Spiral and Elliptical Galaxies I

Spiral and S0 Galaxies I

I I I I

I I

I

Manifested by pronounced disks, with motion dominated by rotation rather than randomness. Little vertical motion. S0 galaxies lack spiral features. Both S0 and spirals can have bars in their nuclear regions. They are composite systems: metal-poor halos, bulges and disk. Bulge regions are very dense, gas-poor, with much random motion (resemble small elliptical galaxies placed in a disk). They host nuclear star clusters, with accumulated gas leading to violent star formation. Spirals are most common galaxy and produce the bulk of light. Massive black holes at center.

Elliptical Galaxies I I

I

I

I

Deceptively simple-looking Devoid of cool gas and star formation, but have abundant hot gas, emitting X-rays. Wide range of luminosities and light concentrations, shapes and rotation. Slowly rotating systems are triaxial, rapidly rotating systems are oblate. Present-day ellipticals are fossils of the early Universe. J.M. Lattimer

AST 346, Galaxies, Part 6

Surface Photometry Isophotes in R band

Contours of CO on R band image

Hα image

i = cos−1 (dminor /dmajor ) = cos−1 0.35 = 69◦ itrue ' 75◦

Inner isophotes are less eccentric than outer: Bulge is ellipsoidal, not a disk. NGC 7331 – An Sb spiral galaxy

J.M. Lattimer

AST 346, Galaxies, Part 6

Surface Photometry mV0 ,T = 8.75, MV0 ,T = mV0 ,T − 5 log10 (D/10 pc) = −21.9 LV ,T = 5 × 1010 L . R∞ Ldisk = 2πIdisk (0) 0 e −R/hR RdR = 2πIdisk (0)hR2 ∼ 3 × 1010 L . ⇐ I (0) = 1.8 × 104 L pc−2 Vr = 820 km/s, D = 13.5 Mpc

disk

⇐ Idisk (0) = 325 L pc−2

3.6 kpc ⇐ sky brightness

I corrected by cos i. NGC 7331 – An Sb spiral galaxy

J.M. Lattimer

AST 346, Galaxies, Part 6

Bulge

NGC 4594, M104, an Sa galaxy Note large bulge and many globular clusters Bulge dominated by older, red stars

J.M. Lattimer

AST 346, Galaxies, Part 6

Relative Luminosities and Colors Galaxies become bluer and fainter the later the type. Ursa Major group, D = 15 Mpc

◦ IK 0 (0) > 19.5

J.M. Lattimer

AST 346, Galaxies, Part 6

Disks Have Varying Thickness

Sd UGC 7321, i ' 87◦ ,

Ir NGC 55, i ' 80◦ ,

LB ∼ 109 L ,

LB ∼ 2 × 109 L ,

J.M. Lattimer

D = 10 Mpc

D = 1.5 Mpc

AST 346, Galaxies, Part 6

Fainter Galaxies Have More Gas Ursa Major group The low-surface brightness galaxies are not efficient in turning gas into stars, like dwarf irregular galaxies.

◦ IK 0 (0) > 19.5

J.M. Lattimer

AST 346, Galaxies, Part 6

Dust and Star Formation Sbc NGC 4321, M100 Bar hidden by dust; young stars dominate spiral arms K-band image, 2.2µm isophotes

J.M. Lattimer

Hα image, K-band isophotes

AST 346, Galaxies, Part 6

The Bulge and Star Formation SBb NGC 3351, M95 The bar lacks young hot stars which are concentrated in knots in the spiral arms. Care must be taken in interpreting images of high-redshift galaxies. ˚ + 2300˚ UV image, 1530A A visible image, K-band isophotes

J.M. Lattimer

AST 346, Galaxies, Part 6

Dust Preferentially Absorbs UV Light

Dust absorbs UV light and re-emits it in the infrared.

T ∼ 20 − 30 K

J.M. Lattimer

AST 346, Galaxies, Part 6

Observing Cool Gas and Increasing Resolution Signal voltages at two telescopes a distance d apart: V1 ∝ cos (2πνt) , V2 ∝ cos (2πν(t − (d/c) cos θ)) Multiply these signals in a correlator, and filter out rapid oscillations. What remains is a fringe pattern

d sin θ. A complete image results if the area of a circle of radius d is covered with dishes. If a source is time-independent, we can put just a few telescopes along a line and use the Earth’s rotation to give us many baselines.

S ∝ cos (2πν(d/c) cos θ) . θ varies slowly as the Earth turns. Two nearby sources produce different fringe patterns, and as an interferometer the telescopes can resolve the angle c/(2dν) = λ/(2d). The resolution is the same as a single instrument with diameter d sin θ. With 2 elements, a source’s position can’t be measured, so we add additional pairs with different baselines J.M. Lattimer

Aperture synthesis

AST 346, Galaxies, Part 6

Cool Gas in NGC 7331 R MHI = 2.4 × 105 M D 2

Fν [1421 MHz(1 − Vr /c)]dVr 3nH /44 photons/cm3 /Myr

D = 14 Mpc 10 = 4 kpc

Fν in Janskys Vr in km/s

⇐ ”Spider diagram”

q northern a southern VLA

21 cm HI gas isophotes

Vr contours

J.M. Lattimer

AST 346, Galaxies, Part 6

Distribution and Mass of Cool Gas 2

c /p

Gas lies in disk centered on a ring; center is relatively gas-poor; it extends to larger R than stars, out to 2R25 .

0 ,1

s as

. vs

M



1M I= 2

dH c s. /p v s M as M 3.6

M

Average column density of HI is same in all spirals, due to self-shielding; higher surface densities make H2 at high densities.

2

/p

5 R2

Sc NGC 891

Gas in outer regions not prone to forming stars, due to differential rotation? In some galaxies, gas is bubbled out of disk, where it falls back. J.M. Lattimer

AST 346, Galaxies, Part 6



c

Searching for Molecular Gas H2 is too hard to observe, so CO emission at mm wavelengths is used as a proxy. But radio instruments are not as sensitive as they are at cm wavelenthgs, and CO/H2 ∼ 10−4 . It’s easier to detect atomic gas. But maps of molecular gas have better spatial resolution due to shorter wavelength.

The ratio of MHI to blue luminosity is often used as a measure of gas-richness of a galaxy; it is independent of D. In S0 and Sa galaxies, this ratio is 0.05 − 0.1M /LB, . In Sc, Sd and Sm galaxies it’s 10 times larger.

CO

In NGC 7331, there is CO emission from a small ring at R = 2.2hR (20 ) containing about 3 × 109 M of H2 . This is commmon, in other spirals CO emission peaks at center. J.M. Lattimer

AST 346, Galaxies, Part 6

Gas Content of S0 Galaxies

The gas content of S0 galaxies is very different from spirals; they have almost no gas. No recent star formation.

S0 UGC 7576

A few S0 galaxies have 1010 M of HI but it generally lies in a tilted ring encircling the galaxy, as in UGC 7576 (polar ring). It was probably captured.

J.M. Lattimer

AST 346, Galaxies, Part 6

Gas Motions and Galaxy Masses i = 30◦

Most galactic mass is ’dark’. For a circular orbit, V 2 /R = G M(< R)/R 2 even for a flattened system. HI gas has flat rotation curves beyond the stellar distribution, suggesting a rising M(< R).

φ=0

R/aH

Spider diagram

In spirals, dominate motion is ordered rotation. Geometry: Vr (R, i) = Vsys + V (R) sin i cos φ

J.M. Lattimer

HI

AST 346, Galaxies, Part 6

Rotation Curve of NGC 7331 and Dark Matter

HI

CO

stellar

J.M. Lattimer

AST 346, Galaxies, Part 6

Rotation Curves of Different Galaxies

← shows Vmax and hR

exponential disk

J.M. Lattimer

AST 346, Galaxies, Part 6

Total Mass Density of Galaxies The Schecter function describes the number density of galaxies: α

Φ(L) = n∗ (L/L∗ ) e −L/L∗ , n∗ ' 0.02h3 Mpc3 L∗ ' 9 × 109 h−2 L α ' −0.46

For spirals: 5h < ∼ M/L < ∼ 25h ρgal = ρL (BJ )M/L ∼ 1 − 5 × 109 h2 M Mpc−3

Total luminosity density: Z ∞ ρL (BJ ) = Φ(L)LdL

< 0.02ρcrit Deuterium abundance implies an even larger baryon density

0

= n∗ L∗ Γ(2 + α) ' 2 × 108 h L Mpc−3 Distance to galaxies: d ' [Vsys /100 km/s]h

Thus L ∝ h−2 , M ∝ R ∝ h−1 . M/L ∝ h

−1

Mpc J.M. Lattimer

2 0.02 < ∼ h ρB /ρcrit < ∼ 0.025

Most baryons are hidden, probably in hot diffuse intergalactic gas. AST 346, Galaxies, Part 6

The Tully-Fisher Relation A single-dish radio telescope can measure HI as a function of velocity, called a global profile. Much of the gas lies where V (R) ∼ constant, so flux is concentrated in two peaks at ±Vmax sin i. Brighter galaxies rotate more rapidly, implying they are more massive. Tully-Fisher relation: α∼4

This correlation is better in the red or infrared: in the blue, starburst episodes cause significant scatter. 2 Without dark matter, M ∝ hR Vmax , 2 2 L ∝ I (0)hR , M/L ∝ Vmax /(I (0)hR ). 4 L ∝ I (0)−1 (M/L)−2 Vmax

2Vmax

α L ∝ Vmax ,

/s) km 5 0 /2 ax

Vm

( 10 L

L=

3

0 ×1

??? J.M. Lattimer

4

K 0 ' 2.2µm

AST 346, Galaxies, Part 6

The Tully-Fisher Relation and the Hubble Constant

J.M. Lattimer

AST 346, Galaxies, Part 6

Lumpiness →

J.M. Lattimer

AST 346, Galaxies, Part 6

B

Observed Spiral Patterns I

Arms are bluer than disk

I

Hα emission shows arms are active star-forming regions

I

HI emission shows cool atomic gas also concentrated in spirals

I

Clearest spirals are of the grand design

Sbc M100 2600 = 2 kpc B-K, Hα

cos(m[φ + f (R, t)]) = 1 Pitch angle i is 5◦ in Sa spirals, 10◦ < i < 30◦ in Sc spirals:

Sbc NGC 3949

1/ tan i = |R∂φ/∂R| = |R∂f /∂R| If i is constant, f = ln R + k, which is a logarithmic spiral. J.M. Lattimer

I

AST 346, Galaxies, Part 6

B-K, HI

Spiral Patterns Spirals are leading (tips pointed forward wrt rotation) or trailing (tips pointed backward wrt rotation). Observed spirals almost always trail. Evidence that spirals are due to density waves (traffic jams), otherwise differential rotation would wind them up. Stars orbit with Ω(R) = V (R)/R; φ = φ0 + Ω(R)t;

f (R, t) = −φ

Since dΩ/dR < 0, it follows that df /dR > 0 and dφ/dR < 0. This is a trailing spiral. 1/ tan ψ = Rt|dΩ/dR| ≈ 25(t/Gyr), ψ ≈ 2◦ (Gyr/t). Stars initially on a radial line are quickly wound into a trailing spiral. J.M. Lattimer

AST 346, Galaxies, Part 6

Spiral Trailing or Leading?

Is the top in front or in back?

J.M. Lattimer

AST 346, Galaxies, Part 6

Prolonging Spiral Patterns A kinematic spiral can result if stars are not on circular paths but on slightly eccentric ones. Consider stars moving about a guiding center Rg with a epicyclic oscillation with frequency κ.

Ωp ∼ 0.3Ω so the spiral pattern lasts longer. An m-armed spiral could be described by ψ = mφg (0).

φg = Ω(Rg )t R = Rg + X cos(κt + ψ) Consider stars at Rg with ψ = 2φg (0); they will lie on an oval with the long axis pointing along φ = 0.

m=2

R = X cos(κt + 2[φg (t) − Ωt]) = X cos([2Ω − κ]t − 2φg (t)) The long axis is defined by (2Ω − κ)t = 2φ or φ = (Ω − κ/2)t = Ωp t. J.M. Lattimer

AST 346, Galaxies, Part 6

m=1

Maintaining Spiral Patterns Spiral-density wave theory maintains that gravitational attraction of stars and gas at different radii can offset the tendency to wind up a pairal pattern, causing the growth of a pattern with frequency Omegap . The general result is that the periodic tugging of stellar motions by a spiral arm will reinforce the pattern only if the perturbing frequency m(Ωp − Ω(R)) < κ(R).

To prevent m = 0 waves from growing κσR > Q= 1 3.36G Σ ∼ In solar neighborhood, Q ∼ 1.4. Trailing arms favored because inner disk exerts a torque on the outer disk allowing angular momentum to be transferred outward and material to move inward. This decreases the rotational energy of the disk. m = 2 Lindblad resonances Plummer potential

Lindblad resonances occur when m(Ωp − Ω(R)) = ±κ(R), and reinforcement occurs between these resonances. Disk stars must have a small random motion to enable reinforcement; they cannot move outside of spiral arms. J.M. Lattimer

ILR

ILR

AST 346, Galaxies, Part 6

Effect of Spiral Arms on Gas Effect on clouds is greater than on stars because of small cloud random motions, ∼ 5 − 10 km/s. The linear speed at which gas enters spiral arms is supersonic: R[Ω(R) − Ωp ] > cs except near the corotation (CR) point Ω(R) = Ωp . Therefore, shocks develop. Dust lanes are on concave side of arms showing the gas enters from that side. SInce 10 Myr is needed to evolve young stars, peak Hα emission is downstream of spiral arms. Radiation from hot stars splits H2 , producing HI emission in arms. J.M. Lattimer

AST 346, Galaxies, Part 6

Barred Disks It is not clear why some galaxies have bars and others do not. Bars are not density waves, but they do promote transfer of angular momentum. Within the corotation point, where Ω(R) = Ωp , a family of closed orbits exist. It is believed the corotation point is external to the bar. The elongated closed orbits converge at the ends and is compressed into shocks (leads to dust lanes along leading edge of bar). In the shock, gas loses energy of forward motion as heat and falls to center, but infall terminated where it meets rounder stable orbits. Gas piles up in a central ring. J.M. Lattimer

AST 346, Galaxies, Part 6

Warped Extended Disk in M83

J.M. Lattimer

AST 346, Galaxies, Part 6

Bulges Bulges are the most densely populated stellar systems, often harboring a black hole at their centers. Milky Way and M31 bulges are more metal-rich than the disk and gas-poor except at the very center. Bulge stars share rotation, larger random motions than disk, σ ∼ Vc . Bulge’s extent is Re , the half-light radius. Studies show Re ' 0.1hR , ranging from 100 pc to several kpc. Origin of bulges is not clear; their high densities could be a result of being older than the disk. Alternatively, they could have formed later as gas spirals to center. Some z > 3 galaxies are apparently building bulges, but a rare case, NGC 7331, has some bulge stars orbiting opposite to the bulge itself, J.M. Lattimer

from matter falling in at late times. Near the center, the angular velocity is nearly constant, so there is little differential rotation to inhibit star formation. In many galaxies, central starbursts are visible, but cannot be maintained longer than 0.1 Gyr. At Milky Way’s center, about 107 M is packed into a nuclear star cluster only 3 pc in radius; these are often seen in spiral and dwarf elliptical galaxies. They are fed by the infall of new gas and continued star formation. The nuclear star clusters can hide black holes. H-burning releases 0.7% of the rest mass as energy, but material falling into a black hole can release 10%. These are probably the sources of active galactic nuclei. AST 346, Galaxies, Part 6

Nuclear Black Holes The black hole in Milky Way’s center is quiescent, visible by gravitational effects. The Milky Way exhibits only a mild degree of nuclear activity, but other galaxies have a more violent center, including jets.

NGC 4258

jets

Water maser (22.2 GHz) reveals a nuclear disk 0.01500 across (0.5 pc). 9 −3 5 ρnuc > ∼ 10 M pc , 10 × that of a globular cluster.

J.M. Lattimer

AST 346, Galaxies, Part 6

Nuclear Black Holes Stars close to a central black hole should move faster than those farther out, leading to an increased velocity dispersion.

MBH = 2 × 108 M (σc /200km/s)4.86

rBH /D

2 V 2 (r ) ≈ G M(< r )/r > ∼ σc  4 MBH σc rBH ≈ 45 8 pc 10 M 100km/s

Most bright ellipticals are radio sources, emitting power 20 P> ∼ 10 W/Hz at 20 cm, about 10 times expected from HII regions and SNR that power radio emission from spirals. Could be evidence for MBH > 106 M . J.M. Lattimer

AST 346, Galaxies, Part 6

Photometry of Elliptical Galaxies Three luminosity groups: I

I

I

Luminous giant ellipticals, L > L∗ = 2 × 1010 L , MB < ∼ −20 Midsize ellipticals, −20 < ∼ MB < ∼ −18 9 Dwarf ellipticals, L < ∼ 3 × 10 L , > MB ∼ −18

Isophotes, contours of equal surface brightness, are usually ellipsoidal. Hubble type En where n = 10 with  = 1 − b/a. Hubble type depends on our perspective. Concentration of light towards center is greater than in disk galaxies, 1/n

I (R) = I (Re )e −b[(R/Re )

n = 4 (deVaucoleurs law) adequately describes luminous and midsize ellipticals; n = 1 describes dwarf and disk galaxies. The total luminosity Z ∞ L= 2πRI (R)dR 0

8!e 7.67 πRe2 I (Re ) = 7.678 ≈ 7.22πRe2 I (Re )

Re = 15.800 in B band IB (Re ) = 24.4 mag arcsec−2 BT0 = 16.4 D = 16 Mpc, L ≈ 1.1 × 108 L Night sky: I ≈ 22.5

dE VCC753

−1] J.M. Lattimer

(n = 4)

AST 346, Galaxies, Part 6

NGC 5846

EFAR J16WG

Note twisted contours

Zw 159-89

NGC 4478

R Band

J.M. Lattimer

AST 346, Galaxies, Part 6

Giant Ellipticals R 1/4 law Re = 15.700 = 1.4 kpc

Re = 4.9500 = 3.8 kpc

mag arcsec−2

The patterns observed here reflect galaxy formation rather than their internal workings.

J.M. Lattimer

AST 346, Galaxies, Part 6

Centers of Ellipticals at High Resolution Viewed from a large distance along the axis z, Z ∞ Z ∞ n(r )rdr √ Σ(R) = 2 n(r )dz = 2 . r 2 − R2 0 R Assuming n(r ) = n0 (r0 /r )α ,  r α−1  r α−1 Z ∞ x 1−α dx 0 0 √ = Σ(R = r0 ) . Σ(R) = 2n0 r0 2−1 R R x 1

cusp α = 0.55

MV = −21.7

MV = −20.9

core

-

J.M. Lattimer

Care should be taken when interpreting a measurement of rc because seeing results in only a lower bound being measured.

AST 346, Galaxies, Part 6

True vs. Observed Shapes of Elliptical Galaxies Oblate spheroid ρ(x) = ρ(m2 )

Fraction between i and i + di is sin i di. A sample with fixed ratio B/A x +y z m2 = + will have a fraction f (q)dq = A2 B2 q dq sin i dq Apparent aspect ratio q = b/a, true p . =p 2 |dq/di| 1 − B /A2 q 2 − B 2 /A2 ratio B/A. 2 zA dx If B/A > Vr − Vsys

J.M. Lattimer

AST 346, Galaxies, Part 6

Faber-Jackson Relation and the Fundamental Plane In analogy to spirals and the Tully-Fisher Relation, ellipticals follow a 4  similar behavior σ LV ≈ . 2 × 1010 L 200 km/s However, difficult to measure light from faint outer parts, errors large. The fundamental plane relation, observationally, is Re ∝ σ 1.2 I −0.8 (Re )

r 0.8 < z < 1.2

J.M. Lattimer

AST 346, Galaxies, Part 6

Rotation and Dispersion Most galaxies rotate less quickly than their shapes imply.

(V /σ)iso '

Less luminous galaxies tend to rotate less slowly.

p

/(1 − )

r MB < −19.5

Boxy galaxies tend to rotate more slowly. Slow rotation must be compensated by anisotropic velocity dispersion σx >> σz PEz KEz σ2 = ≈ 2 z 2 PEx KEx V /2 + σx Triaxiality could explain anisotropy. J.M. Lattimer

AST 346, Galaxies, Part 6

Boxy vs. Disky Galaxies

J.M. Lattimer

AST 346, Galaxies, Part 6

Maximum Rotation Rate Without Random Motions Assume a uniformly rotating fluid, and approximate the gravitational potential by a point source at the origin (Roche approximation): ρ−1 ∇p = ∇h = −∇(ΦG + Φc ) ΦG ' −G M/r , Φc = −(1/2)Ω2 r 2 sin2 φ. This is a perfect differential and can be integrated (Bernoulli Integral): H = h + ΦG + Φc = −G M/Rp Rp and Re are the polar (φ = 0) and equatorial (φ = π/2) radii. Evaluate at equator (h = 0 on the surface): Re Ω2 Re3 = −1 2G M Rp The maximum rotation rate is when the orbital velocity at the equator is the same as the equatorial surface velocity: 3 Ω2max = G M/Re,max which implies Re,max = 3Rp,min /2 or max = 1 − Rp,min /Re,max = 1/3. The fact that many galaxies are more flattened than this implies an additional source of support in the plane; a large velocity dispersion. J.M. Lattimer

AST 346, Galaxies, Part 6

Orbits in a Triaxial Potential

loop box

chaotic

surface of section

loop chaotic box J.M. Lattimer

AST 346, Galaxies, Part 6

Color-Magnitude Relation

Abell 2218 Abell 2218

Virgo and Coma

J.M. Lattimer

AST 346, Galaxies, Part 6

Metallicity-Luminosity Relation

J.M. Lattimer

AST 346, Galaxies, Part 6

Ellipticals Have High Metallicities M87

5 0 4 = < r 0 8 < r 0 4