Charles C. Dyer

Softening in N-body simulations of collisionless systems

The standard Plummer softening force law is physically inconsistent: the force on a particle is calculated as if it were a point mass, but its contribution to the gravitational field for other particles is that of an extended mass. The use of uniform density spheres as models for the particles leads to a consistent force and is physically more reasonable. For a King model with W 0 =5, the optimal size of uniform density spheres is approximately 3 times the optimal Plummer softening length. This allows a larger time step to be used and thus uniform density sphere softening is more efficient. The relaxation rate is smaller for the optimal uniform density sphere softening

Estimates of the Global Masses of two Distant Galaxies Using a New Type of Astrophysical Mass “Laboratory”*

We have applied the polarization alignment-breaking method of measuring global masses of galaxies (developed by Kronberg et al.) to new radio and deep optical images of the strong jet quasar 3C 9 at z = 2.012. We demonstrate the power of this previously unexploited technique by making estimates of the global mass of two intervening galaxies: at z = 0.25 and z 1. This paper also explores the possibilities of the method. It shows that for these two intervening galaxy masses, a detectable gravitational signature in the jet polarization alignment is expected for reasonable galaxy masses. We have clearly detected the expected signature, which provides information on the global mass of each galaxy independently of the other. The more distant z 1 galaxy has a mass of 17 × 1011 M☉ with an estimated uncertainty of ~ ±30%. For the z = 0.25 galaxy, we determine a firm upper limit of 20 × 1011 M☉ (which includes the entire mass up to ~ 100 kpc radius H0 = 75). Future measurements of this type on lensing galaxies up to z ~ 1.8 could place interesting constraints on M and M/L at proper times sufficiently early to constrain galaxy and cosmological evolution.

On the rotation of polarization by a gravitational lens

It is shown that the polarization directions of photons in a beam propagating under the influence of a gravitational lens remain unaffected by the lens in most cases of astrophysical interest

A class of spherically symmetric solutions with conformal killing vectors

Spherically symmetric solutions with a conformal Killing vector in the (r, t) surface allow the null geodesics to be found with relative ease. Knowledge of the null geodesics is essential to calculating the optical properties of a solution via the optical scalar equations. Solutions of this type may be useful for the treatment of the optical properties of an inhomogeneous universe. We first address the question of whether the large class of spherically symmetric solutions found by McVittie possess conformal symmetry. We also investigate the potential for using conformal Killing vectors to aid in the solution of Einsteins Field Equations.

Asymptotically Einstein-de Sitter cosmological black holes and the problem of energy conditions

It is shown that previous asymptotically Einstein–de Sitter cosmological black hole spacetimes violate the energy conditions in some region of spacetime. Thus, cosmological black hole spacetimes (for the Schwarzschild and Reissner–Nordstrom cases) are obtained that satisfy the energy conditions throughout spacetime. The solutions are obtained by performing conformal transformations on the isotropic forms of the isolated black hole metrics.

A technique for using radio jets as extended gravitational lensing probes

A new and potentially powerful method of measuring the mass of a galaxy (or dark matter concentration) which lies close in position to a background polarized radio jet is proposed. Using the fact that the polarization angle is not changed by lensing, an alignment-breaking parameter is defined which is a sensitive indicator of gravitational distortion. The method remains sensitive over a wide redshift range of the gravitational lens. This technique is applied to the analysis of polarimetric observations of the jet of 3C 9 at z = 2.012, combined with a newly discovered 20.3 mag foreground galaxy at z = 0.2538 to weigh the galaxy and obtain an approximate upper limit to the mass-to-light ratio. 15 refs.

On the transition from Weyl to Ricci focusing

Using the weak-field approximation, we show that the Weyl focusing of rays in a beam of light which passes around a number of spherical deflectors may be approximated by the Ricci focusing of the beam due to the enclosed mass.

Complete model of a self-gravitating cosmic string: A new class of exact solutions.

We find solutions of Einsteins field equation for topologically stable strings associated with the breaking of a U(1) symmetry. Strings form in many GUTs and are expected whenever the homotopy group

Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies

\Pi_1(M_0)

Matching of Friedmann-Lemaître-Robertson-Walker and Kasner cosmologies

is non-trivial. The behavior of the fields making up the string is described by the Euler-Lagrange equations. These fields appear in the energy-momentum tensor so we must solve simultaneously for the coupled Einstein-scalar-gauge field equations. Numerical results are obtained using a Taylor-series method. We obtain a 5-parameter family of solutions and discuss their physical characteristics. Significant gravitational lensing can occur due to strings based on this model and are shown for different solutions. Finally, we prove that the assumption of regularity at the string axis is not necessary by looking at the physical properties of the string solutions.