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Register a new userGeneral spherical anisotropic Jeans models of stellar kinematics: including proper motions and radial velocities
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Michele Cappellari
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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
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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.
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.
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.
The Monoceros Ring (MRi) structure is an apparent stellar overdensity that has been postulated to entirely encircle the Galactic plane and has been variously described as being due to line-of-sight effects of the Galactic warp and flare or of extragalactic origin (via accretion). Despite being intensely scrutinised in the literature for more than a decade, no studies to-date have been able to definitively uncover its origins. Here we use $N$-body simulations and a genetic algorithm to explore the parameter space for the initial position, orbital parameters and, for the first time, the final location of a satellite progenitor. We fit our models to the latest Pan-STARRS data to determine whether an accretion scenario is capable of producing an in- Plane ring-like structure matching the known parameters of the MRi. Our simulations produce streams that closely match the location, proper motion and kinematics of the MRi structure. However, we are not able to reproduce the mass estimates from earlier studies based on Pan-STARRS data. Furthermore, in contrast with earlier studies our best-fit models are those for progenitors on retrograde orbits. If the MRi was produced by satellite accretion, we find that its progenitor has an initial mass upper limit of ~$10^{10}$M$_odot$ and the remnant is likely located behind the Galactic bulge, making it diffcult to locate observationally. While our models produce realistic MRi-like structures we cannot definitively conclude that the MRi was produced by the accretion of a satellite galaxy.
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