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Whittle : EXTRAGALACTIC ASTRONOMY
1 : Preliminaries 6 : Dynamics I 11 : Star Formation 16 : Cosmology 2 : Morphology 7 : Ellipticals 12 : Interactions 17 : L.S. Structure 3 : Surveys 8 : Dynamics II 13 : Groups & Clusters 18 : Galaxy Formation 4 : Lum. Functions 9 : Gas & Dust 14 : Nuclei & BHs 19 : Reionization & IGM 5 : Spirals 10 : Populations 15 : AGNs & Quasars 20 : Dark Matter
7. ELLIPTICAL GALAXIES
(1) Introduction
(a) The Myths
Our view of Elliptical galaxies has changed greatly : In the 1970s, Ellipticals were thought to be : Diskless bulges with deVaucouleurs (R1/4) profiles and constant density (King) cores. Oblate spheroids flattened by rotation Void of gas and dust Contain a single ancient population of stars Relaxed dynamically quiescent systems To a large extent, all of the above are now thought to be wrong.
(b) Subdividing the Elliptical Class
In what follows, it will be useful to consider three classes of Ellipticals : Luminous : L greater than 1 - few L, MB brighter than about - 20 Midsize (including massive bulges) : L between 0.1 L & L, MB in the range - 18 to - 20 Dwarfs : L less than 0.1 L, or MB fainter than - 18. Luminous and midsize have somewhat different properties, but form a single sequence in mass. dwarf Es are significantly different.
(c) Parameters
Here are a few recurring parameters we need to be familiar with : Surface Brightness (SB) : several symbols : IB(R) (flux units), or (^) B(R) (mag/ss units; B = B band) Total flux : (a) within projected radius L(<R), or (b) integrated : Ltot (equivalent to MB) Effective Radius : Re defined as the half light radius : L(<Re) = 0.5 Ltot [also Ie = I(Re) and (^) e = (Re)] Stellar Velocity Dispersion : (^) e = < (<Re ) > assumes a Gaussian projected stellar velocity distribution if possible, aperture includes light out to Re Also important, are properties of the core : Central Surface Brightness : (0) Core Radius : rc or Rc, such that I(Rc) = 0.5 I(0) note : sometimes rc (or rb) refers to a break in the near nuclear light profile (eg HST Nuker group) Central Stellar Velocity Dispersion : (^) o = (0) Remember : I(R) and (R) are independent of distance! (for small redshifts)
(d) Deprojection
Note that all the above quantities are projected onto the sky. Ultimately we want true 3D spatial information. ie we want to derive : the luminosity density j(r) from the surface brightness I(R), where R is projected radius r is true (3D) radius for constant M/L ratio, j(r) and I(R) track the space and projected mass densities In general, (see diagram), with z^2 = r^2 - R^2 and dz = r dr / (r^2 - R^2 )1/2, we have (7.1) This is an Abel Integral equation, with solution (7.2) for certain I(R) functions, j(r) can be expressed algebraically for smooth (fitted) profiles, evaluate the integral directly for noisy data, use the Richardson-Lucy iterative inversion Note : if the image is elliptical, a unique inversion is only possible for an axisymmetric figues viewed from the equatorial plane. Just to orient ourselves, consider a single power law of index (typically, 0.5 < < 1.5)
< I(<Re)> = 3.61 Ie (which we abbreviate to < Ie > and equivalently < (^) e >) Asymptotically, at small R, I(R) R-0.8^ while at large R, I(R) R-1. in terms of surface brightness : (R) = (^) e + 8.325[ (R/Re)1/4^ - 1 ] = (0) + 8.325 (R/Re)1/ while originally purely empirical, Binney (1982) has shown that the R1/4^ law arises naturally from a reasonable distribution function. Unfortunately, deprojection isn't straightforward (however, see Young (1975) for tables of j(r) and other properties) The deVaucouleurs law is a special case of a more general, Sersic , law : (7.4) Where b = 1.999 n - 0.327 (N>1) ensures 0.5 Ltot = I(<Re) n=4 gives the deVaucouleurs R1/4^ law with b = 7. n=1 gives an exponential profile with b=1. it turns out (see below) that different n's fit the different classes of Ellipticals
(b) Hubble-Reynolds Law
First Reynolds (1913) and later Hubble (1930) used the following function [ images ] (7.5) for R < ro, I(R) is well behaved, with finite (dI/dR)R= for R>>ro we have I(R) R-^2 so Ltot diverges (though only logarithmically). the related Hubble-Oemler profile avoids this by including an exponential (tidal) cutoff at large R
(c) Modified Hubble Law, Isothermal and King Profiles
The following function avoids some of the above problems, and in addition has other advantages: (7.6) at large R >> ro, similar to the Hubble-Reynolds law : I(R) R-^2 and Ltot diverges however, it has a simple analytic expression for j(r) : (7.7)
at small r < 3ro, this j(r) is similar to isothermal models (though it differs at large r). Isothermal models : are physically grounded : self-gravitating system with Boltzman distribution in energy (potential + kinetic) are physically motivated : violent relaxation (at formation) can lead to this Bolzmann distribution at small R < ro, I(R) turns over in a flat core, which has known dynamical properties : central density (0) = 9 (0)^2 /4 Gro^2 (where (0) is the central velocity disperson) core M/L ratio = (0)/j(0) where j(0)=0.495 I(0)/ro at large R, since j(r) R-^2 we have a flat rotation curve , Vc ~ const however, because of this, at large R, we have I(<R) R and mass quickly diverges! To avoid this divergence King modifed the energy distribution : a modified Boltzmann distribution with cutoff above some threshold. These King Models : are not analytic, but are solutions to an ODE (solved by simple integration). they are two parameter functions : the "core radius" parameter, ro, is related to the overall binding energy (NB ro can be larger than rc, the half-light isophote radius) the energy cutoff leads to a truncation in j(r) at a tidal radius , rt. the models form a sequence in concentration c = log 10 ( rt/ro) [ images ] stellar velocity dispersion is ~const across the core, but drops outside good fits to Globular clusters are found for c ~ 0.75 - 1. moderate fits to some ellipticals are found for c > 2. c ~ 1.7 is reasonably close to the modified Hubble law.
(d) Dehnen Laws (including Hernquist and Jaffe Laws)
Motivated in part by an observed range in profile gradients, Dehnen (1993) introduces a 3 - parameter law : (7.8) with corresponding light profile : (7.9) Note several things : it is the luminosity density that is first specified, the brightness profile is the more complex form. at large R, the total light, Ltot, is finite at small R, for > 1, I(R) R^1 -^ and j(r) rises faster than r-^1 (called cusps ) while for < 1, I(R) ~ const, so j(r) rises slower than r-^1 (called cores ) analytic expressions for I(R) exist for integer and half-integer values of
(3) Radial Light Profiles : Resulting Fits
In general, one should distinguish between the most nuclear regions and the overall profile.
(a) Outside the Center
The various 2 - parameter functions fit with similar quality (typically ~0.2 mag over a 6 mag range). The most commonly used is the R1/4^ law. These fitting functions do not , in general, reproduce the central regions very well There is some real variation in the outer light profiles.
(i) Variation with Luminosity
Galaxies of different luminosity have somewhat different slopes [ images ] The R1/4^ law fits best near MB~ - 21; too steep for MB~ - 22 and too shallow for MB~ - 19 Sersic and Dehnen functions are useful with their variable slope parameters. Lower luminosity Es have steeper slopes : (Sersic n< 4 and Dehnen/Jaffe ~ 2 fit well) Higher luminosity Es have shallower slopes : (Sersic n > 4 and Dehnen/Hernquist ~ 1 fit well)
(ii) Variation with Environment
There is some evidence that outer light profiles can be affected by neighbors : Ellipticals in dense clusters have profiles that are cutoff at large radii likely caused by stars being lost due to tidal evaporation Ellipticals with a near neighbor can have a raised outer profile likely caused by tidal heating which puffs up the outer envelope
(iii) cD galaxies
cD galaxies are well fit by the R1/4^ law out to about 20Re Outside this, their light profiles lie above the fit (eg I(R) R-1.6), in an extended halo [ images ] This halo light may not come from the galaxy but from stars in the cluster the stellar velocity dispersion increases with radius, as expected for cluster stars (note : velocity dispersion usually drops with radius in normal Es) the isophotes can change to match the isopleths of the cluster galaxy distribution.
(iv) Dwarf Ellipticals
There are two classes of Dwarf Ellipticals : compact dEs : these are quite rare, but are clearly a continuation of their more luminous counterparts eg M32 which has a reasonable R1/4^ profile, perhaps slightly steeper, as expected. diffuse dEs : these are common and are quite different from the more luminous Ellipticals The diffuse dEs have exponential light profiles (Sersic with n ~ 1) [ images ] Note that these are, however, not disks (which also have exponential profiles). This figure compares dSph with dS+Irr profiles As we shall see, these diffuse dEs should not be thought of as low luminosity ellipticals.
(b) Central Light Profiles
Before ~1975 the serious influence of seeing, especially in photographic work, was not appreciated. The belief in flat King-like cores was shown to be incorrect with CCD images (eg Kormendy 1977) Significant progress was only possible using HST (principally, by the "Nuker" group). For significant samples, "Nuker" profiles were fitted, and showed :
There are very few cases where I(R) is flat at the center; all continue to rise down to 0.1 arcsec. On the outskirts of the nucleus, all profiles are quite steep, j(r) r-^2 Closer in, the profiles divide into two groups [ images ] : power laws : profile keeps rising steeply : j(r) r-1.9^ with I(R) diverging at R= cuspy cores : profile breaks to shallower power-law : j(r) r-0.8^ with I(R) finite at R= remarkably, these two types depend on the galaxy's total luminosity : Nuclear power laws are found in Lower Luminosity Ellipticals and Spiral bulges (L < ~L*) Nuclear cores are found in Higher Luminosity Ellipticals The reasons for this are not yet well understood (see below, 4c).
(4) Correlations Between Parameters
There are many correlations between the various properties of Ellipticals. The tightness of some are quite remarkable, and point to an underlying homogeneity of this class of galaxy.
(a) Early 2 - Parameter Correlations
(i) Color-Magnitude and Similar Correlations
Several correlations exist between : parameters tracking metallicity (and/or age) : (B-V) and Mg 2 strength parameters of total galaxy mass : MB and (^) e Color-Magnitude Relation more luminous ellipticals are slightly redder [ images ] see figure for Coma and figure for intermediate z cluster (and picture of cluster itself) Mg 2 vs Velocity Dispersion remarkably tight relation : galaxies with deeper potentials have stronger Mg 2 [ images ]. see figure for ellipticals and S0s We conclude : more luminous/massive galaxies are more metal rich (stronger Mg 2 and blue/UV blanketing) The reason : deeper potentials hold ISM longer allowing metals to build up Note : there are similar correlations within individual galaxies Suggests metallicity in fact correlates with escape velocity
(ii) Size & Luminosity vs Surface Brightness (Kormendy) Relation
A couple of correlations suggest larger, more luminous galaxies have lower surface brightness < Ie > correlates with Re : Re < Ie > - 0.83^ +/-^ 0.08^ (see figure from Kormendy) < Ie > correlates with Ltot : Ltot < Ie > - 2/ this follows from the above relation, given Le = 1/2 Ltot = pi < Ie > Re^2 We conclude : larger and more luminous galaxies are fluffier with lower densities An interpretation is not yet too clear, though galaxy formation models must explain it. One inference : low-luminosity ellipticals formed with more gaseous dissipation than giant ellipticals.
Log Dn = Log Re + 0.8 Log < Ie > = Log Re - 0.32 < (^) e > (since < (^) e > = - 2.5 Log < Ie > ) Substituting for Re in the F-P relation, we get : Log Dn + 0.32 < (^) e > = 0.36 < (^) e > + 1.4 Log (^) e Log Dn = 1.4 Log (^) e - 0.02 < (^) e > and we see that the dependency on < (^) e > has essentially vanished, leaving Dn e 1.4^ : a tight 2 - parameter correlation
(iii) Kappa Space : 1 2 3 (Bender et al 1993)
A deliberate attempt to render the F-P "edge-on" using more physical parameters : 1 =^2
2 R
e )^ Log^ M^ (M^ =^ Mass) 2 =^6
2 I
e
2 / R
e )^ Log^ [^ Ie (M/L)
1/3 ]
3 =^3
2 / I
e /^ Re )^ Log^ (M/L) In this K-space we find tight projections in 1 vs 3 (see figure 1 and figure 2 ) this suggests a narrow range of M/L which correlates weakly with total mass
(iv) The Physical Basis of the Fundamental Plane
The following gives some insight into the origin of the F-P relation : Consider : < Ie > =! Ltot / pi Re^2 (just a definition) M/Re = c (^) e^2 (virial equilibrium, KE PE; c = "structure parameter" containing all details) Taken together, these give : Re = (c/2pi) (M/L)-^1 e^2 < Ie >-^1 or equivalently, Log Re = Log [(c/2pi) (M/L)-^1 ] + 2 Log (^) e - Log < Ie > or Log Re = Log [(c/2pi) (M/L)-^1 ] + 2 Log (^) e + 0.4 < (^) e > (since < (^) e > = - 2.5 Log < Ie > ) So, if c and M/L are constants, then we expect Log Re = 2 Log (^) e + 0.4 < (^) e > + Log [(c/2pi) (M/L)-^1 ] Which is close to , but not qute, the F-P relation : Log Re = 1.4 Log (^) e + 0.36 < (^) e > + const To bring these into agreement, we require : (2pi/c) (M/L) M1/5^ L1/ We conclude : The F-P is rooted principally in virial equilibrium To first order, the M/L ratios and dynamical structures of ellipticals are very similar This, in turn, suggests the populations, ages & dark matter properties are highly uniform There is a weak trend for M/L to increase slightly with Mass (" 3 across 5 magnitudes) At any point in this relation, the scatter on M/L is only ~10% The actual M/L values, ~10- 20 (h=1), are consistent with no dark matter (within Re) The narrow scatter on F-P and Mg 2 - relations place limits on the ranges of ages and metallicities : Ages ~ 10 - 13 Gyr; Z ~ 2 - 4 Z(solar)
None of these relations seems to depend on environment : internal properties are relatively robust Current work focusses on whether the F-P is different at higher redshift (implications for evolution)
(v) Use of F-P in Distance Measurement
Much motivation for the above work was to improve methods of distance measurement In general, if a V (km/s) correlates with a luminosity or size, we have a distance indicator, eg : Tully-Fisher : Vrot vs MI Faber-Jackson : (^) e vs MB Both the F-P and the Dn- relations yield a physical length (kpc) from SB & , with low scatter (~10-15%) This has been used to derive distances : used in the distance ladder to get Ho used with cz to map the peculiar velocity field and large scale flows
(c) Core Parameter Correlations
The previous section considered global parameters, defined on scales ~Re One can instead consider core parameters, defined on much smaller scales. One needs to divide the results into Pre-HST and Post-HST :
(i) Pre-HST Results (eg Kormendy 1985)
This makes use of the best ground based data (CFHT; seeing ~ 0.7 arcsec) Here, core parameters are defined near ~Rc, where I(Rc) =! I(0) The principal results are shown here for bulges and ellipticals; Also here or here for wider plots which include dSph, dS-Irr, and GCs (see also S&G 6.6). Main results : Core parameters [ Rc, (0), (^) o ] are closely tied to global parameters [ MB ] more luminous galaxies have larger core radii, with lower central surface brightness this extends the similar result for global parameters into the cores Extreme examples : M32 has Rc = 0.3pc and (0) = 11 V mag/ss! M87 has Rc = 800 pc and (0) = 17 V mag/ss there are three different families present, probably with different formation scenarios : ellipticals and bulges (cDs at one end, M32 at the other) dwarfs : dSph, dS and Irr galaxies are radiacally different they have much lower central SB, they show the opposite trend : more luminous have higher central SB they have exponential light profiles We conclude that dSph and diffuse dEs are NOT simply low luminosity ellipticals, they probably formed from dS or Irr galaxies which lost their gas. Globular clusters are different again they have central densities comparable to the ellipticals, but they do NOT extend the elliptical relations to low luminosities Note that the dwarfs and globular clusters fall well off the F-P for ellipticals
(ii) Post-HST Results (eg Faber et al 1997, the "Nuker" group)
From 3b above, Nuker profile fits provide somewhat different "core" parameters : "break radius", Rb, "break surface brightness" and Ib add to these central dispersion, (^) o; and core luminosity, Lcore = pi Rb^2 Ib Recall that ellipticals and bulges fall into two classes : Power Law profiles with no break (Rb is an upper limit) (lower luminosity galaxies) Core profiles with a break at Rb to a shallower power law (high luminosity galaxies)
However, difficult to generate rising distribution from E0 to E2 with just oblate or prolate Can be fit by distribution of triaxial, closer to oblate than prolate : b/a ~ 0.95 (close to oblate) c/a ~ 0.65 (quite flattened) each have Gaussian dispersion ~0. The conclusion of triaxiality is supported by the presence of isophote twists in many ellipticals PA of major axis changes with radius (so can ) cannot result from projection of oblate or prolate shapes intrinsically twisted galaxies are not stable can occur if triaxial with axial ratios varying with radius.
(b) Isophote Shapes
isophotes are not exact ellipses : typical deviations ~few % in general, one can express the isophote as a Fourier series : (7.14) where : a 0 is the mean radius a 1 , b 1 define the ellipse center a 2 , b 2 define the eccentricity and position angle a 3 , b 3 are useful diagnostics of dust (asymmetries) Note : a 3 and all bn are zero for 4 - fold symmetry a 4 defines the boxiness or diskiness (pointiness is better term) parameter a 4 /a 0 typically in the range - 0.02 to +0. a 4 < 0 : boxy a 4 > 0 : disky examples are shown here a 4 is not very sensitive to presence of an exponential disk; which needs to be quite substantial (~40%), or viewed close to edge on. for sample of Es with a 4 > 0, Rix and White (1990) find data consistent with all having ~20% disk light The a 4 parameters are very important since they correlate with many other variables (see below, § 8)
(c) Ripples and Shells
About 10% - 20% of Ellipticals have sharp edged "ripples", of amplitude 3 - 5% Here is an example (NGC 3923). These shells indicate recent accretion of disk galaxies (discussed more in Topic 12)
(6) Kinematics of Elliptical Galaxies
(a) Methods of Analysis
If stars produced single isolated emission lines, their (projected) velocity field would be easy to find : the distribution of projected velocities N(v) F( ) ie the emission line profile However, Ellipticals have complex absorption line spectra : Similar to a K giant, but broadened by Doppler motion of the stars.[ images ] Consider : S( ) = Stellar Template = a single star spectrum N(v) = relative (normalised) number of stars of projected velocity v (ie vlos) note N(v) is usually called the LOSVD (Line Of Sight Velocity Distribution) G( ) = observed (broadened) galaxy spectrum Loosely speaking, G( ) is the same as S( ) convolved (smoothed) by N(v) We observe G( ) and S( ) and try to obtain N(v). Details : first rebin G( ) and S( ) into pixels of u = c Ln ( ) space, ie km/s/pix rather than A/pix our convolution is in fact, therefore : G(u) = S(u) ® N(u) (where ® is convolution) sum several template stars to match the overall galaxy stellar population template mismatch is a principle source of error subtract a smooth continuum and normalise : we dont want line strength (ie metallicity) to matter remove low frequencies (eg >50A continuum variations) and high frequencies (noise) this is achieved in Fourier space : apply filter to FT and transform back figure Several methods have been devised to extract N(v)
(i) Fourier Quotient (Sargent et al 1977)
Writing Fourier transforms (in k space) in bold face : Starting with the galaxy spectrum : G(u) = S(u) ® N(u) (7.15) From the convolution theorem we have : G (k) = S (k) " N (k) (7.16) giving [ images ] N (k) = G (k) / T (k) (7.17) We cannot simply inverse transform N (k) because noise is introduced by the division instead, we assume N(v) is Gaussian , so N (k) is also Gaussian Estimate N (k) by fitting a Gaussian to the quotient from this fit, we quicky obtain N(v) as a Gaussian thus, the LOSVD is characterized by just cz, , and (effective line strength)
(ii) Cross Correlation (Tonry and Davis 1979)
It is not difficult to show that : G(u) © S(u) = N(u) ® [S(u) © S(u)] (7.18) where © is cross-correlation and ® is convolution (note S(u) © S(u) is also called auto-correlation ) in english : the cross-correlation of the galaxy and template spectra is just
as expected : disky galaxies rotate boxy galaxies dont rotate
(c) Axis of Rotation
Naively, for an axisymmetric rotating galaxy, one expects : major axis slit should show maximum rotation minor axis slit should show no rotation ie kinematic axis = photometric minor axis While for a triaxial rotating galaxy, one expects : the projected photometric minor axis need not align with any true axis the rotation axis can be anywhere in the plane defined by the longest and shortest axes What do the data suggest? Let = the projected kinematic misalignment = angle between kinematic and photometric minor axes For some fiducial radius, Rf, a good estimate of this is : est ~^ arctan^ [Vr(Rf)^ minor^ axis^ /^ Vr(Rf)^ major^ axis] A histogram of (^) est shows [ images ] most are ~ 0 some are 0 - 90 significant minor-axis rotation occurs in boxy Ellipticals (figure) As before : while many Ellipticals are close to axisymmetric, some (the boxy ones) are clearly triaxial [ images ]
(d) Kinematically Distinct Cores and Dust Lanes
~25 % Ellipticals show a separate , rotating component in the nuclear regions (~1kpc; 0.1-0.3 Re) These are called Kinematically Distinct Cores (KDC) Projection effects and difficult detection suggest maybe 30%-60% Ellipticals have KDCs. Example is shown here and here The KDCs show the following : rapid rotation (Vr / )*^ > 1 with a range from "warm" to "cold" : Vr / = 1 to 4. kinematic axis aligned with the photometric axis some KDCs even counter-rotate relative to the host Clearly, they have a different (later?) origin than the main galaxy they have higher metallicity than the rest of the galaxy figure photometrically, they are difficult to identify (eg not necessarily disky isophotes) : they dont contain much mass kinematically prominent in LOSVD because they have low (eg large h 3 ) may be related to subtle gas/dust lanes/disks seen in many (~40%) ellipticals often randomly aligned at large radii but aligned with minor axis at small radii extreme example (NGC 5128) shown here
KDCs (and dust lanes) are likely to be a byproduct of dissipational tidal capture gas and/or star system captured dissipation (loss of orbital energy) occurs : stellar system decays by dynamical friction gas settles, loosing energy by line radiation angular momentum (AM) inherited from merger (not from host) at large radii we have random orientation (of gas/dust) at center, torques/precession aligns with minor axis gas disk undergoes star formation to generates a stellar disk stars age and disk becomes photometrically difficult to identify Conclusion : formation of ellipticals via single event is only part of story ongoing mergers/accretion plays at least some role in construction of present-day ellipticals
(7) Mass to Light Ratios
In principle : Stellar velocities & radius give Mass Photometry gives Light Together, we get M/L ratios In practice, not so straightforward : ideally, need full velocity distribution function at each location now possible to build reasonable models using LOSVD (see Topic 8) usually, however, we need to assume nearly isotropic velocity field.
(a) Inner Parts
Simple estimates : assume approximately isothermal and fit a King profile (see 2c above) gives for central luminosity density, central mass density and central M/L : j(0) = I(0) / 2ro (0) = 9 (0)^2 / 4 G ro^2 M/L = 9 (0)^2 / 2 G I(0) ro Typically, M/L ~ 10 h M / LB, so dark matter does not dominate in the center
(b) Outer Parts & Halo
For proper analysis, need to consider velocity anisotropy r =^ radial^ velocity^ dispersion extreme : radial orbits = tangential velocity dispersion (assume = ) extreme : circular orbits
Velocity Field anisotropic nearly isotropic Shape moderately triaxial almost oblate Core Profile cuspy core steep power law Core Density low high Radio Luminosity radio loud and quiet 1020 - 1025 W/Hz radio quiet < 1021 W/Hz X-ray Luminosity high low Some of these are shown here : a 4 vs V/sig; ellipticity; offset from F-P; radio luminosity : figure and figure a 4 vs V/sig; minor axis rotation : figure a 4 vs radio luminosity; X-ray luminosity; : viewgraph Note that to first order : Boxy and Disky galaxies have the same : color-magnitude relation Mg 2 vs relation Fundamental Plane relation It is still unclear quite how to interpret this dichotomy : The two types may be closely related, or may have quite different histories Semi-empirically, Kormendy and Bender suggest a modification to the Hubble diagram figure Disky Ellipticals form an extension of the S0s Boxy Ellipticals lie at the extreme left end they may or may not be related to the other ellipticals and S0s This all has important implications for Elliptical Formation
(9) Formation of Ellipticals
(Note Mergers and Galaxy Formation discussed more in Topics 12 & 19) Still unclear - - but we have made progress
(a) Two scenarios discussed
(i) Monolithic Dissipative Collapse
Early massive gas cloud undergoes dissipative collapse Huge starburst during collapse Note : sub-mm detection of ~10^10 M cold gas at z ~ 2 - 3 with high SFR. clumpiness during collapse violent relaxation ~ isothermal incomplete violent relaxation non-isothermal & non-isotripic probably rotate "rapidly" "Disky" Ellipticals ???
(ii) Hierarchical Mergers
early universe much denser : eg z ~ 2 density ~ 27 times higher than present mergers/interactions probably common sequence of galactic mergers, starting with pre-galactic substructures galaxies continuue to grow during z ~ 1 - 2 Note : HST finds old ellipticals at z ~ 0. galaxies fall into clusters and merging ceases (encounter velocities too high) random accretions low AM & anisotropic "Boxy" Ellipticals ???
(b) Relevant Issues & Problems
(i) The Need for Dissipation (loss of energy)
High densities (especially in Low-Lum Es) require dissipation during formation eg collapse factors of ~10 needed to convert spiral disks to elliptical cores eg at MB ~ - 16, Dwarf Spiral vs M32 we have rc ~ 700pc vs 1pc and (0) ~ 23 vs 11 unlikely/impossible by mergers of stellar systems alone such mergers cannot increase the (phase-space) density (although dense stellar subsystems can settle to the center intact) Dissptation requires gaseous collapse/merger & subsequent star formation
(ii) Observational Support for Importance of Mergers
ongoing mergers are seen (eg NGC 7252, NGC 6240, Arp 220) they have ~ R#^ profiles (in K light) have high central (gas) densities ~10^2 M pc-^3 comparable to Ellipticals of similar total mass lie close to the F-P for Ellipticals ( from CO; photometry in K) Brightest cluster galaxies are clearly accreting (eg multiple nuclei) ongoing accretion is common in ellipticals : KDCs gas/dust lanes in non-equilibrium configurations ripples & shells However, be careful : dont confuse minor accretion with major merger formation
(iii) Theoretical Support for Importance of Mergers
Compact groups have expected lifetimes ~10^8 -^9 yr must merge n-body simulations of major mergers of two bulge/disk/halo galaxies R# however, highest densities inherited from pre-existing bulges n-body simulations of mergers including gas (in SPH formalism) and star formation (SFR (gas)1.5) yields : rapid gas collapse to center (before merger complete) with nuclear starburst final profile : dense core with "break" in power-law
(iv) Problems to Overcome
Dense Nuclei survive mergers - - so why do giant Es have larger lower density cores if built from denser bulges and Es? Mergers of Es &/or bulges should destroy the F-P GC frequency (per unit luminosity) is ~25 times higher in Es than Spirals (maybe GCs form during merger - - eg as in NGC 1275) difficult to generate metallicity vs luminosity correlation by merging lower luminosity systems (unless metals made during merging starburst)
(c) Hybrid : Merger Induced Dissipational Collapse
Kormendy & Sanders (1992) combine the two formation scenarios :
