12.1 Elliptical Galaxies Elliptical Galaxies Old view: ellipticals are boring, simple systems • Ellipticals contain no gas & dust • Ellipticals are composed of old stars • Ellipticals formed in a monolithic collapse, which induced violent relaxation of the stars, stars are in an equilibrium state Modern view: • Most/all ellipticals have hot x-ray gas, some have dust, even cold gas • Ellipticals do rotate, but most of the kinetic energy support (and galaxy shapes) come from an anisotropic velocity dispersion • Some contain decoupled (counter-rotating) cores, or other complex kinematics • Some have weak stellar disks • Ellipticals formed by mergers of two spirals, or hierarchical clustering of smaller galaxies 2 Dust lanes in E galaxy NGC 1316
Dust is surprisingly common in E’s
Probably it originates from cannibalized spiral galaxies Elliptical Galaxies: Surface Photometry Surface brightness of elliptical galaxies falls off smoothly with radius. Measured (for example) along the major axis of the galaxy, the profile is normally well represented by the R1/4 or de Vaucouleurs law: 1/4 I(R) = I(0) e-kR where k is a constant. This can be rewritten as:
0.25 {−7.67[(R Re ) −1]} I(R) = I e € e where Re is the effective radius - the radius of the isophote containing half of the total luminosity. Ie is the surface brightness at the effective radius. Typically, the effective radius€ of an elliptical galaxy is a few kpc.
4 De Vaucouleurs’ Law
R 1/4 profile fits the data very well over some 2 decades in radius
5 Other Common Profiles Sersic profile:
where S is the surface brightness in linear units (not magnitudes), bn is chosen such that half the luminosity comes from R < Re. This law becomes de Vaucouleurs for n = 4, and exponential for n = 1.
Hubble’s profile:
with S 0 the central surface brightness, and r0 the “core” radius interior to which the surface brightness profile is approx. constant. Note that the integral under the Hubble profile diverges! 6 Breaking the Homology: Density Profiles
Sersic profile index (r 1/n) correlates with the galaxy size (D’Onofrio et al. 1994)
More luminous ellipticals have shallower profiles (Schombert 1986) 7 The Cores and Nuclei of Ellipticals Profiles of elliptical galaxies can deviate from the R1/4 law at both small and large radii. Close to the center: • Some galaxies have cores - region where the surface brightness flattens and is ~ constant • Other galaxies have cusps - surface brightness rises steeply as a power-law right to the center A cuspy galaxy might appear to have a core if the very bright center is blurred out by atmospheric seeing. Thus, HST is essential to studies of galactic nuclei!
It turns out that: • The most luminous ellipticals have HST-resolved cores • Low luminosity ellipticals have power law cusps extending inward as far as can be seen 8 Central Surface Brightness Profiles
To describe these observations, we can use a new profile suggested by the “Nuker” team: (γ −β ) /α & )− γ , & )α / (β −γ ) /α R R I(R) = Ib 2 ( + .1 + ( + 1 ' Rb * -. ' Rb * 01 It is a broken power law: • Slope of -g at small radii • Slope of -b at large radius • Transition€ between the two slopes at a break radius Rb, at which point the surface brightness is Ib • Remaining parameter a controls how sharp the changeover is
9 The “Nuker” Profile
Changing inner slope Changing outer slope
g = 0, 0.5, 1, 1.5 b = 1, 1.5, 2
10 12.2 Elliptical Galaxies: Shapes Typical Elliptical Isophotes
Note the apparent ellipticity gradient
NGC 1533 NGC 4689 12 Shapes of Ellipticals • Ellipticals are defined by En, The observed distribution where n=10e, and e=1-b/a is the ellipticity • Note this is not intrinsic, it is observer dependent!
13 Triaxial Ellipsoids • In general, the 3-D shapes of ellipticals can be triaxial (A,B,C are intrinsic axis radii): – Oblate: A = B > C (a flying saucer) – Prolate: A > B = C (a cigar) – Triaxial A > B > C (a football) • Studies find that ellipticals are mildly triaxial, with typical axis ratios: A:B:C ~ 1 : 0.95 : 0.65 (with some dispersion, ~0.2) • Triaxiality is supported by observations of isophotal twists in some galaxies (would not see these if galaxies were purely oblate or prolate) • It is due to the anisotropic velocity dispersions, which stretch the galaxies in proportion along their 3 principal axes 14 Triaxial Ellipsoids in Projection In a triaxial case, the orientation in the sky of the projected ellipses will not only depend upon the orientation of the body, but also upon the body’s axis ratio
(from Binney & Merrifield) 15 Isophote Twisting Since the ellipticity changes with radius, even if the major axis of all the ellipses have the same orientation, they appear as if they were rotated in the projected image. This is called isophote twisting:
16 Isophote Twists Here is an example of twisted isophotes in a satellite galaxy of Andromeda (M31):
And another:
17 Isophotes: Deviations From Ellipses Isophotes are not perfect ellipses. There may be an excess of light on the major axis (disky), or on the “corners” of the ellipse (boxy):
The diskiness/boxiness of an isophote is measured by the difference between the real isophote and the best-fit elliptical one:
d(f) =
19 Disky and Boxy Ellipticals • Disky/boxy shapes correlate with various other galaxy parameters: – Boxy galaxies more likely to show isophotal twists (and hence be triaxial) – Boxy galaxies tend to be more luminous – Boxy galaxies have stronger radio and x-ray emission – Boxy galaxies are slow rotators, more anisotropic – In contrast, disky galaxies are midsized ellipticals, oblate, faster rotators, less luminous in radio and x-ray • Some believe that more dissipationless mergers lead to more boxy galaxies, whereas any embedded disks imply some dissipative collapse, but the real picture is probably more complicated 20 12.3 Elliptical Galaxies: Kinematics The Kinematics of E-Galaxies Stars in E galaxies have some ordered motions (e.g., rotation), but most of their kinetic energy is in the form of random motions. Thus, we say that ellipticals are pressure-supported systems
To measure the kinematics within galaxies we use absorption lines. Each star emits a spectrum which is Doppler shifted in wavelength according to its motion. Random distribution of velocities then broadens the spectral lines relative to those of an individual star. Systemic motions (rotation) shift the line centroids.
22 Kinematical Profiles of E-Galaxies
dispersion
rotation
• Rotation is present, but generally not a dominant component of the kinetic energy • Velocity dispersion tends to be higher closer to the center 23 2-Dimensional Kinematics of E-Gal’s
Intensity (surface brightness)
Rotation velocity
Velocity dispersion 24 Velocity Anisotropy in Elliptical Galaxies
The ratio of the maximum rotational velocity Vm and the mean velocity dispersion s indicates whether the observed shapes of E’s are due to rotation or anisotropic pressure
Galaxies on this line are flattened by rotation
Galaxies below it are flattened by anisotropy ellipticity
25 Velocity Anisotropy in Elliptical Galaxies
Now normalize by the “isotropic rotator” line
More luminous ellipticals tend to be anisotropic
This can be understood as a consequence of merging 26 Stellar Populations in Ellipticals
• Ellipticals are made mostly Mg line strength vs. radius from old stars, ages > 1 Gyr and generally ~ 10 Gyr • They have a broad range of metallicities (which indicate the degree of chemical evolution), up to 10 times Solar! • More metal rich stars are found closer to the center • This is observed as line strength gradients, or as color gradients (more metal-rich stars are redder) 27 Metallicity-Luminosity Relation also known as the Color-Magnitude Relation There is a relation between the color (a metallicity indicator) and the total luminosity or velocity dispersion for E galaxies: R e d
B l u e Bright Faint Cold Hot
Brighter and dynamically hotter galaxies are redder. This could be explained if small E galaxies were younger or more metal-poor than the large ones. More massive galaxies could be more effective in retaining and recycling their supernova ejecta. 28 Hot Gas in Elliptical Galaxies
M49 Optical M49 X-ray
The gas is metal-rich, and thus at least partly a product of stellar evolution It is at a virial temperature corresponding to the velocity dispersion of stars Another good probe of dark matter in ellipticals… 29 Stellar vs. Dynamical Mass
M★/M¤ M = M★ M = 6 M★ 1011 dyn dyn
Recall that Ωm ~ 6 Ωb
1010 38527 Early-type galaxies from the SPIDER collab. (de Carvalho et al.)
Mdyn/M 10 11 10 10 ¤ 30 More Massive Galaxies Have Larger (M/L)
(M/L) vs. Luminosity a ~ Stellar mass
` (M/L) vs. Mass
(Cappellari et al. 2006) 31 (M/L) vs. Mass From Gravitational Lensing
` Total Mass
` Stellar Mass
(Auger et al. 2010, the SLACS collab.) red = V band, blue = B band 32 (M/L) Increases With Radius
From X-ray profiles and modeling
(Fukazawa et al. 2006)
Fully consistent with dynamical modeling of optical data 33 12.4 Massive Black Holes in Galactic Nuclei
and Dwarf Galaxies Massive Black Holes in Galactic Nuclei
• It turns out that they are ubiquitous: nearly every non-dwarf galaxy seems to have one, but only a small fraction are active today; these super-massive black holes (SMBH) are believed to be the central engines of quasars or other AGN • They are detected through central velocity dispersion or rotation cusps near the center - requiring more mass than can be reasonably provided by stars • Their masses correlate very well with many of their host galaxy properties, suggesting a co-formation and/or co-evolution of galaxies (or at least their old stellar spheroid components) and the SMBHs they contain • Understanding of this connection is still not complete, but dissipative mergers can both drive starbursts and fuel/grow SMBHs 35 Many (all?) ellipticals (& bulges) have black holes- even compact ones like M32!
Can measure BH masses for galaxies via their velocity dispersion 36 Fundamental Corrrelations Between SMBH Masses and Their Host Galaxy Properties ⎛ ⎞ 4.6±0.5 M BH 8 σ c M BH 0 log ( 0.36 0.09)B (1.2 1.9) = (1.7± 0.3)×10⎜ −1⎟ = − ± T + ± M 200km s M 8 ¤ ⎝ ⎠ 2 χ 2 = 0.72 χ r = 23 r Ferrarese & Merritt 2000; Gebhardt et al. 2000 Kormendy & Richstone 1995
€ €
37 The SMBH - Host Galaxy Correlations
M! ~ M! 4.4 M! ~ s
1.6 M! ~ MH
38 Dwarf Galaxies • Dwarf ellipticals (dE) and dwarf spheroidals (dSph) are a completely different family of objects from normal ellipticals - they are not just small E’s • In fact, there may be more than one family of gas-poor dwarf galaxies … • Dwarfs follow completely different correlations from giant galaxies, suggestive of different formative mechanisms • They are generally dark matter (DM) dominated, especially at the faint end of the sequence • One possible scenario is that supernova (SN) winds can remove baryons from these low-mass systems, while leaving the DM, while the more massive galaxies retain and recycle their SN ejecta 39 Parameter Correlations
Kormendy 1985 40 Mean Surface Brightness vs. Absolute Mag.
41 Mass to Light Ratios Dwarf Spheroidals
42 12.5 Galaxy Scaling Relations Galaxy Scaling Laws
• When correlated, global properties of galaxies tend to do so as power-laws; thus “scaling laws” • They provide a quantitative means of examining physical properties of galaxies and their systematics • They reflect the internal physics of galaxies, and are a product of the formative and evolutionary histories – Thus, they could be (and are) different for different galaxy families – We can use them as a fossil evidence of galaxy formation • When expressed as correlations between distance-dependent and distance-independent quantities, they can be used to measure relative distances of galaxies and peculiar velocities: thus, it is really important to understand their intrinsic limitations of accuracy, e.g., environmental dependences 44 The Tully-Fisher Relation • A well-defined luminosity vs. rotational speed (often measured as a H I 21 cm line width) relation for spirals: g L ~ Vrot , g ≈ 4, varies with wavelength Or: M = b log (W) + c , where: – M is the absolute magnitude – W is the Doppler broadened line width, typically measured using the HI 21cm line, corrected for inclination Wtrue= Wobs/ sin(i) – Both the slope b and the zero-point c can be measured from a set of nearby spiral galaxies with well-known distances – The slope b can be also measured from any set of galaxies with roughly the same distance - e.g., galaxies in a cluster - even if that distance is not known • Scatter is ~ 10-20% at best, better in the redder bands 45 Tully-Fisher Relation in Diferent Bands
Sakai et al 1999 46 Why is the TFR So Remarkable? • Because it connects a property of the dark halo - the maximum circular speed - with the product of the net integrated star formation history, i.e., the luminosity of the disk • Halo-regulated galaxy formation/evolution? • The scatter is remarkably low - even though the conditions for this to happen are known not to be satisfied • There is some important feedback mechanism involved, which we do not understand yet • Thus, the TFR offers some important insights into the physics of disk galaxy formation
47 Low surface brightness galaxies follow the same TF law as the regular spirals: so it is really relating the baryonic mass to the dark halo
Zwaan et al. 1995 48 The Faber-Jackson Relation for Ellipticals
Analog of the Tully-Fisher relation for spirals, but instead of the peak rotation speed Vmax, measure the velocity dispersion. This is correlated with the total luminosity:
4 10 ⎛ σ ⎞ LV = 2×10 ⎜ ⎟ L sun ⎝ 200 kms-1 ⎠
49 The Kormendy Relation for Ellipticals
Mean -0.8 surface Re ~ Ie brightness
Larger ellipticals are more diffuse
Effective radius 50 Can We Learn Something About the Formation of Ellipticals From the Kormendy Relation? From the Virial Theorem, ms 2 ~ GmM/R Thus, the dynamical mass scales as M ~ Rs 2 Luminosity L ~ I R 2, where I is the mean surface brightness Assuming (M/L) = const., M ~ I R 2 ~ Rs 2 and I R ~ s 2 Now, if ellipticals form via dissipationless merging, the kinetic energy per unit mass ~ s 2 ~ const., and thus we would predict the scaling to be R ~ I -1 If, on the other hand, ellipticals form via dissipative collapse, then M = const., surface brightness I ~ M R -2, and thus we would predict the scaling to be R ~ I -0.5 The observed scaling is R ~ I -0.8. Thus, both dissipative collapse and dissipationless merging probably play a role 51 Deriving the Scaling Relations
Start with the Virial Theorem:
Now relate the observable values of R, V (or s), L, etc., to their “true” mean 3-dim. values by simple scalings:
kR
One can then derive the “virial” versions of the FP and the TFR:
Where the “structure” coefficients are: Deviations of the observed relations from these scalings must indicate that either some k’s and/or the (M/L) are changing 52 Fundamental Plane of Elliptical Galaxies Commonly expressed as a bivariate scaling relation R ~ s 1.4 I -0.8 Where R is the radius, I the mean surf. brightness, s the velocity disp.
Face-on Edge-on
(Pahre et al. 1988) 53 Different Views of the FP Luminosity instead of radius Mg abs. line strength index (a measure of metallicity) instead of velocity dispersion
FP connects star formation histories and chemical evolution of stellar populations with dynamical and structural parameters of ellipticals 54 Scaling Relations for Ellipticals
Kormendy Faber- rel’n Jackson rel’n
Cooling Fundam. diagram Plane
55 From Virial Theorem to FP
Virial Theorem connects mass, density, and kinetic temperature, and is thus an equation of a plane in that (theoretical) parameter space. Assumptions about the dynamical structure of ellipticals and their (M/L) ratios then map the VT into the tilted FP in the observable s parameter space of measured quantities such as R, , I, L, … 56 Fundamental Plane and M/L Ratios If we assume homology and attribute all of the FP tilt to the changes in (M/L) , (M/L) ~ L a , a ~ 0.2 (vis) or ~ 0.1 (IR)
Possible causes: systematic changes in Mvisible/Mdark, or in their relative concentrations; or in the stellar IMF Cappellaro et al. 2006: Pahre et al. 1995: K-band FP SAURON dynamical modeling log (M/L) + const. (M/L) log
log M + const. 57 For any elliptical galaxy today, big or small, Just Two Numbers determine to within a few percent or less: Mass, luminosity (in any OIR band), Any consistently defined radius Surface brightness or projected mass density Derived 3-d luminosity, mass, or phase-space density Central projected radial velocity dispersion OIR colors, line strengths, and metallicity Mass of the central black hole … and maybe other things as well And they do so regardless of the: Star formation and merging formative/evolutionary history Large-scale environment (to within a few %) Details of the internal structure and dynamics (including S0’s) Projection effects (the direction we are looking from) 58 How Can This Be? • The intrinsic scatter of the FP is at most a few %, and could be 0 • The implication is that elliptical galaxies occupy only a small, naturally selected, subset of all dynamical structures which are in principle open to them • Numerical sim’s can reproduce the observed structures of E’s, and the FP, but they do not explain them • Understanding of the origin of the small scatter of the FP (or, equivalently, the narrow range (Robertson of their dynamical structures) is et al. 2006) an outstanding problem
59 The Galaxy Parameter Space A more general picture Galaxies of different families form 2-dim. sequences in a 3+ dimensional parameter space of physical properties, much like stars form 1-dim. sequences in a 2-dim. parameter space of {L,T} - this is an equivalent of the H-R diagram, but for galaxies 60 The Dark Halos • Many of galaxy scaling relations may be driven by the properties of their dark halos • It is possible to infer their properties from detailed dynamical profiles of galaxies and some modeling • Numerical simulations suggest a universal form of the dark halo density profile (NFW = Navarro, Frenk & White):
ρ(r) δc = 2 ρcrit r r 1 r r ( s )( + s ) (but one can also fit another formula, e.g., with a core radius and a finite central density)
61 Evidence for the NFW profile from simulations
62 Dark Halo Scaling Laws
- 0.35 ro ~ LB ro 0.37 rc ~ LB (fits to Sc-Im only) 0.20 s ~ LB rc
are dSph, dIrr so expect the surface density s S ~ ro rc to be ~ constant over this range of
MB, and it is
Kormendy & Freeman 2003 63