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

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

Hidden Bars and Boxy Bulges

It has been suggested that the boxy and peanut-shaped bulges found in some edge-on galaxies are galactic bars viewed from the side. We investigate this hypothesis by presenting emission-line spectra for a sample of 10 edge-on galaxies that display a variety of bulge morphologies. To avoid potential biases in the classification of this morphology, we use an objective measure of bulge shape. Generally, bulges classified as more boxy show the more complicated kinematics characteristic of edge-on bars, confirming the intimate relation between the two phenomena.Comment: 4 pages, 1 figure, to appear in A&ALett. Colour version of figure a vailable from http://www.astro.rug.nl/~kuijken/nutkinfig2.p

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

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

Kinematic detection of the double nucleus in M31

Using a spectrum obtained under moderate (of order 1 arcsecond) seeing, we show that the double nucleus in M31 produces a strong kinematic signature even though the individual components are not spatially resolved. The signature consists of a significant asymmetric wing in the stellar velocity distribution close to the center of the system. The properties of the second nucleus derived from this analysis agree closely with those measured from high-spatial resolution Hubble Space Telescope images. Even Space Telescope only has sufficient resolution to study the structure of very nearby galactic nuclei photometrically; this spectroscopic approach offers a tool for detecting structure such as multiple nuclei in a wider sample of galaxy cores.Comment: 4 pages of uuencoded compressed postscript, figures included. Accepted for publication in MNRA

Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.Comment: 9 pages, 9 figures, submitted to A&

Hubble Space Telescope weak lensing study of the z=0.83 cluster MS 1054-03

We have measured the weak gravitational lensing signal of MS 1054-03, a rich and X-ray luminous cluster of galaxies at a redshift of z=0.83, using a two-colour mosaic of deep WFPC2 images. The small corrections for the size of the PSF and the high number density of background galaxies obtained in these observations result in an accurate and well calibrated measurement of the lensing induced distortion. The strength of the lensing signal depends on the redshift distribution of the background galaxies. We used photometric redshift distributions from the Northern and Southern Hubble Deep Fields to relate the lensing signal to the mass. The predicted variations of the signal as a function of apparent source magnitude and colour agrees well with the observed lensing signal. We determine a mass of (1.2+-0.2)x10^15 Msun within an aperture of radius 1 Mpc. Under the assumption of an isothermal mass distribution, the corresponding velocity dispersion is 1311^{+83}_{-89} km/s. For the mass-to-light ratio we find 269+-37 Msun/Lsun. The errors in the mass and mass-to-light ratio include the contribution from the random intrinsic ellipticities of the source galaxies, but not the (systematic) error due to the uncertainty in the redshift distribution. However, the estimates for the mass and mass-to-light ratio of MS 1054-03 agree well with other estimators, suggesting that the mass calibration works well. The reconstruction of the projected mass surface density shows a complex mass distribution, consistent with the light distribution. The results indicate that MS 1054-03 is a young system. The timescale for relaxation is estimated to be at least 1 Gyr. Averaging the tangential shear around the cluster galaxies, we find that the velocity dispersion of an Lstar galaxy is 203+-33 km/s.Comment: 21 pages, Latex, with 27 figures (3 figures bitmapped), ApJ, in press. Version (with non-bitmapped figures) available at http://www.astro.rug.nl/~hoekstra/papers.htm