Spiral and Elliptical Galaxies

I Spiral and S0 Galaxies

I Manifested by pronounced disks, with motion dominated by rotation rather than randomness. Little vertical motion.

I S0 galaxies lack spiral features.

I Both S0 and spirals can have bars in their nuclear regions.

I They are composite systems: metal-poor halos, bulges and disk.

I 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.

I Spirals are most common galaxy and produce the bulk of light.

I Massive black holes at center. I Elliptical Galaxies

I Deceptively simple-looking

I Devoid of cool gas and star formation, but have abundant hot gas, emitting X-rays.

I Wide range of luminosities and light concentrations, shapes and rotation.

I Slowly rotating systems are triaxial, rapidly rotating systems are oblate.

I 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 Hα image on R band image −1 i = cos (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 0 0 0 mV ,T = 8.75, MV ,T = mV ,T − 5 log10(D/10 pc) = −21.9 10 LV ,T = 5 × 10 L . ∞ R −R/hR 2 10 Ldisk = 2πIdisk (0) 0 e RdR = 2πIdisk (0)hR ∼ 3 × 10 L .

4 ⇐ I (0) = 1.8 × 10 L pc−2 Vr = 820 km/s, D = 13.5 Mpc

3.6 kpc −2 ⇐ Idisk (0) = 325 L pc disk ⇐ 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

◦ 9 Sd UGC 7321, i ' 87 , LB ∼ 10 L , D = 10 Mpc

◦ 9 Ir NGC 55, i ' 80 , LB ∼ 2 × 10 L , D = 1.5 Mpc

J.M. Lattimer 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 Hα image, K-band isophotes

J.M. Lattimer 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. UV image, 1530A˚ + 2300A˚ 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 d sin θ. A complete image results if distance d apart: the area of a circle of radius d is covered with dishes. If a source is V1 ∝ cos (2πνt) , time-independent, we can put just a V2 ∝ cos (2πν(t − (d/c) cos θ)) few telescopes along a line and use the Multiply these signals in a correlator, Earth’s rotation to give us many and filter out rapid oscillations. What baselines. remains is a fringe pattern 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 Aperture synthesis 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 AST 346, Galaxies, Part 6 Cool Gas in NGC 7331 5 2 R MHI = 2.4 × 10 M D Fν [1421 MHz(1 − Vr /c)]dVr

3nH /44 D = 14 Mpc photons/cm3/Myr 10 = 4 kpc Fν in Janskys Vr in km/s

⇐ ”Spider diagram”

northern southern VLA q a

21 cm HI gas isophotes Vr contours

J.M. Lattimer AST 346, Galaxies, Part 6 Distribution and Mass of Cool Gas 2 /pc

M Gas lies in disk centered on a 2 , 10 ring; center is relatively /pc R 25 gas-poor; it extends to larger M =1 2 R than stars, out to 2R . d HI 25 /pc Mass vs. M Average column density of HI .6 is same in all spirals, due to Mass vs.3 self-shielding; higher surface densities make H2 at high densities. 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 Searching for Molecular Gas

H2 is too hard to observe, so CO emission at mm The ratio of MHI to blue luminosity is often wavelengths is used as a used as a measure of gas-richness of a galaxy; proxy. But radio instruments it is independent of D. In S0 and Sa galaxies, are not as sensitive as they this ratio is 0.05 − 0.1M /LB, . In Sc, Sd are at cm wavelenthgs, and and Sm galaxies it’s 10 times larger. −4 CO/H2 ∼ 10 . It’s easier to detect atomic gas. But maps of molecular gas have better CO spatial resolution due to shorter wavelength. In NGC 7331, there is CO emission from a small ring at 0 R = 2.2hR (2 ) containing 9 about 3 × 10 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 S0 UGC 7576 spirals; they have almost no gas. No recent star formation. A few S0 galaxies have 10 10 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 ◦ Most galactic mass is ’dark’. i = 30 For a circular orbit, 2 2 V /R = GM(< R)/R φ = 0 even for a ﬂattened system. HI gas has ﬂat rotation curves

beyond the stellar distribution, R/aH suggesting a rising M(< R). Spider diagram In spirals, dominate motion is ordered rotation. Geometry: HI Vr (R, i) = Vsys + V (R) sin i cos φ

J.M. Lattimer AST 346, Galaxies, Part 6 Rotation Curve of NGC 7331 and Dark Matter

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 Thus L ∝ h−2, M ∝ R ∝ h−1. number density of galaxies: M/L ∝ h

α −L/L∗ Φ(L) = n∗ (L/L∗) e , For spirals: 5h < M/L < 25h 3 3 ∼ ∼ n∗ ' 0.02h Mpc 9 −2 L∗ ' 9 × 10 h L α ' −0.46 ρgal = ρL(BJ )M/L 9 2 −3 Total luminosity density: ∼ 1 − 5 × 10 h M Mpc Z ∞ < 0.02ρcrit ρL(BJ ) = Φ(L)LdL 0 Deuterium abundance implies an even = n∗L∗Γ(2 + α) larger baryon density 8 −3 ' 2 × 10 h L Mpc < 2 < 0.02 ∼ h ρB /ρcrit ∼ 0.025 Distance to galaxies: Most baryons are hidden, probably in −1 hot diﬀuse intergalactic gas. d ' [Vsys /100 km/s]h Mpc

J.M. Lattimer 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 L ∝ Vmax , α ∼ 4

4 This correlation is better in the red or K 0 ' 2.2µm s) max / km infrared: in the blue, starburst V 2 /205 episodes cause signiﬁcant scatter. (Vmax

2 10 L Without dark matter, M ∝ hR Vmax , × 10 2 2 = 3 L ∝ I (0)hR , M/L ∝ Vmax /(I (0)hR ). L −1 −2 4 L ∝ I (0) (M/L) Vmax ???

J.M. Lattimer AST 346, Galaxies, Part 6 The Tully-Fisher Relation and the Hubble Constant

J.M. Lattimer AST 346, Galaxies, Part 6 Lumpiness → ..Lattimer J.M. S 4,Glxe,Pr 6 Part Galaxies, 346, AST Observed Spiral Patterns BI

I Arms are bluer than disk Hα emission shows arms are Sbc M100 I 2600 = 2 kpc active star-forming regions B-K, Hα B-K, HI I HI emission shows cool atomic gas also concentrated in spirals

I Clearest spirals are of the grand design cos(m[φ + f (R, t)]) = 1 Pitch angle i is 5◦ in Sa spirals, Sbc NGC 3949 10◦ < i < 30◦ in Sc spirals:

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 AST 346, Galaxies, Part 6 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 Ωp ∼ 0.3Ω so the spiral pattern lasts are not on circular paths but on longer. slightly eccentric ones. Consider stars An m-armed spiral could be described moving about a guiding center Rg with by ψ = mφg (0). a epicyclic oscillation with frequency κ.

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 m = 2 m = 1 axis pointing along φ = 0.

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 = Ωpt.

J.M. Lattimer AST 346, Galaxies, Part 6 Maintaining Spiral Patterns Spiral-density wave theory maintains To prevent m = 0 waves from growing that gravitational attraction of stars κσR Q = > 1 and gas at different radii can offset the 3.36GΣ ∼ tendency to wind up a pairal pattern, In solar neighborhood, Q ∼ 1.4. causing the growth of a pattern with Trailing arms favored because inner frequency Omegap. disk exerts a torque on the outer disk The general result is that the periodic allowing angular momentum to be tugging of stellar motions by a spiral transferred outward and material to arm will reinforce the pattern only if move inward. This decreases the the perturbing frequency rotational energy of the disk. m(Ω − Ω(R)) < κ(R). p m = 2 Lindblad resonances Lindblad resonances occur when Plummer potential m(Ωp − Ω(R)) = ±κ(R), and reinforcement occurs between these resonances. Disk stars must have a small random motion to enable reinforcement; they ILR ILR cannot move outside of spiral arms. J.M. Lattimer 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 from matter falling in at late times. stellar systems, often harboring a black Near the center, the angular velocity is hole at their centers. nearly constant, so there is little Milky Way and M31 bulges are more diﬀerential rotation to inhibit star metal-rich than the disk and gas-poor formation. In many galaxies, central except at the very center. starbursts are visible, but cannot be Bulge stars share rotation, larger maintained longer than 0.1 Gyr. random motions than disk, σ ∼ V . 7 c At Milky Way’s center, about 10 M is Bulge’s extent is Re , the half-light packed into a nuclear star cluster only 3 radius. Studies show Re ' 0.1hR , pc in radius; these are often seen in ranging from 100 pc to several kpc. spiral and dwarf elliptical galaxies. They Origin of bulges is not clear; their high are fed by the infall of new gas and densities could be a result of being continued star formation. older than the disk. Alternatively, they The nuclear star clusters can hide black could have formed later as gas spirals holes. H-burning releases 0.7% of the to center. Some z > 3 galaxies are rest mass as energy, but material falling apparently building bulges, but a rare into a black hole can release 10%. case, NGC 7331, has some bulge stars These are probably the sources of active orbiting opposite to the bulge itself, galactic nuclei. J.M. Lattimer 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 8 4.86 MBH = 2 × 10 M (σc /200km/s) hole should move faster than those farther out, leading to rBH /D an increased velocity dispersion.

2 > 2 V (r) ≈ GM(< r)/r ∼ σc 4 rBH MBH σc ≈ 45 8 pc 10 M 100km/s Most bright ellipticals are radio sources, emitting power P ∼> 1020 W/Hz at 20 cm, about 10 times expected from HII regions and SNR that power radio emission from spirals. Could be evidence for 6 MBH > 10 M .

J.M. Lattimer AST 346, Galaxies, Part 6 Photometry of Elliptical Galaxies n = 4 (deVaucoleurs law) adequately Three luminosity groups: describes luminous and midsize I Luminous giant ellipticals, ellipticals; n = 1 describes dwarf and 10 < L > L∗ = 2 × 10 L , MB ∼ −20 disk galaxies. The total luminosity I Midsize ellipticals, Z ∞ < < L = 2πRI (R)dR −20 ∼ MB ∼ −18 0 < 9 I Dwarf ellipticals, L ∼ 3 × 10 L , 7.67 8!e 2 M > −18 = πR I (Re )(n = 4) B ∼ 7.678 e Isophotes, contours of equal surface 2 ≈ 7.22πRe I (Re ) brightness, are usually ellipsoidal. 00 Re = 15.8 in B band −2 Hubble type En where n = 10 with IB (Re ) = 24.4 mag arcsec 0 = 1 − b/a. BT = 16.4 8 D = 16 Mpc, L ≈ 1.1 × 10 L Hubble type depends on our Night sky: I ≈ 22.5 perspective. Concentration of light towards center dE VCC753 is greater than in disk galaxies,

1/n I (R) = I (R )e−b[(R/Re ) −1] e J.M. Lattimer AST 346, Galaxies, Part 6 b ≈ 1999n − 0.327 NGC 5846 EFAR J16WG

Note twisted contours

Zw 159-89 NGC 4478

R Band

J.M. Lattimer AST 346, Galaxies, Part 6 Giant Ellipticals

R1/4 law

00 Re = 15.7 = 1.4 kpc

00 Re = 4.95 = 3.8 kpc

2 The patterns observed − here reﬂect galaxy formation rather than their internal workings. mag arcsec

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 √ . 2 2 0 R r − R α Assuming n(r) = n0(r0/r) ,

α−1 Z ∞ 1−α α−1 r0 x dx r0 Σ(R) = 2n0r0 √ = Σ(R = r0) . 2 R 1 x − 1 R

cusp MV = −21.7 α = 0.55 Care should be taken when interpreting a MV = −20.9 - measurement of rc core because seeing results in only a lower bound being measured.

J.M. Lattimer 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 x 2 + y 2 z2 sin i di. A sample with ﬁxed ratio B/A m2 = + will have a fraction f (q)dq = A2 B2 sin i dq q dq Apparent aspect ratio q = b/a, true = . |dq/di| p1 − B2/A2pq2 − B2/A2 ratio B/A. 2 dx z A If B/A << 1, this distribution is tan i = = − 2 dz x B uniform; observations imply a = mA, b = OR = OQ sin i B/A ∼< 0.2. No ellipticals more OQ = OP+PQ = z−x/ tan i = B2m2/z ﬂattened than q = 0.3, possibly unstable. b OQ sin i B2m q = = = sin i oblate a mA zA r B2 1 = + sin i A2 tan2 i s B 2 = sin2 i + cos2 i A −1 qprolate = qoblate

J.M. Lattimer AST 346, Galaxies, Part 6 Axis Ratio and Luminosity

4.5×

J.M. Lattimer AST 346, Galaxies, Part 6 Ordered vs. Random Velocities

cD NGC 1399

σr >> 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 similar behavior 4 LV σ 10 ≈ . 2 × 10 L 200 km/s However, diﬃcult to measure light from faint outer parts, errors large. 1.2 −0.8 The fundamental plane relation, observationally, is Re ∝ σ I (Re )

0.8 < z < 1.2 r

J.M. Lattimer AST 346, Galaxies, Part 6 Rotation and Dispersion p Most galaxies rotate less (V /σ)iso ' /(1 − ) quickly than their shapes imply. Less luminous galaxies

tend to rotate less slowly. MB < −19.5 Boxy galaxies tend to r rotate more slowly. Slow rotation must be compensated by anisotropic velocity dispersion σx >> σz

2 PEz KEz σz = ≈ 2 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): −1 ρ ∇p = ∇h = −∇(ΦG + Φc ) 2 2 2 ΦG ' −GM/r,Φc = −(1/2)Ω r sin φ. This is a perfect diﬀerential and can be integrated (Bernoulli Integral):

H = h + ΦG + Φc = −GM/Rp

Rp and Re are the polar (φ = 0) and equatorial (φ = π/2) radii. Evaluate at equator (h = 0 on the surface): Ω2R3 R e = e − 1 2GM Rp The maximum rotation rate is when the orbital velocity at the equator is the same as the equatorial surface velocity: 2 3 Ωmax = GM/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

40 = 5 kpc r < 80 r < 40 < T ∼ 2 × 107 K

J.M. Lattimer AST 346, Galaxies, Part 6