Relativistic Dynamical Friction in the Weak Scattering Limit

A test mass, $M$, moving through an ambient medium of light particles with lower average kinetic energy than itself suffers a deceleration caused by its scattering of the light particles. The phenomenon is usually referred to as dynamical friction. The velocity, \v, of the test mass decays on a timescale independent of \v in the non-relativistic case. We derive expressions for dynamical friction in the case that the test mass and the light particles are relativistic, and that the scattering is weak (with impact parameter, $b\gg M$). In the case that the light particles are ultra-relativistic, and isotropic in the frame in which $M$ moves with velocity $v$, we find an explicit expression for the dynamical friction. The well known factor of 2 correcting the Newtonian scattering of photons to give the Einstein angle, $4M/b$, has the largest effect on the resulting friction, which is modified by a factor of roughly $16 / 3\gamma_v$ over the simple non-relativistic case. In the non-relativistic case, the largest contribution to the friction comes from light particles moving slower than $v$. We find that this is not the case for ultra-relativistic scattering, essentially because the scattering angle is independent of \v. Some astrophysical implications are discussed. (Accepted for publication in Monthly Notices.)Comment: 10 pages (no figures), self-unpacking uuencoded PostScript (uufiles), RDF#

Implications of Neutrino Balls as the Source of Gamma-Ray Bursts

(To appear in the Astrophysical Journal) Holdom and Malaney (1994) have suggested a mechanism for gamma-ray bursts which requires that stars be captured by a neutrino ball. Neutrino balls would be, for the most part, denser than main sequence stars, but their density would decrease as their mass increased. We show that small neutrino balls would subject stars to tidal forces sufficient to disrupt them. We thus argue that if neutrino balls existed at the centres of galaxies, only the largest would be able to act as a source of gamma-ray bursts. Such neutrino balls would have a mass of order 10^7\Msun. Tidal capture of stars by a neutrino ball would not be important, but dynamical friction against the neutrinos or star-disc interactions could both be important capture mechanisms. We find that a gamma-ray burst would occur in a galaxy containing such a neutrino ball roughly every 10^2\y, and the fraction of all galaxies contributing to the gamma-ray burst flux would be $\sim 10^{-4}$, assuming that this was the mechanism of all gamma-ray bursts. These numbers have implications for neutrino ball models of active galaxies, assuming that all gamma-ray bursts and all AGN come from neutrino balls. Either a small fraction $\sim 10^{-2}$ of the lifetime of such an object could be spent as an AGN, or that the probability of a neutrino ball becoming an AGN would be $10^{-2}$. It is not possible to rule out the possibility that neutrino balls might exist at the centres of galaxies through direct ground-based observation of stellar kinematics.Comment: 10 pages uuencoded PostScript (no figures), NB-0

Tidal disruption rates of stars in observed galaxies

We derive the rates of capture, Ndot, of main sequence turn off stars by the central massive black hole in a sample of galaxies from Magorrian et al. 1998. The disruption rates are smaller than previously believed with Ndot ~ 10^-4 - 10^-7 per galaxy. A correlation between Ndot and black hole mass, M, is exploited to estimate the rate of tidal disruptions in the local universe. Assuming that all or most galaxies have massive black holes in their nuclei, this rate should be dominated by sub-Lstar galaxies. The rate of tidal disruptions could be high enough to be detected in supernova (or similar) monitoring campaigns---we estimate the rate of tidal disruptions to be 0.01 - 0.1 times the supernova rate. We have also estimated the rates of disruption of red giants, which may be significant (Ndot ~> 10^-4 y^-1 per galaxy) for M ~> 10^8 Msun, but are likely to be harder to observe---only of order 10^-4 times the supernova rate in the local universe. In calculating capture rates, we advise caution when applying scaling formulae by other authors, which are not applicable in the physical regime spanned by the galaxies considered here.Comment: MNRAS, Accepted; 9 pages, Late

Star Captures by Quasar Accretion Disks: A Possible Explanation of the M-sigma Relation

A new theory of quasars is presented in which the matter of thin accretion disks around black holes is supplied by stars that plunge through the disk. Stars in the central part of the host galaxy are randomly perturbed to highly radial orbits, and as they repeatedly cross the disk they lose orbital energy by drag, eventually merging into the disk. Requiring the rate of stellar mass capture to equal the mass accretion rate into the black hole, a relation between the black hole mass and the stellar velocity dispersion is predicted of the form M_{BH} \propto sigma_*^{30/7}. The normalization depends on various uncertain parameters such as the disk viscosity, but is consistent with observation for reasonable assumptions. We show that a seed central black hole in a newly formed stellar system can grow at the Eddington rate up to this predicted mass via stellar captures by the accretion disk. Once this mass is reached, star captures are insufficient to maintain an Eddington accretion rate, and the quasar may naturally turn off as the accretion switches to a low-efficiency advection mode. The model provides a mechanism to deliver mass to the accretion disk at small radius, probably solving the problem of gravitational instability to star formation in the disk at large radius. We note that the matter from stars that is incorporated to the disk has an average specific angular momentum that is very small or opposite to that of the disk, and discuss how a rotating disk may be maintained as it captures this matter if a small fraction of the accreted mass comes from stellar winds that form a disk extending to larger radius. We propose several observational tests and consequences of this theory.Comment: submitted to Ap

Evolution of Giant Planets in Eccentric Disks

We investigate the interaction between a giant planet and a viscous circumstellar disk by means of high-resolution, two-dimensional hydrodynamical simulations. We consider planet masses that range from 1 to 3 Jupiter masses (Mjup) and initial orbital eccentricities that range from 0 to 0.4. We find that a planet can cause eccentricity growth in a disk region adjacent to the planet's orbit, even if the planet's orbit is circular. Disk-planet interactions lead to growth in a planet's orbital eccentricity. The orbital eccentricities of a 2 Mjup and a 3 Mjup planet increase from 0 to 0.11 within about 3000 orbits. Over a similar time period, the orbital eccentricity of a 1 Mjup planet grows from 0 to 0.02. For a case of a 1 Mjup planet with an initial eccentricity of 0.01, the orbital eccentricity grows to 0.09 over 4000 orbits. Radial migration is directed inwards, but slows considerably as a planet's orbit becomes eccentric. If a planet's orbital eccentricity becomes sufficiently large, e > ~0.2, migration can reverse and so be directed outwards. The accretion rate towards a planet depends on both the disk and the planet orbital eccentricity and is pulsed over the orbital period. Planet mass growth rates increase with planet orbital eccentricity. For e~0.2 the mass growth rate of a planet increases by approximately 30% above the value for e=0. For e > ~0.1, most of the accretion within the planet's Roche lobe occurs when the planet is near the apocenter. Similar accretion modulation occurs for flow at the inner disk boundary which represents accretion toward the star.Comment: 20 pages 16 figures, 3 tables. To appear in The Astrophysical Journal vol.652 (December 1, 2006 issue

Massive planet migration: Theoretical predictions and comparison with observations

We quantify the utility of large radial velocity surveys for constraining theoretical models of Type II migration and protoplanetary disk physics. We describe a theoretical model for the expected radial distribution of extrasolar planets that combines an analytic description of migration with an empirically calibrated disk model. The disk model includes viscous evolution and mass loss via photoevaporation. Comparing the predicted distribution to a uniformly selected subsample of planets from the Lick / Keck / AAT planet search programs, we find that a simple model in which planets form in the outer disk at a uniform rate, migrate inward according to a standard Type II prescription, and become stranded when the gas disk is dispersed, is consistent with the radial distribution of planets for orbital radii 0.1 AU < a < 2.5 AU and planet masses greater than 1.65 Jupiter masses. Some variant models are disfavored by existing data, but the significance is limited (~95%) due to the small sample of planets suitable for statistical analysis. We show that the favored model predicts that the planetary mass function should be almost independent of orbital radius at distances where migration dominates the massive planet population. We also study how the radial distribution of planets depends upon the adopted disk model. We find that the distribution can constrain not only changes in the power-law index of the disk viscosity, but also sharp jumps in the efficiency of angular momentum transport that might occur at small radii.Comment: ApJ, in press. References updated to match published versio

The Lopsidedness of Present-Day Galaxies: Results from the Sloan Digital Sky Survey

Large-scale asymmetries in the stellar mass distribution in galaxies are believed to trace non-equilibrium situations in the luminous and/or dark matter component. These may arise in the aftermath of events like mergers, accretion, and tidal interactions. These events are key in the evolution of galaxies. In this paper we quantify the large-scale lopsidedness of light distributions in 25155 galaxies at z < 0.06 from the Sloan Digital Sky Survey Data Release 4 using the m = 1 azimuthal Fourier mode. We show that the lopsided distribution of light is primarily due to a corresponding lopsidedness in the stellar mass distribution. Observational effects, such as seeing, Poisson noise, and inclination, introduce only small errors in lopsidedness for the majority of this sample. We find that lopsidedness correlates strongly with other basic galaxy structural parameters: galaxies with low concentration, stellar mass, and stellar surface mass density tend to be lopsided, while galaxies with high concentration, mass, and density are not. We find that the strongest and most fundamental relationship between lopsidedness and the other structural parameters is with the surface mass density. We also find, in agreement with previous studies, that lopsidedness tends to increase with radius. Both these results may be understood as a consequence of several factors. The outer regions of galaxies and low-density galaxies are more susceptible to tidal perturbations, and they also have longer dynamical times (so lopsidedness will last longer). They are also more likely to be affected by any underlying asymmetries in the dark matter halo.Comment: 42 pages, 13 figures, 3 tables, accepted to Ap