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Register a new userAnisotropic Jeans models of stellar kinematics: second moments including proper motions and radial velocities
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Michele Cappellari
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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.
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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 for 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 computed proper motions of a selected sample of globular clusters projected on the central bulge, employing CCD images gathered along the last 25 years at the ESO-NTT, ESO-Danish and HST telescopes. We presented a method to derive their proper motions, and a set of coordinate transformations to obtain 3D Galactic velocity vectors of the clusters. We analysed 10 globular clusters, namely Terzan 1, Terzan 2, Terzan 4, Terzan 9, NGC 6522, NGC 6558, NGC 6540, AL~3,ESO456--SC38 and Palomar 6. For comparison purposes we also studied the outer bulge cluster NGC 6652. We discuss the general properties of the proper-motion-cleaned Colour-Magnitude Diagrams, derived for the first time for most of them. A general conclusion is that the inner bulge globular clusters have clearly lower transverse motions (and spatial velocities) than halo clusters, and appear to be trapped in the bulge bar.
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.
GALAH+ is a magnitude-limited survey of high resolution stellar spectra obtained by the HERMES spectrograph at the Australian Astronomical Observatory. Its third data release provides reduced spectra with new derivations of stellar parameters and abundances of 30 chemical elements for 584,015 dwarfs and giants, 88% of them in the Gaia magnitude range 11 < G < 14. Here we use these improved values of stellar parameters to build a library of observed spectra which is useful to study variations of individual spectral lines with stellar parameters. This and other improvements are used to derive radial velocities with uncertainties which are generally within 0.1 km/s or ~25% smaller than in the previous release. Median differences in radial velocities measured here and by the Gaia DR2 or APOGEE DR16 surveys are smaller than 30 m/s, a larger offset is present only for Gaia measurements of giant stars. We identify 4483 stars with intrinsically variable velocities and 225 stars for which the velocity stays constant over >=3 visits spanning more than a year. The combination of radial velocities from GALAH+ with distances and sky plane motions from Gaia enables studies of dynamics within streams and clusters. For example, we estimate that the open cluster M67 has a total mass of ~3300 Msun and its outer parts seem to be expanding, though astrometry with a larger time-span than currently available from Gaia eDR3 is needed to judge if the latter result is real.
By taking advantage of the superb measurements of position and velocity for an unprecedented large number of stars provided in Gaia DR2, we have generated the first maps of the rotation velocity, $V_{rm rot}$, and vertical velocity, $V_{rm z}$, distributions as a function of the Galactocentric radius, $R_{rm gal}$, across a radial range of $5<R_{rm gal}<12$~kpc. In the $R-V_{rm rot}$ map, we have identified many diagonal ridge features, which are compared with the location of the spiral arms and the expected outer Lindblad resonance of the Galactic bar. We have detected also radial wave-like oscillations of the peak of the vertical velocity distribution.
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