Paul S. Wesson

An exact solution to Einstein’s equations with a stiff equation of state

A solution to the equations of general relativity is given which is spherically‐symmetric and nonstatic with an inhomogeneous density profile ρ and a pressure p given by the stiff equation of state p=ρc2. The solution may be of use in representing collapsed astrophysical systems or the early stages of an inhomogeneous cosmology.

Accretion and electrostatic interaction of interstellar dust grains; Interstellar grit

This work is divided into 13 sections and 2 appendices, and aims to elucidate the accretion mechanism, which operates via image-theory forces, whenever two interstellar dust grains come close together. Section 1 is an introduction. Section 2 proposes that the distribution of interstellar grains be taken asn(r) ∝r−4 to avoid distortion of the 3K microwave background by radiation from spinning grains. Section 3 examines each of three types of image force accretion processes, finding them to be dominant compared to radiation or gravitational forces by at least a factor of 1019. Section 4 states that only grains made of conducting material (e.g., graphite, ice, iron) are involved in image theory. Section 5 presents reasons for believing that two grains should coalesce on impact. Section 6 examines the motion of charged interstellar grains in Hi and Hii regions. Section 7 demonstrates, by way of four examples involving dust grains ofr=10−7 cm up tor=10−4 cm, that the image effects on conducting grains are not trivial, and that the dynamics involved is not to be compared at all with elementary Coulomb interaction of two changes. Section 8 concludes that accretion with not take place in Hi clouds if thermal (equipartition) velocities prevail among the dust particles. section 9 examines grain interactions in Hii regions: here, following an argument due to Spitzer, consideration is given to the case of a population of dust grains all streaming in the direction of the local magnetic field B at velocities of order 0.1 km s−1. It is shown that accretion takes place effectively, leading to the formation of interstellar ‘grit’, meaning grains of mass 10−8 to 10−7 gm, radius ≃ 0.1 mm; and leaving also a population ofr≳10−6 cm grains, which are observed in polarization and extinction measurements. The existence of the latter is now a deduction and not an ad hoc postulate, as previously, and implies a distribution of the general formn(r) ∝rmean−3, in approximate agreement with that of Section 2. Section 10 considers the accretion mechanism as a cascade process. Section 11 shows that the existence of grains in space ofr ≃ 10−6 cm rules out an origin in supernova or galactic explosions, and supports a passive origin, perhaps in red giants or Mira variables. Section 12 discusses the implications of the results found for polarization observations and cosmogony, the latter being given a new foundation in which planets of different composition form automatically from a solar nebula. Section 13 is a conclusion.

General-relativistic hierarchical cosmology: An exact model

An exact solution of Einsteins equation is stated in which the density (ϱ), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having ϱ ∝R−2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law (ϱ ∝R−θ, approximately, with θ=a number, 0≤θ≤2). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.

The formation of iron, stone, and mixed planetesimals in the early solar system

Abstract The interaction of dust grains with each other in a finite-temperature solar nebula are examined, taking into account the important fact that such grains would carry net steady-state charges like those of grains in interstellar clouds. This charge is given by the well-known Spitzer relation. It provides a screening mechanism that operates during accretion and results in bodies of differing compositions depending on the local temperature in the nebula. In a typical nebula, it is found that planetesimals of 0.1–10 2 -cm size form in a time of order 10 6 –10 7 years. These planetesimals are of iron and stone and mixed composition in the inner solar system, but of mixed composition only in the outer solar system. The predictions of this type of charged-dust accretion can be compared to known data on meteorites and the composition of the planets.

Metric conditions for clusters in hierarchical cosmologies

Algebraic conditions on the continuity of the components of the metric tensor are employed to get an approximate metric in four limiting forms relevant to a condensation in an expanding Einstein/de Sitter substratum. The metric of the condensation is in general spherically-symmetric, nonstatic and asymptotically flat, passing over into the usual Friedmann solution at large distances and late times. The line-element derived supersedes an earlier incorrect formulation of the problem by Einstein and Straus. The metric is applicable in particular to clusters of galaxies, wich cannot avoid being involved in the expansion of the Universe for the density-distributions relevant to average loose clusters as presently observed. It is likely that all clusters, including compact ones, are in a state of dynamical evolution, a conclusion which may remove the missing mass problem. The results found agree, in this respect, with recent work by Noerdlinger and Petrosian, and give effective Hubble parmeters for systems in an expanding substratum.

Numerical experiments on the effect of massive central systems on the virial binding energy of clusters

A program has been developed to evaluated the gravitational binding energy of a clumpy cluster composed ofN particles with a given mass dispersion, a given abundance of binaries and a given massive binary system at the centre. In application to clusters of galaxies nucleated by massivecD binaries, it is found that the gravitational binding energy is typically greater than the equivalent smooth distribution by a factor in the range 2–12. This suggests that the ‘missing’ mass problem in clusters of galaxies can be reduced by an order of magnitude if the correct binding energy is used in the virial theorem.

Particle Physics and Gravitation

In the previous chapter it was seen how modern theories of gravity attach considerable importance to gauge (or scale) invariance. In the present chapter, attention will be directed towards gauge invariance in elementary particle theory and ways in which particle physics might be connected up with gravitation.

Discrete source counts and the rotation of the local Universe in hierarchical cosmology

Attention is given to four reasons for believing that the upper limit on the rotation of the Universe ω set by isotropy of the 3K background may not be appropriate to the local system because of its hierarchical structure. In particular, recent work of Rubinet al. (1973) on the anisotropy of Hubbles parameter (H) as determined by certain galaxies is examined. The anisotropy inH is a 1st order harmonic effect, inconsistent with an origin in an acceleration of the expansion of the Universe (Uα;4≠0), but explicable as being due to a large peculiar velocity of the Local Group. This compromises limits set on ω by isotropy of the 3K field, as does the realization that only weak limits can be set if the last-scattering surface (z*) is notz*→∞ but is at smallz* (as expected in a hierarchy). In a rotating Universe, the 3-spaces of constant density cannot be orthogonal on the world lines of matter: a number test of Gödell based on this is generalized and applied (after consideration of Galactic obscuration) to the local Universe, by taking data on clusters of galaxies from the Abell and Zwicky catalogues. Data from the former give only a marginally significant result for the component ω1 of ω in one direction, but a bootstrap argument is applied which takes significance over from Abells data (considered as a class of galaxies) to Zwickys data (taken as a class of clusters), giving a statistically significant result on the hypothesis that clusters are the fundamental units of the Universe: it seems likely that ω1r≃(const)r-n with 0≲n≲1 over the interval 500–1000 Mpc (H=60 km s−1 Mpc−1) with a total rotation of ω<2ω1, and ω1 = 1.2 (+0.25) x 10-18 s-1 evaluated on data out to 103 Mpc. Strictly, the quoted value of the rotation only applies to a region of space that in some sense has an isotropic limit: if the actual hierarchy has a large density-dependence away from a local origin (i.e., large thinning factor), then the numerical value of the rotation is smaller than the quoted value but still finite and significant.

Expanding clusters of galaxies as components of a relativistic hierarchical cosmology

Approximate metries for clusters embedded in an expanding Robertson/Walker background (Section 1) indicate that in general clusters of galaxies cannot remain uninfluenced by the expansion. The potential for an expanding cluster (Section 2) is seen to suggest that clusters as presently observed are not in static equilibrium and that the missing mass problem can be elucidated via use of the virial theorem (Section 3) given certain density conditions in compact clusters. Non-compact clusters can be treated similarly, and it is found that the behaviour of a low-density cluster is equivalent to that of a domain of a Friedmann (k=0) model Universe (Section 4). The treatment of compact clusters (Section 5) is based on approximate metrics for clusters embedded in a Robertson/Walker background. These comparisons lead to information on the evolution of non-compact clusters and compact clusters (Section 7), and to observable consequences that seem to be borne out successfully (Section 8). Data on clusters themselves tend to show that there exists an expanding supercluster and/ or that Λ>0 (Section 9). Several tests of the hypothesis of expansion of clusters (Section 10) are proposed.

The configuration of a thin, rotating self-similar disk in general relativity

Einsteins equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density σ and an angular velocity ω. Self-similarity as a statement of the absence of scales implies that σ and ω can be written asσ=αc2/4πGr, ω=βc/r, and demands that α and β be pure numbers.