The Internal Dynamics of Globular Clusters

Galactic globular clusters are ancient building blocks of our Galaxy. They represent a very interesting family of stellar systems in which some fundamental dynamical processes have been taking place for more than 10 Gyr, but on time scales shorter than the age of the universe. In contrast with galaxies, these star clusters represent unique laboratories for learning about two-body relaxation, mass segregation from equipartition of energy, stellar collisions, stellar mergers, core collapse, and tidal disruption. This review briefly summarizes some of the tremendous developments that have taken place during the last two decades. It ends with some recent results on tidal tails around galactic globular clusters and on a very massive globular cluster in M31.Comment: An invited review (32 pages, 7 figures) in "The Chaotic Universe: Theory, Observations, Computer Experiments", Proceedings of the ICRA Rome-Pescara workshop, eds. V.G. Gurzadyan and R. Ruffini (Singapore: World Sci.), in pres

The Stellar Dynamics of Omega Centauri

The stellar dynamics of Omega Centauri are inferred from the radial velocities of 469 stars measured with CORAVEL (Mayor et al. 1997). Rather than fit the data to a family of models, we generate estimates of all dynamical functions nonparametrically, by direct operation on the data. The cluster is assumed to be oblate and edge-on but mass is not assumed to follow light. The mean motions are consistent with axisymmetry but the rotation is not cylindrical. The peak rotational velocity is 7.9 km/s at 11 pc from the center. The apparent rotation of Omega Centauri is attributable in part to its proper motion. We reconstruct the stellar velocity ellipsoid as a function of position, assuming isotropy in the meridional plane. We find no significant evidence for a difference between the velocity dispersions parallel and perpendicular to the meridional plane. The mass distribution inferred from the kinematics is slightly more extended than, though not strongly inconsistent with, the luminosity distribution. We also derive the two-integral distribution function f(E,Lz) implied by the velocity data.Comment: 25 Latex pages, 12 Postscript figures, uses aastex, epsf.sty. Submitted to The Astronomical Journal, December 199

Interpolating point spread function anisotropy

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones

Evaluating the effect of stellar multiplicity on the PSF of space-based weak lensing surveys

The next generation of space-based telescopes used for weak lensing surveys will require exquisite point spread function (PSF) determination. Previously negligible effects may become important in the reconstruction of the PSF, in part because of the improved spatial resolution. In this paper, we show that unresolved multiple star systems can affect the ellipticity and size of the PSF and that this effect is not cancelled even when using many stars in the reconstruction process. We estimate the error in the reconstruction of the PSF due to the binaries in the star sample both analytically and with image simulations for different PSFs and stellar populations. The simulations support our analytical finding that the error on the size of the PSF is a function of the multiple stars distribution and of the intrinsic value of the size of the PSF, i.e. if all stars were single. Similarly, the modification of each of the complex ellipticity components (e1,e2) depends on the distribution of multiple stars and on the intrinsic complex ellipticity. Using image simulations, we also show that the predicted error in the PSF shape is a theoretical limit that can be reached only if large number of stars (up to thousands) are used together to build the PSF at any desired spatial position. For a lower number of stars, the PSF reconstruction is worse. Finally, we compute the effect of binarity for different stellar magnitudes and show that bright stars alter the PSF size and ellipticity more than faint stars. This may affect the design of PSF calibration strategies and the choice of the related calibration fields.Comment: 10 pages, 6 figures, accepted in A&

Palomar 13: a velocity dispersion inflated by binaries ?

Recently, combining radial velocities from Keck/HIRES echelle spectra with published proper motion membership probabilities, Cote et al (2002) observed a sample of 21 stars, probable members of Palomar 13, a globular cluster in the Galactic halo. Their projected velocity dispersion sigma_p = 2.2 +/-0.4 km/s gives a mass-to-light ratio M/L_V = 40 +24/-17, about one order of magnitude larger than the usual estimate for globular clusters. We present here radial velocities measured from three different CCD frames of commissioning observations obtained with the new ESO/VLT instrument FLAMES (Fibre Large Array Multi Element Spectrograph). From these data, now publicly available, we measure the homogeneous radial velocities of eight probable members of this globular cluster. A new projected velocity dispersion sigma_p = 0.6-0.9 +/-0.3 km/s implies Palomar 13 mass-to-light ratio M/L_V = 3-7, similar to the usual value for globular clusters. We discuss briefly the two most obvious reasons for the previous unusual mass-to-light ratio finding: binaries, now clearly detected, and more homogeneous data from the multi-fibre FLAMES spectrograph.Comment: 9 pages, 2 Postscript figure

The Mass Function of Main Sequence Stars in NGC6397 from Near IR and Optical High Resolution HST Observations

We have investigated the properties of the stellar mass function in the globular cluster NGC6397 using a large set of HST observations that include WFPC2 images in V and I, obtained at ~4' and 10' radial distances, and a series of deep images in the J and H bands obtained with the NIC2 and NIC3 cameras of NICMOS pointed to regions located ~4.5' and ~3.2' from the center. These observations span the region from ~1 to ~3 times the cluster's half-light radius. All luminosity functions, derived from color magniutde diagrams, increase with decreasing luminosity up to a peak at M_I~8.5 or M_H~7 and then precipitously drop well before photometric incompleteness becomes significant. Within the observational uncertainties, at M_I~12 or M_H~10.5 (~0.09 Msun) the luminosity functions are compatible with zero. By applying the best available mass- luminosity relation appropriate to the metallicity of NGC6397 to both the optical and IR data, we obtain a mass function that shows a break in slope at \~0.3 Msun. No single exponent power-law distribution is compatible with these data, regardless of the value of the exponent. We find that a dynamical model of the cluster can simultaneously reproduce all the luminosity functions observed throughout the cluster only if the IMF rises as m**-1.6 in the range 0.8-0.3 Msun and then drops as m**0.2 below ~0.3 Msun. Adopting a more physical log-normal distribution for the IMF, all these data taken together imply a best fit distribution with characteristic mass m_c~0.3 and sigma~1.8.Comment: 18 pages, 6 figures (ps). Accepted for publication in Ap

Mayall II = G1 in M31: Giant Globular Cluster or Core of a Dwarf Elliptical Galaxy ?

(Abridged version) Mayall II = G1 is one of the brightest globular clusters belonging to M31, the Andromeda galaxy. Our observations with HST/WFPC2 provide data for the (I vs. V-I) and (V vs. V-I) color-magnitude diagrams. From model fitting, we determine a rather high mean metallicity of [Fe/H] = --0.95 +- 0.09, somewhat similar to 47 Tucanae. We find a larger spread in V-I than can be explained by the measurement errors, and we attribute this to an intrinsic metallicity dispersion amongst the stars of G1. So far, only omega Centauri, the giant Galactic globular cluster, has been known to exhibit such an intrinsic metallicity dispersion. Three estimates of the total mass of this globular cluster can be obtained: King mass = 15 x 10^6 with M/Lv ~ 7.5, Virial mass = 7.3 x 10^6 with M/Lv ~ 3.6, and King-Michie mass range from 14 to 17 x 10^6. Although uncertain, all of these mass estimates make G1 more than twice as massive as omega Centauri. Such large masses relate to the metallicity spread whose origin is still unknown (either self-enrichment, an inhomogeneous proto-cluster cloud, or remaining core of a dwarf galaxy). When considering the positions of G1 in the different diagrams defined by Kormendy (1985), G1 always appears on the sequence defined by globular clusters, and definitely away from the other sequences defined by elliptical galaxies, bulges, and dwarf spheroidal galaxies. The same is true for omega Centauri and for the nucleus of the dwarf elliptical NGC 205. This does not prove that all (massive) globular clusters are the remnant cores of nucleated dwarf galaxies.Comment: 24 pages, 5 figures, accepted for publication in AJ (August 2001

Sub-arcsecond imaging and spectroscopy of the radio-loud highly polarized quasar PKS 1610-771

We report on imaging and spectroscopic observations of the radio-loud, highly polarized quasar PKS 1610-771 (z = 1.71). Our long-slit spectroscopy of the companion 4.55 arcseconds NW of the quasar confirms the stellar nature of this object, so ruling out the previously suspected gravitationally lensed nature of this system. PKS 1610-771 looks fuzzy on our sub-arcsecond R and I images and appears located in a rich environment of faint galaxies. Possible magnification, without image splitting of the quasar itself, by some of these maybe foreground galaxies cannot be excluded. The continuum fuzz (made of the closest two objects, viz. A and D) is elongated in a direction orthogonal to the E vector of the optical polarization, as in high-redshift radio-galaxies. The spectrum of PKS 1610-771 appears strongly curved, in a convex way, with a maximum of intensity at ~ 7,600 A (2,800 A rest frame), possibly indicating a strong ultraviolet absorption by dust.Comment: 6 pages, uuencoded gziped tar file including TeX file + postscript figures. Accepted for publication in A&A main journa