Nonuniqueness and Structural Stability of Self-Consistent Models of Elliptical Galaxies

Schwarzschild models of a Plummer sphere were constructed and compared with analytical results to test the robustness of Schwarzschild's method and its efficiency in probing the degeneracy of the solution space. The method was then used to construct and study the nonuniqueness of triaxial equilibria with central density cusps, for which no analytical solutions are known. The stability of some models was also tested via N-body simulations.Comment: 2 pages, to be published in "Galaxy Dynamics" conference, eds. D. Merritt, M. Valluri and J. A. Sellwood, ASP Conf. Serie

Lack of Interaction between the Dust Grains and the Anomalous Radio Jet in the Nearby Spiral Galaxy NGC 4258

We obtained Spitzer/IRAC 3.6-8 micron images of the nearby spiral galaxy NGC 4258 to study possible interactions between dust and the radio jet. In our analysis we also included high-resolution radio continuum, H-alpha, CO, and X-ray data. Our data reveal that the 8 micron emission, believed to originate largely from PAH molecules and hot dust, is an excellent tracer of the normal spiral structure in NGC 4258, and hence it originates from the galactic plane. We investigated the possibility of dust destruction by the radio jet by calculating correlation coefficients between the 8 micron and radio continuum emissions along the jet in two independent ways, namely (i) from wavelet-transformed maps of the original images at different spatial scales, and (ii) from one-dimensional intensity cuts perpendicular to the projected path of the radio jet on the sky. No definitive sign of a correlation (or anticorrelation) was detected on relevant spatial scales with either approach, implying that any dust destruction must take place at spatial scales that are not resolved by our observations.Comment: Accepted for publication in the Astronomical Journal (11 pages, 10 figures, 1 table

Dynamics of Cuspy Triaxial Galaxies with a Supermassive Black Hole

This talk provides a progress report on an extended collaboration which has aimed to address two basic questions, namely: Should one expect to see cuspy, triaxial galaxies in nature? And can one construct realistic cuspy, triaxial equilibrium models that are robust? Three technical results are described: (1) Unperturbed chaotic orbits in cuspy triaxial potentials can be extraordinarily sticky, much more so than orbits in many other three-dimensional potentials. (2) Even very weak perturbations can be important by drastically reducing, albeit not completely eliminating, this stickiness. (3) A simple toy model facilitates a simple understanding of why black holes and cusps can serve as an effective source of chaos. These results suggest that, when constructing models of galaxies using Schwarzschild's method or any analogue thereof, astronomers would be well advised to use orbital building blocks that have been perturbed by `noise' or other weak irregularities, since such building blocks are likely to be more nearly time-independent than orbits evolved in the absence of all perturbations.Comment: a contributed talk at The International Conference on Stellar Dynamics: From Classical to Modern, Sobolev Astronomical Institute, St. Petersburg State University, August 200

The Black Hole Mass and Extreme Orbital Structure in NGC1399

The largest galaxies, and in particular central galaxies in clusters, offer unique insight into understanding the mechanism for the growth of nuclear black holes. We present Hubble Space Telescope kinematics for NGC1399, the central galaxy in Fornax. We find the best-fit model contains a black hole of 5.1 +-0.7 x 10^8 Msun (at a distance of 21.1 Mpc), a factor of over 2 below the correlation of black hole mass and velocity dispersion. We also find a dramatic signature for central tangential anisotropy. The velocity profiles on adjacent sides 0.5" away from the nucleus show strong bimodality, and the central spectrum shows a large drop in the dispersion. Both of these observations point to an orbital distribution that is tangentially biased. The best-fit orbital model suggests a ratio of the tangential to radial internal velocity dispersions of three. This ratio is the largest seen in any galaxy to date and will provide an important measure for the mode by which the central black hole has grown.Comment: 9 pages, accepted for publication in the Astrophysical Journa

Chaos and chaotic phase mixing in cuspy triaxial potentials

This paper investigates chaos and chaotic phase mixing in triaxial Dehnen potentials which have been proposed to describe realistic ellipticals. Earlier work is extended by exploring the effects of (1) variable axis ratios, (2) `graininess' associated with stars and bound substructures, idealised as friction and white noise, and (3) large-scale organised motions presumed to induce near-random forces idealised as coloured noise with finite autocorrelation time. Three important conclusions are: (1) not all the chaos can be attributed to the cusp; (2) significant chaos can persist even for axisymmetric systems; and (3) introducing a supermassive black hole can increase both the relative number of chaotic orbits and the size of the largest Lyapunov exponent. Sans perturbations, distribution functions associated with initially localised chaotic ensembles evolve exponentially towards a nearly time-independent form at a rate L that correlates with the finite time Lyapunov exponents associated with the evolving orbits. Perturbations accelerate phase space transport by increasing the rate of phase mixing in a given phase space region and by facilitating diffusion along the Arnold web that connects different phase space regions, thus facilitating an approach towards a true equilibrium. The details of the perturbation appear unimportant. All that matters are the amplitude and the autocorrelation time, upon which there is a weak logarithmic dependence. Even comparatively weak perturbations can increase L by a factor of three or more, a fact that has potentially significant implications for violent relaxation.Comment: 17 pages, 17 figures -- revised and extended manuscript to appear in Monthly Notices of the Royal Astronomical Societ

A Quintet Of Black Hole Mass Determinations

We report five new measurements of central black hole masses based on Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2 observations with the Hubble Space Telescope (HST) and on axisymmetric, three-integral, Schwarzschild orbit-library kinematic models. We selected a sample of galaxies within a narrow range in velocity dispersion that cover a range of galaxy parameters (including Hubble type and core/power-law surface density profile) where we expected to be able to resolve the galaxy's sphere of influence based on the predicted value of the black hole mass from the M-sigma relation. We find masses for the following galaxies: NGC3585, M(BH) = 3.4(-0.6)(+1.5) x 10(8) M(circle dot;) NGC 3607, M(BH) = 1.2(-0.4)(+0.4) x 10(8) M(circle dot); NGC 4026, M(BH) = 2.1(-0.4)(+0.7) x 10(8) M(circle dot); and NGC 5576, M(BH) = 1.8(-0.4)(+0.3) x 10(8) M(circle dot), all significantly excluding M(BH) = 0. For NGC 3945, M(BH) = 9(-21)(+17) x 10(6) M(circle dot), which is significantly below predictions from M-sigma and M-L relations and consistent with MBH = 0, though the presence of a double bar in this galaxy may present problems for our axisymmetric code.NASA/HST GO-5999, GO-6587, GO-6633, GO-7468, GO-9107NASA NAS 5-26555Astronom

The M-sigma and M-L Relations in Galactic Bulges and Determinations of their Intrinsic Scatter

We derive improved versions of the relations between supermassive black hole mass (M_BH) and host-galaxy bulge velocity dispersion (sigma) and luminosity (L) (the M-sigma and M-L relations), based on 49 M_BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (epsilon_0) in both relations. We find log(M_BH / M_sun) = alpha + beta * log(sigma / 200 km/s) with (alpha, beta, epsilon_0) = (8.12 +/- 0.08, 4.24 +/- 0.41, 0.44 +/- 0.06) for all galaxies and (alpha, beta, epsilon_0) = (8.23 +/- 0.08, 3.96 +/- 0.42, 0.31 +/- 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-sigma relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-sigma relation. We estimate the M-L relationship as log(M_BH / M_sun) = alpha + beta * log(L_V / 10^11 L_sun,V) of (alpha, beta, epsilon_0) = (8.95 +/- 0.11, 1.11 +/- 0.18, 0.38 +/- 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.Comment: 27 pages, 18 figures, 7 tables, ApJ accepte

Phase space transport in cuspy triaxial potentials: Can they be used to construct self-consistent equilibria?

(Abridged) This paper studies chaotic orbit ensembles evolved in triaxial generalisations of the Dehnen potential which have been proposed to model ellipticals with a strong density cusp that manifest significant deviations from axisymmetry. Allowance is made for a possible supermassive black hole, as well as low amplitude friction, noise, and periodic driving which can mimic irregularities associated with discreteness effects and/or an external environment. The degree of chaos is quantified by determining how (1) the relative number of chaotic orbits and (2) the size of the largest Lyapunov exponent depend on the steepness of the cusp and the black hole mass, and (3) the extent to which Arnold webs significantly impede phase space transport, both with and without perturbations. In the absence of irregularities, chaotic orbits tend to be extremely `sticky,' so that different pieces of the same chaotic orbit can behave very differently for 10000 dynamical times or longer, but even very low amplitude perturbations can prove efficient in erasing many -- albeit not all -- these differences. The implications thereof are discussed both for the structure and evolution of real galaxies and for the possibility of constructing approximate near-equilibrium models using Schwarzschild's method. Much of the observed qualitative behaviour can be reproduced with a toy potential given as the sum of an anisotropic harmonic oscillator and a spherical Plummer potential, which suggests that the results may be generic.Comment: 18 pages, including 19 figures; Accepted for publication by MNRAS; higher quality figures available from http://www.astro.ufl.edu/~siopis/papers

A Stellar Dynamical Measurement of the Black Hole Mass in the Maser Galaxy NGC 4258

We determine the mass of the black hole at the center of the spiral galaxy NGC 4258 by constructing axisymmetric dynamical models of the galaxy. These models are constrained by high spatial resolution imaging and long-slit spectroscopy of the nuclear region obtained with the {\em Hubble Space Telescope}, complemented by ground-based observations extending to larger radii. Our best mass estimate is \MBH = (3.3 \pm 0.2) \times 10^7 \MSun for a distance of 7.28 Mpc (statistical errors only). This is within 15% of (3.82\pm 0.01) \times 10^7 \MSun, the mass determined from the kinematics of water masers (rescaled to the same distance) assuming they are in Keplerian rotation in a warped disk. The construction of accurate dynamical models of NGC 4258 is somewhat compromised by an unresolved active nucleus and color gradients, the latter caused by variations in the stellar population and/or obscuring dust. These problems are not present in the $\sim 30$ other black hole mass determinations from stellar dynamics that have been published by us and other groups; thus, the relatively close agreement between the stellar dynamical mass and the maser mass in NGC 4258 enhances our confidence in the black hole masses determined in other galaxies from stellar dynamics using similar methods and data of comparable quality.Comment: 58 pages, submitted to ApJ. Some figures excluded due to size. The entire paper is at http://www.noao.edu/noao/staff/lauer/nuker_papers.htm