Elliptical galaxies

• Nature of ellipticals: primordial or formed by mergers? Historically, perhaps related to discussion about origin of Milky Way halo.
• While merging is preferred in current picture of galaxy formation, question of when the bulk of this occurred is still relevant. Lots of very early merging may look similar to early primordial formation.
  • Key issue may include to what extent merging involves stellar systems (dry mergers) or gaseous systems (wet mergers), or what combination.

Stellar populations in ellipticals

• ellipticals come in range of colors and line strengths. More luminous galaxies have stronger lines/redder colors (recall slope of red sequence in abs mag vs color).
  • Variation can arise either from metallicity and/or age differences

• Breaking the age-metallicity degeneracy with line indices: Worthey Fe4668 vs H$\gamma$ (fig 1) suggests there is a range of ages
  • bulk of stellar pops in E's are at least several Gyr old.
  • some lower velocity dispersion galaxies appear to have lower ages
  • locus of all E's suggest age spread rather than metallicity spread.
  • Absolute age dating is difficult: different results are obtained from different indices. Some indices don't match any models at all.

• strong evidence that there are non-solar abundance ratios, in particular strong enhancement of Mg to Fe as compared with solar (Worthey Fig 3).
  • More luminous Es have stronger Mg overabundance than less luminous E's. With abundance variations and lack of models and calibration for non-solar abundance ratios, it's very to decide about absolute ages.

• Analyis of E line strengths using atmospheres that are adjusted for non-solar abundance ratios, and to a lesser extent, using evolutionary tracks that apply to non-solar abundance ratios (e.g. Trager et al. ApJ 119, 1645; ApJ 120, 165; Thomas, Maraston, Bender).
  • give much more consistent ages (Trager fig 3),
  • continue to suggest that there is a range of SSP ages among Es (Trager fig 7).
  • results of the non-solar abundance ratios are somewhat, but not totally, expected; most alpha-elements are enhanced, but not Ca!
  • some suggestion that the inferred SSP ages (remember SSP!) depend on environment, with cluster galaxies having older ages; current sample is not a volume limited, or in fact, rigorously selected at all (although it tries to be ``representative'')!
  • While unfortunately only based on a relatively small sample of $\sim$ 50 galaxies, some interesting correlations between stellar population parameters.
    • the galaxies appear to lie on a plane (Trager II. Fig 2) in the 4-dimensional space of velocity dispersion, SSP age, SSP metallicity, and SSP enhancement ratio.
    • good correlation between velocity dispersion and enhancement ratio, such that galaxies with higher velocity dispersion are more ``enhanced''.
    • Given velocity dispersion and SSP age, SSP metallicity is well-predicted.

• Note that these integrated light studies are luminosity-weighted, and there exists the possibility that they are just telling us about a small fraction (by mass) of the stellar population. ``Frosting'' models.

• Note that even if bulk of stellar ages are large, issue is still open about whether the stars were necessarily in place in the present-day galaxy for a very long time (e.g. late dry mergers would still show old stellar populations).

• correlation with global properties: relation between luminosity and line strength (which we've seen in Local Group galaxies);
  • in Es, this correlation is even tighter when considering relation between central velocity dispersion and line strength (the $Mg-\sigma$ relation) (BBF.II Fig 3), over large range of $\sigma$.
  • Of equal interest to the Mg-$\sigma$ relation is the quite small scatter around the relation.
  • has been argued that this provides strong constraint on age or metallicity spread at any given $\sigma$, of order 15% in age for larger systems (but 50% in age for smaller systems), or variations in Z of about the same amount;
  • however, the existence of the hyperplane mentioned above suggests that age and metallicity are correlated to produce nearly constant line strength at fixed $\sigma$.

• What does all of this mean? Possible explanations for correlation of enhancement with velocity dispersion:
  • duration of star formation episode decreases at higher velocity dispersion (most conventional interpretation)
  • number of type Ia supernovae decrease at higher velocity dispersion (origin of binaries??),
  • IMF flattens at higher velocity dispersion
    • Buzzoni (Fig 9) however, suggests that IMF can be constrained using IR line strengths, and finds that galaxies are fairly consistent with Salpeter-like IMFs, though of course, at the current time, this only probes IMF slope of low mass stars.
  • late winds are stronger at increasing velocity dispersion (hard to understand),
  • early winds are stronger with decreasing velocity dispersion.

• If most luminous ellipticals have higher metallicity and $\alpha$ enhancement, this suggests that they cannot have been formed by the merging of pre-existing smaller stellar systems. A significant amount of gas must have been present from which stars were formed during/after merger.

• Stellar populations within individual ellipticals: Es have gradients in color/line strength, redder towards center
  • reasonably modest, smaller than suggested by models of a single dissipative collapse.
  • Gradients might be diluted by dissipationless mergers, so perhaps this is suggestive that such a process is important at some level.
  • Some studies find H$\beta$ gradient suggesting that centers of E's may be younger - but beware contamination from emission.
  • Within a galaxy, abundance ratios of Mg and Fe are roughly constant, as opposed to variations from galaxy to galaxy; consistent with a global explanation for non-solar abundance ratios.

• E+A (or k+a) galaxies: galaxies with strong Balmer lines. Relatively rare, but likely are indicative of post-starburst galaxies with significant star formation  1 Gyr ago. (see Goto MNRAS 357, 937, 2006)
  • Not associated with cluster environment
  • Some show morphological signs of recent interactions

Structure of ellipticals

• 3D shapes of ellipticals: oblate vs. prolate vs. triaxial. Determine true shapes by looking at distribution of ellipticities
  • distribution function is different for fainter and brighter E's.
  • For bright giant E's, distribution is inconsistent with either prolate or oblate intrinsic shapes: not enough circular galaxies (Tremblay and Merritt Fig 3).
  • fainter galaxies, however, distribution is consistent with oblate, prolate, or triaxial.
  • Triaxiality is also inferred for some giant Es from observation of isophotal twisting, which you can't get from oblate or prolate shape (de Zeeuw, Fig 1).

• Origins of shapes is related to dynamics of ellipticals: consider velocities of stars in Es.
  • Can measure rotation as well as velocity dispersion as function of radius.
  • Relative importance of organized over random motion can be characterized by $v_{rot}/\sigma$. For an oblate model with isotropic velocity distribution which is flatted by rotation, get $v_{rot}/\sigma = \sqrt{\epsilon/(1-\epsilon)}$.
  • giant Es have less rotation than this, implying anisotropic velocity disperions.
  • low luminosity (high SB) Es, however, may be isotropic with flattening caused by rotation (de Zeeuw Fig 3).
  • low SB E's appear to have anisotropic velocity dispersion: measured in LG E's 185 (factor of three low in $v_{rot}/\sigma$), 147, 205 (factor of 10 low).
  • Significant fraction of ellipticals may have dynamical subcomponents, e.g. kinematically decoupled cores (e.g. SAURON NGC4365

• Departures from ellipses: boxy and disky isophones.
  • Many ellipticals are not precisely elliptical.
  • In most cases, major deviation from ellipticity is measured by the amplitude of the $\cos 4\theta$ term in a given elliptical isophote. Positive $a_4$ are disky, negative are boxy.
  • deviations from elliptical shape is correlated with dynamics, such that slower rotators are more likely to be boxy, and faster rotators more likely to be disky (Kormendy and Bender Fig 2)
  • appears to be two kinds of boxiness, one found in giant Es and one found in bulges, which in fact are relatively rapid rotators. Likely that these come from different origins: plausibly, mergers in the case of giant Es and bars/disk evolution in the case of bulges.
  • Possibly isophotal deviations form a continuous sequence, from S to S0 to disky E's to true E's to boxy E's.
  • also possible that true E's are just disky Es viewed face-on (Kormendy and Bender Fig 3), and that there are two distinct classes of Es.
  • Relation between shape and population. Disky galaxies are apparently younger: is the disk an accreted population or intrinsically different?

• Central properties: cuspy vs. core ellipticals.
  • Central surface brightness profiles appear to be bimodal. Common representation is given by ``Nuker'' law:
    
    $$I(r) = 2^{(\beta-\gamma)\over\alpha}I_b({r_b\over r})^\gamma [1+({r\over r_b})^alpha]^{(\gamma-\beta)\over\alpha}$$
    
    

  • Profile type is correlated with luminosity. Luminous ellipticals tend to have ``cuspy cores'' with a break radius and shallower central density profile.
  • Lower luminosity ellipticals have power laws all the way in.
  • The core properties are correlated with the global shapes and dynamics: cuspy core galaxies are boxy and anisotropic, cuspy galaxies are disky and rotating.

• Black holes and BH-$\sigma$ relation.
  • Based on gas and stellar kinematics from high spatial resolution observations, ellipticals harbor supermassive black holes in their centers.
  • Relation between BH mass and velocity dispersion

• Formation of ellipticals by mergers
  • Idea of elliptical formation by mergers first proposed by Toomre& Toomre
  • Numerical simulations (e.g. Barnes & Hernquist) show that mergers of two roughly equal-mass stellar disks give remnants with $r^{1/4}$ profile, with relatively little rotation, via tidal disruption
  • Other simulations (e.g., Burkert & Naab):
    • details of resultant isophotal shape depends on details of merger, i.e. the mass ratio of progenitors; higher mass ratio mergers give diskier remnants.
    • kinematics also depends on mass ratio
    • May be difficult to form luminous ellipticals via spiral:spiral mergers; however, mergers of elliptical systems may be able to reproduce these (e.g. Naab et al. ApJL 636, 81 (2006) Fig 3)

Ellipticals: relation between global parameters and the fundamental plane

• there is a relation between the three fundamental global observables: surface brightness (or luminosity), size, and velocity dispersion. Original refs: Dressler et al ApJ 313, 42, Djorgovski and Davis ApJ 313,59.
  • galaxies do not populate the entire 3-space of I, r, and $\sigma$, but instead populate only a plane in this space.
  • observed relation given by Virgo ellipticals is
    
    $$r_e\propto (\sigma_0^2)^{0.7} I_e^{-0.85}$$
    
    

  • called the fundamental plane

• What is the origin of this relation?
  • Might expect something like this if three assumptions are true: Es are in virial equilibrium, M/L varies systematically with luminosity, and Es form a ``homologous'' family, all, e.g., with deVaucouleurs profiles.
  • In this case, one expects
    
    $$L = c_1 I_e r_e^2$$
    
    
    
    
    $$M = c_2 {\sigma_0^2 r_e\over G}$$
    
    
    where the first relation is a definition, the second is the virial theorem, and the constants have to do with the shapes of the galaxies.
  • Combining these, we get
    
    $$r_e = {c_2\over c_1} ({M\over L})^{-1} \sigma_0^2 I_e^{-1}$$
    
    
    If one has $M/L \propto L^{\sim 0.2}$, one then recovers the observed fundamental plane. Alternatively, one could have constant $M/L$ with a structure which varies relative to one or more of the fundamental variables.
  • However, still need to understand origin of assumptions:
    • Why should parameters, e.g. mass-to-light, vary smoothly with luminosity? Recall this mass-to-light includes dark matter.
    • if ellipticals have dark matter halos, don't require luminous inner parts to be in virial equilibrium
  • relatively little scatter around the fundamental plane, implying that the assumptions are reasonably valid over a large range of elliptical properities, which implies some significant regularities in the galaxy formation process.

• Galaxies do not fully populate the entire plane defined by our relation, Consider the projection of the fundamental plane onto the different 2-D spaces (Djorgovski Fig 2).
  • surface brightness-$\sigma$ plane is presumably related to underlying physical parameters density and virial temperature. In this plane, can only form galaxies where cooling is effective, i.e. at larger densities and hotter temperatures. This restricts the area in the space in which we can find galaxies.
  • Additional features of the galaxy formation process may introduce additional restrictions into allowed locations of galaxies on the fundamental plane. Most luminous ellipticals are located along one line (with some scatter) in the fundamental plane, and most diffuse Es are located along another.
  • Consequently, when the plane is projected onto the other two axes, one can see a correlation.
    • In the luminosity(size)-$\sigma$ plane, one finds that $L\propto \sigma^4$ which is known as the Faber-Jackson relation; however, since the locus of Es isn't perfectly linear and the plane defined by the Es isn't perpendicular to this dimension, the scatter around F-J is larger than the scatter around the FP. One can define a new radius which incorporates surface brightness, such that the new radius vs $\sigma$ views the FP edge-on; such a size measurement is called $D_n$ where $D_n$ is the isophotal diamter of the B=20.75 isophote. This $D_N-\sigma$ relation provides a very useful distance estimator - if the FP is really fundamental.
    • In the surface brightness-size plane, one sees a relation in which smaller galaxies have higher surface brightness for normal Es; the diffuse Es have totally different behavior where smaller galaxies have lower SB. These are sometimes known as the Kormendy relations, and are one of the main bases for separating these two types of objects.

• The location of galaxies within the plane suggests important processes about galaxy formation. For these purposes, it's convenient to designate new axes for the 3-space within which galaxies lie, following BBF, ApJ 399, 462. This ``$\kappa$-space'', has $\kappa_1\propto M$, $\kappa_2\propto (M/L)I_e^3$, and $\kappa_3\propto (M/L)$. In this space, the fundamental plane is nearly face-on in the $\kappa_1$-$\kappa_2$ plane, and $\kappa_1$-$\kappa_3$ plane is edge-on to the fundamental plane by definition. Galaxies then fall in this space according to BBF Figures 2a/2b.
  • Note that there are two apparent sequences in the fundamental plane, one occupied by giant Es, intermediate Es, bulges, and some compact Es, and another occupied by dwarf galaxies. There is a clear limitation within the plane, which must have something to do with galaxy formation.

  • Looking perpendicular to the plane, we find that bright dwarfs are found systematically above the plane, which may suggest that they have higher M/L ratios. Dwarf spheroidals are way off plane, but note that this assumes virial equilibrium. Bulges lie below the plane, which may be caused by lower M/L or possibly by disk contamination. Note that anisotropic velocity dispersions are found both at low mass and at high mass.

  • Most of the physical processes which might be important in galaxy formation/evolution move galaxies within the $\kappa_1$-$\kappa_2$ plane (BBF Figure 4). For example, dissipation increases surface brightness at constant mass. Merging increases mass, possibly size depending on model. Winds decrease mass and surface brightness; they also move points off of the plane, possibly suggestive for dSphs. Tidal stripping makes objects higher SB and smaller.

• Ideas about origin of location of galaxies in fundamental plane: E sequence as a merging sequence, with SB declining with increasing mass, velocity anisotropy increasing. The fact that the lower mass Es have more rotation suggests that dissipation gets less important as one goes to higher mass Es. Systems with rotation have higher SB. Bulges fit in this sequence. Compact Es are like bulges, but don't have associated disks. So the entire sequence is a merging sequence, where the importance of gas increases as one goes towards lower mass.

• Still puzzling about Mg-$\sigma$ relation, however, in relatively dissipationless merging hypothesis; however, maybe merging doesn't increase velocity dispersion? Note that scatter around the Mg-$\sigma$ relation does not appear to be correlated with any scatter or location in the FP.

• On the contrary, dwarf galaxies may be more shaped by mass-loss than by merging - but it's unclear what the progenitor galaxies are.

Dark matter in ellipticals

• What about dark matter?(see review by Gerhard 2006). Theoretically, it is clearly expected.
• harder to observe directly than in spirals because of lack of good dynamical tracer, e.g. a rotating component
• for non rotating components, velocity dispersion is insufficient to measure masses because of unknown velocity anisotropy.
• potential tracers
  • planetary nebulae
  • globular clusters
  • velocity distribution of stars
  • X ray halos
  • gas disks (rare, but do exist)
• from stellar velocity distributions, most elliptics show evidence of increasing M/L as a function of radius, indicating the presence of dark matter in the inner regions
• Has been some debate about PN observations at larger radii, with some observations suggesting declining circular velocities. However, understanding of velocity anisotropy is important to the conclusion
• X ray halos, when they exist, generally indicate the presence of dark matter halos
• Finally, ellipticals have extended dark matter halos as traced by satellite galaxies, although it requires stacking many galaxies to see the signature(e.g., Prada et al. 2003), and also from weak lensing studies.