Distribution of Gamma-Ray Bursts in Halo Neutron Star-Comet Models

The motions of comets and neutron stars have been integrated over five billion years in the Galactic potential to determine a gamma-ray burst distribution, presuming that bursts are the result of interactions between these two families of objects. The comets originate in two distinct populations - one from ejection by stars in the Galactic disk, and the other from ejection by stars in globular clusters. No choice of the free parameters resulted in agreement with both the isotropy data and the $\log(N>F) - \log(F)$ data.Comment: 4 pages LaTex and two style files, tarred, compressed, and uuencoded. One postscript figure. To appear in Astrophysics and Space Science as part of the proceedings of the 29th ESLAB Symposium 'Toward the Source of Gamma-Ray Bursts' held in Noordwijk, 1995. A postscript version can be found at http://astro.queensu.ca/~mark/preprints.htm

On Stationary, Self-Similar Distributions of a Collisionless, Self-Gravitating, Gas

We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution functions where the mass density and gravitational potential are strict power laws in $r$, the distance from the symmetry point. We treat as special cases, systems built from purely radial orbits and systems that are isotropic in velocity space. We then discuss systems with arbitrary velocity space anisotropy finding a new and very general class of distribution functions. These distributions may prove useful in modelling galaxies. Distribution functions in cylindrical and planar geometries are also discussed. Finally, we study spatially spheroidal systems that again exhibit strict power-law behaviour for the density and potential and find results in agreement with results published recently.Comment: 23 pages, regular Tex, figures in separate .uu file to follo

Relaxing and Virializing a Dark Matter Halo

Navarro, Frenk, and White have suggested that the density profiles of simulated dark matter halos have a ``universal'' shape so that a given halo can be characterized by a single free parameter which fixes its mass. In this paper, we revisit the spherical infall model in the hope of recognizing in detail the existence and origin of any such universality. A system of particles is followed from linear perturbation, through first shell crossing, then through an accretion or infall phase, and finally to virialization. During the accretion phase, the system relaxes through a combination of phase mixing, phase space instability, and moderate violent relation. It is driven quickly, by the flow of mass through its surface, toward self-similar evolution. The self-similar solution plays its usual role of intermediate attractor and can be recognized from a virial-type theorem in scaled variables and from our numerical simulations. The transition to final equilibrium state once infall has ceased is relatively gentle, an observation which leads to an approximate form for the distribution function of the final system. The infall phase fixes the density profile in intermediate regions of the halo to be close to r^{-2}. We make contact with the standard hierarchical clustering scenario and explain how modifications of the self-similar infall model might lead to density profiles in agreement with those found in numerical simulations.Comment: 26 pages, Latex, plus 11 figure

The Deutsch Field Gamma-Ray Pulsar - Paper I: The Model Basics

A new model for the high-energy emission from pulsars is developed by considering charged particle motion in the fields of a spinning, highly magnetised and conducting sphere in vacuum. A generally applicable approximation to the particle motion in strong fields is developed and applied to the numerical modelling, and the radiation emitted by curvature emission is summed to generate light curves. The model predicts many of the observed features of pulsar light curves. This paper outlines the basic properties of the model; a subsequent paper will discuss the statistical properties of a population of model pulsars and apply the model to the known gamma-ray pulsars.Comment: 11 pages LaTex, 10 postscript figures included with psfig. The paper can also be found at ftp://astro.queensu.ca/pub/mark/preprints/paper1.ps.Z as a compressed postscript file. Submitted to MNRA

Wavelet Analysis of Inhomogeneous Data with Application to the Cosmic Velocity Field

In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present authors, we devised a method for inferring the velocity potential from the radial component of the cosmic velocity field assuming an ideal sampling. Unfortunately the sparseness of the real data as well as errors of measurement require us to first smooth the velocity field as observed on a 3-dimensional support (i.e. the galaxy positions) inhomogeneously distributed throughout the sampled volume. The wavelet formalism permits us to introduce a minimal smoothing procedure that is characterized by the variation in size of the smothing window function. Moreover the output smoothed radial velocity field can be shown to correspond to a well defined theoretical quantity as long as the spatial sampling support satisfies certain criteria. We argue also that one should be very cautious when comparing the velocity potential derived from such a smoothed radial component of the velocity field with related quantities derived from other studies (e.g : of the density field).Comment: 19 pages, Latex file, figures are avaible under requests, published in Inverse Problems, 11 (1995) 76

Charge separation instability in an unmagnetized disk plasma around a Kerr black hole

In almost all of plasma theories for astrophysical objects, we have assumed the charge quasi-neutrality of unmagnetized plasmas in global scales. This assumption has been justified because if there is a charged plasma, it induces electric field which attracts the opposite charge, and this opposite charge reduces the charge separation. Here, we report a newly discovered instability which causes a charge separation in a rotating plasma inside of an innermost stable circular orbit (ISCO) around a black hole. The growth rate of the instability is smaller than that of the disk instability even in the unstable disk region and is forbidden in the stable disk region outside of the ISCO. However, this growth rate becomes comparable to that of the disk instability when the plasma density is much lower than a critical density inside of the ISCO. In such case, the charge separation instability would become apparent and cause the charged accretion into the black hole, thus charge the hole up.Comment: 15pages, 1 figur

Black holes and Galactic density cusps -- I. Radial orbit cusps and bulges

In this paper, we study the distribution functions that arise naturally during self-similar radial infall of collisionless matter. Such matter may be thought of either as stars or as dark matter particles. If a rigorous steady state is assumed, then the system is infinite and is described by a universal distribution function given the self-similar index. The steady logarithmic potential case is exceptional and yields the familiar Gaussian for an infinite system with an inverse-square density profile. We show subsequently that for time-dependent radial self-similar infall, the logarithmic case is accurately described by the Fridmann and Polyachenko distribution function. The system in this case is finite but growing. We are able to embed a central mass in the universal steady distribution only by iteration, except in the case of massless particles. The iteration yields logarithmic corrections to the massless particle case and requires a `renormalization' of the central mass. A central spherical mass may be accurately embedded in the Fridmann and Polyachenko growing distribution however. Some speculation is given concerning the importance of radial collisionless infall in actual galaxy formation.Comment: 10 pp, 3 fig

Hydrogen Clouds and the MACHO/EROS Events

We propose that the recently reported MACHO/EROS events correspond to gravitational amplification by dark clouds rather than compact objects. These clouds must be very dense with $M\sim 0.1 ~M_\odot$ and R\la 10^{14}~{\rm cm}. In all likelihood, the clouds will be members of a family of objects with different sizes and masses. We therefore expect events of longer duration than the ones reported by the MACHO and EROS groups but with light curves very different from the ones derived assuming point mass lenses. We suggest that one such event has already been observed in radio measurements of the quasar 1502+106. The abundances of free electrons, metals, complex molecules, and dust grains are constrained to be very small suggesting that the clouds are formed from a primordial mixture of hydrogen and helium. Cosmic rays and background UV radiation ionize a halo around the cloud. Radio waves from distant sources will be scattered by the electrons in this halo, an effect which may have already been observed in quasars such as 1502+106. We argue that dark clouds are a viable alternative to compact objects for baryonic dark matter in the halo.Comment: 11 pages, LaTe

Non-radial motion and the NFW profile

The self-similar infall model (SSIM) is normally discussed in the context of radial orbits in spherical symmetry. However it is possible to retain the spherical symmetry while permitting the particles to move in Keplerian ellipses, each having the squared angular momentum peculiar to their 'shell'. The spherical 'shell', defined for example by the particles turning at a given radius, then moves according to the radial equation of motion of a 'shell' particle. The 'shell' itself has no physical existence except as an ensemble of particles, but it is convenient to sometimes refer to the shells since it is they that are followed by a shell code. In this note we find the distribution of squared angular momentum as a function of radius that yields the NFW density profile for the final dark matter halo. It transpires that this distribution is amply motivated dimensionally. An effective 'lambda' spin parameter is roughly constant over the shells. We also study the effects of angular momentum on the relaxation of a dark matter system using a three dimensional representation of the relaxed phase space.Comment: accepted for publication in Astronomy and Astrophysics. date received: 31-03-03 date accepted: 10-06-0