Galaxias Elípticas
Qué pasa si n = 1 y n = 4?
Isophotal Shapes For normal elliptical galaxies the axis ratio lies in the range 0.3 <b/a 1, corresponding to types E0 to E7. Isophote twisting Boxy ellipticals are usually bright, rotate slowly, and show stronger than average radio and X-ray emission, while disky ellipticals are fainter, have significant rotation and show little or no radio and X-ray emission (e.g. Bender et al., 1989; Pasquali et al., 2007). In addition, the diskiness is correlated with the nuclear properties as well; disky ellipticals typically have steep cusps, while boxy ellipticals mainly harbor central cores (e.g. Jaffe et al., 1994; Faber et al., 1997).
Tarea.- Considere la Ec. 2.22 y obtenga la Ec. 2.24
Ie = L / (2πR2e)
Colors Elliptical galaxies in general have red colors, indicating that their stellar contents are dominated by old, metal-rich stars. In addition, the colors are tightly correlated with the luminosity such that brighter ellipticals are redder (Sandage & Visvanathan, 1978). The slope and (small) scatter of this color magnitude relation puts tight constraints on the star-formation histories of elliptical galaxies. Ellipticals also display color gradient. In general, the outskirt has a bluer color than the central region. Peletier et al. (1990) obtained a mean logarithmic gradient of Δ(U R)/Δlog r = 0.20±0.02 mag in U R, and of Δ(B R)/Δlog r = 0.09±0.02 mag in B R, in good agreement with the results obtained by Franx et al. (1989b). Kinematic Properties Giant ellipticals generally have low rotation velocities. Observationally, this may be characterized by the ratio of maximum line-of-sight streaming motion vm (relative to the mean velocity of the galaxy) to σ, the average value of the line-of-sight velocity dispersion interior to Re/2. This ratio provides a measure of the relative importance of ordered and random motions within the galaxy. For isotropic, oblate galaxies flattened by the centrifugal force generated by rotation, vm/σ ε /(1 ε ), with ε the ellipticity of the spheroid. Note how in bright ellipticals, vm/σ lies well below this prediction
Scaling Relations The kinematic and photometric properties of elliptical galaxies are correlated. In particular, ellipticals with a larger (central) velocity dispersion are both brighter, known as the Faber Jackson relation, and larger, known as the Dnσ relation (Dn is the isophotal diameter). When plotted in the three-dimensional space spanned by logσ0, logre and log<i>e, elliptical galaxies are concentrated in a plane known as the fundamental plane. The values of a and b have been estimated in various photometric bands. For example, Jørgensen et al. (1996) obtained a = 1.24±0.07, b = 0.82±0.02 in the optical, while Pahre et al. (1998) obtained a = 1.53±0.08, b = 0.79±0.03 in the nearinfrared. More recently, using 9,000 galaxies from the Sloan Digital Sky Survey (SDSS), Bernardi et al. (2003b) found the best fitting plane to have a=1.49±0.05 and b= 0.75±0.01 in the SDSS r-band with a rms of only 0.05. The Faber Jackson and Dn-σ relations are both two-dimensional projections of this fundamental plane.these relations can not only be used to determine the distances to elliptical galaxies, but are also important for constraining theories for their formation.
Gas Content Hot ( 107 K) X-ray emitting gas usually dominates the interstellar medium (ISM) in luminous ellipticals, where it can contribute up to 10^10 Mo to the total mass of the system. This hot gas is distributed in extended X-ray emitting atmospheres (Fabbiano, 1989; Mathews & Brighenti, 2003), and serves as an ideal tracer of the gravitational potential in which the galaxy resides. In addition, many ellipticals also contain small amounts of warm ionized (10^4K) gas as well as cold (< 100K) gas and dust. Typical masses are 10^2 10^4 Mo in ionized gas and 10^6 10^8 Mo in the cold component. Contrary to the case for spirals, the amounts of dust and of atomic and molecular gas are not correlated with the luminosity of the elliptical. In many cases, the dust and/or ionized gas is located in the center of the galaxy in a small disk component, while other ellipticals reveal more complex, filamentary or patchy dust morphologies (e.g. van Dokkum & Franx, 1995; Tran et al., 2001). This gas and dust either results from accumulated mass loss from stars within the galaxy or has been accreted from external systems. The latter is supported by the fact that the dust and gas disks are often found to have kinematics decoupled from that of the stellar body (e.g. Bertola et al., 1992).
The dichotomy between disky and boxy ellipticals is reinforced by their nuclear properties: high-resolution images from the Hubble Space Telescope have shown that the central regions of disky ellipticals typically have steep cusps, while many boxy ellipticals have gently rising inner luminosity profiles or central cores (Ferrarese et al., 1994; Lauer et al., 1995; Rest et al., 2001). If the surface brightness profiles, I(R), are inverted to obtain the three-dimensional luminosity density profiles, ν(r), the distribution of the inner logarithmic slope of these profiles, S dlnν/dlnr, appears bimodal, with most galaxies having S near 0.9 or 1.8. The kinematics of elliptical galaxies have to be determined from absorption line spectroscopy. Before this, it was generally believed that both ellipticals and the bulges of disk galaxies are oblate systems with near-isotropic velocity dispersions and are flattened by rotation While bright, boxy ellipticals are slow rotators, supported by anisotropic velocity dispersions, the fainter, disky ellipticals typically have much higher rotation velocities, often consistent with them being purely rotationally flattened
Velocity fields of 25% of all ellipticals have a kinematically decoupled core (KDC) whose angular momentum vector is misaligned with respect to that of the bulk of the galaxy. In extreme cases, the core can even be counterrotating with respect to the outer regions. KDCs are usually attributed to dynamically distinct subsystems that are the remnants of accreted companions. However, kinematic twists can also result from the projection of the major families of circulating orbits in a triaxial potential, without the core being a separate dynamical subsystem (Statler, 1991). Evidence for Dark Halos According to the standard paradigm for galaxy formation, elliptical galaxies should reside in dark halos. However, finding direct, dynamical evidence for dark halos around elliptical galaxies has proven difficult because of the lack of suitable and easily interpretable tracers at large radii. One possibility is to use the stellar kinematics, obtained from absorption line spectroscopy of the integrated stellar light. However, since the surface brightness of elliptical galaxies drops rapidly with radius, it is difficult to obtain reliable measurements much beyond one effective radius. To date, stellar kinematics have been measured out to 2Re in a few cases IFUs??. These typically show that the line-ofsight velocity dispersion profile is roughly constant beyond 1Re. Although consistent with a mass-to-light ratio profile that increases outward, as expected if the system is embedded in a dark halo, a constant σp(r) can also signal a velocity distribution that becomes more tangentially anisotropic with increasing radius. Comparing such data with dynamical models has indicated that, in general, the mass-to-light ratios increase with radius, consistent with the presence of dark halos, although there are also cases where the data is consistent with a constant M/L all the way out to 2Re (e.g. Rix et al., 1997; Kronawitter et al., 2000). Bright ellipticals are often surrounded by extended X-ray emitting coronae of hot gas. As we have seen in 8.2.1, under the assumption that the X-ray emitting gas is in hydrostatic equilibrium, the total gravitational mass enclosed within a radius r is given by Eq. (8.16). A comparison with Eq. (13.12) shows that this hydrostatic equation is similar to the stellar dynamical equivalent, but with the stellar velocity dispersion v2r replaced by the gas temperature T and with β (r) = 0. For a few bright ellipticals, both the temperature, T(r), and the density, ρ(r), of the gas can be determined from X-ray measurements, and Eq. (8.16) can be solved for the total mass profile M(r). In all cases the mass-to-light ratios thus derived reach values of 100M/L on scales of 100kpc, providing strong evidence for the presence of dark halos (e.g. Forman et al., 1985; Mushotzky et al., 1994).
The Masses of Elliptical Galaxies. I. a Redetermination of the Mass of M32. Burbidge, E. M., Burbidge, G. R., & Fish, R. A. The Astrophysical Journal, vol. 133, p.393, 1961.
Evidence for Supermassive Black Holes
The Formation of Elliptical Galaxies
Before the current structure formation paradigm was established, there were two competing scenarios for the formation of elliptical galaxies: The Monolithic Collapse Scenario In the monolithic collapse scenario elliptical galaxies form in a single burst of intense star formation at high redshift, which is coincident with their collapse to equilibrium and is followed by passive evolution of their stellar populations to the present day (Partridge & Peebles, 1967; Larson, 1975). This scenario was inspired by the fact that elliptical galaxies appear to be a remarkably homogeneous class of objects with uniformly old stellar populations. The morphology and size of the final object depend critically on when star formation occurs relative to collapse, and, in particular, on whether substantial radiative energy losses can increase the binding energy of the system before the stars form. In the dissipationless extreme, all the gas associated with the object is turned into stars either prior to the collapse or during its early stages. The collapse then effectively conserves energy and according to the spherical collapse model, the final system has an average density that is 200 times that of the average density of the universe at the time of collapse. Given the observed sizes and masses of elliptical galaxies, this implies that they must all have formed at redshifts greater than 20. This is quite incompatible with our current understanding of the star-formation history of the Universe according to which only a very small fraction of all stars formed before z = 6 The monolithic collapse scenario In this scenario elliptical galaxies form on a short time scale through collapse and virialization from idealized uncollapsed initial conditions (whose prior evolution is not considered). If the star-formation time scale is short compared to the free-fall time scale the collapse is effectively dissipationless. If the two time scales are comparable, then radiative energy losses are important and one speaks of dissipational collapse. The main characteristic of this scenario is that the stars form simultaneously with the assembly of the final galaxy. The merger scenario In this scenario, an elliptical forms when two or more pre-existing and fully formed galaxies merge together. The main differences with respect to the monolithic collapse scenario is that formation of the stars occurs before, and effectivley independently of, the assembly of the final galaxy.
A second conflict between this dissipationless collapse scenario and our current understanding of cosmic structure comes from the fact that violent relaxation does not differentiate between stars and dark matter and so cannot separate them. This is incompatible with the observation that the visible regions of ellipticals contain rather little dark matter, but are surrounded by dark matter halos with masses at least 10 times the stellar mass of the galaxy and sizes which are well over an order of magnitude greater. Clearly any collapse model should apply to the total mass associated with the virialized system, but it then needs to explain why the stars occupy a very small region at the center of the final object. with re some characteristic radius of the stellar system, and ζ a form factor that depends on the density distributions of the stars and dark matter. In the absence of a dark matter halo, a Hernquist sphere has ζ 0.303, if re is defined as the effective radius, while realistic models with a dark matter halo typically have ζ 0.6±0.1 (Boylan-Kolchin et al., 2005). The situation is different if substantial dissipation can occur during collapse, requiring a starformation time scale which is comparable to or somewhat longer than the collapse time scale. The gas can then segregate from the dark matter at the center of the potential well before turning into stars, and the final galaxy can end up with a binding energy that is substantially greater During such an extended collapse, stars form at later times out of gas that was enriched in metals by earlier generations. This can result in metallicity gradients similar to those seen in many real ellipticals (e.g. Larson, 1974a). The Sizes of Elliptical Galaxies In general, the size of an equilibrium galaxy is related to its mass and binding energy via the virial theorem which states that E =W/2. Here is the potential energy of the stellar system, and we have assumed spherical symmetry. The subscripts s and h refer to stars and the dark matter halo, respectively. The potential energy thus consists of a term that describes the self-energy of the stellar system plus a cross-term that describes the interaction energy of the stellar system with the dark matter halo. In general, we can cast Eq. (13.33) in the form
In the case of the monolithic collapse scenario, consider a perturbation consisting of both gas and dark matter with a homogeneous density distribution, and having a total mass of Mvir at turn-around. The initial energy of the gas at turnaround is then simply Thus, in the monolithic collapse scenario the binding energy of the gas has to become more negative by a factor 7 before it forms stars, in order to explain the observed sizes of elliptical galaxies. where fgas = Mgas/Mvir and rt is the turnaround radius. Suppose that, while the dark matter collapses and virializes, the gas dissipates its binding energy (due to radiative cooling) until it is instantaneously turned into stars at a time when the absolute value of its binding energy has increased to Ef =η Ei. From that point on the stellar system experiences dissipationless, gravitational collapse resulting in a virialized stellar system, embedded in a virialized dark matter halo. According to the virial theorem we then have that where we have assumed that all the gas is turned into stars. Relating this to the initial binding energy of the gas, and using that ζf 0.6, we obtain that where rvir is the virial radius of the final dark matter halo, which we have taken to be half the turnaround radius (see 5.4.4). Using the Sloan Digital Sky Survey, Shen et al. (2003) found that the effective radii of elliptical galaxies are related to their stellar masses, M, according to Substituting this into Eq. (13.37) and assuming that the average density of a dark matter halo is 100 times the critical density for closure (see 5.4.4), we finally obtain that
Several issues remain. It can be shown that the observed properties of ellipticals lead to inferred collapse factors of their baryonic component which are comparable to those inferred for the material collecting in galaxy disks. Why then does the gas end up in a rotationally supported configuration in one case but not in the other? This would require ellipticals either to form from protogalaxies with substantially lower initial angular momentum, or for their formation process to be much more efficient at transferring angular momentum from baryons to dark matter. This is not implausible; the distribution of spin parameters of dark matter haloes is broad and galaxy formation simulations often reveal efficient angular momentum transfer to the extent that it turns out to be much easier to make spheroid-dominated systems like ellipticals than disk-dominated systems like late-type spirals (e.g. Katz & Gunn, 1991; Katz, 1992). A more difficult problem for the monolithic collapse model comes from its principal assumption that the final assembly of an elliptical galaxy occurs simultaneously with the formation of the bulk of its stars over a relatively short time interval, perhaps a Gyr or two. The great majority of normal elliptical galaxies appear to have old stellar populations with a mean age of 10 Gyr or more, implying that the formation events should have occurred at z > 2 and that the galaxies should have evolved passively thereafter. However, the total mass density in relatively massive, passively evolving galaxies appears to be a factor of 3 4 lower at z 1 than it is today (Bell et al., 2004; Brown et al., 2007; Faber et al., 2007; Taylor et al., 2009). Thus at least 70% of present-day ellipticals were either still forming stars at z = 1 or had not yet been assembled. In either case this contradicts the simple monolithic collapse hypothesis.
The Merger Scenario