Galaxy mass functions

949

SDSS Images of Spiral Galaxies (Sa to Sd):

Lecture Ten: Disc/Disk/Spiral Galaxies

Figure 5. Bivariate distribution for M/L versus mass. The contours rephttp://www.astro.rug.nl/~etolstoy/pog16 resent the volume-corrected number densities: logarithmically spaced with four contours per factor of 10. The lowest dashed contour corresponds to Also made use of Binney & Merrifield, 10−4 Mpc−3 per 0.5 × 0.2 bin. The dotted lines represent the observable e contours represent Galactic Astronomy, Chp. 4.2 & 4.4 limits for an r < 17.8 mag limit and different redshift limits (ignoring ple: logarithmically & Gallagher, chapter 5 23rd May 2016 k-corrections). The grey dashed line region represents Sparke galaxies that can only west dashed contour be observed at z < 0.008 where Hubble-flow corrections are significant lowest solid contour (cz < 2400 km s−1 ). ne regions represent

stimated by Blanton the median and 1σ by the middle dotted

:more than one component (central bulge, disk, bar, spiral arms, rings=), Blanton 2009 :large amounts of dust (not transparent)

Galaxy photometry

dw arf s

Edge on: i = 90o

Face on i = 0o

Number

spirals most of the galaxies are here most of the mass is here

icals ellipt

ct that the r-band n required for the ax but it should be ss are viewed over M/L. Fig. 5 shows e limits at various

The surface brightness profiles of disk galaxies are complex:

Their appearance depends both on the stellar distribution and that of gas and dust, and on the angle from which we observe them.

of Blanton et al. DSS main galaxy in the range 18–

comes incomplete ate distribution in ion represented by orrected). There is h is approximately masses, the distripleteness at µR50,r s for lower masses corrections for SB

Photometry of disk galaxies

Appearance depends on the distribution of stars, gas, the angle at which we see them, and even the bandpass in which we observe them

Luminosity

Figure 6. GSMF extending down to 107 M⊙ determined from the NYUVAGC. The points represent the non-parametric GSMF with Poisson error bars; at M < 108.5 M⊙ the data are shown as lower limits because of the SB incompleteness (Fig. 4). The dashed line represents a double-Schechter

Surface Brightness Profile

Galaxy photometry

of galaxy components as a function of (R,z)

Our classification of galaxies into different morphological types is dependent on our visual impression of their images, so understanding the distribution of their light is crucial for understanding their physics The determination of brightness in an image is called “photometry” (measuring light), but this process also covers determination of shapes and brightness profiles

multiple components

Surface Brightness

Surface brightness profile

The surface brightness I(x) is the amount of light contained in an area at a particular point x in an image.

An isophote is closed curve connecting points of equal surface brightness.

Consider a square area with a side of length D of a galaxy at distance d. This length will subtend an angle, α = D/d.

A Surface brightness profile is produced by azimuthally averaging along isophotes (elliptical annuli).

If the total luminosity of the galaxy in that area is L, then the received flux is, F=L/(4πd2) So the surface brightness is:

I(x) = F/↵2 =

L ⇥ 4⇡d2

✓

d D

◆2

=

L 4⇡D2

15

(L⦿pc-2)

µB

Surface brightness is independent of distance (d) since flux decreases as 1/d2, but the area subtended by 1 sq arcsec increases as d2 (until cosmological dimming, 1/(1+z)4, becomes important)

µ (x) =

2.5 log I (x) + constant

In the B-band, the constant is 27 Thus

IB = 10

0.4(µB 27)

mag/arcsec2, which

L

,B pc

night sky level

25

Magnitude per square arcsecond is usual units of surface brightness:

!

20

30

radius

(mag arcsec-2)

corresponds to 1 L⦿

pc-2 Note: the largest isophote usually represents the lowest level that can be seen above the instrumental noise (not physical boundary)

2 NGC 7331

Surface brightness profile

Surface brightness profile

b = cos(i) a

b is the projection of a along the minor axis

The density of stars in the disc drops by a factor of e as we move out in radius R by one scale length hR

If a disc is circular & very thin, it will appear as an ellipse with axis ratio cos i when we view it at an angle i from face-on.

The effective radius Re, the radius of a circle that includes half of the light.

This means that the surface brightness is greater by a factor 1 /cos i than if we saw the disk face on. Using this we can correct our observations to the correct average surface brightness at distance R from the centre.

μI

Here the diameter along the minor axis of the disk isophotes is only 0.35 that measured along the major axis, and so we can infer that the galaxy is inclined at about 70° from face-on.

The disc has an exponential profile:

I(R) = I0 exp( R/hR )

µ(R) = µ0 + 1.09

The bulge follows an r1/4 (or de Vaucouleurs) law:

I(R) = Ie 10

3.33((R/Re )1/4 1)

µ(R) = µe + 8.3268

NGC 7331

"✓

R Re

◆1/4

✓

R hR

◆

#

1

Surface Brightness of Discs

Fitting surface brightness profiles disc galaxies are composite systems,

Freeman 1970 (ApJ, 161, 802) , for a wide range in luminosity, little scatter

• almost all spirals have disk surface brightness around Io (B-band) = 21.5 ± 0.5 ! • partly a selection effect since low-surface brightness (LSB) galaxies are harder to identify ! • many LSB disks identified since e.g., extreme case - Malin 1 (Io = 25.5 and Rd=55 kpc!)

bulge

disk

µ(B)

SO Sa Sb Sc Sd

2-component

Im TYPE

B/T =

Re2 Ie Re2 Ie + 0.28h2R I0

The importance of the bulge increases moving towards earlier types

1985ApJS...59..115K

Contribution of the bulge to the total light of a galaxy

1985ApJS...59..115K

Bulge-to-Disc ratio

Size vs. surface brightness

Sb and earlier disc galaxies follow a relation between effective radius and the (effective) surface brightness of their bulges: the bigger the galaxy, the lower the SB

There is a similar relation between the scale length and central surface brightness of discs: the bigger the disc, the lower the central SB

Simien & de Vaucouleurs 1986

Colours of disc galaxies

Gas in disc galaxies HI gas in the Ursa major group more HI

less HI

Galaxies get bluer as the disks become more prominent (and fainter, too, because diskdominated galaxies tend to be less massive than bulge-dominated galaxies)

Faint galaxies have proportionally more HI than bright galaxies and have lower central surface brightness.

Spectra of disc galaxies

Scale Height

Disc galaxies looks as you might expect given their colours: early-type spirals have older stars and few if any emission lines from starformation regions late-type spirals have younger stars and emission lines from star-formation regions

Bulges

Figure 21: The S0-galaxy NGC 4762, which has a very bright thick disk, as was first described The z-extent indicated by the arrows is where the thin disk dominates. On the right the outer extent of the thick disk is slanted w.r.t. the symmetry plane (producing an approximately diamond shape), indicative of a double exponential light distribution. These Sometimes a second component can be fit to the vertical direction, as if there were images were produced with the use of the Sloan Digital Sky Survey. Tsikoudi Typically hbyz~0.1h R (1980).

'About half of all disk galaxies contain a thick diskstructure. but inclination effects, scattered light, and a flattened halo can all mimic a thick disk. a central bar-like der Kruit & Searle, 1981b); in van der Kruit (1984) it is shown that this distribution can be

interpreted as a superposition of a thin and thick disk plus a small, central bulge. Recent studies 'The long to short axis can be as disk is 1.44 ± 0.03 kpc and its radial scalelength is 4.8 ± 0.1 showratio that the scaleheight of its thick kpc, only slightly longer than that of the thin disk (Ibata, Mouhcine & Rejkuba, 2009). The large as 5:1. relationship between the scalelengths of the thin and thick disk is an important constraint on the various formation mechanisms of thick disks, as discussed below.

Bulges 'About half of all disk galaxies contain Bars a central bar-like structure. 'The long to short axis ratio can be as large as 5:1.

7.3

Kinematics and Chemical Properties

Little information is available on the kinematics and chemical properties of thick disks in galaxies other than the Milky Way. The larger scaleheight of the Galactic thick disk means that its velocity dispersion is higher than for the thin disk (about 40 km s 1 in the vertical direction near the sun, compared to about 20 km s 1 for the thin disk (e.g. Quillen & Garnett, 2000). The stars of the thick disk are usually identified by their larger motions relative to the Local Standard of Rest, but kinematic selection is inevitably prone to contamination by the more abundant thin disk stars. Recently it has become clear that the Galactic thick disk is a discrete component, kinematically and chemically distinct from the thin disk. It now appears that thick disk stars can be more reliably selected by their chemical properties. Galactic plane, the rotational lag of the thick disk relative to the LSR is only about Can be quite Near long,thewith axial ratios as km s 1 (Chiba & Beers, 2000; Dambis, 2009), but its rotational velocity appears to decrease large as 5:1 30 with height above the plane. The stars of the thick disk are old ( > 10 Gyr) and more metalpoor than the thin disk. The metallicity distribution of the thick disk has most of the stars with

Bars

'When viewed edge-on: boxy shape (not round) of the light distribution.

Seen edge-on, bars are flattened, boxy

'When viewed edge-on: boxy shape (not round) of the light distribution. In some cases the isophotes are squashed, and the bulge/bar has a peanut-like shape.

structures and can even be “peanut” In some cases the isophotes shaped are squashed, and the bulge/bar has a peanut-like shape.

52

Spiral structure in disc galaxies

Spiral structure in disc galaxies

There are three main types of spiral arms 10% "Grand Design", two well defined spiral arms

60% Multiple-arm spiral arms

30% Flocculent spirals - no well defined arms "ratty" structure

Spiral structure occurs in all bands, but is much smoother and less pronounced Spiral in redder bands

B

M83 K

structure and patterns

Shapes of spiral galaxies are approximately invariant under a rotation around their centres. A galaxy that looks identical after rotation of 2 /m has m-fold symmetry. A galaxy with an m-fold symmetry has m-spiral arms. Most spirals have 2 arms, Figure hence8: they a twofold symmetry M83 in have blue light at the left and in the K-band on the right.

The bar is much more

obvious in the near-IR. (Unpublished images by Park & Freeman).

The shapes of spiral galaxies are typically where the disk is assumed exponential with scalelength h and total mass M . Since the rotation velocity V is related to the total mass, it is a criterion that relates to the relative Spiral patterns are classified invariant under rotation about their centers according to orientationmass in disk and halo. It can be rewritten to say that within the radial distance from the disk

rot

compared to rotation

center corresponding to the edge of the disk, the dark matter halo contains up to 60–70% of the total mass (van der Kruit & Freeman, 1986). Such galaxies are in fact sub-maximal. Sellwood

A galaxy that looks identical of concludes that these criteria are only necessary for disks that have no dense centers, directionafter a rotation(2010a) since central concentrations of mass in disks themselves could also provide global stability. It was 2π/m has m-fold symmetry and has m spiralshown already some decades ago (Kalnajs, 1987) that halos are not very e⇥cient in stabilising disks acompared to budges. @trailing arms We will not discuss the formation of bars in galaxies, as this subject has been covered in @leading

detail by Kormendy & Kennicutt (2004) in relation to pseudo-bulges, and by Sellwood (2010a). We do want to stress the fundamental point that the incidence of bars is much larger than

Spirals are further classified by whether the traditionally thought; a typical fraction that figured in previous decades –although admittedly for strongly barred galaxies as in Sandage (1961)– was of the order of a quarter to a third. arms are leading or trailing the rotation Current estimates are much higher; Sheth et al. (2008) found in the COSMOS field that in the local Universe about 65% of luminous spiral galaxies are most barred. spiral This fraction arms is a strong direction function of redshift, dropping to 20% at a redshift of 0.8. The Spitzer Survey of Stellar Structure are trailing

Spiral structure in disc galaxies

Why doesn't this happen?

Density Waves

in Galaxies S4 G (Sheth et al., 2010) aims among others at studying this in the near IR. As an example, we show in fig. 8 a blue and near-IR image of the large spiral M83. Although it appears mildly barred in the optical, it is clear that in K-band the bar is very prominent and extended. Throughout the previous century much attention has been paid to the matter of the formation and maintenance of spiral structure. It was extensively reviewed by Toomre (1977, 1981). Spiral structure in itself is unquestionably an important issue (see the quote to Richard Feynman in the introduction in Toomre’s review), as it is so obvious in galaxy disks and appears to play a determining role in the evolution of disks through the regulation of star formation and therefore the dynamical, photometric and chemical evolution. We will not discuss theories of spiral structure itself as progress in this area has recently been somewhat slow. We refer the reader to the contributions of Kormendy & Norman (1979), Sellwood & Carlberg (1984), Elmegreen, Elmegreen & Leitner (2003) and Sellwood (2008, 2010a,b). Spiral structure is often

Density waves move through galaxy compressing matter as it passes and24setting off star formation

It seems likely that spiral arms are created by a density perturbation that moves along at a speed different from the objects around it. The density wave resists the spiral's tendency to wind up and causes a rigidly rotating spiral pattern. Like slow moving traffic on the highway. Pattern Speed - fixed angular speed of density wave rotating through galaxy.

There is an initial “seed” perturbation in the spiral disc. These come from either initial asymmetries in the disk and/or halo (galaxy formation processes), or induced via galaxy encounters. Thus there are regions of slightly higher density than their surroundings. The higher density accelerates matter into the wave.

Density Waves

Self-propagating star formation density wave theory can't explain flocculant spirals, but these can be explained by self-propagating star-formation. star formation produces supernovae, which shock the gas, and triggers more star formation, and then differential rotation stretches out the regions of star formation into trailing fragmentary arms with no global symmetry.

HI Rotation curves of disc galaxies

HI Rotation curves of disc galaxies In central regions, contours are parallel to the minor axis Further out, they are nearly radial The kinematic major axis is the line connecting the points where the radial velocities deviate the most from the systemic velocity The denser the contours, the more rapid the change in V(R)

Contours of constant V(R)cosϕ

Rotation curves of disc galaxies

Rotation of a galactic disc Line profiles

Doppler effect

Velocity field Viewed edge-on, the radial velocity measured is Vsys the systemic velocity of the galaxy.

Vr (R, i = 90 ) = Vsys + V (R) cos

When viewed at an inclination i, the radial velocity is projected to

Vr (R, i) = Vsys + V (R) cos sin i

HI Rotation curves of disc galaxies

HI Rotation Curve: NGC3198

Optical disc

Open circles - scale length hR of stellar disc and peak rotation speed for each galaxy Begeman 1987

HI Rotation curves of disc galaxies

HI rotation curves & Dark Matter

This is the rotation for the We can compare curve the HI rotation curve to that predicted from the previous V(R) galaxy. luminous (stellar and gaseous) matter, using the observed surface brightness shown as function R and density of the starsof andradius gas

It is along theThe (photometric) rotation curve V(R)major depends axis. on

Dark Matter

mass, not luminosity, so we need to transform the surface brightness profile into a mass profile using M/L

This axis is generally (but not always) But what is M/L for the disk? around coincidentthewith the kinematic axis. Sun we found, M/L~1–3 major M⊙ The contributions of the disk and bulge can be added since the potentials add linearly:

We can compare this rotation curve 2 2 V 2 (R) = Vdisk (R) + Vbulge (R) in the galaxy.

For all disc galaxies the luminous matter is never enough to make up all the mass inferred from the dark matter halo luminous mass torotation that curve: provided by the Note: the mass inferred from the HI rotation is a lower limit, as there maybe a lot of dark matter outside the region where there is gas and stars.

To calculate the predicted circular velocity we use the observed surface brightness distribution of gas and of stars (preferably in R-band to be sensitive to older stellar populations which trace mass better).

Uncertainties and degeneracies. II Uncertainties and degeneracies. II

Uncertainties Generally the M/L and used isdegeneracies the one that gives Generally the M/L used is the one that gives

the maximum amplitude to disk contribution the maximum amplitude to disk contribution Given the still uncertainties in thewith disk M/L, the disk (and consistent observations) to the (and still consistent with observations) to the given rotation curve. contribution is highly uncertain given rotation curve. — without extra information. This is known as the maximum disk.

This is known as the maximum disk.

disc The model Maximum dark halo can be changed to have a

minimum disk (left), or no disk Uncertainties and degeneracies. IIat all (right)

The model dark halo can be changed to have a minimum disk (left), or nothe disk atused all (right) Generally M/L is the one that gives

the maximum amplitude to disk contribution (and still consistent with observations) to the given rotation curve. This is known as the maximum disk. The model dark halo can be changed to have a minimum disk (left), or no disk at all (right)

Minimum disc

No disc

Single dish (unresolved) HI measurements.

The Tully-Fisher Relation

The Tully-Fisher Relation

A relationship exists between the luminosity of a spiral galaxy and its maximum rotation velocity.

L

4 Vmax

amplitude of flat part of HI rotation curve

More luminous galaxies rotate faster How does this come about? Circular velocity and mass are related through The flux and luminosity are related

Assuming that M/L is constant More scatter in B due to stellar population effects The exponent changes with bandpass

L Link between the stellar mass (luminosity) of a disc and the mass of the Dark Matter halo. Verheijen 2001 Tully & Fisher 1977

1/2

✓

M L

◆

/I

1/2 2

v

I=

v2 =

GM r

M / rv 2

L 4⇡r2

M =L⇥

✓

M L

L/v

Assuming that M/L and I are constant

✓ ◆1/2 L I ✓ ◆1/2 L / v2 I

r2 / ◆

4

/ rv 2

✓

M L

◆

2

I

1

L / v4 Stars & Dark Matter are linked…