Stellar kinematics in disk galaxies

Cover: The overhead view of this whirlpool shows a striking resemblance to a spiral galaxy. Photo: Don Farrall.

Printed by Universal Press, Veenendaal

R IJKSUNIVERSITEIT G RONINGEN

Stellar kinematics in disk galaxies

P ROEFSCHRIFT ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, Dr. D.F.J. Bosscher, in het openbaar te verdedigen op vrijdag 14 juli 2000 om 16.00 uur

door Joris Gerssen geboren op 29 december 1969 te Amsterdam

Promotores: Prof. Dr. K.H. Kuijken Prof. Dr. M.R. Merrifield

Beoordelingscommissie: Prof. Dr. P.C. van der Kruit Prof. Dr. T.S. van Albada Prof. Dr. P.T. de Zeeuw

Contents

Nederlandse samenvatting

7

1

Introduction 1.1 Thesis outline





















13 16

2

The shape of the velocity ellipsoid in NGC 488 2.1 Analysis



















2.2 NGC 488 


















2.2.1 Stellar absorption line data











2.2.2 Analysis 
















2.2.3 The emission line data 












2.3 Discussion 




















19 20 21 22 22 25 25

3

Disk heating in NGC 2985 3.1 Modelling 


















3.2 Observations and Reduction













3.2.1 Spectroscopy















3.2.2 Photometry 















3.3 Analysis



















3.4 discussion 


















3.4.1 Comparison to other galaxies 












29 30 31 31 32 32 34 35

4

The pattern speed of the bar in NGC 4596 4.1 Observations and Analysis














4.2 Results 



















4.2.1 The pattern speed














4.2.2 Bar major axis















4.2.3 Nuclear disk 















4.3 Discussion 




















39 40 42 42 42 44 45

5

Planetary nebulae kinematics in M94 5.1 Slitless Spectroscopy















5.2 Observations




















49 50 52

5

6 Data Reduction 
















5.3.1 Calibration 















5.3.2 Object identification













5.3.3 Comparing Spectral Modes











Long-slit data

















Results 



















5.5.1 Luminosity function













5.5.2 Rotation curve















5.5.3 Velocity dispersion













5.5.4 Combined Kinematic Model 










Conclusions




















52 52 53 54 54 55 56 58 58 59 60

6

Dark halos in S0 galaxies: NGC 5866 6.1 Observations


















6.2 Reduction 


















6.3 Results 



















6.3.1 Radial velocities 














6.3.2 Velocity dispersions













6.4 Modelling 


















6.5 Discussion 




















63 64 65 65 66 67 68 69

7

Summary and outlook 7.1 Summary 


















7.2 Future and ongoing projects













7.2.1 Secular evolution of disk stars 










7.2.2 Planetary Nebulae spectrograph










7.2.3 Lenticular galaxies













7.2.4 Bar pattern speeds
















73 73 75 75 76 77 77

5.3

5.4 5.5

5.6

Nawoord

81

Publications in refereed journals

83

Nederlandse samenvatting

Hoewel sterren op het eerste gezicht willekeurig verdeeld lijken, zijn ze in werkelijkheid gegroepeerd in collecties van miljarden sterren. Dergelijke eilanden van sterren, in het verder lege heelal, worden sterrenstelsels genoemd. Onze eigen ster, de zon, bevindt zich in zo’n eiland. Alle sterren die we ’s nachts kunnen zien maken deel uit van dit eiland en staan, astronomisch gezien, vlakbij de zon. De meerderheid van de sterren in ons eigen sterrenstelsel is echter veel te zwak om individueel gezien te worden maar het collectieve licht van al deze sterren is wel te zien als een zwakke band van diffuus licht. De Griekse naam voor deze band van licht is Galaxias ofwel Melkweg en sterrenstelsels worden daarom ook wel melkwegstelsels genoemd. Sterrenstelsels bestaan dankzij de gravitatiekracht. Het is de onderlinge aantrekkingskracht van de sterren in een melkwegstelsel die ervoor zorgt dat alle sterren bij elkaar blijven. Dit impliceert echter dat sterren moeten bewegen. Zoals de beweging van de aarde ervoor zorgt dat de aarde niet op de zon botst maar er netjes omheen draait, zo is de beweging van sterren er de oorzaak van dat sterren ondanks hun onderlinge aantrekkingskracht niet op elkaar zullen botsen. Het is echter nog geen 100 jaar geleden dat het inzicht dat het heelal bestaat uit eilanden van sterren werd verworven. De voornaamste reden dat het zo lang heeft geduurd is dat sterrenstelsels zeer lichtzwak zijn. Zelfs het meest nabije stelsel, onze directe buurman de Andromedanevel, is met het blote oog nauwelijks meer dan een wazig vlekje van licht. Met behulp van telescopen kunnen wel veel meer van deze nevels worden waargenomen maar zelfs dan blijven het meestal niet meer dan wazige vlekjes. Het is pas sinds de introductie van fotografie in de astronomie dat er meer bekend werd over de aard van deze nevels. Met een camera is het namelijk mogelijk om een object urenlang — desnoods nachtenlang — te belichten. Op zulke lang belichte opnamen veranderen de wazige nevels vaak in spectaculaire afbeeldingen met een grote verscheidenheid aan structuren. De Amerikaanse astronoom Edwin Hubble bracht in die verscheidenheid een classificatie aan die nog steeds gebruikt wordt. Figuur 1 toont zijn oorspronkelijke diagram. Ruwweg onderscheidde hij drie typen sterrenstelsels. De weinig details vertonende elliptische stelsels bevinden zich links in het diagram. Aan de rechterkant bevinden zich sterrenstelsels die juist veel structuur vertonen, vaak in de vorm van een soort draaikolk. Deze stelsels worden nog onderverdeeld in nevels met een balk (een min of meer rechthoekige band van licht) in het midden, de balkspiraalstelsels, en in nevels zonder een balk, de spiraalstelsels. Afgezien van de balk in het midden lijken deze laatste twee zeer sterk op elkaar. Beide hebben een afgeplatte vorm en ze worden daarom ook wel schijfstelsels genoemd. Ons eigen sterrenstelsel is van dit type en dat 7

8 verklaart meteen waarom we de Melkweg ’s nachts als een smalle band van licht zien. Belangrijker echter nog dan dit classificatieschema was dat Hubble als eerste de afstanden tot deze nevels wist te bepalen en zodoende kon aantonen dat ze in omvang vergelijkbaar zijn met ons eigen Melkwegstelsel. In e´ e´ n keer was daarmee duidelijk geworden dat sterrenstelsels de belangrijkste bouwstenen van het heelal zijn.

F IGUUR 1— Het oorspronkelijke classificatieschema van Hubble. Vanwege de vorm wordt het ook wel het ‘stemvork diagram’ genoemd. Uit: The Realm of the Nebulae (Hubble, 1936).

Inzicht in de opbouw van melkwegstelsels kan worden verkregen door het bestuderen van stersnelheden. Zoals eerder opgemerkt moeten sterren bewegen omdat ze anders op elkaar zullen storten. De snelheden waarmee de sterren moeten bewegen zijn gerelateerd aan de grootte van de gravitatiekracht, en deze kracht hangt alleen af van de massa’s en de onderlinge afstanden tussen de sterren. Door het bestuderen van stersnelheden kunnen we dus leren hoe de massa verdeeld is in een melkwegstelsel. Het blijkt dat sterren in melkwegstelsels zowel systematische bewegingen zoals rotatie om het centrum kunnen vertonen, als willekeurige bewegingen, waarbij ze kris kras langs elkaar vliegen. De kans dat twee sterren ooit op elkaar botsen is echter zeer klein want ondanks het feit dat ze verzameld zijn in een sterrenstelsel is de gemiddelde afstand tussen de sterren nog altijd een lichtjaar groot, ofwel ongeveer 7 miljoen keer groter dan de gemiddelde diameter van een ster. Een andere manier om iets te leren over de verdeling van massa is door te kijken naar afbeeldingen van melkwegstelsels, zoals bijvoorbeeld figuur 2. Dit is een voorbeeld van een spiraalstelsel waar we schuin tegen aankijken. Het nadeel van beelden zoals deze is dat ze altijd twee dimensionaal zijn. Uit een foto valt geen informatie over de diepte af te leiden. Het bepalen van de werkelijke vorm met behulp van alleen fotometrische informatie is daarom niet mogelijk. Een ander probleem is dat wanneer we de totale hoeveelheid licht in een plaatje vertalen naar massa, deze massa altijd lager is dan de totale massa van een melkwegstelsel bepaald uit de stersnelheden. Blijkbaar is er in melkwegstelsels een grote hoeveelheid massa

9 aanwezig die geen licht uitzendt en deze massa wordt daarom donkere materie genoemd. De hoeveelheid donkere materie in een melkwegstelsels is ongeveer tien keer groter dan alle zichtbare materie maar wat deze donkere materie precies is, is nog steeds niet bekend. Een van de beste manieren om meer inzicht te verkrijgen in de verdeling van deze materie is door het vergaren van snelheidsinformatie.

F IGUUR 2— Een typisch spiraalstelsel. Dit stelsel heeft de prozaische naam NGC 488. De foto is als negatief afgebeeld voor een beter contrast. De afstand tot dit melkwegstelsel is ongeveer 50 miljoen lichtjaar wat betekent dat we het stelsel zien zoals het er 50 miljoen jaar geleden uitzag. Dit is astronomische gezien een korte tijdspanne en dit stelsel zal in die periode dan ook niet noemenswaardig veranderen.

In dit proefschrift worden een aantal onderzoeken beschreven waarbij gebruik wordt gemaakt van stersnelheden om verschillende aspecten van melkwegstelsels te bestuderen. Om de snelheden van sterren te bepalen wordt gebruik gemaakt van een techniek die spectroscopie wordt genoemd. Het komt erop neer dat het licht van een ster uiteen wordt gerafeld in een spectrum. Zonlicht dat tot een regenboog uiteen wordt gerafeld is een bekend voorbeeld. Wanneer men goed kijkt naar een sterspectrum dan blijkt dat er op tal van plaatsen (golflengten) in het spectrum donkere lijntjes zitten. Deze plaatsen zijn donkerder omdat atomen in de atmosfeer van een ster het licht, dat in het midden van de ster ontstaat, op deze specifieke golflengten absorberen. Een dergelijk type spectrum wordt daarom een absorptielijnspectrum genoemd. De posities van de lijnen hangen af van het soort atomen in de steratmosfeer en van de snelheid van de ster. Net als bij geluid varieert de golflengte van licht (de kleur) met snelheid. Denk bijvoorbeeld aan het verschil in geluid van een sirene van een ambulance die op ons afkomt en e´ e´ n die van ons af rijdt. Voor licht geldt precies hetzelfde. Door in een gemeten sterspectrum

10 de posities van de lijnen te vergelijken met de lijnen in een referentie-spectrum (waarvan de snelheid bekend is) is het mogelijk om de snelheid van een ster te bepalen. Wanneer we het spectrum van een melkwegstelsel waarnemen dan zien we niet het licht van e´ e´ n enkele ster maar van vele miljoenen sterren tegelijk. Deze sterren zullen niet allemaal dezelfde snelheid hebben. Sommige sterren bewegen wat sneller dan andere (met als gevolg dat de lijnen in dit spectrum een beetje naar de rode kant van het spectrum zijn verschoven) en andere bewegen weer wat langzamer (waardoor de lijnen naar de blauwe kant zullen opschuiven). Wat we waarnemen is het gecombineerde licht van al deze, iets ten opzichte van elkaar verschoven spectra. En dus zullen de lijnen in een melkwegstelselspectrum een stuk breder zijn dan in een individuel sterspectrum. Door nu de breedte van de lijnen in een melkwegstelsel te vergelijken met de breedte van de lijnen in een sterspectrum is het mogelijk om de verdeling van snelheden in een melkwegstelsel te bepalen. De eerste twee projecten die in dit proefschrift worden beschreven, de kris-kras bewegingen en de patroonsnelheden, maken gebruik van deze absorptielijn-spectroscopie techniek om de stersnelheden te bestuderen. Het laatste project, planetaire nevels, dat in dit proefschrift wordt beschreven maakt gebruik van een andere vorm van spectroscopie om snelheden in melkwegstelsels te bepalen. Kris-kras bewegingen Naast rotatie vertonen de sterren in een spiraalstelsel ook willekeurige bewegingen. Hoewel deze laatste moeilijker te meten zijn dan de systematische rotatie leveren ze nieuwe informatie op over de opbouw van een melkwegstelsel. Bovendien verschaffen ze informatie over de levensloop van melkwegstelsels aangezien de kris-kras snelheden toenemen met verloop van tijd. Wanneer sterren worden geboren hebben ze een relatief lage willekeurige snelheid van 10 kilometer per seconde die later kan oplopen tot wel 100 kilometer per seconde. Deze toename is een belangrijke indicator voor de ontwikkeling van een melkwegstelsel. Om deze toename te kunnen meten is het nodig de willekeurige bewegingen van sterren in drie dimensies te bepalen. Tot nu toe was het echter alleen mogelijk voor sterren in de directe omgeving van de zon om de drie dimensionele verdeling van snelheden te bepalen. In dit proefschrift wordt een techniek beschreven waarmee ook in andere melkwegstelsels de drie dimensionale verdeling van de willekeurige snelheden kan worden bepaald. De toepassing van deze nieuwe techniek op twee spiraalstelsels laat zien dat de gemeten snelheidsverdeling in deze stelsels goed overeenkomen met de theoretisch voorspelde waarden. Patroonsnelheden Tenminste een derde van alle schijfstelsels is van het type balkspiraal, zie nogmaals figuur 1. Net als de rest van het stelsel bestaat ook de balk voornamelijk uit sterren. De aanwezigheid van een balk kan de ontwikkeling van een melkwegstelsel sterk beinvloeden en het is daarom van belang om de eigenschappen van een balk zo nauwkeurig mogelijk te bepalen. Een van de belangrijkste eigenschappen is de snelheid waarmee een balk ronddraait, de zogenaamde patroonsnelheid. Om een volledige omwenteling te maken heeft een balk doorgaans zo’n 100 miljoen jaar nodig. Het rechtstreeks bepalen van de patroonsnelheid is daarom niet mogelijk. Sinds het midden van de jaren 80 bestaat er een techniek om deze patroonsnelheid op een andere manier te bepalen. De succesvolle toepassing hiervan liet echter op zich wachten tot er betere instrumenten en software waren ontwikkeld. In dit proefschrift tonen we aan dat

11 het nu wel mogelijk is om deze techniek met succes toe te passen. Het bepalen van de rotatie is vooral belangrijk omdat de meest recente theorie¨en voorspellen dat de rotatiesnelheid van balken snel moet afnemen als gevolg van interactie met de donkere materie. Maar de tot nu toe gemeten balken roteren echter allemaal met een hoge patroonsnelheid en niets lijkt erop te duiden dat deze snelheid aan het afnemen is. Een grotere verzameling van gemeten patroonsnelheden kan mogelijk meer duidelijkheid verschaffen. Planetaire nevels De helderheid van sterrenstelsels is niet constant over hun oppervlak maar neemt naar buiten toe juist zeer snel af. Dat is goed te zien in figuur 2, het midden is volledig overbelicht (en dus op het plaatje zwart want het is een negatief) maar naar de rand toe wordt het licht van de sterren snel zwakker. Het bepalen van stersnelheden met behulp van spectroscopie zal dus beperkt moeten blijven tot de relatief heldere binnen delen van een melkwegstelsel. Om toch iets over de verdeling van stersnelheden in de buitendelen van sterrenstelsels te kunnen leren zal een alternatieve methode gezocht moeten worden. Planetaire nevels zijn sterren die zich in de laatste fase van hun leven bevinden. In die doodstrijd stoten ze hun buitenste gaslagen af. Daardoor worden ze niet alleen een stuk groter maar het betekent ook dat het sterlicht nu door de gaslaag wordt uitgezonden. Dit heeft tot gevolg dat het sterlicht geconcentreerd wordt in een paar heldere emissie-lijnen in plaats van verdeeld te zijn over duizenden zwakke absorptie-lijntjes. Dat maakt het relatief eenvoudig om planetaire nevels te vinden en om hun snelheden spectroscopisch te bepalen. De aanduiding planetaire nevel wordt gehanteerd omdat deze objecten gezien door een kleine telescoop enigzins op planeten lijken, maar ze hebben hoegenaamd niets met planeten uit te staan. In spiraalstelsels is het dikwijls mogelijk om bewegingen (kinematica) in de buitendelen van melkwegstelsels te bepalen met behulp van gas. Het nadeel van gas is dat het alleen de globale verdeling van massa kan traceren en niet de locale massa. Daarvoor is informatie over de willekeurige beweging van sterren noodzakelijk. In dit proefschrift wordt een techniek beschreven die gebruik maakt van planetaire nevels om de stersnelheden in de buitendelen van een spiraalstelsel en in een S0 (spreek uit es-nul) te bepalen. S0-stelsels vormen een intermediaire klasse tussen de elliptische stelsels en de spiraalstelsels. Ze hebben weinig tot geen gas waardoor planetaire nevels als enige in aanmerking komen om de massa verdeling in de buitendelen van deze systemen te bestuderen. Hoe verder een sterrenstelsel verwijderd is, des te verder kijken we terug in de tijd aangezien de snelheid van het licht eindig is. Door ver weg gelegen stelsels te bestuderen kunnen we in principe de ontwikkeling van deze systemen rechtstreeks volgen. Helaas is hoeveelheid licht die we van deze ver weg gelegen stelsels ontvangen beperkt. Voor gedetailleerde informatie over de interne structuur van sterrenstelsels zijn we dus aangewezen op de nabije stelsels zoals beschreven in dit proefschrift. Een combinatie van dit soort gedetailleerd onderzoek met de globale informatie van de ver weg gelegen melkwegstelsels kan er toe leiden dat we een beter begrip krijgen van de vorming en ontwikkeling van melkwegstelsels, de bouwstenen van het heelal.

12

1 Introduction

T

HE advent of the 8 to 10 meter class of telescopes and the Hubble Space Telescope made it possible to study galaxies at large look-back times. The evidence amassed from these studies shows that at high redshifts galaxies look very different (i.e. smaller and more irregular) from their counter parts seen today and provide the first direct evidence for the evolution of galaxies (e.g. Ellis 1998, Dickinson 2000.) However, a complete understanding of the formation and evolution of galaxies requires detailed knowledge about the internal structure of these systems. Unfortunately, information about the third dimension — the direction perpendicular to the sky — of a galaxy cannot be obtained using only photometry. However, in combination with stellar absorption line spectroscopy it is possible to explore a galaxy’s third dimension. The internal stellar structure — which makes up the bulk of a galaxy’s visible matter — canbe with a function that depends only on the phase specified  . Knowledge space coordinates of the stars, about the kinematics of stars is therefore  essential since the distribution function depends on both position and velocity, although without additional information about the shape of the potential the derived distribution function is not necessarily unique. In a steady-state the Jeans theorem states that a galaxy’s phase-space coordinates depend  on at most three integrals of motion (e.g. Binney & Tremaine 1987) and can therefore be constrained with a three dimensional dataset. The line-of-sight velocity distributions acquired over a galaxy’s projected surface represent just such a dataset and can in principle be used to fully constrain the distribution function. In practise, however, galaxies are not in a steadystate. After all they do evolve with time. However, galaxies are usually sufficiently close to a steady state that a dynamical analysis can still be warranted. At larger radii from the centre of a galaxy, where the relaxation times are longer, the stellar kinematics will still partially reflect the formation mechanism by which a galaxy formed. Stellar kinematic studies thus provide information about galaxies that would otherwise be inaccessible. Unfortunately, such investigations are hampered by the low surface brightnesses of galaxies. Furthermore, to accurately determine the line-of-sight velocities, spectral resolutions of 5000 or more are typically required. And this relatively high dispersion weakens the signal even more. Observations relying on stellar absorption lines are therefore necessarily confined to the central regions of a galaxy where the surface brightness is highest.

13

14

CHAPTER 1 INTRODUCTION

A more convenient way of measuring the kinematics of galaxies is to use HI gas, since emission lines are generally easier to observe than stellar absorption lines. However gas represents at most 10 percent of the visible mass and quite often it is lacking in detectable quantities altogether, for instance in elliptical galaxies and in the majority of S0 galaxies. Moreover, gas traces the global potential of a galaxy since the gas particles are on nearly circular orbits due to their collisional nature. To trace the local mass density requires information about the stellar kinematics.

Stellar kinematics The first attempts to measure the kinematics of galaxies were made by Slipher in 1912. Using stellar absorption line spectroscopy he showed that galaxies, on average, all recess from us with large radial velocities. Hubble famously extended this work in the mid twenties to discover the expansion of the universe. A vivid description of this development can be found in Man discovers the Galaxies by Berendzen et al (1976.) The next decades saw the use of absorption lines mainly limited to probe the distances to successively more distant galaxies. Although Minkowski pioneered the study of velocity dispersions in the fifties (see Minkowski 1962), it was not until the early seventies that stellar absorption lines became a viable tool to study the internal kinematics of galaxies. Several techniques were then developed that all use the spectrum of an individual star as a template to which the galactic spectrum can be compared (Simkin 1974, Sargent et al 1977.) In this way kinematical properties such as the line-of-sight stellar velocity dispersions and stellar radial velocities can be derived, see fig. 1.1. Initially only the brightest objects such as elliptical galaxies and the bulges of spiral galaxies were observed (e.g. Illingworth 1977.) The measurement of stellar velocity dispersions in the fainter disk components of galaxies was first attempted by van der Kruit & Freeman (1984, see also Bottema 1993.) Most results so far have been derived from longslit spectroscopy and therefore only provide one-dimensional information. Integral field spectrographs (e.g. SAURON, Miller et al 1999) are now slowly becoming available. With such two-dimensional kinematical information many of the ambiguities that can arise when using only one-dimensional information are avoided. Just like HI mapping integral field techniques yield velocity fields but in addition, also provide the surface distribution of the stellar velocity dispersions. However, the rapid decline of the surface brightness of galaxies with radius limits the use of stellar absorption line techniques to about two disk scale length. The stellar kinematics at radii large than about two disk scale length are most effectively probed by a technique that does not rely on integrated light. Over the last few years planetary nebulae have proven to be adequate tracers of the stellar distribution at large radii (e.g. Hui 1993.) A dedicated instrument, Planetary Nebulae Spectrograph, to routinely measure the kinematics of planetary nebulae populations in galaxies is now under construction. The large field of view (10 by 10 arcmin) of this instrument and its high efficiency will provide kinematical information similar to an integral field spectrograph, although with a sparser sampling but over a much larger fraction of a galaxy.

Velocity profiles The amount by which a template spectrum has to be broadened to fit the galactic spectrum is called the velocity profile or line-of-sight velocity distribution. The basic idea is that the ob-

15 served galactic spectrum can be approximated by a stellar spectrum (the template) convolved with the velocity distribution of the stars along the line-of-sight (the velocity profile or VP),

!"#$&%('*) The earliest stellar velocity dispersion work of Minkowski used out of focus spectra of template stars to estimate the amount of broadening. With the introduction of computers and the availability of the Fast Fourier Transform algorithm it became feasible to numerically perform the deconvolution. Today the analysis of absorption line data is essentially unchanged although the techniques to deconvolve have become more sophisticated. The techniques developed to extract the velocity profiles can be broadly classified as either parametric or non-parametric methods. The advantage of parametric methods is that they have robust, well-defined errors. However, parametric methods do assume a specific shape for the velocity profile, often a Gaussian. Starting with van der Marel & Franx (1993) and Gerhard (1993) several techniques have been developed to extract higher-order Gaussian moments from the observed spectra, such as the skewness. Non-parametric methods (e.g. Rix & White 1992) place no restriction on the shape of the velocity profile but have the disadvantage that the error analysis is generally less tractable. The Unresolved Gaussian Decomposition algorithm of Kuijken & Merrifield (1993) is an example of a non-parametric method that has complete freedom of the velocity profile shape but also provides a good handle on the uncertainties associated with the derived shape. In this thesis both UGD and higher-order Gaussian moment techniques have been employed to extract velocity profiles from the data.

F IGURE 1.1— An example of a galactic spectrum (bottom line) and a K0 stellar template (top line) shifted to the radial velocity of the galaxy. Notice that the main difference between the two spectra is the width on the absorption lines. The difference in width is a measure of the stellar velocity dispersion.

CHAPTER 1 INTRODUCTION

16

1.1 Thesis outline Several aspects of the stellar kinematics in disk galaxies are addressed in this thesis:

+

+

In the first part of the thesis we present a technique to derive the three dimensional distribution of stellar velocity dispersions in galactic disks, and apply this technique to the early type spiral galaxies NGC 488 (chapter 2) and NGC 2985 (chapter 3). These results represent the first measurements of stellar velocity ellipsoids outside of the Solar neighbourhood, and suggest a trend between the dynamical history of a galactic disk and its Hubble type.

+

The rate at which a bar rotates, the bar pattern speed, is a defining parameter of any barred galaxy. Most measures of this parameter have so far relied on indirect techniques. More direct information about pattern speeds of bars, however, is highly desirable since the evidence gathered to-date suggests that bars rotate as fast as they are physically allowed to. This behaviour is at odds with the findings of recent numerical simulations (Debattista & Sellwood 1998) which predict that the tumbling rate of bars should decrease rapidly due to the dynamical friction exerted by the dark halo. Accurate measurements of the pattern speed and of the halo properties (see below) are needed to resolve this issue. In chapter 4 we present an application of the Tremaine & Weinberg method (1984) to directly measure the bar pattern speed in the SBa galaxy NGC 4596 and demonstrate that this technique is a practical means of obtaining this important parameter. Absorption line spectroscopy is restricted to radii extending no more than one to two disk scale length. However, in recent years planetary nebulae have proven to be wellsuited tracers of the stellar kinematics at large radii in elliptical galaxies (Hui 1993.) Detecting planetary nebulae and measuring their radial velocities is usually a two-step process. In chapter 5 we present a technique with which we can simultaneously detect and measure the kinematics of a planetary nebulae population. This method is essentially similar to the technique employed by the Planetary Nebulae Spectrograph (Arnaboldi et al 1999) now under construction. We have tested this method using the nearby spiral galaxy M94 and found that we can reliably determine the stellar velocity dispersions to beyond four disk scale lengths. We have started a project to measure the stellar rotation curves in a sample of S0 and SB0 galaxies using the planetary nebulae technique. Our main goal is to establish whether the halo properties of the S0/SB0 systems are similar to the halo properties of ordinary spiral galaxies, where the halo properties can be derived from HI rotation curves, and to examine whether there is any difference between the halo properties of barred and non-barred S0 galaxies. In chapter 6 the first results for the S0 galaxy NGC 5866 are presented.

The results presented in this thesis show that stellar spectroscopy provides a versatile tool to study different aspects of the internal structure of galaxies. Stellar absorption lines can be used to explore galactic structure in the inner parts of galaxies (i.e within about two scale length), and at larger radii the emission lines of planetary nebulae can be used to probe galactic properties that are otherwise inaccessible.

1.1 Thesis outline

17

New developments like integral field spectroscopy, the large new telescopes such as the Very Large Telescope and the Planetary Nebulae Spectrograph guarantee that in the near future stellar spectroscopy studies will continue to provide new insights into the internal structure of galaxies. A combination of the detailed structure, obtainable only for nearby galaxies, and the morphology of their distant counter parts will ultimately lead to a better understanding of the formation and evolution of the building blocks of the universe, the galaxies.

References Arnaboldi M., Capaccioli M., Douglas N.G. et al 1999, Proceedings of the SAIT symposium, Naples 1999 Berendzen R., Hart R., Seeley D., 1976 Man Discovers the Galaxies. Science History Publications, New York Binney J., Tremaine S., 1987 Galactic Dynamics. Princeton University Press, Princeton Bottema R., 1993, A&A, 275, 16 Debattista V.P., Sellwood J.A., 1998, ApJ, 493, L5 Dickinson M., 2000, Proceedings of the XIXth Moriond Astrophysics Meeting, eds. Hammer F., Thuan T.X., Cayatte V., Guiderdoni B., Tranh Than Van J., p. 257 Ellis R.S., 1998, Nature, 395, A3 Gerhard O.E., 1993, MNRAS, 265, 213 Hui X., 1993, PASP, 105, 1011 Illingworth G., 1977, ApJ, 218, 43 Kuijken K., Merrifield M.R., 1993, MNRAS, 264, 712 Miller B.W., Bureau M., Verolme E. et al, astro-ph/9906091 Minkowski R., 1962, IAU Symposium 15, p. 112 Rix H-W., White S.D.M., 1992, MNRAS, 254, 389 Sargent W.L.W., Schechter P.L., Boksenberg A., Shortridge K., 1977, ApJ, 212, 326 Simkin S.M., 1974, A&A, 31, 129 Tremaine S., Weinberg M.D., 1984, ApJ, 282, L5 van der Kruit P.C., Freeman K.C., 1984, ApJ, 278, 81 van der Marel R.P., Franx M., 1993, ApJ, 407, 525

18

2 The shape of the velocity ellipsoid in NGC 488 Originally published as J. Gerssen, K. Kuijken, M. R. Merrifield, MNRAS 288, 618 (1997)

Theories of stellar orbit diffusion in disk galaxies predict different rates of increase of the velocity dispersions parallel and perpendicular to the disk plane, and it is therefore of interest to measure the different velocity dispersion components in galactic disks of different types. We show that it is possible to extract the three components of the velocity ellipsoid in an intermediate-inclination disk galaxy from measured line-of-sight velocity dispersions on the major and minor axes. On applying the method to observations of the Sb galaxy NGC 488, we find evidence for a higher ratio of vertical to radial dispersion in NGC 488 than in the solar neighbourhood of the Milky Way (the only other place where this quantity has ever been measured). The difference is qualitatively consistent with the notion that spiral structure has been relatively less important in the dynamical evolution of the disk of NGC 488 than molecular clouds.

I

T is observationally well established that the velocity dispersion of main sequence stars increases with advancing spectral type. This fact has been recognised ever since velocity dispersions were first measured in the solar neighbourhood (e.g. King 1990). Initially these observations were explained as the result of equipartition of energy because the mass of the stars decreases along the main sequence. However the two-body relaxation time scale is much too long to have any effect on the stellar velocity ellipsoid, prompting explanations relying on collective effects instead. Some of the different functional forms that have been suggested for the velocity dispersion-age relation are reviewed by Lacey (1991). This increase in velocity dispersion, or heating, depends on the roughness of the gravitational potential in the disk, so knowledge about the shape of the velocity ellipsoid will tell us a great deal about the dynamical history of a disk. Until recently direct measurements of the three-dimensional shape of the velocity ellipsoid have been restricted to the solar neighbourhood. Observations of the stellar velocities in external spiral galaxies have concentrated on systems that are either close to edge-on or

19

20

CHAPTER 2 THE SHAPE OF THE VELOCITY ELLIPSOID IN NGC 488

face-on (van der Kruit and Freeman 1986; Bottema 1995) and will therefore only provide information about a single component of the velocity dispersion. From these measurements only indirect inferences can be drawn about the shape of velocity ellipsoids in galaxies because the results of a small sample of different galaxies are being compared in a statistical way. Moreover, this shape will be subject to rather large uncertainties because the errors of the face-on and edge-on galaxies are compounded, and because relating face-on and edge-on galaxies is rather delicate. In this pilot study we show that it is possible to derive the shape of the velocity ellipsoid within a single galaxy. We use the fact that an intermediate-inclination galaxy shows different projections of the velocity dispersion at different galactocentric azimuths. In section 2 the method by which we extract the velocity dispersions information is described. In section 3 we apply this analysis to the large early type spiral NGC 488 and in section 4 we discuss the results obtained for NGC 488 and compare them to the velocity ellipsoid in the solar neighbourhood.

2.1 Analysis

,- /.0 $12

the line-of-sight velocity dispersion as a function of In cylindrical polar coordinates . (intrinsic) position angle in a thin axisymmetric disk is

35478: 6 9$;=< 6 .-> 74 &?6 @BAC9 6 !. D $9 ;=< 67E > 476 @GAH9 6 E F

(2.1)

I

which can be written as

6KE 3 476 476 74 6 6 E 476 476 (2.2) J 9$;=<  8 > ? > J F @BA # LM 8 L ? @GAH9 J .ND J . variation that depends only on the compoThus, it consists of an element with a @GAH9 .

nents of the dispersion in the plane of the galaxy, and an element with no dependence on that depends on all three components of the velocity dispersion. Observations along at least two axes (preferably the major and minor axes, which provide maximum leverage), are therefore required to extract both coefficients. Furthermore, in disk galaxies, in which most orbits are well-described by the epicycle approximation the radial and azimuthal dispersions obey the relation 46 I 

? 4 86  JPO I >RQ  47c 86 b Le,fQ ,  <  4786  L J > J NS U Q SNW Q Q Q, g

(2.4)

2.2 NGC 488

21

TABLE 2.1— Parameters of NGC 488

Hubble type Inclination Distance Max. rotational velocity Angular size Photometric scale length

Sb

hCiHj

30 Mpc (for k:l of 75) 360 km/s 5.2 x 3.9 arcmin 40”in B

The first term on the RHS of equation 2.4 describes of the velocity ellipsoid. 4 6 the L 4 tilting F6 ). Orbit integration by Binney The two limiting cases of this tilting term are zero and ( 8 & Spergel (1983) and by Kuijken & Gilmore (1989) suggest that in the solar neighbourhood the truth lies close to midway between the two extremes. As will be seen below, the uncertainty in this term is not a concern in the present analysis. In summary, the three components of the stellar velocity ellipsoid can be deduced from measurements of the line-of-sight dispersions along two position angles in a galaxy disk. The two sets of measurements, together with the ratio of tangential and radial velocity dispersions appropriate for nearly circular orbits, provide the three equations necessary to deproject the ellipsoid. If the asymmetric drift can also be measured, e.g. when a rotation curve for cold interstellar gas is available, the system is overdetermined, allowing a consistency check on the result.

2.2 NGC 488 We choose the large early type spiral NGC 488 for this analysis because of its regular optical appearance and its intermediate inclination. Table 2.1 lists some properties of this galaxy. Note the very high rotational velocity (Peterson 1980). B and I band images of NGC 488 were obtained with the 48 inch telescope at Mt. Hopkins observatory in September 1992. Bulge-disk decompositions were performed on these images to assess the extent to which the bulge contaminated the velocity dispersions of the disk. The light profiles obtained from these images along the major and minor axis are textbook ,em$n o bulge, examples of an exponential disk and a see fig. 2.1. After subtracting a straight line fit to the linear part of light profile we found that beyond a radius of 20 arcsec the diskto-bulge light ratio increases rapidly. At 20 arcsec this ratio is about 7 and at 30 arcsec it is already 25. Data points at radii smaller than 20 arcsec were therefore excluded from the analysis. The derived scale lengths ( p 40 arcsec along the B band major axis) are in good agreement with the literature values (e.g. Schombert & Bothun 1987). The ratio of the minor I to major axis scale lengths implies an inclination of h jrqWsCj , again in good agreement with the literature value of hHi j . The scale lengths of the I band image are approximately 20% shorter than the B band scale lengths. This effect is usually attributed to obscuration by dust, but de Jong (1995) finds that such colour gradients are best explained by differences in the star formation history as a function of radius.

CHAPTER 2 THE SHAPE OF THE VELOCITY ELLIPSOID IN NGC 488

22

F IGURE 2.1— Major-axis I-band light profile of NGC 488. The line shows an exponential fit to the disk luminosity.

2.2.1 Stellar absorption line data Two longslit spectra of NGC 488 were obtained with the Multiple Mirror Telescope in January 1994 using the Red Channel Spectrograph: a 3 hour integration spectrum along the major axis and a 2 hour integration along the minor axis. Both spectra were centered around ˚ Calibrating arc lamp exposures were taken every 30 minutes. The the Mg b triplet at 5200A. ˚ dispersion per pixel is p 0.7A. The longslit spectra were reduced to log-wavelength bins in the standard way, using IRAF packages. Adjacent spectra were averaged to obtain a signal-to-noise ratio of at least 25 per bin, and the absorption-line profiles of these co-added spectra were analysed. Analysis of the absorption line profiles using the algorithms of Kuijken & Merrifield (1993) and van der Marel & Franx (1993) revealed no significant departures from a gaussian distribution in the stellar velocity distributions, so all velocity dispersions were derived by the traditional gauss-fitting methods using a single template star (HD 2841, spectral type K5III) to spatially co-added spectra. We note that the models of Kuijken & Tremaine (1991), based on the Shu (1969) distribution function, predict small skewness for the distribution of azimuthal velocity distribution within 1 disk scale length; such a marginally non-gaussian shape would not affect our analysis significantly. 2.2.2 Analysis We applied the analysis described in section 2 to the spectra. Due to the noise present in the data we could not obtain the three components of the velocity dispersion directly (Merrifield & Kuijken, 1994) and adopted therefore a model fitting-approach. We assumed the following models for the velocity dispersions:

48



4 8 t G  LZ,e[u wv l

(2.5)

2.2 NGC 488

23

x

TABLE 2.2— Best-fitting parameters for the model distributions. The quoted errors are one sigma errors.

Parameter

S o l (km/s) y 4 8t 4 F t l (km/s) l (km/s) u (arcsec) 4F[48 4F 

fit 1 336 q 0.21 q 253 q 164 q 38 q

8 0.04 32 27 4

0.65 q 0.16

fit 2 327 q 0.27 q 237 q 176 q 38 q

5 0.04 38 30 4

0.74 q 0.22

4 F t G zLZ,e[u2 l

(2.6)

We also ,e assumed that the circular velocity could be described by a power-law S U S o l [ hHi|{ z} and used equation 2.4 to relate S U to the stellar rotation speed. 4!~€ B‚/ƒ 4!~€„ …‚$ƒ These model distributions were fitted simultaneously to our observables ,
using the non linear fit routines described in Press et al. (1992). The, best-fit and S parameters that we obtained are shown in table 2.2. In fit 1 the tilting term 4 is 4 6 inL equation 46 F . Both fit set to zero, while in fit 2 it set6 equal to the other extreme possible value, 8 the data equally well. The † value of fit 1 is only marginally better than that of fit 2, and so these data cannot distinguish between the two extreme models for the tilting term. It is, however, interesting to note that sufficiently accurate data might allow the tilting term to be measured by such a comparison, perhaps providing constraints on the shape of the potential close to the disk. The error in the derived 4 axis ratio 4 of the velocity ellipsoid is slightly larger than one would naively expect because 8 and F are anti-correlated. Adopting the average between fits 1 and 2 as representing the most realistic tilting term, we obtain

4F 4 8  i ˆ‡ iZq(i IŠ‰ (2.7) We have tested this procedure on a large ( pŒ‹|i|i ) set of artificial major and minor axis

spectra, created from the template star to resemble the observed galactic spectra as closely as possible, with a different poisson noise realisation for each spectrum. The best-fit parameters obtained from these spectra scatter with the same dispersion as the errors obtained from any individual fit to a spectrum. Therefore, we conclude that the parameters returned by the fit programme are reliable. An , obvious 1 extension to our fitting procedure would be to use different scale lengths for the and dispersion components. Unfortunately the data are not of sufficient quality to allow for a six parameter fit. One of the six eigenvalues that we obtained from diagonalising the correlation matrix was much larger than the other five, a clear indication that a six parameter fit is stretching the data a bit too much. Interestingly, the kinematic scale length of the disk appears to be comparable to the photometric one. This is not the expectation from local isothermal approximation for disks, which predicts a scale length double the photometric one. The most likely explanation is probably the fact that we measure the scale length in the B band while the stellar mass distribution is

24

CHAPTER 2 THE SHAPE OF THE VELOCITY ELLIPSOID IN NGC 488

F IGURE 2.2— The best-fitting model distributions (solid line is fit 1 and the dashed line is fit 2) and the data. At radii smaller than 20 arcsec the bulge contaminates the disk light so data within that region were not included in the fit. The triangles in the lowest panel are the emission-line data of Peterson (1980).

2.3 Discussion

25

best traced in the K band, the near infra-red. Empirically it is found that scale lengths in the K band are shorter than the B band up to a factor of about 2 (de Jong 1995, fig. 4 and Peletier et al. 1996). Alternatively the approximation of a local isothermal distribution breaks down. 2.2.3 The emission line data The fits described above are to the stellar data only. The lowest panel in fig. 2.2 shows the emission line data of Peterson and the predictions from our two fits. Both our fits are fully consistent with these data, and provide extra confirmation of the validity of our analysis. (A simple power-law fit to the emission-line data plotted in fig. 2.2 gives a power index of 0.18 q 0.13.) Unfortunately there are no measured emission line velocities in the inner part of the disk. Peterson gives velocities around 195 km/s near a radius of 10 arcsec which are a little higher than our fits would predict. However there is no reason why a power-law rotation curve should persist into those central, bulge dominated regions.

2.3 Discussion This is the first direct measurement of the vertical-to-radial velocity dispersion ratio anywhere outside the solar neighbourhood. Previous determinations have all been indirect, and hence suffer from large uncertainities. The method we have described here is quite straightforward, and could be applied to many systems. I‰ , which is effectively the average ratio near one photoThe derived value of i ‡ iqŽi metric scale length, is somewhat higher than the solar neighbourhood value of 0.52 q 0.03 that Wielen (1977) derived from the McCormick sample of K and M dwarfs. However, the error of 0.03 is the purely statistical error, but the scatter between the published observational estimates of this ratio suggests that the true error may be larger (see Lacey 1991). Any difference between the two ratios is consistent with the findings about the relative effects of the two dominant heating mechanisms, molecular clouds and spiral structure, as we now show. Heating by molecular clouds was originally proposed by Spitzer and Schwarzschild (1951). They proposed that stars in star-cloud encounters gain kinetic energy at the expense of the clouds because of the huge masses of the latter. Subsequent analysis by Lacey (1984) and  -body simulations by Villumsen (1985) showed however that this mechanism saturates rather quickly (once the stars have sufficient energy that they spend most of their time outside the cloud layer the heating rate drops) and could not fully explain the observed heating. An alternative proposal to heat the disk, due to Barbanis and Woltjer (1967), explains the heating as the result of stars scattering from spiral irregularities in the galactic potential. Carlberg and Sellwood (1985) have extended this work and showed that this can indeed heat up the disk. However this process cannot heat the stars efficiently in the vertical direction because the vertical oscillation frequency of stars is much larger than the frequency at which a spiral wave sweeps past the stars orbiting the disk. Hence the stars respond almost adiabatically to this force. Giant molecular clouds create large spiral wakes, often much larger than a cloud itself (Julian and Toomre 1966). This interplay between clouds and spiral irregularities is not yet completely understood but it is clear that they are not independent. Jenkins and Binney (1990) examined the combined effects of both processes based on Monte Carlo simulations of the Fokker-Planck equation describing these processes. They expressed the relative importance

26

CHAPTER 2 THE SHAPE OF THE VELOCITY ELLIPSOID IN NGC 488

of heating by spiral structure 4 [ to4 8 heating by clouds by a parameter denoted  and calculated the corresponding ratio of F (see their fig. 2). From the observed shape of the velocity ellipsoid and velocity dispersion-age relations they concluded that in the solar neighbourhood ‰ i ). the heating of the disk is dominated by spiral structure (‘p 6 The mean surface density of the cloud layer near the sun is 1.8 ’(“ pc ” (Clemens, Sanders and Scoville 1988). From the FCRAO extragalactic CO survey (Young et al. 1995) 6 a mean surface density for NGC 488 is derived of 3.5 ’(“ pc ” . (Young et al. find that the CO layer in NGC 488 is best described by a uniform distribution with a radius of 1.65  ‹hCi€q IŠ˜ i Jy km/s.), higher than in the solar neighbourhood. arcmin and a CO flux of •–N— NGC 488 is classified as an Sb galaxy. It has a very regular tightly wound spiral pattern (the pitch angle is only 5 j ). It is therefore quite likely that the potential associated with this spiral pattern is much smoother that that of our own Galaxy, which has an Sbc Hubble type. Both these observations imply that the parameter  must be smaller for NGC 488 than for the solar neighbourhood. 4 [ 4 8 According to the predictions of Jenkins and Binney a smaller  corresponds to a larger F ratio. 4 [48 ratio for NGC 488 is higher than for the Milky Way, We do indeed find that the F however the difference is only one sigma. We conclude therefore that the shape of the velocity ellipsoid that we have determined is qualitatively consistent with the picture sketched by Jenkins and Binney. The technique we have described in this paper would be straightforward to apply to a larger sample of disk galaxies. With higher quality data, it would also be possible to extend the analysis to map out the radial variation of the velocity ellipsoid shape, a quantity which has never been observationally constrained. Both projects would provide important measurements for comparison with the theoretical treatments of the heating processes in stellar disks.

Acknowledgments The data presented in this paper were obtained using the Multiple Mirror Telescope, which is a joint facility of the Smithsonian Institute and the University of Arizona. Much of the analysis was performed using IRAF, which is distributed by NOAO. We thank the referee, Cedric Lacey for his helpful comments.

References Barbanis B., Woltjer L., 1967, ApJ, 150, 461 Binney J., Spergel D. N., 1983, IAU Colloquium No. 76 Bottema R., 1995 PhD thesis, University of Groningen Carlberg R. G., Sellwood J. A., 1985, ApJ, 292, 79 Clemens D. P., Sanders D. B., Scoville N. Z., 1988 ApJ, 327, 139 Cuddeford P., Binney J., 1994, MNRAS, 266, 273 de Jong R. S., 1995 PhD thesis, University of Groningen de Jong R. S., 1996, A&A, 313, 45 Jenkins A., Binney J., 1990, MNRAS, 245, 305 Julian W. H., Toomre A., 1966, ApJ, 146, 810 King I. R., 1990, in The Milky Way as a Galaxy, eds Buser R., King I. R., p. 172 Kuijken K., Gilmore, G., 1989, MNRAS, 239, 571 Kuijken K., Tremaine S., 1991 in Dynamics of Disc Galaxies, ed. Sundelius B., p. 71

2.3 Discussion Kuijken K., Merrifield M. R., 1993, MNRAS, 264, 712 Lacey C. G., 1984, MNRAS, 208, 687 Lacey C. G., 1991, in Dynamics of Disc Galaxies, ed. Sundelius B., p. 257 Merrifield M., Kuijken K., 1994, ApJ, 432, 575 Peletier R. F. et al., 1996 A&A, 300, L1 Peterson C. J., 1980, AJ, 85, 226 Press et al., 1992, Numerical Recipes, Cambridge University Press, Cambridge Schombert J. M., Bothun G. D., 1987, AJ, 93, 60 Shu F. H., 1969, ApJ, 158, 505 Spitzer L., Schwarzschild M., 1951, ApJ, 114, 385 van der Kruit P. C., Freeman K., 1986, ApJ, 303, 556 van der Marel R. P., Franx M., 1993, ApJ, 407, 525 Villumsen J. V., 1985, ApJ, 290, 75 Wielen R., 1977, A&A, 60, 263 Young J. S., et al., 1995, ApJSupl, 98, 219

27

28

3 Disk heating in NGC 2985 Originally published as J. Gerssen, K. Kuijken, M. R. Merrifield, MNRAS in press (2000)

Various processes have been proposed to explain how galaxy disks acquire their thickness. A simple diagnostic for ascertaining this “heating” mechanism is provided by the ratio of the vertical to radial velocity dispersion components. In a previous paper we have developed a technique for measuring this ratio, and demonstrated its viability on the Sb system NGC 488. Here we present follow-up observations of the morphologically similar Sab galaxy NGC 2985, still only the second galaxy for which this ratio has been determined outside of the solar neighbourhood. The result is consistent with simple disk less than one. heating models which predict ratios of

™šG›G™!œ

T

HE three dimensional distribution of velocities within a galactic disk contains a wealth of information about disk structure. One aspect that is immediately tractable with this information is the dynamical history of a disk. It has long been known that the random velocity of disk stars increases over their lifetime, a process dubbed disk heating. The two main contributors to this heating process – i.e. the increase of velocity dispersions over time – are molecular clouds, which scatter and heat stars more or less isotropically, and spiral irregularities, which primarily heat stars in the plane of the disk. Jenkins & Binney (1990, see also Jenkins 1992) have numerically studied the combined effect of these two processes. 4 [48 By varying the relative importance of the two mechanisms they showed that the ratio F decreases when the contribution of spiral arm structure increases. Although they made their predictions to explain 4 the solar 4 neighbourhood data, their results can also be applied to other galaxies provided 8 and F can be measured. Only in the immediate solar neighbourhood can the full distribution of stellar positions and velocities be obtained directly. The stellar velocities can be fitted by a trivariate Gaussian

 rž B2 Ÿ LR¡^J ¢ 4 86 6 >  ¢ ? J L 4 6 ¢ ? 6 £ > J ¢ 4 F6 6 8 ? ¥F ¤¦

(3.1)

a function originally proposed by Schwarzschild (1907). Such a distribution is known as a velocity ellipsoid since the density of stars is constant on ellipsoids with semi-axes lengths 29

30

CHAPTER 3 DISK HEATING IN NGC 2985

given velocity dispersion components. Solar neighbourhood observations show that 4 8c§ by4 ?¨the § 4 F which is consistent with the predictions of the gradual-heating mechanisms described above. Other, more erratic heating occurs for instance during a minor merger event such as the accretion of a small satellite (Sellwood, Nelson & Tremaine, 1998). Depending on the geometry, this irregular heating process can lead to a substantial thickening of the disk and to a velocity ellipsoid that is significantly different than in the solar neighbourhood. In a previous paper (Gerssen, Kuijken & Merrifield 1997, hereafter Paper 1) we have shown that much can be inferred about the shapes of the velocity ellipsoids in external galaxies from spectra obtained along different position angles. Most studies of stellar velocity dispersions have however concentrated on systems that are either close to edge-on or face-on and therefore only provide information about a single component of the velocity dispersion. But in an intermediate-inclination galaxy spectra obtained along radius vectors with different position angles will show different projections of the velocity ellipsoid. In Paper 1 we showed that we can derive the ratio of the vertical to radial velocity dispersion in NGC 488 from longslit spectra obtained along the major axis, where the line-of-sight velocities are a combination of the azimuthal and the vertical components, and along the minor axis, which gives a combination of the radial and vertical components. Along an arbitrarily positioned spectrum the velocity dispersion in a thin axisymmetric disk can be written as

47©56 ª¬«  53 4786 9$;=< 6 .-> 74 ?6 @GAH9 6 N. D $9 ;=< 6KE > 476 @GAH9 6 E F

(3.2)

There 4 ©=ª/« are in fact only two independent quantities that can be extracted from the variation of with position angle (see Paper 1). Additional spectra, obtained along a third position angle, will therefore only supply redundant information – if the disk is perfectly axisymmetric. A further constraint is necessary if we want to retrieve all three components of the velocity dispersion. Most of the disk stars’ orbits are nearly circular and can be adequately described using the epicycle approximation. This description leads to a relation between the radial and azimuthal components of the velocity dispersion (e.g. Binney & Tremaine 1987) which yields the third constraint, provided that the observed velocity profiles are not significantly skewed:

4 ?6 I > Q 4 86  J O I R Q

 J , Q S ,WU g XS U Q Qd , where the disk photometrical scale length and the radius are in arcsec.

(3.4)

By assuming ,
can a model distribution for the circular velocity the observed stellar rotation curve S be fitted directly using this equation. The circular velocity, SNU , is modelled as a power law, SXU  S l ,} . If the galaxy contains a cold gas disk, SXU can be either included in the fitting procedure or serve as a consistency 4!~€„ …check ‚$ƒ on 4N~€the  ‚$ƒ results. The other two observables, and , are modelled assuming exponential distributions for both the radial and the vertical velocity dispersion components.

4 8  4 8 t G zLZ,e[u2 l 4 F  4 F t B  zLZ,e[u l

u Note that there is no a priori reason to believe that the scalelength

(3.5) (3.6)

is the same for both the vertical and the radial component. Given the present data, it is not possible to constrain both scalelengths independently. There are a total of five free parameters 4 4 tou be determined in our model. Three parameters determine the velocity ellipsoid: 8t l , F t l , ; and two describe the potential: S l and y .

3.2 Observations and Reduction We have applied the analysis described above to the Sab galaxy NGC 2985. It is a typical multi-armed spiral with an inclination of 36 j (Grosbol, 1985). Its distance, using an Hubble constant of 75, is 18 Mpc and the amplitude of the inclination corrected HI rotation curve is about 250 km/s (WHISP database), see table 3.1. 3.2.1 Spectroscopy Longslit absorption line spectra along the major axis (3.5 hours integration) and the minor axis (4 hours) of NGC 2985 were obtained with the ISIS spectrograph on the William Herschel Telescope in the first week of January 1997. These spectra were centered around the

32

CHAPTER 3 DISK HEATING IN NGC 2985

˚ Calibrating arc lamp exposures were taken every 30 minutes. The Mg b feature near 5200 A. ˚ dispersion per pixel is p¯i h A. The longslit spectra were reduced to log-wavelength bins in the standard way, using IRAF packages. Adjacent spectra were averaged to obtain a signal-to-noise ratio of at least 25 per bin, and the absorption-line profiles of these co-added spectra were analysed. Velocity dispersions and radial velocities have been extracted from the absorption-line profiles using the traditional Gauss-fitting method after we had first established that the profiles are indeed close to having Gaussian shape. The observed spectra are compared with a template spectrum (HD107288, type K0III) convolved with a Gaussian. The Gaussian that best fits the data in a least square sense then yields the stellar radial velocities and the stellar velocity dispersions. The derived velocity dispersions along the major axis are significantly better behaved (larger extent and less erratic behaviour) on the redshifted side of the centre than on the blueshifted side. This behaviour was also observed with the software of van der Marel (1994). It is even apparent in the kinematic data of Heraudeau et al (1999). We have therefore decided to only use the redshifted side of the major axis in the subsequent analysis. Hence we have only half as many data points on the major axis as we have on the minor axis, which looks regular on both sides of the centre. Around 20 arcsec from the nucleus there is some indication of a break in the profiles. Beyond this radius the velocity dispersion profiles flatten, suggesting that the disk component starts dominating the velocity dispersions. ˚ emission The spectral range of the longslit absorption spectra also included the 5007 A line. Fitting the mean of the emission line in each co-added spectrum gives us a direct measure of the circular velocity. 3.2.2 Photometry The extent of the bulge can be assessed from a bulge-disk decomposition performed on a WHT ® band image obtained from the ING archive. Ellipses were fitted to the isophotes and an azimuthally averaged luminosity profile was extracted. The bulge component and the disk component of this profile were then simultaneously fitted assuming an exponential distribution for the disk component and either an exponential profile, Fig. 3.1, (Andredakis & Sanders, 1994) or a De Vaucouleurs profile for the bulge.6 Using a De Vaucouleurs profile gives a slightly better † value than using an exponential profile. The latter, however, is mathematically more sound since its derivative does not go to zero at the origin and it is physically more attractive because a De Vaucouleurs profile will at some (large) radius dominate the total light distribution again. With a double exponential distribution the bulge is significantly smaller than with an exponential disk and a De Vaucouleurs bulge. However, even in the latter case the disk dominates beyond a radius of 20 arcsec (but then only by a factor of a few). Taking the average of the two different fitting procedures to represent the true disk scalelength we derive an exponential disk scalelength in the ® band of 30 q 4 arcsec, close to the literature value of 35 arcsec (Grosbol, 1985).

3.3 Analysis The model projected distributions of section 2 were fitted simultaneously to the observables. However, unlike in Paper 1 we were unable to apply the non-linear fitting (Press et al. 1992) routines successfully, probably because the present data set is noisier and contains fewer data

3.3 Analysis

33

F IGURE 3.1— Azimuthally averaged radial surface brightness profile of NGC 2985 ( -band). Both the disk and the bulge component have been fitted with an exponential profile. The solid line is the sum of the two components.

°

points. Fitting is therefore accomplished using a combination of a simulated annealing (a.k.a. biased random walk, Rix & White 1992) method and the downhill simplex method (Press et al. 1992). Since the number of data points is rather small we have included the emission line data directly into the fitting procedure. This allowed us to better constrain the model distributions although it also meant that we had to sacrifice the consistency check on the result. Error estimates were obtained numerically since the minimisation of a function does not provide direct estimates of the uncertainties involved. One-sigma 6 errors have been estimated from a brute force calculation. In this procedure we calculated † values 6 by varying all five fitting parameters in a broad range around their best-fit values (i.e. † is sampled on a five6 dimensional grid). One-sigma errors correspond to an increase of unity in † over its best-fit

TABLE 3.2— Best-fit parameters and their corresponding one-sigma errors obtained from a brute force calculation. The errors in brackets are obtained from bootstrapping the data.

Parameter 4

y

4

u

S

8t l  ±  9 ” mG (arcsec) F t l ±  ±  9 m” mB 9” l

Best-fit 149 q 12 (15) 73 q 9 (15) 127 q 10 (15) 136 q 14 (28) 0.18 q 0.03 (0.07)

34

CHAPTER 3 DISK HEATING IN NGC 2985

6  I

value. The projection of the grid inclosure where ²:† onto the principal axes determines the one-sigma uncertainty in each individual parameter. A two dimensional projection of this grid is shown in Fig. 3.3. Here the grid is projected onto the plane spanned by the radial and vertical velocity dispersion axes. The distribution of points, ‘the error cloud’, not only yields the one-sigma errors but it also provides a measure of the covariance between the two parameters. The confidence intervals have also been estimated from a Monte-Carlo study of a large number of new data sets, with each new data set drawn randomly from the original data set. This bootstrapping procedure resulted in slightly larger error-bars but did not change the numerical values of the parameters suggesting that the brute force calculation is probably a bit to restrictive 4 in its4 estimate of the uncertainties. For the two parameters that we are most interested in, 8 and F , the difference appears to be at a minimum anyway. The obtained best-fit parameters are listed in table 1 and the corresponding 6 model distributions are together with the data presented in Fig.3.2. The associated † value of 50, however, is a bit higher than what is formally required by chi-square fitting. But the scatter of the data points around the best-fit models, 6 especially along the major axis velocity dispersion is rather large and the large value of † can probably be attributed to that. It even appears that the best-fit profile along the major axis actually lies too low given the data points. Along this axis the observed dispersions are a combination of the tangential and the vertical velocity dispersion components while the minor axis measures the radial and vertical components. Implying that the dispersions along the minor axis should 4 be higher 4 ?³§ than 4 F along the major axis if the components are distributed in the canonical way, 8W§ . However, the difference between the circular velocity and the stellar rotation speed (top panel of Fig. 2) is roughly proportional to the radial velocity dispersion, see equation 3.4. A higher best-fit major axis profile therefore also implies a smaller difference between the circular velocity and the rotational velocity, which is certainly not warranted by this data set. u The best-fit kinematical scalelength parameter, , is about twice as large as the photometrical scalelength. A result predicted by the local isothermal approximation of stellar disks (e.g. van der Kruit & Freeman, 1986).

3.4 discussion

4 [4

8 The results derived in the previous section imply a ratio of the velocity ellipsoid of F is 0.85 q 0.1. The one-sigma error includes the covariance – evident from the fact that the distribution of points in Fig. 3.3 is not completely circular – between the two parameters. With the error estimates obtained from bootstrapping the ratio becomes 4  0.85 4 8 q 0.13. . Indeed, accordAll the one-sigma points in Fig. 3.3 are located below the line F ing to4 the generic picture of the gradual heating of stellar disks (Jenkins & Binney, the [ 4 8 – starting from an isotropic distribution of velocity dispersions – will1990) ratio F become smaller than one given enough time. If only giant molecular clouds are responsible for heating this ratio will approach 0.75 and, if spiral structure also contributes to the disk heating the ratio will be lower. The derived ratio is therefore just consistent with the picture where disk heating is dominated by giant molecular clouds.

3.4 discussion

35

F IGURE 3.2— The best-fitting model distributions (solid lines for the stellar kinematics and a dotted line for the emission line kinematics) and the line-of-sight velocity data. Within 20 arcsec the bulge dominates the total light distribution. This region has therefore been excluded in the analysis. The open circles in the upper panel are ˚ while the filled circles measure measurements of the circular velocity determined from the emission line at 5007 A the stellar rotation derived from the absorption lines.

3.4.1 Comparison to other galaxies The obtained velocity ellipsoid axis ratio is a little higher but comparable to the value found IŠ‰ ). The slightly rounder velocity ellipsoid found in NGC 2985 for NGC 488 ( i ‡ i:q]i may reflect a genuine difference in the internal heating mechanisms. Since both galaxies are multi-armed type spiral galaxies but the Sab galaxy NGC 2985 is of slightly earlier type than NGC 488, which is an Sb galaxy. However, in both galaxies the axis ratios (average values around one disk scale length) are somewhat higher than in the solar neighbourhood (at about two disk scale lengths), where the most accurate measurements using the Hipparcos data indicate a ratio of 0.53 q 0.07 (Dehnen & Binney 1998). This behaviour is again consistent with the predictions of simple disk heating mechanisms since our own Galaxy is of type Sbc and therefore has a higher contribution from heating by spiral structure resulting in a flatter velocity ellipsoid. This effect is illustrated in Fig. 3.4. The observed trend may be slightly fortuitous given the large error-bars on each point. However, photometric observations of edge-on galaxies (van der Kruit and de Grijs, 1999 and references therein) indicate a similar trend, i.e. late type spiral galaxies are more flattened than early type spiral galaxies. A larger sample is clearly needed to clarify the significance of this trend. The relevant measurements for a single galaxy typically require one night on a 4m class telescope. Dou-

36

CHAPTER 3 DISK HEATING IN NGC 2985

F IGURE 3.3— Distribution of the allowed range of values of the extrapolated central radial and vertical velicity dispersions. Small dots are random choices of the model paramaters (projected onto , ) which are consistent with the data at the 2- level, large dots are consistent at 1- . The white contour delineates the 1- region. The upper dashed line indicates an isotropic velocity ellipsoid. The results obtained for NGC488 (Paper 1) are also indicated.

´ œ0µ"¶G· ´ š µ ¶G· ´ ´ ´ ´šT¸‘´ œ

F IGURE 3.4— Observed velocity ellipsoid ratios as a function of morphological RC3 type. The observed ratios in both NGC 2985 and NGC 488 are average values at one disk scalelength while the value derived for the Galaxy is obtained at two disk scalelengths. The horizontal error bars reflect the uncertainty associated with classifying galaxies.

bling or tripling the sample size can thus be done in a relative short time span and should unequivocally establish the validity of the current disk heating theories.

3.4 discussion

37

ACKNOWLEDGEMENTS The WHT is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof´isica de Canarias. Much of the analysis in this paper was performed using IRAF, which is distributed by NOAO.

References Andredakis Y.C., Sanders R.H., 1994, MNRAS, 267, 283 Binney J., Tremaine S., 1987 Galactic Dynamics. Princeton University Press, Princeton Dehnen W., Binney J., 1998, MNRAS, 298, 387 de Vaucouleurs G., de Vaucouleurs A., Corwin H.G., Buta R.J. et al, 1991, Third Reference Catalog of Bright Galaxies. Springer Verlag, New York (RC3) Gerssen J., Kuijken K., Merrifield M.R., 1997, MNRAS, 288, 618 (Paper 1) Grosbol P.J., 1985 A&AS, 60, 261 Heraudeau Ph., Simien F., Maubon G., Prugniel Ph., 1999, A&ASS, 136, 509 Jenkins A., 1992, MNRAS, 257, 620 Jenkins A., Binney J., 1990, MNRAS, 245, 305 Kuijken K., Tremaine S., 1991 in Dynamics of disc Galaxies. G¨otenborg Univ. and Chalmers Univ. of Technology, G¨otenborg, Sweden, p. 71 Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P., 1992, Numerical Recipes. Cambridge University Press, Cambridge Rix H-W., White S.D.M., 1992, MNRAS, 254, 389 Schwarzschild K., 1907 in G¨otingen Nachr., p. 614 Sellwood J.A., Nelson R.W., Tremaine S., 1998, ApJ, 506, 590 Shu F. H., 1969, ApJ, 158, 505 van der Kruit P.C., Freeman K.C., 1986, ApJ, 303, 556 van der Kruit P.C., de Grijs R., 1999 A&A, in press van der Marel R.P., 1994, MNRAS, 270, 271

38

4 The pattern speed of the bar in NGC 4596 Originally published as J. Gerssen, K. Kuijken, M. R. Merrifield, MNRAS 306, 926 (1999)

The pattern speed is a defining parameter of any barred galaxy. A large number of model dependent techniques have therefore been developed to derive the pattern speed. However, the only model-independent technique for measuring this quantity – the TremaineWeinberg method – has hitherto been applied to just one case, the SB0 galaxy NGC 936. In this paper, we apply the technique to a second system, the SBa galaxy NGC 4596. The km s kpc . This result is resulting estimate for the pattern speed is corroborated by a spectrum obtained along the major axis of the bar in this system. The co-rotation radius associated with this pattern speed lies just beyond the end of the bar indicating a fast bar. Combining the bar major axis spectra with data obtained from a Hubble Space Telescope WFPC2 image, we also find strong evidence for a nuclear disk.

¹Kº³»½¼¾À¿^ÁwÂ

A

ÃXÄ

ÃÅÄ

large fraction of all disk galaxies exhibit central bar-like structures. In a comprehensive review, Sellwood & Wilkinson (1993) estimate this fraction to be 30 percent. However, near-infrared observations often show bar-like structures where none are visible in the optical images (Mulchaey & Regan 1997). In addition, bars present in edge-on systems are generally not visible, but their presence may be inferred from kinematical observations (Kuijken & Merrifield 1995, Bureau 1998). The occurrence of bars might therefore be significantly higher than the quoted 30 percent. Theoretical work on building self-consistent models of barred galaxies has made great strides over the past two decades (e.g. Sellwood 1995). A key parameter in all these models is the angular rate at which the bar pattern rotates – the bar’s “pattern speed.” Unfortunately, comparisons between models and real galaxies are hampered because the pattern speed is difficult to determine observationally. Indirect measurements of the pattern speed based on identifying morphological features like rings with resonance radii (Buta & Combes 1996) or matching a model to the observed gas streamlines (Athanassoula 1992) seem empirically to work quite well and give reliable estimates of quantities such as the densities and velocity 39

40

CHAPTER 4 THE PATTERN SPEED OF THE BAR IN NGC 4596

fields. However, if we want to relate the theoretical models unequivocally to real galaxies, we clearly need a model-independent way of determining the pattern speed. Tremaine & Weinberg (1984, hereafter TW) showed that, by invoking the continuity equation, a number of observationally-accessible quantities can be related to determine the pattern speed of a bar directly. Application of this technique has so far been limited to two galaxies, (1987) made the first study of the pattern speed, and Merrifield & Kuijken (1995, henceforth MK) refined his analysis using higher quality data. Recently, Bureau et al. (1998) have used this method to measure the pattern speed of a bar detected only in HI in the blue compact dwarf galaxy NGC 2915. This rather low number of successful applications stems from the difficulty to apply the method in practice. Since stars are continually forming and evolving, the continuity equation for both stars and gas is never strictly met. Further, dust extinction can systematically distort both the mean velocity and the mean location of stars along the spectrograph slit. In slightly irregular galaxies features with different pattern speeds may invalidate the analysis. Finally, the non-axisymmetric signal of a bar is intrinsically weak, so high quality data must be employed if the characteristic signature is to be detected. In this paper, we present an application of the TW method to the strongly barred galaxy NGC 4596 using the implementation of this method described in MK. Briefly, this implementation requires the determination of the mean line-of-sight velocities and mean positions of stars along lines parallel to a barred galaxy’s major axis. The mean velocity can be obtained from Doppler analysis of long-slit spectral observations with the slit oriented parallel to the major axis; the corresponding mean position follows from the integrated light admitted through the slit. The pattern speed can then be calculated from the slope of a linear fit between the mean velocities and the mean positions obtained for different slit positions. One asset of this implementation is that the errors are handled in a reliable and quantifiable manner. The Virgo cluster galaxy NGC I o 4596 is a very early type barred galaxy classified as SBa. Its dust mass is only ‹ hÇÆ i M “ (Roberts et al, 1991), and its total B-V colour of 0.9 (RC3) implies a star formation rate of less than one M “ per year, a result similar to what is usually found in „$ƒ type spirals (Kennicutt, Tamblyn & Congdon, 1994). The position ,TÈ early pÉh kpc) is offset from the major axis by about 45 degrees, the optimal angle of the bar ( configuration when applying the TW method (see MK).

4.1 Observations and Analysis Long-slit spectra of NGC 4596 were obtained using the blue arm of the ISIS spectrograph on the William Herschel Telescope on the 22nd and 23rd of May 1996. The data were obtained J ˚ giving using the 1200 line/mm grating, with m spectra centred on the Mg b feature at pc‹ i|i A, ±  9 ” . Three long-slit spectra, one along the galaxy major a velocity resolution of pʋi axis and two offset parallel to it, were obtained for the purpose of determining the pattern speed. In addition, we obtained a long-slit spectrum with the slit aligned along the bar’s major axis. A schematic view of the slit positions is shown in Figure 4.1, and the observations are summarised in Table 4.1. The spectra were reduced using IRAF. All frames were bias subtracted and flatfielded and corrected for vignetting. The spectra were wavelength calibrated and binned onto a logarithmic scale using the calibration frames taken before or after each exposure. The frames were sky subtracted, and spectra of foreground stars superposed on the long-slit spectra were

4.1 Observations and Analysis

41

NE 38 MAJOR SW 38

BAR 1’

F IGURE 4.1— Contours of the bulge, bar and disk in NGC 4596 from Kent (1990) with our observed slit positions overlaid. The slit positions labeled NE38 and SW38 are offset from the major axis by 38 arcsec. The dashed line indicates the position of the bar major axis, where we also obtained spectra. The rectangular box indicates the position of the HST image discussed in Section 4.2.3.

removed by linear interpolation. These foreground stars need to be removed because their presence would otherwise affect the mean of the light and radial velocity distributions. Finally, the 20 outermost lines of each long-slit spectrum were clipped before averaging the remaining lines to form a single one-dimensional spectrum. The TW method formally requires an infinitely-long slit. However, the outermost lines contribute mainly noise instead of signal to the velocity profiles. The pattern speed derived with and without the outermost lines are essentially the same, though the former has an uncertainty that is about 20 percent larger than the latter. Velocity profiles for the integrated spectrum were measured using the Unresolved Gaussian Decomposition method of Kuijken & Merrifield (1993). This method does not presuppose any specific shape for the velocity profiles, and is therefore particularly well suited to measuring asymmetries in velocity profiles. A K0 giant and a G2V star were used as template stars in this process. Both templates worked equally well. Only for the major axis spectrum did the K0 star provide a better match to the galaxy spectrum than the G2V star. The UGD method was applied first using only a single Gaussian component with varying dispersion in order to get an estimate for the velocity dispersion. The mean velocity of the single component fit obtained along the major axis was taken as the systemic velocity of NGC 4596 and the single component fits to the two offset spectra were subsequently fixed at this velocity. Then a more complete set of Gaussian components was adopted in order to allow for the departures from Gaussianity in the velocity distribution. The positioning of these components, based on the crude estimate of the dispersion derived from the single Gaussian fit, is described in more detail in MK. A detailed description of the error analysis can also be found there. The mean position of the stars along each long-slit spectrum was determined by simply collapsing all wavelengths of the long-slit spectrum on to a one dimensional spatial intensity profile, and then determining the mean of that profile. Errors in this procedure are completely

CHAPTER 4 THE PATTERN SPEED OF THE BAR IN NGC 4596

42

spectrum

exp. time (s)

ne38 major sw38 bar The entries for

Ì$Í

TABLE PA ( )

Ë

~eÐÒÑHÓ Ô

~eÐÒÑHÓ Ô /Õ × Ö Ø ÙÛÚÝÜ ~eÐÒÑHÓ Ô =Õ Þ Ü Î$Ï (arcsec) 71 2010.0 ß 9.2 99.97 118 1973.7 ß 5.4 113.1 71 1946.5 ß 13.5 127.1

4.1— Summary of the spectral analysis and results.

Ì ÍwÎ/Ï

vel. disp.

Î/Ï

1800 130 1864 (118.0) 2100 300 130 1794 (188.8) 2171 1800 130 1864 (118.0) 2100 1200 73 list the minimum, step size and maximum velocities for the means of the UGD components.

negligible compared to the errors in the mean radial velocity. A summary of the analysis is given in table 4.1.

4.2 Results 4.2.1 The pattern speed The resulting velocity and light profiles, together with their respective means, are presented in Figure 4.2. The linear fit between the mean velocities and the mean positions along the slit for the three data sets yields a slope of

àrá 9 ;"< E  J h*q(i s ±  9 ” m  â B@ 9  @ ” m

(4.1)

In order to assess the sensitivity of the derived pattern speed to the accuracy with which we have modeled the non-Gaussian nature of the velocity distribution, we repeated the analysis using the single-Gaussian fits to the velocity distribution. The triangular points and dotted line in Figure 4.2 show the results of this analysis. There is a slight offset in the mean velocities, but the net impact on the slope of the relation is entirely negligible. We have also assessed the validity of the error analysis in the estimates of mean velocities (which dominate the total error budget in this analysis). We simulated galaxy data by artificially broadening the template stellar spectra and adding noise. The scatter in the resulting estimated mean velocities was found to be closely comparable to the errors in the estimates. There was a slight tendency for the errors to be overestimated by a few percent. This effect can probably be attributed to the imposition of a positivity constraint in the derived velocity distributions: this constraint leads to a suppression of the noise in the velocity distribution, which is not accounted for in the error analysis. In any case, this small overestimate in the error analysis makes no significant difference to the derived slopeE of the line in Figure 4.2.  ˜Cã j and a distance to Adopting Kent’s (1990) values of a galaxy inclination of I ‡± ä @ m , the slope of the line in Figure 4.2 corresponds to a pattern speed NGC 4596± of ‹ mX  J  I ˜ 9 of ‹ q ” m ± @ ” m . This value is marginally higher than, but quite consistent with, the ±  ˜ 9 ” @ ” that Kent (1990) estimated more indirectly. value of h 4.2.2 Bar major axis Corroborative evidence for the derived pattern speed comes from analysis of the long-slit spectrum obtained along the major axis of the bar. The mean velocity as a function of position along this axis was calculated by co-adding adjacent one dimensional spectra to obtain a signal-to-noise ratio of at least 25. The mean radial velocities of these averaged spectra were then determined directly in pixel space (van der Marel 1994) assuming Gaussian velocity distributions and using the same giant K0 star used in the derivation of the pattern speed as a

4.2 Results

43

F IGURE 4.2— The central panel shows the mean line of sight velocities versus luminosity centroid position for the three slits parallel to the major axis (circles). The slope of the linear fit yields (dotted line). The dotted line is a measure of the pattern speed derived assuming Gaussian shapes for the velocity profiles (triangles, which are slightly offset horizontally for clarity). Dashed lines indicate the mean of the light profiles (bottom panels) and of the integrated velocity distributions (right panels) from which the central plot was derived. The velocity profiles plotted here are over-sampled, which is responsible for the large error bar on each individual point.

åNºKæÝç è0é

44

CHAPTER 4 THE PATTERN SPEED OF THE BAR IN NGC 4596

F IGURE 4.3— The rotation curve obtained from a spectrum along the bar major axis. Outside the nucleus the bar is rotating like a solid body (triangles), the solid line is a simple linear fit to the triangles. In the inner regions however, a sharp peak in the rotation curve near 3 arcsec is clearly visible (circles).

template. The resulting rotation curve is presented in Figure 4.3. The spatial scale along this position angle has been deprojected to the spatial scale of the major axis. Outside the central few arcseconds, the rotation curve showsà solid E  rotation È „$ƒ 9$;=< body I hJ q along± the bar. A simple linear fit to these data gives a slope of m m    â  ˜ 9 ” @B9 @ ” . In the plane of the disk, this velocity can be written as the sum of i i the pattern speed plus the streaming motion in the bar:

à È „/ƒ , ¯àráê > ¢ 8 9 ;"< .> ¢ ? @GAH9 .0

(4.2)

8 ¢ ?Nì are the polar components of the mean streaming velocity, êí , @BAC9 . , and where .  s ˜ ë j ¢ is the I˜ difference between the position angle of the major axis ( i j ) and the position ˜ angle of the bar ( ‡ j ) in the plane of the disk. Along the bar major axis ¢ 8 will be almost ê zero and can therefore be neglected. The m orbits that are believed to make up the bulk of the bar (Contopoulos & PapayannopoulosÈ „/1980) the same direction as the galaxy, . in, Which àrá à ƒ § àrá rotate G @ H A 9 is indeed what we observe, so ¢ ? has the same sign as . Hence, I h § J h @GAC9 s ˜ j  I I . Thus the sense of internal streaming in the bar is as expected. 4.2.3 Nuclear disk Prompted by the fast-rotating nuclear component apparent in Figure 4.3, we extracted a WFPC2 image of the central regions of NGC 4596 from the HST archive. Fitting the isophotes in the innermost few arcsec using the ELLIPSE task in the package of  @ with the ˜ â @B9 STSDAS IRAF , we found that the isophotes are all aligned in the central p galactic disk. At larger radii, the position angles of the ellipses gradually level off to the position angle of the bar (see Figure 4.4).

4.3 Discussion

45

F IGURE 4.4— The top left panel shows the position angles of ellipses fitted to an HST image of the nucleus of NGC 4596. The position angles of the ellipses remain more or less constant within the first 2.5 arcsec and then gradually level off to the position angle of the bulge. In the bottom left panel the derived ellipticities as a function of radius are plotted. The left panel shows the luminosity profile along the bar major axis derived from the data published by Kent (1990). The profile shows the flat bar plateau commonly found in early-type galaxies. The hatched region denotes the range in which the corotation radius lies.

The dimension of the area of constant position angle closely corresponds to the radius at which the peculiar peak in the rotation curve occurs. Kent (1990) also observed this peak in his long-slit spectra, and found that this feature is strongest along the bar major axis. If we can identify this area with a nuclear disk, its position angle coincides roughly with the major axis of the outer parts of the galaxy. The kinematical axis, however, seems to be aligned with the bar. Coupled with the observation that this projected nuclear disk is rounder than the projected galactic disk ( î = 0.21), these results imply that either the potential is not spherical in the centre of this galaxy or that the nuclear disk is not in the plane of the galaxy.

4.3 Discussion We have made only the second successful application of the TW method for calculating stellar-bar pattern speeds. In order to interpret ,* the it is instructive to calculate what is ï ƒ .result, known as the “co-rotation radius” of the bar, This radius is the point in the galaxy at which stars same angular frequency as the bar pattern. Combining the derived à á rotate with the(1990) value of , ï ƒ with Kent’s model for the circular velocity curve of the NGC 4596, we m¬ñ ò find that is h sCð l ñ ó kpc in this galaxy. Figure 4.4 the luminosity profile along the , ï ƒ shows ” major axis of the bar, with the range of allowed marked. The point at which bar ± the @ ends is apparent as the “shoulder” in the surface brightness profile at a little over h . This , È „$ƒ to , ï ƒ of I I ‹|ð l ññ ô$6 õô . Thus, the bar ends at close to, but a little inside, yields a ratio of ”l the co-rotation radius. MK found the same result when they applied the TW method to the bar in NGC 936.

46

CHAPTER 4 THE PATTERN SPEED OF THE BAR IN NGC 4596

In a barred potential, the orbits of stars are aligned parallel to the bar distortion inside the co-rotation radius, but perpendicular to it outside (Contopoulos & Papayannopoulos 1980). Since only stars whose orbits are aligned along the major axis of the bar contribute to its excess density, any self-consistent bar must end inside its own co-rotation radius. Thus, the two directly measured co-rotation radii are as small as they are physically to be. This àrá allowed limit also means that , the bars cannot rotate any faster: larger values of would correspond ï ƒ , which are forbidden. Thus, these bars can be described as “fast to smaller values of rotators.” The speed at which these bars rotate is interesting because numerical simulations by Debattista & Sellwood (1998), following work by Weinberg (1985) and Hernquist & Weinberg (1992), have shown that bars forming in dense dark matter halos are rapidly decelerated by dynamical friction. Thus, unless we have caught the bars in NGC 936 and NGC 4596 exceptionally soon after they formed, these galaxies cannot contain centrally-concentrated dark matter halos. This conclusion conflicts with the results of some cosmological cold dark matter simulations of galaxy dark halo formation, which predict that all galaxies should form with a common centrally-concentrated dark matter distribution (Navarro, Frenk & White 1996). These conflicting results could be resolved if the inner part of the halo, i.e. the part coinciding with the bar and the disk, somehow acquires a net rotation. Tremaine & Ostriker (1998) have identified a number of possible mechanisms that can spin up the inner halo. However, it should be borne in mind that high halo densities in the cores of galaxies also serve to inhibit the formation of bars (Ostriker & Peebles 1973). Thus, these two galaxies, which were chosen specifically because they contain strong bars, may constitute a biased subset of central halo densities. If we are to assess whether low central dark matter density is a generic property of galaxies, we need to look at the pattern speeds of a fairer sample of galaxies, including some with weaker bars. The results obtained on the blue compact dwarf galaxy NGC 2915 by Bureau et al (1998) are interesting in this respect. However, in late type galaxies the underlying assumption of continuity, required by the TW method, will be violated due to vigorous star formation and large amounts of gas present in these galaxies. It also remains to be demonstrated whether the spiral disturbances in such an HI disk can be characterised by a spatially constant real pattern speed, i.e. no winding or growth. Applying the TW method to the stellar kinematics of galaxies of a slightly later type than SB0 (NGC 936) and SBa (NGC 4596) however, not only seems feasible but it will also facilitate a comparison between the TW method and results derived using gas flow methods. Another interesting problem that the implementation of the TW method described here could tackle is the direct measurement of the pattern speed of a – fairly open – spiral arm pattern (although the spiral pattern has to be steady if these measurements are to succeed). The galaxy presented here, NGC 4596, is a strongly barred galaxy. It will, of course, be more difficult to detect the kinematic signature of the pattern speed in weakly-barred or later type systems. However, the combination of high throughput spectrographs on large telescopes should soon allow us to meet this challenge.

Acknowledgements Much of the analysis in this paper was performed using IRAF, which is distributed by NOAO. MRM is supported by a PPARC Advanced Fellowship (B/94/AF/1840).

4.3 Discussion

47

References Athanassoula E., 1992, MNRAS, 259, 345 Bureau M., 1998, PhD thesis, Australian National University Bureau M., Freeman K.C., Pfitzner D.W., Muerer G.R., 1998, AJ submitted Buta R., Combes F., 1996, Fund. Cosmic Physics, 17, 95 Contopoulos G., Papayannopoulos Th., 1980, A&A, 92, 33 Debattista V. P., Sellwood J. A., 1998 ApJ, 493, L5 Hernquist L., Weinberg M. D., 1992, ApJ, 400, 80 Kennicutt R.C., Tamblyn P., Congdon C. W., 1994, ApJ, 435, 22 Kent S. M., 1987, AJ, 93, 1062 Kent S. M., 1990, AJ, 100, 377 Kuijken K., Merrifield M. R., 1993, MNRAS, 264, 712 Kuijken K., Merrifield M. R., 1995, ApJ, 443, L13 Merrifield M. R., Kuijken K., 1995, MNRAS, 274, 933 (MK) Mulchaey J. S., Regan M. W., 1997, ApJ, 482, L135 Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ, 462, 563 Ostriker J. P., Peebles P. J. E., 1973, ApJ, 186, 467 Roberts et al., 1991, ApJS, 75, 751 Sellwood J. A., Wilkinson A., 1993, Rep. Prog. Phys., 56, 173 Sellwood J. A., 1995, in Buta R., Crocker D. A., Elmegreen B. G., eds., Barred Galaxies, IAU Colloquium 157, p. 259 Tremaine S., Ostriker J. P., 1999, MNRAS, 306, 662 Tremaine S., Weinberg M. D., 1984, ApJ, 282, L5 (TW) van der Marel R. P., 1994, MNRAS, 270, 271 Weinberg M. D., 1985, MNRAS, 213, 451

48

5 Planetary nebulae kinematics in M94 Originally published as N.G. Douglas, J. Gerssen, K. Kuijken, M.R. Merrifield, MNRAS in press (2000)

The planetary nebula populations of relatively nearby galaxies can be easily observed and provide both a distance estimate and a tool with which dynamical information can be obtained. Usually the requisite radial velocities are obtained by multi-object spectroscopy once the planetary nebulae have been located by direct imaging. Here we report on a technique for measuring planetary nebula kinematics using the double-beam ISIS spectrograph at the William Herschel Telescope in a novel slitless mode, which enables the detection and radial velocity measurements to be combined into a single step. The results on our first target, the Sab galaxy NGC 4736, allow the velocity dispersion of the stellar population in a disk galaxy to be traced out to four scale lengths for the first time and are consistent with a simple isothermal sheet model.

T

HE he outer kinematics of galaxies have played a crucial role in our understanding of their structure. The dark matter halos are most important there, so that conclusions about their shape, mass and extent may be drawn that are less dependent on assumed mass-tolight ratios of the observed stars. Most of the angular momentum resides at large radii, and relaxation times are longest there, possibly enabling echos of the formation process to be observed directly. However, the required observations are rather difficult. The integrated stellar light of a galaxy rapidly becomes too weak at large radii to do spectroscopy. In the case of elliptical galaxies, the old stellar populations have now in a few cases been probed as far as two effective radii (e.g., Carollo et al. 1995; Gerhard et al. 1997). Some tracers, such as globular clusters and HI emission, can be observed at larger radii, but neither provides a reliable tracer of the kinematics of the relaxed, old stellar population. Moreover systems like S0s and ellipticals generally lack an extensive gaseous disk. Fortunately an alternative tracer of the kinematics out to large radii has been identified by Hui et al. (1993), who showed that the radial velocities of a galaxy’s planetary nebula (PN) population constitute a suitable diagnostic. Planetary nebulae (PNe) appear in the post-main sequence phase of stars in the range 0.8 - 8 M “ . Fortunately, in all but the very youngest of systems the PN population is strongly correlated with the older, and therefore dynamically

49

50

CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

relaxed, population of low-mass stars. This statement is true not only because of the statistics of stellar formation and evolution, but also because the PN lifetime is itself a strongly decreasing function of progenitor mass (Vassiliadis & Wood 1994). PNe emit almost all of their light in a few bright emission lines, particularly the O[III] ˚ There is evidence that the PN O[III] luminosity function is essentially constant line at 5007A. with galaxy type and metallicity (Jacoby et al 1992), so that the observed bright-end cut-off magnitude ’÷ö (Ciardullo et al 1989) represents a ‘standard candle’ with which distances can J I m ù be determined. 6 m At a distance of 10 Mpc, this cut-off corresponds to a flux of iøÆ i!” erg cm ” s ” , making PNe within one dex of this limit easily detectable in one night with a 4-m As a rule of thumb, approximately 100 such PNe are found to be present per I i ó Ltelescope. “ of B-band luminosity (Hui 1993), so they are seen in sufficient number to study the kinematics of the stellar population of the host galaxy. The usual approach in making such kinematic studies has been to identify the PN population by narrow-band imaging and then to re-observe the detected PN spectroscopically to obtain radial velocities. However, other strategies exist that avoid the need for several observing runs. For example, Tremblay et al. (1995) used Fabry-Perot measurements in a PN kinematics study of the SB0 galaxy NGC 3384. In this paper, we describe a novel alternative, based on slitless spectroscopy, and discuss its application to the Sab galaxy M94.

5.1 Slitless Spectroscopy Our method for obtaining the kinematics of PNe is outlined in Figure 5.1. The galaxy under study is imaged through narrow-band filters around the two strongest emission lines in a typical PN spectrum, Hy and O[III]. The H y image is recorded directly, but the O[III] light is dispersed. Comparison of the dispersed and undispersed images then allows the kinematics of the PNe to be measured, without prior knowledge of the location of the PNe. Two modes of analysis are possible: Dispersed/Undispersed Imaging (DUI): In the dispersed blue arm the PNe will be visible through their O[III] emission as point sources, displaced from their ‘true’ positions by an amount related to their radial velocity, against a background of dispersed galactic light. The red arm will detect the PNe through their H y emission, along with any other objects with line or continuum emission in the pass band of the filter. Assuming that the PNe can be unambiguously identified in the Hy image, their position in the O[III] image will give the radial velocity. We chose to disperse the blue rather than the red light since PN have a higher flux at O[III] than at H y , and gratings are less efficient than mirrors. Counter-Dispersed Imaging (CDI): The method of counter-dispersed imaging was described in an earlier paper (Douglas & Taylor 1999). In this mode, pairs of dispersed O[III] images are made with the entire spectrograph rotated by 180 degrees between exposures. The difference in the position of a given PN in the two dispersed images again reflects its radial velocity. In this case the undispersed Hy image can be used as a consistency check on the derived positions of the PNe. We have implemented our method on the ISIS medium-dispersion spectrograph at the Cassegrain (f/10.94) focus of the 4.2m William Herschel Telescope. The slit unit was removed during the observations, and the O[III] and H y light paths were separated with a dichroic before being passed through appropriate narrow-band filters. The filters ( ú 5026/47 I arcmin and ú 6581/50) were custom-made for this project in order to exploit the full hÇÆ

5.1 Slitless Spectroscopy

51

planetary nebulae

Red Arm

Blue Arm 12 m

m

ati gr

irr or

l/m

fla t

00

dichroic

ng

narrow-band Hα filter

narrow-band O[III] filter

F IGURE 5.1— Diagram showing schematically how one can use a dual-beam spectrograph to study PN kinematics. The narrow-band images in the two arms allow one to identify the PNe and measure their line intensities in both the [OIII]5007A˚ and H lines. The dispersive element in the blue arm shifts each PN image by an amount proportional to its redshift. In the red arm the grating has been replaced by a mirror.

û

undispersed Hα image

dispersed O[III] image

field of the instrument in slitless mode, and to give adequate velocity coverage. We used a 6 1200 g/mm (first order) grating in the blue arm. Both arms contained 1024 -pixel Tek CCD detectors. Thus, dispersed images in the blue (calibration showed the dispersion ±  we9 ” obtained m per pixel) to be about 24 and simultaneous direct images in the red. DUI observations are accomplished in a single exposure; CDI requires two exposures. The overall efficiency of this setup, including telescope, instrument, filter and CCD, was found from observations of a standard star (Feige 34) to be 14% in the blue and 20% in the J J O[III] photons per second from red for air mass of 0. We therefore expected to detect p the brightest 6 PN when viewed at 6.6 Mpc. Dark sky (V=21.4) would produce p 2 counts 6 per arcsec per second, and the4 background light of the galaxy 1–5 counts> per arcsec . A J reasonable goal is to obtain a 4 detection over the top decade (üþýÿü ö ‹ ) of the PN population, corresponding to p 4 hours of integration if the seeing conditions are of the order of one arcsec. The required integration time is approximately proportional to the square of the seeing.

52

CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

TABLE 5.1— Galaxy parameters

Name Position (J2000) Hubble  ‚ type V
 l B Angular size Inclination Scale length Position angle

NGC 4736 (M94) 12h50m53.061s +41d07m13.65s SA(r)ab 308 q 1 km/s I|I J Æ 8.99 ‰ I arcmin  35 j 57 q 10 arcsec 105 j

5.2 Observations The observations were carried out on 1997 April 11 and 12. For this pilot project NGC 4736 (M94) was chosen. It has a large angular size and is at a distance of 6 Mpc (Bosma et al 1977). The galaxy shows some peculiar morphological features, most notably an inner and an outer optical ring with radii of 1 and 5.5 arcmin respectively. The stellar light is too faint for direct optical spectroscopy outside 1 arcmin, and our goal was to measure PN kinematics to three times this radius. Key parameters of NGC 4736 are listed in Table 5.1, and the observing log is given in Table 5.2. Two fields were observed, 3 arcmin west of centre on the major axis, and 3 arcmin north of centre on the minor axis. The major axis was observed at two orientations (allowing CDI mode) while the minor axis was observed in one orientation only. We took the major axis position angle to be 90 j , as would seem appropriate from the relevant isophotes (see Figure 5.3). Total integration times were 6.0hrs on the Western field (4.6hrs in one orientation, and 1.4hrs with the spectrograph rotated by 180 degrees), and 3hrs on the Northern field. The observing conditions were close to photometic with seeing, as judged from stellar images in the red arm, less than 1.1 arcsec at all times. We also observed a flux standard star for photometry and a Galactic PN as a radial velocity reference. A second star was observed as a spectral reference. The custom-made [OIII] and Hy filters had a central wavelength and peak transmission ˚ ˚ ˚ and 50A, ˚ of 5026A/0.823 and 6581A/0.915, respectively. The nominal FWHM was 47A ˚ while the effective photometic bandwidth was evaluated graphically and found to be 38.7A ˚ respectively. and 45.7A,

5.3 Data Reduction 5.3.1 Calibration The dispersion in the blue arm was measured by inserting a slit and using an arc lamp, and ˚ found to be 0.3992 A/pixel. The spectrum of the star HD66637 was then observed through the same slit and wavelength-calibrated. Subsequent observations of the same star at numerous positions in the field (after removal of the slit) established that the dispersion could be taken as constant over the field. The combination of these observations with the undispersed red

5.3 Data Reduction

53



TAB LE 5.2— Log of our observations at the WHT, La Palma Observatory. PA is the position angle of the spectrograph and T the total integration time (where two values are given these refer to the red/blue arms respectively).

Field

PA

T 60 2/10 16,453 5 4,868

UT April 11 20:35 21:15 21:20 - 2:13 2:03 2:36 - 4:52

HD66637 Feige 34 N4736 - major axis PN 49+88.1 N4736 - major axis

90 90 90 90 270

HD66637 Feige 34 N4736 - minor axis

90 90 0

Airmass 1.06 1.07 1.35 - 1.07 1.06 1.12 - 1.54

0.1/10 3/60 10,800

April 12 20:29 20:57 21:02 - 0:08

1.06 1.09 1.42 - 1.03

arm positions of HD66637 gave an unambiguous solution for the transformation between objects in the red (direct image) and blue (dispersed image). (Note that with this technique the radial velocity of the star does not enter into the calculation.) To check the zero point of the velocity scale, we moved the telescope from the reference star to the Galactic nebula PN 49.3+88.1, for which the heliocentric radial velocity L I h I ±  planetary 9 ” L m I(Schneider is listed as In ten pointings over the field of the specm , in agreement ˜ s iq ˜ J et.±  al9 1983). trograph we measured ” calculated observatory L I˜|˜ ±  9 ” m . Unfortunately we discoveredwithlaterthethat frame redshift of at certain telescope orientations the flexure is large enough to cause significantly larger errors. However, such flexure only introduces an offset in absolute velocity, and does not compromise our ability to study a galaxy’s internal kinematics. In order to derive an absolute calibration for the velocity scale, we have also obtained a long slit observation of two of the objects detected in this  analysis (see 5.4). The spectrograph field of view with the slit unit removed consists of an approximately unvignetted area of about 4 arcmin Æ 1 arcmin, but we obtained useful data outside this region. Correcting the observed fluxes for the vignetting is only straightforward for the red (undispersed) arm. In the blue arm the correction is complicated by the fact that the image is dispersed. The sky flat measured in the blue arm was found to closely approximate the aperture function in the red arm, shifted by a small number of pixels, transformed to blue arm coordinates and then convolved with the filter profile at the appropriate dispersion. We therefore carried out the complete analysis after correcting only for the pixel-to-pixel variation of the CCD responses, determined in the usual way. Once the PNe were identified it was possible to determine their wavelength and their positions in the aperture prior to being shifted by the spectrograph, so that the O[III] magnitudes could then be corrected analytically both for the filter response, which was fitted with a polynomial, and for vignetting. 5.3.2 Object identification Scripts based on IRAF procedures were used for all of the data reduction.

54

CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

Due to spectrograph flexure, individual exposures needed to be aligned before being added. This was accomplished by a simple shift (at least one PN was visible in each individual exposure). The images were then combined by computing a weighted and scaled median. A spatial median filter was applied to the combined frame, and the result subtracted from the original image to yield a field of unresolved objects against a background with a mean of zero. The PNe and any other point sources in the red and blue images were extracted by two methods: (A) Blinking and hand-tagging, followed by a PSF-fitting step to evaluate the shape and size parameters. For DUI mode observing it was usually found to be easier to search the range of possible (red) coordinates corresponding to an object seen in the blue (see Fig. 5.2). (B) an automated procedure based on object lists generated with DAOPHOT. A 2D-gaussian fit to each detected image was used to select PN candidates. The FWHM of a candidate was required to be within a small range of that of the seeing disk (PNe are unresolved) and the axial ratio close to the value 1.28 expected from our instrumental configuration (the ellipticity arises from the anamorphic effect of the grating). The object lists were then correlated to search for potential PN image pairs. 5.3.3 Comparing Spectral Modes We identified PNe in NGC 4736 along the minor axis with DUI mode observations and along the major axis using CDI (with DUI mode data being redundant). Although CDI requires two distinct integrations, we found that data obtained from CDI results in a higher number of detected PN per unit integration time. For visual identification using blinking, CDI is considerably easier since the two images have the same plate scale and similar properties with respect to sky noise and confusion. Therefore to illustrate the numerical superiority of using two dispersed O[III] images we rely on the automated search results for 4 the major axis observations only. 36 PNe were identified in this field from matching 2.5 sources in the counterdispersed O[III] images. The limiting factor here was the shorter integration time with one of the two spectrograph orientations: had both integration times been equal we would presumably have found yet more PNe. By comparison, only 24 PNe were detected from the DUI mode analysis of the same field. Therefore, we conclude that a significant number of PNe are too faint in H y for the DUI mode to detect them.

5.4 Long-slit data It has been mentioned that instrument flexure, particularly between sets of observations in CDI mode, can lead to an uncertainty in the absolute velocity scale. To remove this uncertainty we attempted to obtain the velocity of at least one object in the major axis field via the Willian Herschel Telescope service data program. As the PNe are faint, with effective Vband magnitude of around 25, the slit had to be positioned ‘blind’ on the basis of the position computed from the dispersed data. Fortunately the astrometry does not depend on velocity, but only on correct identification of PN pairs, and on the centroiding of the dispersed images of stars in the field. We requested a spectrum using ISIS in long-slit mode and with the slit at a position and PA chosen such as to fall across two objects. This provided a good test of the astrometry. The service observation was attempted on 1999 July 28. Both objects were acquired, and their

5.5 Results

55

F IGURE 5.2— An example of the ‘postage stamp’ method for detecting red counterparts. The boxes on the right each contain one point source identified in the blue frame. The boxes on the left side show the corresponding parts of the red frame. Any red counterpart must be located somewhere within the box since the size of the box is such that it encompasses the velocity range spanned by the filter. The horizontal location of the counterpart is a measure of the object’s radial velocity. In the vertical direction we require the positional agreement to be within one pixel.

separation along the slit agreed with that calculated. One of the objects, suspected of being an HII region, as such. The radial velocities obtained had an internal error of ±  9 ” was m , asconfirmed judged from the values obtained from different lines, and were used to about 10 calibrate the major axis data (Table 5.3).

5.5 Results The PNe identified along the major axis are listed in Table 5.3 and those along the minor axis in Table 5.4. Their positions are also shown in Fig 5.3. As suggested by the successful longslit experiment, the positional uncertainty of the order of 1-2 arcsec. The internal error in ±  9 ” m .isThe minor axis velocities have an offset that has the velocities is approximately 10

56

CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

F IGURE 5.3— Digitised Sky Survey image of NGC 4736 (North at top) with the observed fields marked with boxes and the PNe shown as open circles.

not been determined, but the values as presented have an average velocity near systemic, as would be expected. The derivation of velocities from DUI mode data, as was used for the minor axis, is in fact much less sensitive to flexure. However, in order to reduce the number ± 9” m of candidate objects in the red image, only radial velocities between 200 and 500 were searched for, so this table has to be used with caution. 5.5.1 Luminosity function We placed a premium on detecting as many PNe as possible, even in the partially vignetted region of the instrument. Considerable corrections have been applied, and the magnitudes should therefore only be taken as indicative. The luminosity function of the objects detected is presented in Fig. 5.4. The ü ö cutoff (24.4) for the assumed distance of 6 Mpc is indicated. At the faint end the luminosity function is, of course, significantly incomplete while at the bright end some objects are brighter than the cutoff. The latter are probably HII regions and have therefore not been included in the analysis of the kinematics. The number of PNe found in the major axis field (CDI mode) is in rough agreement with  㠋ã, predictions. From the basic data on NGCm 4736 compiled by Mulder (1995) (üa­   J I s i Mpc) we have r­ i ‡ Æ i l “ , and on the basis of the results of Hui et al (1993) the expected number of PN in the top decade of the PNLF in M94 would therefore be around 2000. Mulder also found the galaxy to be fairly well-fitted by an exponential disk

5.5 Results

RA (J2000) 12:50:49.46 12:50:49.42 12:50:49.35 12:50:48.93 12:50:48.62 12:50:48.40 12:50:48.53 12:50:47.97 12:50:47.87 12:50:47.73 12:50:47.61 12:50:47.59 12:50:47.50 12:50:47.17 12:50:46.92 12:50:46.93 12:50:46.32 12:50:46.40 12:50:46.13 12:50:46.17 12:50:45.27 12:50:45.11 12:50:44.65 12:50:44.26 12:50:43.79 12:50:43.76 12:50:43.29 12:50:43.03 12:50:42.95 12:50:42.66 12:50:42.58 12:50:42.48 12:50:42.19 12:50:41.40 12:50:41.17 12:50:41.17 12:50:40.87 12:50:40.74 12:50:40.55 12:50:40.26 12:50:40.15 12:50:38.62 12:50:38.67 12:50:38.55 12:50:38.02 12:50:37.90 12:50:36.34 12:50:35.24 12:50:34.75 12:50:34.15 12:50:25.18 12:50:48.71 12:50:42.79

57

Dec (J2000) 41:07:09.5 41:07:40.3 41:07:17.5 41:07:51.2 41:07:22.9 41:06:17.3 41:07:45.8 41:07:10.8 41:07:09.8 41:06:33.2 41:07:00.2 41:06:56.9 41:06:26.2 41:06:27.4 41:06:05.5 41:06:35.3 41:06:18.3 41:07:46.8 41:06:11.2 41:08:13.6 41:06:36.8 41:06:27.8 41:06:51.3 41:07:39.2 41:06:11.4 41:06:48.3 41:07:54.9 41:06:07.7 41:07:49.5 41:06:11.8 41:06:36.6 41:07:52.8 41:08:15.0 41:07:01.5 41:06:21.0 41:07:46.4 41:05:57.5 41:06:11.7 41:07:46.4 41:08:00.7 41:06:51.3 41:07:04.9 41:08:05.0 41:06:44.4 41:06:20.9 41:08:06.1 41:06:48.0 41:06:10.8 41:06:18.3 41:05:58.2 41:06:16.4 41:06:32.7 41:07:48.9

Rvel 459 472 463 483 444 309 450 508 378 296 345 391 525 429 413 378 357 466 380 491 478 308 369 432 353 348 457 485 473 405 428 425 476 433 413 339 414 410 417 400 383 409 391 418 423 464 430 425 408 379 415 378 454

  23.44 23.18 23.48 22.54 23.18 24.80 24.63 25.46 25.78 24.56 24.45 25.33 25.52 25.34 25.14 25.41 25.60 24.95 24.24 24.34 24.91 25.30 24.82 25.78 24.95 25.18 22.59 24.91 26.39 22.65 25.00 24.88 24.58 24.98 25.21 24.26 25.53 24.72 25.33 24.74 25.41 25.35 25.00 25.54 25.14 25.65 24.93 24.87 25.50 25.18 25.22

FWHM 3.52 3.59 3.31 3.29 3.31 3.24 3.54 3.9 2.79 3.9 3.61 3.38 3.5 3.54 3.45 3.47 3.05 4.38 3.94 3.57 4.37 3.73 3.66 2.67 3.33 2.79 3.52 3.17 2.7 3.92 4.34 3.5 3.07 3.5 3.47 4.7 3.47 4.37 3.61 4.04 2.77 3.71 4.2 2.89 3.68 3.05 3.07 3.45 3.31 2.91 4.3 5.45 3.54

TABLE 5.3— Fifty-three point sources in the major axis field. Rvel (heliocentric) is the measured relative radial velocity from the slitless spectroscopy plus an offset established by an additional calibration (see  5.4).   = -2.5 log( ) - 13.74 is the apparent V-band magnitude of the objects, where  is the flux in erg cm  s . The magnitudes have been corrected for vignetting as described earlier. The vignetting correction could not be reliably applied for two objects as they were too close to the edge of the aperture, and their magnitudes are not given. FWHM (in pixels) refers to the major axis of the gaussian fit.

à ÃÅÄ

CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

58



TAB LE 5.4— Fourteen point sources in the minor axis field. The coordinates are derived directly from the position in the red image (see text).    gives the ratio of the fluxes (in erg cm  s ) seen in the red and blue images. Other symbols are as in Table 5.3, except that the radial velocities have not been checked against an external reference and may have a small common offset.

à ÃÅÄ

RA (J2000) 12:50:52.02 12:50:53.68 12:50:50.03 12:50:50.16 12:50:51.57 12:50:56.25 12:50:52.22 12:50:48.81 12:50:57.74 12:50:46.14 12:50:49.62 12:50:52.93 12:50:53.86 12:50:51.57

d

Dec (J2000) 41:11:22.3 41:10:15.8 41:09:22.2 41:09:01.5 41:08:58.3 41:08:42.6 41:08:35.6 41:08:25.3 41:08:19.7 41:08:13.2 41:08:04.5 41:08:02.5 41:07:56.1 41:07:52.1

Rvel 330 263 341 311 270 265 268 367 252 408 363 496 310 367

! 

  

26.26 24.37 26.56 25.67 24.74 25.54 24.35 26.21 25.35

1.26 0.38 1.11 0.82 0.62 0.65 0.48 1.57 0.65

24.84 25.63 23.35 23.62

1.28 2.47 2.61 8.87

FWHM 3.36 3.17 3.71 4.04 3.1 4.74 3.54 2.72 4.25 3.61 5.02 4.46 3.31 3.76



with scale length 57 arcsec. The region we examined includes 0.029 of the light of such an exponential, which should therefore include 59 PNe in the brightest decade. This number compares well with the 53 actually found, though the agreement may be somewhat fortuitous given the incompleteness at the faint end. 5.5.2 Rotation curve In Fig 5.5 the line-of-sight velocities of the 53 objects in the major axis field are plotted as function of radius, after subtraction of the systemic velocity. Flat rotation is seen until the last measured point at almost 5 scale lengths. For comparison we overplot the HI/CO rotation curve of Sofue (1997), projected into the plane of the sky. ± Considering objects near a distance  9 ” m , in agreement of 1 armin along the major axis the mean velocity is 98 with the gas ±  9 ” m at that point. rotation velocity of 103 ±  9 ” m , consistent with the The uncorrected minor axis data have± a velocity mean of 329 m  9” . systemic velocity, and a dispersion of 68 5.5.3 Velocity dispersion Generally, the vertical structure in disks of spiral galaxies is reasonably well described by an isothermal sheet approximation (van der Kruit & Searle 1982; Bottema 1993). In this model, the vertical velocity dispersion is found to follow an exponential decline with radius with scale length twice that of the surface density. With the additional assumption that the dispersion ellipsoid has constant axis ratios throughout the disk, one finds that the line-ofsight velocity dispersion follows the same decline, independent of the galaxy’s inclination. Figure 5.6 shows the velocity dispersion in bins of distance along the major axis. Seven objects were eliminated from the kinematic analysis as their brightnesses suggested that they

5.5 Results

59

F IGURE 5.4— The luminosity function of the 64 objects for which magnitudes could be determined. The cutoff peak for PNe is clearly defined. The objects brighter than this cutoff are probably bright HII regions.

d

are HII The curve is the least-squares exponential fit with central velocity dispersion ±  regions. 9 ” m and scale length " = 130 111 close to the published d value for the  9 ” m )are I J arcsec. I ‹ ± These central stellar velocity dispersion ( i*q obtained from absorption-line spectra J  ICI h arcsec), (Mulder and van Driel, 1993) and to twice the photometric scale length ( suggesting that the isothermal sheet approximation is reasonable. 5.5.4 Combined Kinematic Model The binning in Fig 5.6 effectively assumes that the PNe all lie close to the major axis. In fact, they are located up to one arcminute from the axis, at azimuths up to 45 j , so a more sophisticated approach is required. We therefore projected the PNe on to a thin disk of fixed ¬. coordinates. inclination (35 j ), giving # The nebulae’s line-of-sight velocities can then be compared with a model consisting of ad three-dimensional isothermal sheet with a flat rotation curve. This4 model five parameters, namely the three components of the central velocity 4 4 has 8 , the scale length " , and the rotation amplitude. A maximum likelihood dispersion F ? method was then used to fit the model. We added 12 PNe from the minor axis field (Table 5.4) to help constrain the fit (two were excluded from the fit as probable HII regions). In practice the4 6 data not adequate to constrain all five parameters. Using the canon 4were 846 [ [ J 4 from the epicyclic ical relationship ? approximation (Binney & Merrifield 1998, d 8 to vary over eq. 11.18) and allowing F the range 0.2 to 2.0, we found a robust maxi I h|hZq ˜ i arcsec, central velocity dispersion mum scale length " 4 ©=ª/«  likelihood ±  9 ” m with  I ‡|‡ q I|I ±  9 ” m . These results IŠJ iq ˜ i solution , and circular rotation speed ¢ U ±  9 ” m ) and with (twice) are consistent with the HI rotation speed at 1 arcmin radius (180 the photometric scale length (57 arcsec).

60

CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

F IGURE 5.5— Line-of-sight velocities of the 53 objects in the major axis field plotted as a function of distance along the axis. The dotted line shows the gas rotation curve, from Sofue (1997.)

It was not possible to constrain the shape of the velocity ellipsoid with these data – such an analysis would 4 F [ require 4 8 I a more complete ‡ azimuthal 4 coverage of the galaxy. However if we assume i ‹³ý ý i then we infer ‹ ý 8 ý ICI i ±  9 ” m at one photometric scale length, consistent with the trend between rotation speed and disk velocity dispersion found by Bottema (1993). Thus far we have ignored measurement error in the velocities, which will tend to increase 4 the measured velocity dispersion. This turns out to be a small effect: allowing for a 1 error ± m  9 ” , the fitted dispersion becomes approximately 3% smaller and the scale length of 10 is unchanged.

5.6 Conclusions In this paper we have demonstrated how the kinematics of the PN population in a galaxy can be measured by slitless spectroscopy through narrow-band filters with a dual-beam spectrograph. We compared two possible modes: dispersed/undispersed imaging, in which a dispersed O[III] image is compared to an undispersed H y image; and counterdispersed imaging, in which two O[III] images, dispersed in opposite directions, are analysed. It turns out that the latter method is more effective: evidently the H y fluxes of faint PNe are not reliably high enough to allow both spectral lines to be used. Our pilot experiment was performed on the large nearby Sab galaxy M94. It has revealed

5.6 Conclusions

61

120

100

80

60

40

20

0 0

2

4

6

F IGURE 5.6— The dispersion in radial velocities computed by binning the radial velocity measurements, together with the bestfit exponential curve.

a PN population in the disk whose rotation curve remains flat, and whose velocity dispersion declines radially exponentially, consistent with the predictions of a simple isothermal sheet model. PNe were detected out to five exponential scale lengths, well beyond the reach of kinematic measurements based on integrated-light absorption-line spectroscopy. The number of PNe detected was consistent with expectations. The present experiment was limited to two fields in this large galaxy. Complete coverage of the galaxy should yield around 2000 PNe, and would allow a detailed kinematic model to be fitted, including a determination of the axis ratio of the velocity ellipsoid following the technique of Gerssen et al. (1997). Obtaining such data for a small sample of nearby galaxies in just a few nights of 4-m telescope time is a practical proposition.

Acknowledgements The WHT is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof´isica de Canarias. We wish to acknowledge the help and support of the ING staff. We are also grateful for some excellent additional data provided by ING astronomers in service mode. The IRAF data reduction package is written and supported by the IRAF programming group at the National Optical Astronomy Observatories (NOAO) in Tucson, Arizona.

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CHAPTER 5 PLANETARY NEBULAE KINEMATICS IN M94

References Binney, J., Merrifield, M.R., 1998, “Galactic Astronomy”, Princeton University Press. Bosma A., van der Hulst J.M., Sullivan W.T., 1977, A&A, 57, 373 Bottema, R., 1993, A&A, 275, 16 Carollo, C.M., de Zeeuw, P.T., van der Marel, R.P., Danziger, I.J., 1995, ApJL, 441, 25 Ciardullo R., Jacoby G.H., Ford H.C., Neil J.D., 1989, ApJ, 339, 53 Douglas N., Taylor K, 1999, MNRAS 307, 190 Gerhard, O., Jeske, G., Saglia, R.P., Bender, R., 1998, MNRAS, 295, 197 Gerssen J., Kuijken K., Merrifield M.R., 1997, MNRAS 288, 618 Hui X., 1993, PASP, 105, 1011 Hui X., et al., 1993, ApJ, 414, 463 Jacoby G.H., Branch D., Ciardullo R., Davies R.L., Harris W.E., Pierce M.J., Pritchet C.J., Tonry J.L., Welch D.L., 1992, PASP, 104, 599 Mulder P.S., 1995, Ph.D. Thesis, Groningen Mulder P.S., van Driel W., 1993, A&A, 272, 63 Schneider S.E., Terzian Y., Purgathofer A., Perinotto M., 1983, ApJSS 52, 399 Sofue, Y., 1997, PASJ 49, 17 Tremblay B., Merrit D., Williams T.B., 1995, ApJ, 443, L5 Van der Kruit, P.C., Searle, L., 1982, A&A, 110, 61 Vassiliadis & Wood, 1994, ApJS 92, 125

6 Dark halos in S0 galaxies: NGC 5866 J. Gerssen, A.J. Romanowsky, N. G Douglas, K. Kuijken, M. R. Merrifield, A. Mathieu

Due to the lack of suitable tracers the kinematics at large radii in S0 galaxies are poorly constrained. Only planetary nebulae are able to trace the stellar kinematics at large distances from the centre in these systems. In this paper we present the stellar kinematics of the S0 galaxy NGC 5866 obtained from planetary nebulae observations. A self-consistent model is calculated from stellar absorption line kinematics near one scale length. The observed planetary nebulae kinematics are consistent with the velocities predicted by the model.

T

HE S0 class of galaxies — or lenticulars — shares with spiral galaxies the same basic components such as disks, bulges and bars. However, it is still unclear whether these similarities also point to a single formation scenario. Since present-day galaxies are not fully relaxed dynamical entities, especially at large radii where relaxation times are the longest, the kinematical properties of a galaxy will partially reflect the mechanism by which the galaxy formed. A kinematic investigation of the different types of galaxies will thus provide a key to compare their formation histories. In spiral galaxies the kinematics can normally be derived out to large radii from HI gas. The flatness of the measured rotation curves is usually interpretated as evidence for the presence of dark matter halos. If lenticular galaxies are formed by the same process as spiral galaxies we would expect them to have dark halo components as well. Unfortunately, lenticular galaxies in general lack an extensive gaseous component, and the existence of a halo therefore has to be inferred in another way. Some 20 percent of all S0 galaxies do actually contain detectable HI but the derived rotation curves are often of low quality due to the low column densities (van Driel & van Woerden 1991). The results nonetheless seem to indicate that the rotation curves remain flat in these systems. Polar ring galaxies provide another measure of the circular speed at large radii (Reshentikov & Combes 1994), but it is unclear whether these systems are representative

63

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CHAPTER 6 DARK HALOS IN S0 GALAXIES: NGC 5866

of S0 galaxies in general, and globular cluster systems do not trace the kinematics of the relaxed old stellar population in a galaxy. Fortunately, planetary nebulae have proven to be well-suited kinematic tracers to probe the outer regions of both elliptical galaxies (Hui 1993) and spiral galaxies (Douglas et al 2000, hereafter paper 1). Planetary nebulae (hereafter PNe) are bright emission-line objects which radiate their flux ˚ which accounts for about 15 percent in just a few lines, most notably the [OIII] line at 5007A of the total flux. The PNe distribution in a galaxy follows that of the underlying stellar light implying that PNe are present at radii where techniques relying on integrated stellar light are unavailable and that PNe adequately trace the stellar kinematics. In paper 1 we presented a technique based on slitless spectroscopy with which we can simultaneously detect PNe and measure their radial velocities. With this technique we image the galaxy through a narrow ˚ filter centered on [OIII] and disperse the light using a grating. The grating band (50 A) will displace the PNe (point sources) by an amount proportional to their radial velocities. The galaxy will subsequently be imaged for a second time but with the dispersion direction reversed (by rotating the spectrograph over 180 degrees). Each PNe will thus be imaged twice and the separation between the two members of a pair is a direct measure for its radial velocity. In this paper we present the results that we have obtained on the PNe population in the S0 galaxy NGC 5866 and compare these results to stellar absorption lines observations. We then construct a model for this galaxy and fit this model to the stellar absorption line data covering the central scale length, and test whether the model predictions can explain the observed PNe kinematics at several scale length, this will be our null hypothesis.

6.1 Observations We have observed the S0 galaxy NGC 5866 using the ISIS spectrograph on the William Herschel Telescope in April 1997 and July 1998. This galaxy is seen nearly edge-on, evident from its prominent dust lane although on a long exposure its appearance is more similar to an E6/E7 galaxy. The stellar light is dominated by a large bulge. In fact, dynamical modelling by Pignatelli & Galletta (1999) suggests a disk-to-bulge mass ratio of 0.31. Table 6.1 lists some other properties of this galaxy. TABLE 6.1— Parameters of NGC 5866

Hubble type Y Scalelength in Effective radius Distance Inclination Angular size

S0.3 28 arcsec 33 arcsec 13 Mpc p 90 degrees 4.7 x 1.9 arcmin

The unvignetted field of view of ISIS in a slitless configuration is four by one arcmin. On the first run in April 1997 we observed the galaxy along the major axis (position angle 308 j ) and centered on the nucleus. The total integration time was 6.5 hours. The second observing run in June 1998 provided the 180 j rotated position angle (i.e. along position angle

6.2 Reduction

65

128 j ). The total integration time was again 6.5 hours. Both 6.5 hours science exposures were actually broken up in several shorter (20 to 30 minute) exposures. The overall image quality of the second run is somewhat less than on the first run because of the atmospheric conditions and telescope pointing problems. ISIS is a double armed spectrograph and we were therefore able to simultaneously record images through a narrow band filter centered on the H y emission line, the second brightest line in most PNe spectra. This light has not been dispersed because PNe are generally weaker in H y than in [OIII]. Still, it often proved difficult to find an Hy counterpart to a PN detected in [OIII] and the Hy data have therefore only been used indirectly in the reduction process.

6.2 Reduction The data have been reduced using IRAF. All the usual reduction steps were applied. Each frame, however has only been corrected for pixel-to-pixel sensitivity variation and not for the narrow band filter profile. Since the location of the PNe on the CCDs depend on both position and radial velocities, a correction for the filter profile cannot be made because the radial velocity of each PN is initially unknown. Once the PNe are detected and their radial velocities measured the PNe fluxes can be determined but for the kinematical analysis presented here this is not important. The background galactic light is removed by running a median filter over the images. After background subtraction the noise levels will not be constant over the image but will vary accordingly with the amount of subtracted light. To compensate for this effect we constructed a sigma image (i.e. a frame in which each pixel is a measure of the local one-sigma noise) and divided the background subtracted image by this sigma image. Possible PNe candidates were identified by eye, blinking the two different position angles. This method proves to be far more efficient than using automated routines based on IRAF scripts. A more detailed description of the reduction process and the PNe identification can be found in paper 1. We experienced rather large instrumental flexure during the observations and all the short science exposures therefore had to be shifted to a common reference position before they could be combined. This means that the absolute radial± velocities cannot be determined to  9 ” m ). This situation is described better than the largest shifts of about 5 to 6 pixels ( p 150 in more detail in paper 1. However, the internal kinematics are entirely unaffected since all this uncertainty amounts to is an unknown but equal offset for all PNe. The real accuracy of the derived radial velocities depends± on how well the centroiding of the detected PNe  9 ” m and can be done. Each pixel measures 24 an accuracy half a pixel is a rather I [%$ ofJ comes conservative estimate of centroiding accuracy. Another factor from combining I i ±  9 ” m on the two different position angles resulting in an uncertainty of p the measured radial velocities.

6.3 Results Some 60 PNe candidates are seen in the April 1997 data. Combining them with the somewhat lesser quality June 1998 data resulted in 34 pairs of PNe for which the radial velocities could be derived. Fig. 6.1 shows the location of each planetary nebula overlaid , , on a contour image of NGC 5866. More PNe are found at positive , than at negative due to the presence of a number of foreground star found at negative . This stellar – continuum – light when dispersed will cause long light trails and essentially renders that part of the CCD useless for

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CHAPTER 6 DARK HALOS IN S0 GALAXIES: NGC 5866

F IGURE 6.1— The detected PNe population overlaid on a contour image of NGC 5866 obtained with the JKT. The PNe marked with a square are blue shifted and the stars are red shifted PNe. The size of each symbol is proportional to the radial velocity of each planetary nebula. The solid line indicates the position of the cut along the & direction which we used to verify whether the PNe do indeed follow the stellar light.

the detection of PNe. In the central parts of the galaxy PNe are lacking because there the galactic light is too bright to detect PNe against it and the outer most radius at which we are able to detect PNe is set by the size of the CCD. , To assess whether the PNe follow the stellar light we binned the 24 PNe with positive 1 along the direction in bins of 10 arcsec width to determine the number density as a function of scale height. The number density of the PNe closely follows the stellar light distribution, see fig. 6.2. Thus, the PNe are indeed adequate tracers of the stellar distribution. 6.3.1 Radial velocities From fig. 6.1 it is clear that the PNe population shows rotation about the centre. This is even more apparent in fig. 6.3. mean velocities, determined separately for both positive and ±  9 The ±  9 ” m respectively. ” m and negative radii are 911 763 the mean to represent the ±  9 ” m . The literature valuesTaking systemic velocity±  we find 837 for the heliocentric velocities m ± m range from 672  ‚  9 ” to 970 ±  9 ” m . An average of all the literature values that quote er‡ J|ã q hHi 9 ” , still somewhat off from the PNe determined systemic rors yields a V'(
 velocity. But as mentioned earlier the uncertainty on the absolute radial velocity determination of the PNe is rather large, and is furthermore compounded by the small number statistics involved in deriving the mean velocity. Overplotted in fig. 6.3 is the stellar rotation curve of Fisher (1997) derived from stel-

6.3 Results

67

F IGURE 6.2— Surface brightness profile along the positive z-cut of fig. 6.1. Overplotted are the number of PNe found in bins of 10 arcsec width, assuming refection symmetry around the major axis. The plotted errors are the Poisson errors.

lar absorption line spectra. These data extend far enough to suggest that the stellar rotation curve becomes flat. The outermost stellar data just touches the innermost PNe data, clearly demonstrating that these two different detection techniques complement each ±  other 9” m very well. However, the PNe exhibit significantly lower rotation than the stars (75 m ±  9 ” ). Combined with the spatial distribution of the PNe this suggests that the versus 200 observed PNe population is not confined to the disk but is instead more akin to a bulge or a halo population. 6.3.2 Velocity dispersions Another advantage of PNe over other tracers of the kinematics is that the PNe can be used to get a direct estimate of the stellar velocity dispersion. Estimates of the stellar velocity dispersion were obtained by binning the PNe into radial and azimuthal bins, Fig. 6.4. Instead of simply projecting the position of each PN onto the major axis to obtain their radial positions we took the intersection of the isophote that coincides with a particular PN and the major axis as a measure of the radius of that specific PN. The azimuthal velocity dispersions are derived by assuming four-fold symmetry on the sky and projecting all PNe onto a single quadrant. Due to the small number of PNe in each bin the uncertainties associated with them are rather large. The velocity dispersion along the radial direction appears to be more or less constant, unlike the stellar absorption line data which shows a steady decline with radius. Along the azimuthal direction it is more difficult to discern the behaviour of the velocity dispersion since nearly all PNe are contained in just the two central bins. Here too, the velocity dispersions seem to remain constant although there is a hint that they actually drop with increasing

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CHAPTER 6 DARK HALOS IN S0 GALAXIES: NGC 5866

F IGURE 6.3— The radial velocities of the detected PNe as a function of position along the major axis of NGC 5866. The cross indicates the systemic velocity and the solid line is the stellar rotation curve of Fisher (1997) offset to the PNe systemic velocity.

height from the major axis. The constancy of the velocity dispersion, at least along the radial direction, is consistent with the conjecture from the previous section that the PNe constitute a bulge or halo population and are not part of the disk. 4*) +  ‰ ôwmzóm ±  9 m
The velocity dispersion of the total PNe population measures ‹𔠔 . This value is corrected for the slight overestimation that occurs when the dispersion of an ensemble of points with non-zero errors is determined (Danese et al 1980). Comparing this value to the stellar data is not straightforward since the stellar velocity dispersions derived from absorption line data are not constant. A simple linear extrapolation of Fisher’s major axis velocity dispersions, however, shows that at the innermost radius of the PNe distribution both velocity dispersion are about equal.

6.4 Modelling In order to interpret the PNe results we have constructed a dynamically self-consistent model of NGC 5866 from additional photometric and stellar kinematical data. The model is used to test the null hypothesis that the observed PNe kinematics agree with the model predictions. , The first step in the construction of the model is to derive the luminosity density. - band surface photometry obtained from the ING archive is used to deproject the light distribution. Since NGC 5866 is close to edge-on the deprojection is in principle unique. However, real data is noisy making the deprojection less unambiguous in practise. We used the method developed by Romanowsky & Kochanek (1997) to deproject this galaxy. Their method has the advantage that there are no hidden constraints built in to produce a unique inversion. The

6.5 Discussion

69

200

200

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F IGURE 6.4— The left panel shows the velocity dispersion of the PNe along the major axis obtained by binning the PNe into bins of 20 arcsec width. The right panel shows the azimuthal behaviour of the velocity dispersion in bins of 10 degrees width. The major axis is at 90 degrees in this panel.

deprojection algorithm assumes axisymmetry and reflection symmetry about the major axis (i.e. 4-fold symmetry.) To calculate velocities we assume a constant mass-to-light ratio, axisymmetry and a twointegral dynamical model. The mass density then follows trivially from the luminosity density and the potential is obtained using the procedure outlined in Binney The solu4 6 et al 4 (1990). 6 tions to the Jeans equation for a two-integral model then yield the and ? components of the velocity dispersion (Satoh 1980). To scale the predicted velocities to the observed major and minor axis values we have projected the model line-of-sight velocities onto the plane of the sky and compared them to the stellar absorption line data of Fisher (1997) in a least square out the projected model velocities in its components, 4 6 ‚/Ð > WeS ‚/6 have , 6 ‚/Ð.-  sense. Ð (e.g.notvanseparated ¢ der Marel 1991). Instead of using the major axis data to scale   the model we used a spectrum obtained parallel to the major axis but offset from it by 6 arsec to avoid problems with the dust lane. Although the major and minor axis data sets were fitted independently they give essentially the same result. In fig. 6.5 the predicted model kinematics along both the major and the minor axis are overplotted with the PNe kinematics.

6.5 Discussion Clearly, the null hypothesis (mass traces light) cannot be discarded on the basis of this model and data. The inclusion of a dark matter halo in the model calculations is therefore not required by the data. However, the complete absence of a dark halo appears to be unlikely. Tremblay et al (1995), for instance, used PNe to probe the dark matter distribution in the SB0 galaxy NGC 3384. Although the kinematics of the 68 PNe they measured cannot fully explain the total mass that has been estimated for this system from a 200 kpc HI ring, it does show that there is an unseen component of matter present.

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CHAPTER 6 DARK HALOS IN S0 GALAXIES: NGC 5866

F IGURE 6.5— The model predicted stellar kinematics and the stellar absorption line data of Fisher (1997) used to scale the models. The solid line is the scaled major axis prediction while the dashed line depicts the minor axis. The triangles show the PNe kinematics using the same radial bins as in fig. 6.4.

One possible explanation could be that the dark halo already dominates at the radii of the stellar absorption line data. The model will then not be self-consistent but the PNe kinematics and the stellar kinematics should both follow the model predictions. Qualitatively the PNe data should fall somewhere between the major and minor axis model predictions since the detected PNe population is not confined to the disk, fig. 6.5. The average azimuthal angle of all the PNe suggests that the PNe kinematics should follow the major axis prediction more closely that the minor prediction, however the actual behaviour of the PNe seems to indicate the opposite. L,  i s J , The mass-to-light ratio of the model (converted to the S -band using S Prugniel & Heraudeau 1998) is about Although this value is higher than what is typically [ 15. × ratios are usually in the range one to five, it falls right found in disk galaxies, where the ’ [ × range (10 to 20) of elliptical galaxies (Lauer 1985.) S0 galaxies in the middle of the ’ constitute an intermediate class of galaxies in between spiral galaxies and elliptical galaxies, However, Burstein (1999) points out that the distinction between (giant) elliptical galaxies and S0 galaxies is probably blurred, implying that S0 galaxies are probably more closely related to elliptical galaxies that to spiral galaxies. However, Emsellem et al (1999) find a ’ [ × of about 6.5 for the S0 galaxy NGC 3115. The stellar[ light in NGC 5866 is dominated by the large bulge and Bottema (1999) shows that the ’

values of bulges are typically somewhat higher than what is found for disks. The[ derived value for NGC 5866, although a

values found in other galaxies. little large, is therefore not inconsistent with the ’ Clearly, the results presented here need to be reexamined carefully, since it seems unlikely that the S0 galaxy NGC 5866 is truly without a dark halo. Observations of more PNe will provide a better constraint on the halo kinematics. The dedicated Planetary Nebulae Spec-

6.5 Discussion

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trograph (Arnaboldi et al 1999) with its large field-of-view and high throughput will shortly make it possible to effectively detect additional PNe. A single S0 galaxy, however, cannot yield any statistical information about the halos properties of these systems, and a larger sample of S0 galaxies is therefore essential. A comparison of the properties derived from such a sample with the properties of spiral galaxies will establish whether or not both systems have the same formation mechanisms.

References Arnaboldi M., Capaccioli M., Douglas N.G. et al 1999, Proceedings of the SAIT symposium, Naples 1999 Binney J., Davies R.L., Illingworth G.D., 1990, ApJ, 361, 78 Bottema R., 1999, A&A, 348, 77 Burstein D., astro-ph/9908355 Danese L., De Zotti G., di Tullio G., 1980, A&A, 82, 322 Douglas N.G., Gerssen J., Kuijken K., Merrifield M.R., 2000, MNRAS in press (paper 1) Emsellem E., Dejonghe H., Bacon R., 1999. MNRAS, 303, 495 Fisher D., 1997, AJ, 113, 950 Hui X., 1993, PASP, 105, 1011 Lauer T. R., 1985, ApJ, 292, 104 Pignatelli E., Galletta G., 1999, A&A, 349, 369 Prugniel Ph., Heraudeau Ph., 1998, A&AS, 128, 299 Reshentikov V.P., Combes F., 1994, A&A, 291, 57 Romanowsky A. J., Kochanek C. S., 1997, MNRAS, 287, 35 Satoh C., 1980, PASJ, 32, 41 Tremblay B., Merritt D., Williams T.B., 1995, ApJ, 443, L5 van Driel W., van Woerden H., 1991 A&A, 243, 71 van der Marel R. P., 1991, MNRAS, 253, 710

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7 Summary and outlook

I

N this thesis several aspects of the stellar kinematics in disk galaxies have been addressed. Due to the low surface brightness of these systems the number of studies that have addressed these issues has been fairly limited. However, kinematic studies, especially stellar kinematics because stars make up the bulk of a galaxy’s visible matter, remain crucial for understanding the full structure of a galaxy. In the previous chapters we have shown that stellar kinematics can be used to derive the three dimensional structure of the stellar velocity dispersions in inclined disk galaxies. We have shown that the same information can be derived at larger radii using planetary nebulae as tracers of the stellar kinematics. In the gas poor lenticular galaxies, planetary nebulae are the only practical way to determine the kinematics at large radii and we have therefore initiated a project to study the halo properties of these systems using planetary nebulae. In addition, we reconfirmed that the Tremaine & Weinberg (1984) method is a viable technique to derive the pattern speed of stellar bars. The stellar kinematics results presented here have been derived using both stellar absorption line techniques and emission lines techniques. Below we summarise the derived results and techniques and present some additional work. We close this chapter with a description of ongoing projects and suggestions for future research.

7.1 Summary Absorption line kinematics In chapters 2 and 3 we have measured the stellar velocity dispersion using our own implementation of the Gauss-Hermite expansion developed by van der Marel & Franx (1993). Although this method can in principle detect deviations from Gaussian shaped velocity profiles, in practice we did not observe such deviations. In a rotating disk the line-of-sight velocities are expected to show asymmetries. However, limited velocity resolutions usually result in observed velocity profiles that are approximately Gaussian. The derived stellar velocity dispersions along the major and minor axes in the early type galaxies NGC 488 (chapter 2) and NGC 2985 (chapter 3) allowed us to constrain the shapes of the velocity ellipsoids in these systems. Although the error bars on the velocity dispersion 73

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CHAPTER 7 SUMMARY AND OUTLOOK

ratios are still rather large, the derived values differ from the solar neighbourhood in a manner consistent with disk heating theories and suggest a trend between the velocity ellipsoid ratio and Hubble type. In chapter 4 we derived the pattern speed of the bar in NGC 4596 using the Tremaine & Weinberg (1984) method. This method relies on an accurate measurements of the mean lineof-sight velocities along axes parallel to the bar. Non-parametric methods which can extract arbitrarily shaped velocity profiles are ideally-suited to derive this quantity. We have used the Unresolved Gaussian Decomposition algorithm of Kuijken & Merrifield (1993) to measure the stellar velocities in the bar of NGC 4596. The derived pattern speed implies that the bar in this galaxy ends close to the co-rotation radius. This is only the second barred galaxy for which the pattern speed has been determined directly. A larger sample of model independent measured pattern speeds is desirable since the derived pattern speeds are at odds with cosmological predictions, but this study has shown that such a sample is straightforward to obtain. In addition to the Tremaine & Weinberg method used to derive the pattern speeds of bars directly, we have also attempted to measure this quantity from a spectrum taken along the bar minor axis. Along this axis the radial velocities will be close to zero. However, near the co-rotation radius a sign reversal in these velocities will occur because the orbital structure changes across this radius. The average distribution of radial velocities on opposite sides of the co-rotation radius should display different signs, and we have attempted to measure this effect in NGC 4596 and in the SBb galaxy NGC 5383. For both galaxies we used 1800s longslit exposures taken along the minor axis with the same instrumental configuration described in chapter 4. The smallness of the effect which is further compounded by the limited accuracy with which the sky background can be subtracted, meant that we could not reliably measure the effect (see also Kormendy 1983.) Emission line kinematics Emission lines are generally easier to observe than stellar absorption lines. Unfortunately most emission lines originate in the HI gas layer or in HII regions and therefore trace global galactic parameters. To trace the local properties inside a galaxy requires knowledge about the kinematics of the old stellar population. The results presented in the first part of the thesis derive this information from stellar absorption lines. While this works fine for the relatively bright inner parts of a disk it is vastly impractical at radii larger than about two disk scale lengths. Planetary nebulae have proven to be excellent tracers of the stellar population at large radii in elliptical galaxies. In chapter 5 we presented a new method to simultaneously detect and measure the kinematics of a planetary nebulae population. We showed that the stellar rotation curve and the stellar velocity dispersion in the Sb galaxy M94 can be reliably derived using planetary nebulae, thereby demonstrating that planetary nebulae are also excellent tracers of the kinematics of the old stellar population in spiral galaxies. Unlike spiral galaxies, S0 galaxies lack sufficient amounts of HI gas hampering the inference of halo properties in these systems. In chapter 6 we present stellar kinematic observation at large radii in the S0 galaxy NGC 5866 derived from its planetary nebulae population, and discuss the implications of these observations.

7.2 Future and ongoing projects

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7.2 Future and ongoing projects The large new telescopes like VLT or Gemini make it possible to extent stellar absorption line spectroscopy to larger radii. However, it is probably more worthwhile to focus on different projects that were hitherto impossible with the four meter class of telescopes. Such project may, for example, include the kinematics of the faint shell structures observed around many elliptical galaxies or to probe the internal kinematics of more distant galaxies. The latter has already been attempted using emission lines (Vogt et al 1997) but the internal structure of stellar systems is best probed by stellar absorption line techniques. Another difficulty that distant galaxies present is their limited angular extent. Often the apparent size of a distant disk is about as large as a single seeing element, complicating the interpretation. A space-borne spectrograph like STIS has the angular resolution to resolve distant disk galaxies but the light gathering power of HST in not enough to observe the stellar absorption line kinematics in such systems. The stellar kinematics of nearby systems, however, still present numerous challenges and opportunities to study the internal structure of galaxies. Below we outline a number of such projects. 7.2.1 Secular evolution of disk stars The work on the three dimensional structure of stellar velocity dispersion presented in the first part of this thesis can be extended to larger radii using the planetary nebulae technique described in chapter 5. Integrated stellar light techniques are largely confined to about one to two disk scale length, while planetary nebulae are most effectively detected at somewhat larger radii where the reduced galactic background light provides a better contrast for the detection of planetary nebulae. Both techniques therefore complement each other very well. Fig. 7.1 clearly demonstrates the difference in radii accessible with the two different techniques. The planetary nebulae technique uses essentially the same instrumental setup required for longslit absorption line spectroscopy. Both techniques can therefore employed on a single observing run which makes it possible to acquire a data set that consistently merges the stellar kinematics on both small and large galactic scales. An obvious candidate for such a project will be M94 for which the planetary nebulae kinematics along the major axis are already available. With the stellar velocity dispersions available over nearly the full extent of a disk variations of the ratio /*0212/43 with radius can be assessed. Current disk heating theories were developed to explain only the solar neighbourhood value. Although the results presented in the last figure of chapter 3 suggest that at least at radii of about one to two disk scale length they adequately explain the observed values. In addition, systematic differences between the kinematics at small and at large scales are eliminated in this study, providing the best test yet of the basic question whether planetary nebulae are indeed good tracers of the stellar kinematics. With a larger sample of galaxies a systematic study of disk heating can be made. Such a study will show unequivocally which process or processes are responsible for one of the most basic properties of galactic disks — their finite thickness.

CHAPTER 7 SUMMARY AND OUTLOOK

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M94

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F IGURE 7.1— The left panel shows the line-of-sight velocity dispersion along the major and minor axis of NGC 488 obtained from stellar absorption line spectra. The dotted lines are the best-fit stellar kinematic model. The right panel shows the same information for the major axis of M94, but derived from PNe. Clearly, PNe trace the stellar kinematics to much larger radii than possible with absorption line spectroscopy.

7.2.2 Planetary Nebulae spectrograph The Planetary Nebulae Spectrograph (PNS) presently under construction will greatly facilitate the studies of secular evolution. The PNS is a slitless spectrograph working according to the same principle described in chapter 5. However, it simultaneously records the dispersed image and the counter-dispersed image of the galaxy under study in a small wavelength range ˚ The 10 by 10 arcmin field-of-view of this dedicentered on the [OIII] emission line at 5007 A. cated instrument makes it possible to observe most galaxies with just a single pointing instead of having to observe the major and minor axis separately. The galaxies NGC 488 and NGC 2985 are of course prime candidates for a study of stellar velocity dispersions at large radii with this new instrument since we already know their distribution of stellar velocity dispersions at small radii from our stellar absorption line observations. The angular extent of both galaxies is such that they comfortably fit the PNS field-of-view. Using the technique described in chapter 5 it would require several pointings to achieve the same coverage. The ratios of the velocity ellipsoids are expected to be different from their small scale counterparts since the relaxation times at large radii are considerably longer. The kinematics at large radii also reflect, to some extent, the formation processes involved and this will have its bearings on the derived velocity ellipsoid ratios. Another observation that can be made using planetary nebulae is the mass density in Low Surface Brightness galaxies. LSB galaxies constitute around 30 percent of the total galaxy population, yet almost nothing is known about their stellar mass density and the distribution of dark matter within these systems. Using planetary nebulae to measure the vertical component of the stellar velocity dispersion allows one to estimate the mass density 576 from the relation, /90 8 1;:40=;@BAC576 obtained from the isothermal sheet approximation. By assuming

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a lower limit for the vertical scale height :40 , (from the super thin class of galaxies) a useful upper limit on the stellar mass density in LSB galaxies can be obtained. 7.2.3 Lenticular galaxies We have initiated a programme to study the stellar kinematics at large radii in lenticular galaxies using planetary nebulae. The aim of this programme is to quantify the halo properties of these systems. In addition, the required planetary nebulae kinematics have the added advantage that they can also trace the stellar velocity dispersions. Differences between the halo properties of lenticular galaxies and spiral galaxies, where the halo properties are normally derived from HI rotation curves, will provide information about the formation mechanisms of the different systems. If lenticular galaxies lost their gas due to tidal stripping, as some theories suggest, the dark halos may have been tidally truncated in the process, which will be reflected in the halo kinematics. To measure the planetary nebulae kinematics we will initially use the technique described in chapter 5 until the Planetary Nebulae Spectrograph becomes available. However, in systems where the planetary nebulae population has already been detected with the traditional on/off band technique it makes sense to perform the necessary follow up spectroscopic observations using fiber fed spectrographs. In all other instances the Planetary Nebulae Spectrograph will be the preferred instrument due to its high efficiency and its large field-of-view. Another important issue that this study will address is the comparison between the halo properties of barred and non-barred lenticular galaxies. The observed tumbling rates of most bars do not show any signs of deceleration implying that the central halo densities are too low to exert significant dynamical friction. However, according to the predictions of hierarchical structure formation (Navarro, Frenk & White 1996) the central halo densities should be fairly high. Although high central halo densities do stabilise disk galaxies, they also serve to inhibit bar formation. Thus, bars probably do not form, as was once thought, through a global instability but may grow by a slow or secular process (Sellwood 1999.) One of the lenticular galaxies we use in this study — the SB0 type NGC 2787 — is also in our sample of galaxies with measured bar pattern speeds, see below. This will permit a direct comparison between the inferred halo properties and the rate at which the bar tumbles. 7.2.4 Bar pattern speeds The presence of barred structures in galactic disks will affect all the major components of disk galaxies such as the bulge, the halo and of course the disk itself. Bars themselves also seem to evolve since they are much less frequent beyond redshifts of 0.5 than they are at the present epoch (Abrahams et al 1999.) Bars therefore play an important role in understanding the evolution of galaxies. We have shown in chapter 4 that one of the most basic parameters of a bar, its pattern speed, can be reliably determined using the model independent method of Tremaine & Weinberg (1984.) Based on these results we have started to collect data for a sample of barred galaxies. Once a pattern speed has been determined the co-rotation radius can be derived using a rotation curve. This radius is usually expressed by a parameter D , which measures the ratio of the co-rotation radius to the length of the bar. Indirect measurements of pattern speeds in about 15 galaxies yield, EFDHG IKJ(G LNMOPRQSXWZYV[> , Elmegreen (1996.) Bars therefore seem to end inside co-rotation, which is expected on dynamical grounds because

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CHAPTER 7 SUMMARY AND OUTLOOK

in a barred potential only the stellar orbits within the co-rotation radius are aligned with the bar. Any self-consistent bar must therefore end within the co-rotation radius. Results derived from gas kinematics indicate the same behaviour (Sanders & Tubbs 1980.) We are currently in the process of extending the sample of directly measured pattern speeds. Data for two more barred galaxies, the SB0 galaxy NGC 2787 and the SBbc galaxy NGC 3992, have been collected and data for several more — southern hemisphere — galaxies will be collected shortly. Preliminary analysis of the NGC 2787 data suggests that the bar in this system, which is comparable to NGC 4596 (chapter 4), behaves in much the same way. The complete sample will not only facilitate a comparison with model dependent methods of determining bar pattern speeds, but it will also allow us to put constraints on the central concentration of dark matter halos within barred galaxies.

References Abrahams R.G., Merrifield M.R., Ellis R.S., Tanvir N.R., Brinchmann J., 1999, MNRAS, 308, 569 Elmegreen B.G., 1996 in Barred Galaxies. IAU Colloqium 157, Buta R., Crocker D.A., Elmegreen B.G., eds., p. 197 Gebhardt K., Richstone D., Kormendy J., et al 2000, AJ, 119, 1157 Gerhard O.E., 1993, MNRAS, 265, 213 Kuijken K., Merrifield M.R., 1993, MNRAS, 264, 712 Kormendy J., 1983, ApJ, 275, 529 Larsen N., Norgaard-Nielsen H.U., Kjaergaard P., Dickens R.J., 1983, A&A, 117, 257 Navarro J.F., Frenk C.S., White S.D.M., 1996, ApJ, 462, 563 Rix H-W., White S.D.M., 1992, MNRAS, 254, 389 Sanders R.H., Tubbs A.D., 1980, ApJ, 235, 803 Sellwood J. A., 1999 in Galaxy Dynamics. ASP Conference Series Combes F., Mamon G.A., Charmandaris V., eds. Tremaine S., Weinberg M.D., 1984, ApJ, 282, L5 van der Marel R.P., Franx M., 1993, ApJ, 407, 525 Vogt N.P., et al 1997, ApJ, 479, L21

Appendix The accuracy with which the line-of-sight velocity profiles are extracted from the data can, in principle, be improved using additional reduction steps. We have attempted two such steps, described below. Although the signal-to-noise of our data, in retrospect, was too low to successfully apply these procedures, the suggested improvements can be beneficial to future observations which is why we briefly describe them here. Template mismatch Often a single template star is not a fair representation of the galaxy light. Any mismatch between a template spectrum and a galactic spectrum will result in a less accurate determination of the stellar kinematics. We have therefore tried to use two templates simultaneously by means of a linear fitting algorithm. However, in all cases nearly all the weight was given to just one of the two templates. Probably because the templates were too dissimilar in spectral type. Gebhardt et al (2000) encountered a similar situation. More elaborate composite template spectra and simulations of the effects of template mismatch on the reconstructed velocity profile are discussed by Rix & White (1992.)

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Amplitude – dispersion correlation A well know property (Larsen et al 1983) of fitting lineprofiles with Gaussian velocity profiles is the existence of a correlation between the amplitude \ and the dispersion / . We have indeed observed this behaviour in the full correlation matrix working with artificial data. In order to reduce the uncertainties associated with the measured velocity dispersions we have attempted to correct for this correlation by applying the following procedure:

/*]_^`/*]9acbedgfhfKij/*].k\ ]ml o

n

\ ] o /*].V \ ]

To apply this prescription an average gamma profile (i.e. the Gaussian amplitudes as a function of radius) is needed. However with the signal-to-noise of the real data this is rather problematic. We have tried scaling the surface brightness profile of NGC 2985 (chapter 3) to obtain an average gamma profile. However, this only proved satisfactory for the very central regions of the galaxy. At somewhat larger radii a discrepancy occurred. This is probably the result of template mismatch but it could also reflect a decrease in metallicity with radius. If the abundances of Mg and Fe — the two main absorption lines used to extract the velocity profiles — are not constant with radius then the average stellar light profile cannot be a good approximation of the gamma profile. An observational bias directed against the suggested correction is the fact that in spiral arms the amplitude gamma will be larger than in inter-arm regions but at the same time the velocity dispersions are on average smaller because of the overabundance of young stars.

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Nawoord Dit proefschrift kon alleen maar tot stand komen dankzij de hulp van veel personen. Op deze plaats wil ik dan ook iedereen bedanken die in meer of mindere mate heeft bijgedragen aan de realisering van dit boekje. In het bijzonder wil ik mijn begeleiders Koen en Mike bedanken. Dankzij hun adviezen en suggesties konden de verschillende projecten, beschreven in dit proefschrift, met succes worden afgerond. Tevens demonstreerde beide — de een iets meer dan de ander — bijna voortdurend het begrip “werking op afstand”. Van de samenwerking met Nigel, Aaron en Anne heb ik veel profijt gehad, vooral in de tweede helft van mijn onderzoek. Het onderzoek beschreven in dit boekje is in zekere zin een vervolg op het werk van Roelof en diens — meestal opbouwende — commentaar is altijd zeer nuttig geweest. Ook de overige bewoners van het Kapteyn Instituut ben ik dank verschuldigd voor al hun bijdragen/afleiding. Speciaal natuurlijk mijn kamergenoten Rolf, Remco en Stephanie, zij hebben immers nog het meest met mij te stellen gehad. Het Kapteyn Instituut en het Leids Kerkhoven-Bosscha Fonds hebben dit proefschrift gedeeltelijk gefinancierd en tevens de verschillende reizen die ik heb ondernomen financieel ondersteund. Voor het veraangenamen van de tijd die niet aan astronomie werd gespendeerd wil ik met name Carina, Michel, Greta, Erwin, en Dam/Esornibor bedanken. Tenslotte wil ik mijn ouders bedanken. Zij hebben mij de gelegenheid gegeven om mijn eigen weg te gaan, en me in mijn keuzes altijd gesteund.

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Publications in refereed journals Kinematic detection of the double nucleus in M31 Gerssen J., Kuijken K., Merrifield M.R., 1995, MNRAS, 277, L21 The shape of the stellar velocity ellipsoid in NGC 488 Gerssen J., Kuijken K., Merrifield M.R., 1997, MNRAS, 288, 618 The pattern speed of the bar in NGC 4596 Gerssen J., Kuijken K., Merrifield M.R., 1999, MNRAS, 306, 926 Using slitless spectroscopy to study the kinematics of the planetary nebulae population in M94 Douglas N.G., Gerssen J., Kuijken K., Merrifield M.R., 2000, MNRAS in press Disk heating in NGC 2985 Gerssen J., Kuijken K., Merrifield M.R., 2000, MNRAS in press

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