X-ray Wakes as Probes of Galaxy Cluster Dynamics

If a galaxy resides in a cluster, then its passage through the pervasive intracluster medium will produce a detectable signature in the X-ray emission from the cluster. The simplest kinematic information that can be extracted from this signature is the galaxy's direction of motion on the plane of the sky. This paper explores the constraints on cluster dynamics that could be derived from such information. In particular, we show that it is possible to define a projected anisotropy parameter, B(R), which is directly analogous to the usual orbital anisotropy parameter. We describe an estimator for this quantity, Bhat(R), which can be derived in a robust and straightforward manner. Using a simple dynamical model, we demonstrate the ambiguity between the distribution of mass and the distribution of galaxy orbits when interpreting the traditional measures of cluster kinematics (the projected density of galaxies and their line-of-sight velocity dispersion). As an example, we show how two very different dynamical models can fit the kinematic properties of the Coma cluster. We demonstrate that the measurement of Bhat using a relatively small sample of wake directions (N_{wake} ~ 50) would provide an effective mechanism for lifting this degeneracy. Thus, by combining X-ray measurements of wake directions with number counts and line-of-sight velocities derived from optical data, it will prove possible to measure both the orbit distribution and the form of the gravitational potential in clusters of galaxies.Comment: 6 pages, LaTeX, including 2 figures, using mn and epsf style files. Accepted for publication in MNRA

Dark Matter on Galactic Scales (or the Lack Thereof)

This paper presents a brief review of the evidence for dark matter in the Universe on the scales of galaxies. In the interests of critically and objectively testing the dark matter paradigm on these scales, this evidence is weighed against that from the only other game in town, modified Newtonian dynamics. The verdict is not as clear cut as one might have hoped.Comment: 10 pages, 5 figures. Invited review talk presented at IDM2004 5th International Workshop on the Identification of Dark Matter, Edinburgh, Scotland, September 200

Refining the Oort and Galactic constants

The local stellar kinematics of the Milky Way offer a useful tool for studying the rotation curve of the Galaxy. These kinematics -- usually parameterized by the Oort constants A and B -- depend on the local gradient of the rotation curve as well as its absolute value (Theta_0), and the Sun's distance to the Galactic center (R_0). The density of interstellar gas in the Milky Way is shown to vary non-monotonically with radius, and so contributes significantly to the local gradient of the rotation curve. We have therefore calculated mass models for the Milky Way that include this component, and have derived the corresponding radial variation in the Oort constants. Between 0.9R_0 and 1.2R_0, the Oort functions, A(R) and B(R), differ significantly from the general Theta/R dependence. Various previously-inexplicable observations are shown to be consistent with these predictions. These models can explain the 40% difference between the values for 2 A R_0 derived from radial velocity data originating in the inner and outer Galaxy. They also go some way toward explaining the different shapes of the velocity ellipsoids of giant and dwarf stars in the solar neighbourhood. However, a consistent picture only emerges if one adopts small values of R_0 = 7.1 +/- 0.4 kpc and Theta_0 = 184 +/- 8 km/s. With these Galactic constants, the Milky Way's rotation curve declines slowly in the outer Galaxy; V_rot(20 kpc) = 166 kms. Our low value for R_0 agrees well with the only direct determination (7.2 +/- 0.7 kpc, Reid 1993). Using these Galactic constants, we find that the proper motion of Sgr A^* is consistent with the observational constraints. The radial velocities and proper motions of our best fit model are entirely consistent with the radial velocities of Cepheids and the Hipparcos measurements of their proper motions.Comment: 11 pages, LaTeX, including 5 figures, using mn and epsf style files. Accepted for publication in MNRA

Disc heating in NGC 2985

Various processes have been proposed to explain how galaxy discs acquire their thickness. A simple diagnostic for ascertaining this ``heating'' mechanism is provided by the ratio of the vertical to radial velocity dispersion components. In a previous paper we have developed a technique for measuring this ratio, and demonstrated its viability on the Sb system NGC 488. Here we present follow-up observations of the morphologically similar Sab galaxy NGC 2985, still only the second galaxy for which this ratio has been determined outside of the solar neighbourhood. The result is consistent with simple disc heating models which predict ratios of $\sigma_z / \sigma_R$ less than oneComment: 5 pages, 4 figures. Accepted for publication in MNRA

Two measures of the shape of the Milky Way's dark halo

In order to test the reliability of determinations of the shapes of galaxies' dark matter halos, we have made such measurements for the Milky Way by two independent methods, which make use of the stellar kinematics in the solar neighbourhood and the observed flaring of the Galactic HI layer to estimate the flattening of the Galactic dark halo. These techniques are found to produce a consistent estimate for the halo shape, with a shortest-to-longest axis ratio of q ~ 0.8, but only if one adopts somewhat non-standard values for the distance to the Galactic centre, R_0, and the local Galactic rotation speed, Theta_0. For consistency, one requires values of R_0 < 7.6 kpc and Theta_0 < 190 km/s. Although differing significantly from the current IAU-sanctioned values, these upper limits are consistent with all existing observational constraints. If future measurements confirm these lower values for the Galactic constants, then the validity of the gas layer flaring method will be confirmed. Further, dark matter candidates such as cold molecular gas and massive decaying neutrinos, which predict very flat dark halos with q < 0.2, will be ruled out. Conversely, if the Galactic constants were found to be close to the more conventional values, then there would have to be some systematic error in the methods for measuring dark halo shapes, so the existing modeling techniques would have to be viewed with some scepticism.Comment: Accepted for publication in MNRAS. 10 pages, 6 figures, uses mn.sty and epsf.st

The shape of the velocity ellipsoid in NGC 488

Theories of stellar orbit diffusion in disk galaxies predict different rates of increase of the velocity dispersions parallel and perpendicular to the disk plane, and it is therefore of interest to measure the different velocity dispersion components in galactic disks of different types. We show that it is possible to extract the three components of the velocity ellipsoid in an intermediate-inclination disk galaxy from measured line-of-sight velocity dispersions on the major and minor axes. On applying the method to observations of the Sb galaxy NGC 488, we find evidence for a higher ratio of vertical to radial dispersion in NGC 488 than in the solar neighbourhood of the Milky Way (the only other place where this quantity has ever been measured). The difference is qualitatively consistent with the notion that spiral structure has been relatively less important in the dynamical evolution of the disk of NGC 488 than molecular clouds.Comment: 5 pages LaTex, including 2 figures, mn.sty, submitted to MNRA

Central Stellar Populations of S0 Galaxies in The Fornax Cluster

Based on FORS2-VLT long-slit spectroscopy, the analysis of the central absorption line indices of 9 S0 galaxies in the Fornax Cluster is presented. Central indices correlate with central velocity dispersions as observed in ellipticals. However, the stellar population properties of these S0s indicates that the observed trends are produced by relative differences in age and alpha-element abundances and not in metallicity ([Fe/H]) as previous studies have found in elliptical galaxies. The observed scatter in the line indices vs. velocity dispersion relations can be partially explained by the rotationally-supported nature of many of these systems. The presence of tighter line indices vs. maximum (circular) rotational velocity relations confirms this statement. It was also confirmed that the dynamical mass is the driving physical property of all these correlations and in our Fornax S0s it has to be estimated assuming rotational support.Comment: To appear in the Proceedings of IAU Symposium 241: "Stellar Populations as Building Blocks of Galaxies", 10-16 December, 2006 at La Palma, Canary Islands, Spai