Jeans Instability in a Universe with Dissipation

TL;DR

This paper investigates Jeans gravitational instability in static and expanding universes considering viscous and thermal effects using five and thirteen field theories, revealing how viscosity influences perturbation damping and growth.

Contribution

It derives a general dispersion relation incorporating shear viscosity and heat flux effects in the context of viscous cosmological models, extending previous analyses.

Findings

Shear viscosity affects the damping of harmonic perturbations.

Density and temperature contrasts grow or decay depending on wavelength and viscosity.

Jeans mass profiles are compared with molecular cloud data.

Abstract

The problem of Jeans gravitational instability is investigated for static and expanding universes within the context of the five and thirteen field theories which account for viscous and thermal effects. For the five-field theory a general dispersion relation has been derived with the help of relevant linearized perturbation equations, showing that the shear viscosity parameter alters the propagating modes for large and small wavelengths. The behavior of density and temperature contrasts are analyzed for the hard-sphere model in detail. In the small wavelengths regime, increasing the amount of shear viscosity into the system forces the harmonic perturbations to damp faster, however, in the opposite limit larger values of shear viscosity lead to smaller values of density and temperature contrasts. For the hyperbolic case, the dispersion relation becomes a polynomial in the frequency with two orders higher in relation to the five-field theory, indicating that the effects associated with the shear viscosity and heat flux are non-trivial. The profile of Jeans mass in terms of the temperature and number density is explored by contrasting with several data of molecular clouds. Regarding the dynamical evolution of the density, temperature, stress and heat flux contrasts for a universe dominated by pressureless matter, we obtain also damped harmonic waves for small wavelengths. In the case of large wavelengths, the density and temperature contrasts grow with time (due to the Jeans mechanism) while the stress and heat flux contrasts heavily decay with time.