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

Buckling Bars and Boxy Bulges

It has been suggested that the peanut-shaped bulges seen in some edge-on disk galaxies are produced when bars in these galaxies buckle. This paper reviews the modelling which seeks to show how bars buckle, and I present a very simple new model which captures the essential physics of this process. I then discuss the problems in establishing observationally the connection between peanut-shaped bulges and bars: confirmation of the link has proved difficult because boxy bulges are only apparent in edge-on galaxies whereas bars are only easily detectable in more face-on systems. Finally, I present a new technique which avoids this difficulty by searching for the distinctive kinematic signature of an edge-on bar; application of this method to spectra of peanut-shaped bulges reveals that they are, indeed, associated with hidden bars.Comment: uuencoded compressed postcript, 9 pages. Invited talk at IAU Colloquium #157: Barred Galaxies. The figures (some of which are rather large) are available over the WWW from our preprint server at http://www.astro.soton.ac.uk/pubs/Publications.htm

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

The Kinematics of Galactic Stellar Disks

The disks of galaxies are primarily stellar systems, and fundamentally dynamical entities. Thus, to fully understand galactic disks, we must study their stellar kinematics as well as their morphologies. Observational techniques have now advanced to a point where quite detailed stellar-kinematic information can be extracted from spectral observations. This review presents three illustrative examples of analyses that make use of such information to study the formation and evolution of these systems: the derivation of the pattern speed of the bar in NGC 936; the calculation of the complete velocity ellipsoid of random motions in NGC 488; and the strange phenomenon of counter-rotation seen in NGC 3593.Comment: 11 pages, LaTeX (including 7 figures), uses paspconf.sty and epsf.sty, to be published in Proceedings of the EC Summer School on 'Astrophysical Discs', eds J. A. Sellwood and J. Goodman, ASP Conf. Serie

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

The pattern speed of the bar in NGC 936

We have used the Tremaine-Weinberg method to measure the angular speed of rotation for the bar in the SB0 galaxy NGC 936. With this technique, the bar's pattern speed, Omega_p, can be derived from the luminosity and stellar-kinematic information in long-slit spectral observations taken parallel to the major axis of the galaxy. The kinematic measurement required is the mean line-of-sight velocity of all stellar light entering the slit. This quantity can only be calculated reliably if any asymmetry in the shape of the broadening function of the spectral lines is also measured, and so we present a method which allows for such asymmetry. The technique also returns a true measure of the RMS uncertainty in the estimate. Application of the analysis to a set of long-slit spectra of NGC 936 returns four separate measures of Omega_p which are mutually consistent. Combining these data produces a best estimate for the bar pattern speed of Omega_p = 60 +/- 14 km/s/kpc (assuming a distance of 16.6 Mpc). This result refines the only previous attempt to make this measurement, which yielded an estimate for Omega_p in NGC 936 of 104 +/- 37 km/s/kpc (Kent 1987). The new measurement places the co-rotation radius just beyond the end of the bar, in agreement with theoretical calculations.Comment: uuencoded compressed postscript file. 6 pages. Accepted for publication in MNRAS

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