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Register a new userDynamical family properties and dark halo scaling relations of giant elliptical galaxies
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Ortwin Gerhard
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Based on a uniform dynamical analysis of line-profile shapes for 21 luminous round elliptical galaxies, we have investigated the dynamical family relations of ellipticals: (i) The circular velocity curves (CVCs) of elliptical galaxies are flat to within ~10% for R>~0.2R_e. (ii) Most ellipticals are moderately radially anisotropic; their dynamical structure is surprisingly uniform. (iii) Elliptical galaxies follow a Tully-Fisher (TF) relation, with v_c^max=300 km/s for an L_B^* galaxy. At given v_c^max, they are ~1 mag fainter in B and appear to have slightly lower baryonic mass than spirals even for maximum M/L_B. (iv) The luminosity dependence of M/L_B is confirmed. The tilt of the Fundamental Plane is not caused by dynamical non-homology, nor only by an increasing dark matter fraction with L. It is, however, consistent with stellar population models based on published metallicities and ages. The main driver is therefore probably metallicity, and a secondary population effect is needed to explain the K-band tilt. (v) These results make it likely that elliptical galaxies have nearly maximal M/L_B (minimal halos). (vi) Despite the uniformly flat CVCs, there is a spread in cumulative M/L_B(r). Some galaxies have no indication for dark matter within 2R_e, whereas others have local M/L_Bs of 20-30 at 2R_e. (vii) In models with maximum stellar mass, the dark matter contributes ~10-40% of the mass within R_e. (viii) The corresponding halo core densities and phase-space densities are at least ~25 times larger and the halo core radii ~4 times smaller than in spiral galaxies of the same v_c^max. The increase in M/L sets in at ~10 times larger acceleration than in spirals. This could imply that elliptical galaxy halos collapsed at high redshift or that some of the dark matter in ellipticals might be baryonic. (abridged)
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(ABRIDGED) We examine the fundamental scaling relations of elliptical galaxies formed through mergers. Using hundreds of simulations to judge the impact of progenitor galaxy properties on merger remnants, we find that gas dissipation provides an important contribution to tilt in the Fundamental Plane relation. Dissipationless mergers of disks produce remnants that occupy the virial plane. As the gas content of disk galaxies is increased, the tilt of the Fundamental Plane relation increases and the slope of the Re-M_* relation steepens. For gas fractions fgas > 30%, the simulated Fundamental Plane scalings approach those observed in the K-band. In our simulations, feedback from supermassive black hole growth has only a minor influence on the stellar-mass scaling relations of spheroidal galaxies, but may play a role in maintaining the observed Fundamental Plane tilt at optical wavelengths by suppressing residual star formation in merger remnants. We estimate that approx 40-100% of the Fundamental Plane tilt induced by structural properties owes to trends in the central total-to-stellar mass ratio M_total/M_* produced by dissipation. Lower mass systems obtain greater phase- space densities than higher mass systems, producing a galaxy mass-dependent central M_total/M_* and a corresponding tilt in the Fundamental Plane.
We investigate the black hole (BH) scaling relation in galaxies using a model in which the galaxy halo and central BH are a self-gravitating sphere of dark matter (DM) with an isotropic, adiabatic equation of state. The equipotential where the escape velocity approaches the speed of light defines the horizon of the BH. We find that the BH mass ($m_bullet$) depends on the DM entropy, when the effective thermal degrees of freedom ($F$) are specified. Relations between BH and galaxy properties arise naturally, with the BH mass and DM velocity dispersion following $m_bulletproptosigma^{F/2}$ (for global mean density set by external cosmogony). Imposing observationally derived constraints on $F$ provides insight into the microphysics of DM. Given that DM velocities and stellar velocities are comparable, the empirical correlation between $m_bullet$ and stellar velocity dispersions $sigma_star$ implies that $7<F<10$. A link between $m_bullet$ and globular cluster properties also arises because the halo potential binds the globular cluster swarm at large radii. Interestingly, for $F>6$ the dense dark envelope surrounding the BH approaches the mean density of the BH itself, while the outer halo can show a nearly uniform kpc-scale core resembling those observed in galaxies.
I review our understanding of classic dynamical scaling relations, relating luminosity, size and kinematics of early-type galaxies. Using unbiased determinations of galaxy mass profiles from stellar dynamical models, a simple picture has emerged in which scaling relations are driven by virial equilibrium, accompanied by a trend in the stellar mass-to-light ratio (M/L). This picture confirms the earliest insights. The trend is mainly due to the combined variation of age, metallicity and the stellar initial mass function (IMF). The systematic variations best correlate with the galaxy velocity dispersion, which traces the bulge mass fraction. This indicates a link between bulge growth and quenching of star formation. Dark matter is unimportant within the half-light radius, where the total mass profile is close to isothermal ($rhopropto r^{-2}$).
Given the recently deduced relationship between X-ray temperatures and stellar velocity dispersions (the T-sigma relation) in an optically complete sample of elliptical galaxies (Davis & White 1996), we demonstrate that L>L_* ellipticals contain substantial amounts of dark matter in general. We present constraints on the dark matter scale length and on the dark-to-luminous mass ratio within the optical half-light radius and within the entire galaxy. For example, we find that minimum values of dark matter core radii scale as r_dm > 4(L_V/3L_*)^{3/4}h^{-1}_80 kpc and that the minimum dark matter mass fraction is >~20% within one optical effective radius r_e and is >~39-85% within 6r_e, depending on the stellar density profile and observed value of beta_spec. We also confirm the prediction of Davis & White (1996) that the dark matter is characterized by velocity dispersions that are greater than those of the luminous stars: sigma_dm^2 ~ 1.4-2 sigma_*^2. The T-sigma relation implies a nearly constant mass-to-light ratio within six half-light radii: M/L_V ~ 25h_80 M_sun/L_V_sun. This conflicts with the simplest extension of CDM theories of large scale structure formation to galactic scales; we consider a couple of modifications which can better account for the observed T-sigma relation.
Dynamical modeling and strong lensing data indicate that the total density profiles of early-type galaxies are close to isothermal, i.e., rho_tot ~ r^gamma with gamma approx -2. To understand the origin of this universal slope we study a set of simulated spheroids formed in isolated binary mergers as well as the formation within the cosmological framework. The total stellar plus dark matter density profiles can always be described by a power law with an index of gamma approx -2.1 with a tendency toward steeper slopes for more compact, lower-mass ellipticals. In the binary mergers the amount of gas involved in the merger determines the precise steepness of the slope. This agrees with results from the cosmological simulations where ellipticals with steeper slopes have a higher fraction of stars formed in situ. Each gas-poor merger event evolves the slope toward gamma ~ -2, once this slope is reached further merger events do not change it anymore. All our ellipticals have flat intrinsic combined stellar and dark matter velocity dispersion profiles. We conclude that flat velocity dispersion profiles and total density distributions with a slope of gamma ~ -2 for the combined system of stars and dark matter act as a natural attractor. The variety of complex formation histories as present in cosmological simulations, including major as well as minor merger events, is essential to generate the full range of observed density slopes seen for present-day elliptical galaxies.
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