Stellar Proper Motions Research Articles

Systematic differences between the positions and proper motions of stars from the PPMXL and UCAC4 catalogs

The PPMXL and UCAC4 catalogs are compared by representing the differences between the positions and proper motions of stars as decompositions into a set of orthogonal vector harmonics with allowancemade for themagnitude equation. A list of 41 316 676 common stars has been compiled using the star identification procedure in the J band (2MASS photometric system). The mean differences between the stellar positions and proper motions have been referred to the centers of 1200 HealPix pixels on the sphere. These data have been generated in the equatorial coordinate system for the stars belonging to 12 J magnitude bins with a width of 0.5m for mean values from 10.m25 to 15.m75. For each sample of stars, the differences have been approximated by vector spherical harmonics. A new statistical criterion that is oriented to using HealPix data pixelization and that allows the significance of all the accessible harmonics to be determined is proposed to extract the signal from noise. An analytical method that includes the effects dependent on the magnitude of the stars has been proposed for the first time in the vector spherical harmonics technique, i.e., a new model of systematic differences based on a system of basis functions that are the products of vector spherical harmonics and Legendre polynomials has been generated. The influence of the magnitude equation on the determination of the mutual orientation and rotation of the PPMXL and UCAC4 reference frames has been studied. It has been established that the extreme systematic differences do not exceed in absolute value 20 mas and 4 mas yr−1 for the positions and proper motions, respectively. The largest differences between the PPMXL and UCAC4 catalogs are shown to be explained by their random rather than systematic errors.

HUBBLE SPACE TELESCOPEPROPER MOTIONS ALONG THE SAGITTARIUS STREAM. I. OBSERVATIONS AND RESULTS FOR STARS IN FOUR FIELDS

We present a multi-epoch Hubble Space Telescope (HST) study of stellar proper motions (PMs) for four fields spanning 200 degrees along the Sagittarius (Sgr) stream: one trailing arm field, one field near the Sgr dwarf spheroidal tidal radius, and two leading arm fields. We determine absolute PMs of dozens of individual stars per field, using established techniques that use distant background galaxies as stationary reference frame. Stream stars are identified based on combined color-magnitude diagram and PM information. The results are broadly consistent with the few existing PM measurements for the Sgr galaxy and the trailing arm. However, our new results provide the highest PM accuracy for the stream to date, the first PM measurements for the leading arm, and the first PM measurements for individual stream stars; we also serendipitously determine the PM of the globular cluster NGC~6652. In the trailing-arm field, the individual PMs allow us to kinematically separate trailing-arm stars from leading-arm stars that are 360 degrees further ahead in their orbit. Also, in three of our fields we find indications that two distinct kinematical components may exist within the same arm and wrap of the stream. Qualitative comparison of the HST data to the predictions of the Law & Majewski and Penarrubia et al. N-body models show that the PM measurements closely follow the predicted trend with Sgr longitude. This provides a successful consistency check on the PM measurements, as well as on these N-body approaches (which were not tailored to fit any PM data).

Residual HCRF rotation relative to the inertial coordinate system

VLBI measurements of the absolute proper motions of 23 radio stars have been collected from published data. These are stars with maser emission, or very young stars, or asymptotic-giant-branch stars. By comparing these measurements with the stellar proper motions from the optical catalogs of the Hipparcos Celestial Reference Frame (HCRF), we have found the components of the residual rotation vector of this frame relative to the inertial coordinate system: (\omega_x,\omega_y,\omega_z) = (-0.39,-0.51,-1.25)+/-(0.58,0.57,0.56) mas/yr. Based on all the available data, we have determined new values of the components of the residual rotation vector for the optical realization of the HCRF relative to the inertial coordinate system: (\omega_x,\omega_y,\omega_z) = (-0.15,+0.24,-0.53)+/-(0.11,0.10,0.13) mas/yr.

Compiling catalogs of stellar coordinates and proper motions via coprocessing of archival photographic and modern CCD observations

A catalog of positions and proper motions of stars in the fields around open clusters was compiled at the Research Institute—Nikolaev Astronomical Observatory (NAO) with the use of the results of photographic observations conducted in the 20th century (at the NAO zonal astrograph with D = 11.6 cm and F = 2.04 m) and modern CCD observations performed with the Mobitel NAO telescope (D = 50 cm and F = 3 m) with a Alta U9000 3056 × 3056 CCD camera. The difference in epochs is approximately 30 years. The initial processing of photographic images was carried out with the use of the MIDAS/ROMAFOT software package, and the CCD data were processed using the Astrometrica software. The data reduction and integration was performed with the use of proprietary software. A photographic catalog of approximately 900000 stars (8–16 m , J1981.6) and a CCD catalog of 780000 stars (9–17 m , J2012.2) were obtained, and the integrated catalog of positions, proper motions, and stellar magnitudes of approximately 700000 stars up to 17 m was then compiled. The errors in catalog positions along both coordinates varied from 20 mas (for 8–13 m stars) to 40 mas (for 14–17 m stars). The standard deviation of proper motions was approximately 5 mas/year along both coordinates. The stellar magnitudes were estimated. The estimated standard deviation of stellar magnitudes in the Tycho-2 system was 0.04 m . The catalogs may be accessed from the NAO site.

Kinematic analysis of stellar radial velocities by the spherical harmonics

A method for a kinematic analysis of stellar radial velocities using spherical harmonics is proposed. This approach does not depend on the specific kinematic model and allows both low-frequency and high-frequency kinematic radial velocity components to be analyzed. The possible systematic variations of distances with coordinates on the celestial sphere that, in turn, are modeled by a linear combination of spherical harmonics are taken into account. Theoretical relations showing how the coefficients of the decomposition of distances affect the coefficients of the decomposition of the radial velocities themselves have been derived. It is shown that the larger the mean distance to the sample of stars being analyzed, the greater the shift in the solar apex coordinates, while the shifts in the Oort parameter A are determined mainly by the ratio of the second zonal harmonic coefficient to the mean distance to the stars, i.e., by the degree of flattening of the spatial distribution of stars toward the Galactic plane. The distances to the stars for which radial velocity estimates are available in the CRVAD-2 catalog have been decomposed into spherical harmonics, and the existing variations of distances with coordinates are shown to exert no noticeable influence on both the solar motion components and the estimates of the Oort parameter A, because the stars from this catalog are comparatively close to the Sun (no farther than 500 pc). In addition, a kinematic component that has no explanation in terms of the three-dimensional Ogorodnikov-Milne model is shown to be detected in the stellar radial velocities, as in the case of stellar proper motions.

A bag of tricks: Using proper motions of Galactic stars to identify the Hercules ultra-faint dwarf galaxy members

Hercules is the prototype of the ultra-faint dwarf (UFD) galaxies. To date, there are still no firm constraints on its total luminosity, due to the difficulty of disentangling Hercules bona-fide stars from the severe Galactic field contamination. In order to better constrain Hercules properties we aim at removing foreground and background contaminants in the galaxy field using the proper motions of the Milky Way stars and the colour-colour diagram. We have obtained images of Hercules in the rSloan, BBessel and Uspec bands with the Large Binocular Telescope (LBT) and LBC-BIN mode capabilities. The rSloan new data-set combined with data from the LBT archive span a time baseline of about 5 yr, allowing us to measure for the first time proper motions of stars in the Hercules direction. The Uspec data along with existing LBT photometry allowed us to use colour-colour diagram to further remove the field contamination. Thanks to a highly-accurate procedure to derive the rSloan-filter geometric distortion solution for the LBC-red, we were able to measure stellar relative proper motions to a precision of better than 5 mas yr^-1 down to rSloan=22 mag and disentangle a significant fraction (\>90\%) of Milky Way contaminants. We ended up with a sample of 528 sources distributed over a large portion of the galaxy body (0.12 deg^2). Of these sources, 171 turned out to be background galaxies and additional foreground stars, from the analysis of the Uspec - BBessel vs. BBessel - rSloan colour-colour diagram. This leaves us with a sample of 357 likely members of the Hercules UFD. We compared the cleaned colour-magnitude diagram (CMD) with evolutionary models and synthetic CMDs, confirming the presence in Hercules of an old population (t=12\pm 2 Gyr), with a wide spread in metallicity (-3.3\<[Fe/H]\<-1.8).

Rigorous treatment of barycentric stellar motion

High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused for example by unseen companions. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the Solar System Barycentre, in terms of observable quantities including error propagation. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions which relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. We present rigorous and explicit formulae for the transformation of stellar positions, parallaxes, proper motions, and radial velocities from one epoch to another, assuming uniform rectilinear motion and taking into account light-time effects. The Jacobian matrix of the transformation is also given, allowing accurate and reversible propagation of errors over arbitrary time intervals. The light-time effects are generally very small but exceeds 0.1 mas or 0.1 m/s over 100 yr for at least 33 stars in the Hipparcos Catalogue. For high-velocity stars within a few tens of pc from the Sun light-time effects are generally more important than the effects of the curvature of their orbits in the Galactic potential.

From Flamsteed to Piazzi and Lalande: new standards in 18th century astrometry

Aims. The present high accuracy of stellar positions and proper motions allows us to determine the positional accuracy of old stellar catalogues. This has already been done for the most important catalogues from before the 18th century. Our aim is to extend this study to several 18th century catalogues.Methods. To do this, I studied ten catalogues: those of Flamsteed and Romer, four catalogues of La Caille, and catalogues of Tobias Mayer, Bradley, Piazzi, and Lalande. A comparison with modern data, mostly from Hipparcos, compiled in the Simbad database of the CDS allowed me to determine the position errors of these catalogues. I also compared the stellar visual magnitudes given in eight of these catalogues with photometric V magnitudes.Results. Thanks to novel instruments, the rms positional accuracy improved from thousands to hundreds of arcsec in older catalogues to less than one minute in that of Flamsteed, and to 2−6 arcsec in the other catalogues I examined. These improvements allowed for the first time relatively accurate proper motions to be determined by 19th century astronomers.

Investigation of the Galactic bar based on photometry and stellar proper motions

A new method for selecting stars in the Galactic bar based on 2MASS infrared photometry in combination with stellar proper motions from the Kharkiv XPM catalogue has been implemented. In accordance with this method, red clump and red giant branch stars are preselected on the color-magnitude diagram and their photometric distances are calculated. Since the stellar proper motions are indicators of a larger velocity dispersion toward the bar and the spiral arms compared to the stars with circular orbits, applying the constraints on the proper motions of the preselected stars that take into account the Galactic rotation has allowed the background stars to be eliminated. Based on a joint analysis of the velocities of the selected stars and their distribution on the Galactic plane, we have confidently identified the segment of the Galactic bar nearest to the Sun with an orientation of 20°–25° with respect to the Galactic center-Sun direction and a semimajor axis of no more than 3 kpc.

Proper motions for HST observations in three off-axis bulge fields

Aims. This is the second in a series of papers that attempt to unveil the kinematic structure of the Galactic bulge through studying radial velocities and proper motions. We report here ~15000 new proper motions for three low foreground-extinction off-axis fields of the Galactic bulge. Methods. Proper motions were derived from a combination of Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2) and Advanced Camera for Surveys (ACS) images taken 8 and 9 years apart, and ACS observations taken 9 and 10 years apart, and they reach accuracies better than 0.9 mas/yr for more than ~10000 objects with magnitudes F814W < 24. Results. The proper motion distributions in these fields are similar to those of Galactic minor axis bulge fields. We observe the rotation of main sequence stars below the turn-off within the Galactic bulge, as in the minor axis fields. Conclusions. Our stellar proper motions measurements show a significant bulge rotation for fields as far from the galactic plane as b=-8.

Candidate stellar occultations by Centaurs and trans-Neptunian objects up to 2014

Context. We study trans-Neptunian objects (TNOs) from stellar occultations.Aims. We predict stellar occultations from 2012.5 to the end of 2014 by 5 Centaurs and 34 TNOs.Methods. These predictions were achieved in two ways: first, we built catalogues with precise astrometric positions of the stellar content around the paths on the sky of these targets, as seen by a ground-based observer; second, the observed positions of the targets were determined with the help of these same catalogues so that we could improve their ephemerides and the reliability of the predictions. The reference system is the International Celestial Reference System (ICRS) as realised by the Fourth US Naval Observatory CCD Astrograph Catalog (UCAC4). All the sky paths as well as the selected targets were observed from Oct. 2011 to May 2013 with the ESO/MPG 2.2 m telescope equipped with the Wide Field Imager (WFI). All astrometric results were obtained with the platform for reduction of astronomical images automatically (PRAIA) after correcting the images for overscan, bias, and flatfield.Results. The catalogues with the stellar content around the sky path of each selected target are complete down to magnitude R = 19 and have an average positional accuracy of about 50 milliarcseconds. This same average accuracy also holds for the observed positions of the targets. In the catalogues from the sky paths, stellar proper motions for non-UCAC4 objects were derived from the combination of the current epoch WFI observations with either the 2MASS or the USNO-B1 catalogues. The offsets between the observed and (JPL) ephemeris positions of the targets frequently reach absolute values of some hundreds of milliarcseconds.Conclusions. We present here stellar occultation predictions for the selected 5 Centaurs and 34 TNOs from 2012.5 to the end of 2014. This work is also an extension of two previous prediction works by us, the first one for Pluto, Charon, Nix, and Hydra, and the second for ten other large TNOs. The use of catalogues from the observations of the sky paths in the astrometry of the TNOs and Centaurs enhanced the coherence between their positions and those of the respective occulted candidate stars. New observations of these TNOs and Centaurs are continuously used to redetermine their ephemerides.

Toward the event horizon—the supermassive black hole in the Galactic Center

The center of our Galaxy hosts the best constrained supermassive black hole in the universe, Sagittarius A* (Sgr A*). Its mass and distance have been accurately determined from stellar orbits and proper motion studies, respectively, and its high-frequency radio, and highly variable near-infrared and x-ray emission originate from within a few Schwarzschild radii of the event horizon. The theory of general relativity (GR) predicts the appearance of a black hole shadow, which is a lensed image of the event horizon. This shadow can be resolved by very long baseline radio interferometry and test basic predictions of GR and alternatives thereof. In this paper we review our current understanding of the physical properties of Sgr A*, with a particular emphasis on the radio properties, the black hole shadow, and models for the emission and appearance of the source. We argue that the Galactic Center holds enormous potential for experimental tests of black hole accretion and theories of gravitation in their strong limits.

DISTANCE AND PROPER MOTION MEASUREMENT OF THE RED SUPERGIANT, PZ CAS, IN VERY LONG BASELINE INTERFEROMETRY H2O MASER ASTROMETRY

We present the very long baseline interferometry H2O maser monitoring observations of the red supergiant, PZ Cas, at 12 epochs from 2006 April to 2008 May. We fitted maser motions to a simple model composed of a common annual parallax and linear motions of the individual masers. The maser motions with the parallax subtracted were well modeled by a combination of a common stellar proper motion and a radial expansion motion of the circumstellar envelope. We obtained an annual parallax of 0.356+/-0.026 mas and a stellar proper motion of {\mu}*{\alpha}cos{\delta}=-3.7+/-0.2 and {\mu}*{\delta}=-2.0+/-0.3 mas/yr eastward and northward, respectively. The annual parallax corresponds to a trigonometric parallax of 2.81+0.22-0.19 kpc. By rescaling the luminosity of PZ Cas in any previous studies using our trigonometric parallax, we estimated the location of PZ Cas on a Hertzsprung-Russell diagram and found that it approaches a theoretically evolutionary track around an initial mass of ~25M(sun). The sky position and the distance to PZ Cas are consistent with the OB association, Cas OB5, which is located in a molecular gas super shell. The proper motion of PZ Cas is close to that of the OB stars and other red supergiants in Cas OB5 measured by the Hipparcos satellite. We derived the peculiar motion of PZ Cas of Us = 22.8+/-1.5, Vs = 7.1+/-4.4, and Ws = -5.7+/-4.4 km/s. This peculiar motion has rather a large Us component, unlike those of near high-mass star-forming regions with negatively large Vs motions. The uniform proper motions of the Cas OB5 member stars suggest random motions of giant molecular clouds moving into local potential minima in a time-dependent spiral arm, rather than a velocity field caused by the spiral arm density wave.

Comparison of the four catalogues by pairs, the Hipparcos, new Hipparcos, EOC‐2 and IL, by using μδ for the common 1120 stars

AbstractWe present comparison results of our Independent Latitude (IL) catalogue of μδ determinations for 1120 bright stars with the Hipparcos, new Hipparcos and Earth Orientation Catalogue (EOC‐2) values. Also, we took into consideration the EOC3 and EOC4 (recent versions of EOC catalogues). Our μδ values are based on zenith telescope observations from seven Independent Latitude (IL) observatories. The IL measures are spanning a time baseline of up to 90 years which is the key advantage to the accurate determination of μδ. The short interval of the Hipparcos satellite observations is a disadvantage for a good accuracy of stellar proper motion, especially in the case of double and multiple stars. For this reason many astrometric catalogues have appeared after the publication of the Hipparcos including our IL catalogue. These catalogues are an appropriate combination of the Hipparcos satellite and ground‐based data which yields more accurate stellar coordinates and/or their proper motions. Among various types of ground‐based observations the latitude and universal time variations obtained from several million observations of stars reduced to the Hipparcos reference system were used for this purpose. These observations were obtained during almost the entire last century and were originally used to determine the Earth Orientation Parameters. It is also possible to use these data in the inverse task of checking the accuracy of stellar coordinates and/or their proper motions listed in the Hipparcos Catalogue. Such latitude and universal time variations data are the basis of the EOC and IL catalogues. In this paper, we computed the differences in μδ values between pairs of catalogues and analyzed the results to characterize the μδ errors for the four catalogues with a special focus on our IL catalogue. The standard errors of μδ for IL stars observed over more than 20 years are mostly smaller than or equal to the Hipparcos errors, and close to the accuracy level of the EOC‐2 (EOC‐3, EOC‐4) and the new Hipparcos. The resulting investigations of errors of differences of μδ, show that all four catalogues have relatively small random and systematic errors which are close to each other meaning that the corresponding μδ values have a high accuracy. Our sample also contains detected double and multiple stars for which the effects of the orbital and proper motions are difficult to separate. The differences of μδ values for these stars generally exceed those obtained for single stars. Also, these discrepancies could be attributed to effect of possible, still unrecognized, astrometric binaries. These investigations about the proper motions and double stars are in line with the activity of the IAU Working Group on Astrometry by Small Ground‐Based Telescopes. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Aberration in proper motions for stars in our Galaxy

Accelerations of both the solar system barycenter (SSB) and stars in the Milky Way cause a systematic observational effect on the stellar proper motions, which was first studied in the early 1990s and developed by J. Kovalevsky (aberration in proper motions, 2003, A&A, 404, 743). This paper intends to extend that work and aims to estimate the magnitude and significance of the aberration in proper motions of stars, especially in the region near the Galactic center. We adopt two models for the Galactic rotation curve to evaluate the aberrational effect on the Galactic plane. Based on the theoretical developments, we show that the effect of aberration in proper motions depends on the galactocentric distance of stars; it is dominated by the acceleration of stars in the central region of the Galaxy. Within 200 pc from the Galactic center, the systematic proper motion can reach an amplitude larger than 1000 uas/yr by applying a flat rotation curve. With a more realistic rotation curve which is linearly rising in the core region of the Galaxy, the aberrational proper motions are limited up to about 150 uas/yr. Then we investigate the applicability of the theoretical expressions concerning the aberrational proper motions, especially for those stars with short period orbits. If the orbital period of stars is only a fraction of the light time from the star to the SSB, the expression proposed by Kovalevsky is not appropriate. With a more suitable formulation, we found that the aberration has no effect on the determination of the stellar orbits on the celestial sphere. The aberrational effect under consideration is small but not negligible with high-accurate astrometry in the future, particularly in constructing the Gaia celestial reference system realized by Galactic stars.

Estimation of the solar galactocentric distance and galactic rotation velocity from near-solar-circle objects

We have tested the method of determining the solar Galactocentric distance R_0 and Galactic rotation velocity $V_0$ modified by Sofue et al. using near-solar-circle objects. The motion of objects relative to the local standard of rest has been properly taken into account. We show that when such young objects as star-forming regions or Cepheids are analyzed, allowance for the perturbations produced by the Galactic spiral density wave improves the statistical significance of the estimates. The estimate of R_0=7.25\pm0.32 kpc has been obtained from 19 star-forming regions. The following estimates have been obtained from a sample of 14 Cepheids (with pulsation periods P>5^d): R_0=7.66\pm0.36 kpc and V_0=267\pm 17 km s^{-1}. We consider the influence of the adopted Oort constant A and the character of stellar proper motions (Hipparcos or UCAC4). The following estimates have been obtained from a sample of 18 Cepheids with stellar proper motions from the UCAC4 catalog: R_0=7.64\pm0.32 kpc and V_0=217\pm 11 km s^{-1}.

Cluster membership probability: polarimetric approach

Interstellar polarimetric data of the six open clusters Hogg 15, NGC 6611, NGC 5606, NGC 6231, NGC 5749 and NGC 6250 have been used to estimate the membership probability for the stars within them. For proper-motion member stars, the membership probability estimated using the polarimetric data is in good agreement with the proper-motion cluster membership probability. However, for proper-motion non-member stars, the membership probability estimated by the polarimetric method is in total disagreement with the proper-motion cluster membership probability. The inconsistencies in the determined memberships may be because of the fundamental differences between the two methods of determination: one is based on stellar proper-motion in space and the other is based on selective extinction of the stellar output by the asymmetric aligned dust grains present in the interstellar medium. The results and analysis suggest that the scatter of the Stokes vectors q(%) and u(%) for the proper-motion member stars depends on the interstellar and intra-cluster differential reddening in the open cluster. It is found that this method could be used to estimate the cluster membership probability if we have additional polarimetric and photometric information for a star to identify it as a probable member/non-member of a particular cluster, such as the maximum wavelength value (\lambda_max), the unit weight error of the fit (\sigma_1), the dispersion in the polarimetric position angles (\epsilon), reddening (E(B-V)) or the differential intra-cluster reddening (\Delta E(B-V)). This method could also be used to estimate the membership probability of known member stars having no membership probability as well as to resolve disagreements about membership among different proper-motion surveys.

DID THE INFANT R136 AND NGC 3603 CLUSTERS UNDERGO RESIDUAL GAS EXPULSION?

Based on kinematic data observed for very young, massive clusters that appear to be in dynamical equilibrium, it has recently been argued that such young systems set examples where the early residual gas-expulsion did not happen or had no dynamical effect. The intriguing scenario of a star cluster forming through a single starburst has thereby been challenged. Choosing the case of the R136 cluster of the Large Magellanic Cloud, the most cited one in this context, we perform direct N-body computations that mimic the early evolution of this cluster including the gas-removal phase (on a thermal timescale). Our calculations show that under plausible initial conditions as consistent from observational data, a large fraction (> 60%) of a gas-expelled, expanding R136-like cluster is bound to regain dynamical equilibrium by its current age. Therefore, the recent measurements of velocity dispersion in the inner regions of R136, that indicate that the cluster is in dynamical equilibrium, are consistent with an earlier substantial gas expulsion of R136 followed by a rapid re-virialization (in approx. 1 Myr). Additionally, we find that the less massive Galactic NGC 3603 Young Cluster (NYC), with a substantially longer re-virialization time, is likely to be found deviated from dynamical equilibrium at its present age (approx. 1 Myr). The recently obtained stellar proper motions in the central part of the NYC indeed suggest this and are consistent with the computed models. This work significantly extends previous models of the Orion Nebula Cluster which already demonstrated that the re-virialization time of young post-gas-expulsion clusters decreases with increasing pre-expulsion density.

Mass estimates from stellar proper motions: the mass of ω Centauri

We lay out and apply methods to use proper motions of individual kinematic tracers for estimating the dynamical mass of star clusters. We first describe a simple projected mass estimator and then develop an approach that evaluates directly the likelihood of the discrete kinematic data given the model predictions. Those predictions may come from any dynamical modelling approach, and we implement an analytic King model, a spherical isotropic Jeans equation model and an axisymmetric, anisotropic Jeans equation model.We apply these approaches to the enigmatic globular cluster omega Centauri, combining the proper motion from van Leeuwen et al (2000) with improved photometric cluster membership probabilities. We show that all mass estimates based on spherical isotropic models yield $(4.55\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, where our modelling allows us to show how the statistical precision of this estimate improves as more proper motion data of lower signal-to-noise are included. MLM predictions, based on an anisotropic axisymmetric Jeans model, indicate for $\omega$ Cen that the inclusion of anisotropies is not important for the mass estimates, but that accounting for the flattening is: flattened models imply $(4.05\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, 10% lower than when restricting the analysis to a spherical model. The best current distance estimates imply an additional uncertainty in the mass estimate of 12%.

DEEPHUBBLE SPACE TELESCOPEIMAGING IN NGC 6397: STELLAR DYNAMICS

Multi-epoch observations with ACS on HST provide a unique and comprehensive probe of stellar dynamics within NGC 6397. We are able to confront analytic models of the globular cluster with the observed stellar proper motions. The measured proper motions probe well along the main sequence from 0.8 to below 0.1 M$_\odot$ as well as white dwarfs younger than one gigayear. The observed field lies just beyond the half-light radius where standard models of globular cluster dynamics (e.g. based on a lowered Maxwellian phase-space distribution) make very robust predictions for the stellar proper motions as a function of mass. The observed proper motions show no evidence for anisotropy in the velocity distribution; furthermore, the observations agree in detail with a straightforward model of the stellar distribution function. We do not find any evidence that the young white dwarfs have received a natal kick in contradiction with earlier results. Using the observed proper motions of the main-sequence stars, we obtain a kinematic estimate of the distance to NGC 6397 of $2.2^{+0.5}_{-0.7}$ kpc and a mass of the cluster of $1.1 \pm 0.1 \times 10^5 \mathrm{M}_\odot$ at the photometric distance of 2.53 kpc. One of the main-sequence stars appears to travel on a trajectory that will escape the cluster, yielding an estimate of the evaporation timescale, over which the number of stars in the cluster decreases by a factor of e, of about 3 Gyr. The proper motions of the youngest white dwarfs appear to resemble those of the most massive main-sequence stars, providing the first direct constraint on the relaxation time of the stars in a globular cluster of greater than or about 0.7 Gyr.