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Register a new userThe Virial Relation and Intrinsic Shape of Early-Type Galaxies
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Sascha Trippe
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Early-type galaxies (ETGs) are supposed to follow the virial relation $M = k_e sigma_*^2 R_e / G$, with $M$ being the mass, $sigma_*$ being the stellar velocity dispersion, $R_e$ being the effective radius, $G$ being Newtons constant, and $k_e$ being the virial factor, a geometry factor of order unity. Applying this relation to (a) the ATLAS3D sample of Cappellari et al. (2013) and (b) the sample of Saglia et al. (2016) gives ensemble-averaged factors $langle k_erangle =5.15pm0.09$ and $langle k_erangle =4.01pm0.18$, respectively, with the difference arising from different definitions of effective velocity dispersions. The two datasets reveal a statistically significant tilt of the empirical relation relative to the theoretical virial relation such that $Mpropto(sigma_*^2R_e)^{0.92}$. This tilt disappears when replacing $R_e$ with the semi-major axis of the projected half-light ellipse, $a$. All best-fit scaling relations show zero intrinsic scatter, implying that the mass plane of ETGs is fully determined by the virial relation. Whenever a comparison is possible, my results are consistent with, and confirm, the results by Cappellari et al. (2013). The difference between the relations using either $a$ or $R_e$ arises from a known lack of highly elliptical high-mass galaxies; this leads to a scaling $(1-epsilon) propto M^{0.12}$, with $epsilon$ being the ellipticity and $R_e = asqrt{1-epsilon}$. Accordingly, $a$, not $R_e$, is the correct proxy for the scale radius of ETGs. By geometry, this implies that early-type galaxies are axisymmetric and oblate in general, in agreement with published results from modeling based on kinematics and light distributions.
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We use the Atlas3D sample to perform a study of the intrinsic shapes of early-type galaxies, taking advantage of the available combined photometric and kinematic data. Based on our ellipticity measurements from the Sloan Digital Sky Survey Data Release 7, and additional imaging from the Isaac Newton Telescope, we first invert the shape distribution of fast and slow rotators under the assumption of axisymmetry. The so-obtained intrinsic shape distribution for the fast rotators can be described with a Gaussian with a mean flattening of q=0.25 and standard deviation sigma_q = 0.14, and an additional tail towards rounder shapes. The slow rotators are much rounder, and are well described with a Gaussian with mean q = 0.63 and sigma_q =0.09. We then checked that our results were consistent when applying a different and independent method to obtain intrinsic shape distributions, by fitting the observed ellipticity distributions directly using Gaussian parametrisations for the intrinsic axis ratios. Although both fast and slow rotators are identified as early-type galaxies in morphological studies, and in many previous shape studies are therefore grouped together, their shape distributions are significantly different, hinting at different formation scenarios. The intrinsic shape distribution of the fast rotators shows similarities with the spiral galaxy population. Including the observed kinematic misalignment in our intrinsic shape study shows that the fast rotators are predominantly axisymmetric, with only very little room for triaxiality. For the slow rotators though there are very strong indications that they are (mildly) triaxial.
We study the HI K-band Tully-Fisher relation and the baryonic Tully-Fisher relation for a sample of 16 early-type galaxies, taken from the ATLAS3D sample, which all have very regular HI disks extending well beyond the optical body (> 5 R_eff). We use the kinematics of these disks to estimate the circular velocity at large radii for these galaxies. We find that the Tully-Fisher relation for our early-type galaxies is offset by about 0.5-0.7 magnitudes from the relation for spiral galaxies. The residuals with respect to the spiral Tully-Fisher relation correlate with estimates of the stellar mass-to-light ratio, suggesting that the offset between the relations is mainly driven by differences in stellar populations. We also observe a small offset between our Tully-Fisher relation with the relation derived for the ATLAS3D sample based on CO data representing the galaxies inner regions (< 1 R_eff). This indicates that the circular velocities at large radii are systematically 10% lower than those near 0.5-1 R_eff, in line with recent determinations of the shape of the mass profile of early-type galaxies. The baryonic Tully-Fisher relation of our sample is distinctly tighter than the standard one, in particular when using mass-to-light ratios based on dynamical models of the stellar kinematics. We find that the early-type galaxies fall on the spiral baryonic Tully-Fisher relation if one assumes M/L_K = 0.54 M_sun/L_sun for the stellar populations of the spirals, a value similar to that found by recent studies of the dynamics of spiral galaxies. Such a mass-to-light ratio for spiral galaxies would imply that their disks are 60-70% of maximal. Our analysis increases the range of galaxy morphologies for which the baryonic Tully-Fisher relations holds, strengthening previous claims that it is a more fundamental scaling relation than the classical Tully-Fisher relation.
We measure the average mass properties of a sample of 41 strong gravitational lenses at moderate redshift (z ~ 0.4 - 0.9), and present the lens redshift for 6 of these galaxies for the first time. Using the techniques of strong and weak gravitational lensing on archival data obtained from the Hubble Space Telescope, we determine that the average mass overdensity profile of the lenses can be fit with a power-law profile (Delta_Sigma prop. to R^{-0.86 +/- 0.16}) that is within 1-sigma of an isothermal profile (Delta_Sigma prop. to R^{-1}) with velocity dispersion sigma_v = 260 +/- 20 km/s. Additionally, we use a two-component de Vaucouleurs+NFW model to disentangle the total mass profile into separate luminous and dark matter components, and determine the relative fraction of each component. We measure the average rest frame V-band stellar mass-to-light ratio (Upsilon_V = 4.0 +/- 0.6 h M_sol/L_sol) and virial mass-to-light ratio (tau_V = 300 +/- 90 h M_sol/L_sol) for our sample, resulting in a virial-to-stellar mass ratio of M_vir/M_* = 75 +/- 25. Finally, we compare our results to a previous study using low redshift lenses, to understand how galaxy mass profiles evolve over time. We investigate the evolution of M_vir/M_*(z) = alpha(1+z)^{beta}, and find best fit parameters of alpha = 51 +/- 36 and beta = 0.9 +/- 1.8, constraining the growth of virial to stellar mass ratio over the last ~7 Gigayears. We note that, by using a sample of strong lenses, we are able to constrain the growth of M_vir/M_*(z) without making any assumptions about the IMF of the stellar population.
The kinematic morphology-density relation for early-type galaxies posits that those galaxies with low angular momentum are preferentially found in the highest-density regions of the universe. We use a large sample of galaxy groups with halo masses 10^12.5 < M_halo < 10^14.5 M_sun/h observed with the Mapping Nearby Galaxies at APO (MaNGA) survey to examine whether there is a correlation between local environment and rotational support that is independent of stellar mass. We find no compelling evidence for a relationship between the angular momentum content of early-type galaxies and either local overdensity or radial position within the group at fixed stellar mass.
We present a detailed diagnostic study of the observed temperatures of the hot X-ray coronae of early-type galaxies. By extending the investigation carried out in Pellegrini (2011) with spherical models, we focus on the dependence of the energy budget and temperature of the hot gas on the galaxy structure and internal stellar kinematics. By solving the Jeans equations we construct realistic axisymmetric three-component galaxy models (stars, dark matter halo, central black hole) with different degrees of flattening and rotational support. The kinematical fields are projected along different lines of sight, and the aperture velocity dispersion is computed within a fraction of the circularized effective radius. The model parameters are chosen so that the models resemble real ETGs and lie on the Faber-Jackson and Size-Luminosity relations. For these models we compute T_* (the stellar heating contribution to the gas injection temperature) and T_gm (the temperature equivalent of the energy required for the gas escape). In particular, different degrees of thermalisation of the ordered rotational field of the galaxy are considered. We find that T_* and T_gm can vary only mildly due to a pure change of shape. Galaxy rotation instead, when not thermalised, can lead to a large decrease of T_*; this effect can be larger in flatter galaxies that can be more rotationally supported. Recent temperature measurements T_x, obtained with Chandra, are larger than, but close to, the T_* values of the models, and show a possible trend for a lower T_x in flatter and more rotationally supported galaxies; this trend can be explained by the lack of thermalisation of the whole stellar kinetic energy. Flat and rotating galaxies also show lower L_x values, and then a lower gas content, but this is unlikely to be due to the small variation of T_gm found here for them.
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