Cappellari (2008) presented a flexible and efficient method to model the stellar kinematics of anisotropic axisymmetric and spherical stellar systems. The spherical formalism could be used to model the line-of-sight velocity second moments allowing f
or essentially arbitrary radial variation in the anisotropy and general luminous and total density profiles. Here we generalize the spherical formalism by providing the expressions for all three components of the projected second moments, including the two proper motion components. A reference implementation is now included in the public JAM package available at http://purl.org/cappellari/software
We study the total mass-density profile for a sample of 14 fast-rotator early-type galaxies (stellar masses $10.2<log M_ast/M_odot<11.7$). We combine observations from the SLUGGS and Atlas3D surveys to map out the stellar kinematics in two-dimensions
, out to a median radius for the sample of four half-light radii $R_e$ (or 10 kpc), and a maximum radius of 2.0-6.2 $R_e$ (or 4-21 kpc). We use axisymmetric dynamical models based on the Jeans equations, which allow for a spatially varying anisotropy, and employ quite general profiles for the dark halos, and in particular do not place any restriction on the profile slope. This is made possible by the availability of spatially extended two-dimensional kinematics. We find that our relatively simple models provide a remarkably good description of the observed kinematics. The resulting total density profiles are well described by a nearly-isothermal power law $rho_{rm tot}(r)propto r^{-gamma}$ from $R_e$/10 to at least 4$R_e$, the largest average deviation being 11%. The average logarithmic slope is $langlegammarangle=2.19pm0.03$ with observed rms scatter of just $sigma_gamma=0.11$. This scatter out to large radii, where dark matter dominates, is as small as previously reported by lensing studies around $rapprox R_e/2$, where the stars dominate. Our bulge-halo conspiracy places much tighter constraints on galaxy formation models. It illustrates the power of two-dimensional stellar kinematics observations at large radii. It would now be important to test the generality of our results for different galaxy types and larger samples.
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 w
hich 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 ($rhopropto r^{-2}$).
The distribution of galaxies on the mass-size plane as a function of redshift or environment is a powerful test for galaxy formation models. Here we use integral-field stellar kinematics to interpret the variation of the mass-size distribution in two
galaxy samples spanning extreme environmental densities. The samples are both identically and nearly mass-selected (stellar mass M*>6e9 Msun) and volume-limited. The first consists of nearby field galaxies from the Atlas3D parent sample. The second consists of galaxies in the Coma Cluster (Abell 1656), one of densest environments for which good resolved spectroscopy can be obtained. The mass-size distribution in the dense environment differs from the field one in two ways: (i) spiral galaxies are replaced by bulge-dominated disk-like fast-rotator early-type galaxies (ETGs), which follow the SAME mass-size relation and have the SAME mass distribution as in the field sample; (ii) the slow rotator ETGs are segregated in mass from the fast rotators, with their size increasing proportionally to their mass. A transition between the two processes appears around the stellar mass M_crit=2e11 Msun. We interpret this as evidence for bulge growth (outside-in evolution) and bulge-related environmental quenching dominating at low masses, with little influence from merging, while significant dry mergers (inside-out evolution) and halo-related quenching driving the mass and size growth at the high-mass end. The existence of these two processes naturally explains the diverse size evolution of galaxies of different masses and the separability of mass and environmental quenching.
This is an addendum to the paper by Cappellari (2008, MNRAS, 390, 71), which presented a simple and efficient method to model the stellar kinematics of axisymmetric stellar systems. The technique reproduces well the integral-field kinematics of real
galaxies. It allows for orbital anisotropy (three-integral distribution function), multiple kinematic components, supermassive black holes and dark matter. The paper described the derivation of the projected second moments and we provided a reference software implementation. However only the line-of-sight component was given in the paper. For completeness we provide here all the six projected second moments, including radial velocities and proper motions. We present a test against realistic N-body galaxy simulations.
Since Edwin Hubble introduced his famous tuning fork diagram more than 70 years ago, spiral galaxies and early-type galaxies (ETGs) have been regarded as two distinct families. The spirals are characterized by the presence of disks of stars and gas i
n rapid rotation, while the early-types are gas poor and described as spheroidal systems, with less rotation and often non-axisymmetric shapes. The separation is physically relevant as it implies a distinct path of formation for the two classes of objects. I will give an overview of recent findings, from independent teams, that motivated a radical revision to Hubbles classic view of ETGs. These results imply a much closer link between spiral galaxies and ETGs than generally assumed.
The evolution of masses and sizes of passive (early-type) galaxies with redshift provides ideal constraints to galaxy formation models. These parameters can in principle be obtained for large galaxy samples from multi-band photometry alone. However t
he accuracy of photometric masses is limited by the non-universality of the IMF. Galaxy sizes can be biased at high redshift due to the inferior quality of the imaging data. Both problems can be avoided using galaxy dynamics, and in particular by measuring the galaxies stellar velocity dispersion. Here we provide an overview of the efforts in this direction.
We investigate the accuracy of mass determinations M_BH of supermassive black holes in galaxies using dynamical models of the stellar kinematics. We compare 10 of our M_BH measurements, using integral-field OASIS kinematics, to published values. For
a sample of 25 galaxies we confront our new M_BH derived using two modeling methods on the same OASIS data.
We measured stellar velocity dispersions sigma and dynamical masses of 9 massive (M~10^11 Msun) early-type galaxies (ETG) from the GMASS sample at redshift 1.4<z<2.0. The sigma are based on individual spectra for two galaxies at z~1.4 and on a stacke
d spectrum for 7 galaxies with 1.6<z<2.0, with 202-h of exposure at the ESO Very Large Telescope. We constructed detailed axisymmetric dynamical models for the objects, based on the Jeans equations, taking the observed surface brightness (from deep HST/ACS observations), PSF and slit effects into account. Our dynamical masses M_Jeans agree within ~30% with virial estimates M_vir=5*Re*sigma^2/G, although the latter tend to be smaller. This suggests that sizes are not underestimated by more than a similar fraction. Our M_Jeans also agrees within a factor <2 with the M_pop previously derived using stellar population models and 11 bands photometry. This confirms that the galaxies are intrinsically massive. The inferred mass-to-light ratios M/L_U in the very age-sensitive rest frame U-band are consistent with passive evolution in the past ~1 Gyr (formation redshift z_f~3). A bottom-light stellar Initial Mass Function (IMF) appears to be required to ensure close agreement between M_Jeans and M_pop at z~2, as it does at z~0. The GMASS ETGs are on average more dense than their local counterpart. However a few percent of local ETGs of similar dynamical masses also have comparable sigma and mass surface density Sigma_50 inside Re.
We present a simple and efficient anisotropic generalization of the semi-isotropic (two-integral) axisymmetric Jeans formalism which is used to model the stellar kinematics of galaxies. The following is assumed: (i) a constant mass-to-light ratio M/L
and (ii) a velocity ellipsoid that is aligned with cylindrical coordinates (R,z) and characterized by the classic anisotropy parameter beta_z=1-sigma_z^2/sigma_R^2. Our simple models are fit to SAURON integral-field observations of the stellar kinematics for a set of fast-rotator early-type galaxies. With only two free parameters (beta_z and the inclination) the models generally provide remarkably good descriptions of the shape of the first (V) and second (V_rms=sqrt{V^2+sigma^2}) velocity moments, once a detailed description of the surface brightness is given. This is consistent with previous findings on the simple dynamical structure of these objects. With the observationally-motivated assumption that beta_z>0, the method is able to recover the inclination. The technique can be used to determine the dynamical mass-to-light ratios and angular momenta of early-type fast-rotators and spiral galaxies, especially when the quality of the data does not justify more sophisticated modeling approaches. This formalism allows for the inclusion of dark matter, supermassive black holes, spatially varying anisotropy, and multiple kinematic components.
