Anisotropic Jeans models of stellar kinematics: second moments including proper motions and radial velocities

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.Comment: 2 pages, 1 figure, LaTeX. Software implementing the JAM method used in this paper is available at http://purl.org/cappellari/id

The Quest for the Dominant Stellar Population in the Giant Elliptical NGC 5018

Newly obtained HST/WFPC2 images of the disturbed elliptical galaxy NGC 5018 show that the average amount of internal reddening due to the its complex ``dust web'' is as low as E(B-V)~0.02 within the IUE aperture, thus implying that its observed and intrinsic energy distributions do not differ significantly down to UV wavelengths. This, in turn, is quite relevant to the current debate on the age of its dominant stellar population.Comment: 2 pages, 1 figure. Proceedings of the conference "Galaxy Disks and Disk Galaxies", ASP Conference Series, eds. J.G. Funes, S.J. and E.M. Corsin

The stellar initial mass function of early type galaxies from low to high stellar velocity dispersion: homogeneous analysis of ATLAS3D^{\rm 3D} and Sloan Lens ACS galaxies

We present an investigation about the shape of the initial mass function (IMF) of early-type galaxies (ETGs), based on a joint lensing and dynamical analysis, and on stellar population synthesis models, for a sample of 55 lens ETGs identified by the Sloan Lens ACS (SLACS) Survey. We construct axisymmetric dynamical models based on the Jeans equations which allow for orbital anisotropy and include a dark matter halo. The models reproduce in detail the observed \textit{HST} photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion ($\sigma$) within the SDSS fibers. Comparing the dynamically-derived stellar mass-to-light ratios $(M_*/L)_{\rm dyn}$, obtained for an assumed halo slope $\rho_{\rm h}\propto r^{-1}$, to the stellar population ones $(M_*/L)_{\rm pop}$, derived from full-spectrum fitting and assuming a Salpeter IMF, we infer the mass normalization of the IMF. Our results confirm the previous analysis by the SLACS team that the mass normalization of the IMF of high $\sigma$ galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and $\sigma$ for both the SLACS and \ATLAS samples, which explore quite different $\sigma$ ranges. The two samples are highly complementary, the first being essentially $\sigma$ selected, and the latter volume-limited and nearly mass selected. We find that the two samples merge smoothly into a single trend of the form $\log\alpha =(0.38\pm0.04)\times\log(\sigma_{\rm e}/200\,\mathrm{km~s}^{-1})+(-0.06\pm0.01)$, where $\alpha=(M_*/L)_{\rm dyn}/(M_*/L)_{\rm pop}$ and $\sigma_{\rm e}$ is the luminosity averaged $\sigma$ within one effective radius $R_{\rm e}$. This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval $\sigma_{\rm e}\approx90-270\,\mathrm{km~s}^{-1}$.Comment: 18 pages, 8 figures. Accepted for publication in MNRA

The benchmark black hole in NGC 4258: dynamical models from high-resolution two-dimensional stellar kinematics

NGC 4258 is the galaxy with the most accurate (maser-based) determination for the mass of the supermassive black hole (SMBH) in its nucleus. In this work we present a two-dimensional mapping of the stellar kinematics in the inner 3.0 x 3.0 arcsec = 100 x 100 pc of NGC 4258 using adaptative-optics observations obtained with the Near-Infrared Integral Field Spectrograph of the GEMINI North telescope at a 0.11 arcsec (4 pc) angular resolution. The observations resolve the radius of influence of the SMBH, revealing an abrupt increase in the stellar velocity dispersion within 10 pc from the nucleus, consistent with the presence of a SMBH there. Assuming that the galaxy nucleus is in a steady state and that the velocity dispersion ellipsoid is aligned with a cylindrical coordinate system, we constructed a Jeans anisotropic dynamical model to fit the observed kinematics distribution. Our dynamical model assumes that the galaxy has axial symmetry and is constructed using the multi-gaussian expansion method to parametrize the observed surface brightness distribution. The Jeans dynamical model has three free parameters: the mass of the central SMBH, the mass-luminosity ratio of the galaxy and the anisotropy of the velocity distribution. We test two types of models: one with constant velocity anisotropy, and another with variable anisotropy. The model that best reproduces the observed kinematics was obtained considering that the galaxy has radially varying anisotropy, being the best-fitting parameters with 3$\sigma$ significance $M_\bullet=4.8^{+0.8}_{-0.9}\times 10^7\,{\rm M_\odot}$ and $\Gamma_k = 4.1^{+0.4}_{-0.5}$. This value for the mass of the SMBH is just 25 per cent larger than that of the maser determination and 50 per cent larger that a previous stellar dynamical determination obtained via Schwarzschild models.Comment: Accepted for publication in MNRAS, 19 pages, 19 figure

Orbital structure of triaxial galaxies

We have developed a method to construct realistic triaxial dynamical models for elliptical galaxies, allowing us to derive best-fitting parameters, such as the mass-to-light ratio and the black hole mass, and to study the orbital structure. We use triaxial theoretical Abel models to investigate the robustness of the method.Comment: 2 pages (1 figure), to appear in the proceedings of the IAU Symposium 220 "Dark matter in galaxies", eds. S. Ryder, D.J. Pisano, M. Walker and K. Freema