Using frequency maps to constrain the distribution function of the Milky Way stellar halo

Resolved surveys of the Milky Way's stellar halo can obtain all 6 phase space coordinates of tens of thousands of individual stars, making it possible to compute their 3-dimensional orbits. Spectral analysis of large numbers of halo orbits can be used to construct frequency maps which are a compact, yet informative representation of their phase space distribution function (DF). Such maps can be used to infer the major types of orbit families that constitute the DF of stellar halo and their relative abundances. The structure of the frequency maps, especially the resonant orbits, reflects the formation history and shape of the dark matter potential and its orientation relative to the disk. The application of frequency analysis to cosmological hydrodynamic simulations of disk galaxies shows that the orbital families occupied by halo stars and dark matter particles are very similar, implying that stellar halo orbits can be used to constrain the DF of the dark matter halo, possibly impacting future direct dark matter detection experiments. An application of these methods to a sample of \sim 16,000 Milky Way halo and thick disk stars from the SDSS-SEGUE survey yields a frequency map with strong evidence for resonant trapping of halo stars by the Milky Way disk, in a manner predicted by controlled simulations in which the disk grows adiabatically. The application of frequency analysis methods to current and future phase space data for Milky Way halo stars will provide new insights into the formation history of the dierent components of the Galaxy and the DF of the halo.Comment: 4 pages, 3 figures, to appear in the proceedings of the conference "Assembling the Puzzle of the Milky Way", to be published electronically by the European Physical Journal. Eds. Celine Reyle, Annie Robin and Mathias Schulthei

Cluster tidal fields: Effects on disk galaxies

A variety of observations of galaxies in clusters indicate that the gas in these galaxies is strongly affected by the cluster environment. We present results of a study of the dynamical effects of the mean cluster tidal field on a disk galaxy as it falls into a cluster for the first time on a bound orbit with constant angular momentum (Valluri 1992). The problem is studied in the restricted 3-body framework. The cluster is modelled by a modified Hubble potential and the disk galaxy is modelled as a flattened spheroid

Orbital instability and relaxation in stellar systems

The orbits of stars in galaxies are generically chaotic: the chaotic behavior arises in part from the intrinsically grainy nature of a potential that is composed of point masses. Even if the potential is assumed to be smooth, however, orbits in non-axisymmetric galaxies can be chaotic due to the presence of central density cusps or black holes. The chaotic nature of orbits implies that perturbations will grow exponentially and this in turn is expected to result in a diffusion in phase space. We show that the degree of orbital evolution is not well predicted by the growth rate of infinitesimal perturbations, i.e. by the Liapunov exponent. A more useful criterion is whether perturbations continue to grow exponentially until their scale is of order the size of the system. We illustrate these ideas in a potential consisting of N fixed point masses. Liapunov exponents are large for all values of N, but orbits become increasingly regular in their behavior as N increases; the reason is that the exponential divergence saturates at smaller and smaller distances as N is increased. The objects which impede diffusion are the invariant tori. When there are few stable tori, an ensemble of chaotic orbits evolves rapidly toward a nearly stationary state. This mixing process occurs on timescales of a few crossing times in triaxial potentials containing massive central singularities, consistent with the rapid evolution observed in N-body simulations of galaxies with central black holes.Comment: Invited review to appear in "The Chaotic Universe", eds. R. Ruffini, V.G. Gurzadyan (World Scientific) 1999, 9 pages, 4 figure

Collisional removal of HI from the inner disks of Virgo cluster galaxies

There is sufficient observational evidence to show that many Virgo Cluster spirals are HI deficient in their inner disks (in addition to being HI deficient globally, as previously established). It is shown here that collisions between galaxies in a cluster can lead to the removal of HI gas from these galaxies while leaving the H2 gas, undisturbed. This follows directly from the application of the Spitzer-Baade collisional gas removal mechanism to galaxies consisting of stars and a two-component interstellar medium (ISM) consisting of HI and H2, with HI having the largest filling factor. This can account for both the observed HI deficiency in the inner regions and the normal H2 content of these galaxies. The frequency of galaxy collisions in the Virgo Cluster is shown to be large enough to make collisional gas removal a viable mechanism

The Low End of the Supermassive Black Hole Mass Function: Constraining the Mass of a Nuclear Black Hole in NGC 205 via Stellar Kinematics

Hubble Space Telescope (HST) images and spectra of the nucleated dwarf elliptical galaxy NGC 205 are combined with 3-integral axisymmetric dynamical models to constrain the mass (M_BH) of a putative nuclear black hole. This is only the second attempt, after M33, to use resolved stellar kinematics to search for a nuclear black hole with mass below 10^6 solar masses. We are unable to identify a best-fit value of M_BH in NGC 205; however, the data impose a upper limit of 2.2x10^4 M_sun (1sigma confidence) and and upper limit of 3.8x10^4 M_sun (3sigma confidence). This upper limit is consistent with the extrapolation of the M_BH-sigma relation to the M_BH < 10^6 M_sunregime. If we assume that NGC 205 and M33 both contain nuclear black holes, the upper limits on M_BH in the two galaxies imply a slope of ~5.5 or greater for the M_BH-sigma relation. We use our 3-integral models to evaluate the relaxation time (T_r) and stellar collision time (T_coll) in NGC 205; T_r~10^8 yr or less in the nucleus and T_coll~10^11 yr. The low value of T_r is consistent with core collapse having already occurred, but we are unable to draw conclusions from nuclear morphology about the presence or absence of a massive black hole.Comment: Latex emulateapj, 15 pages, 16 figures, Version accepted for Publication in ApJ, 20 July 2005, v628. Minor changes to discussion