Abstract
We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular equation of state (ideal gas) and imperfect fluid terms due to the relative energy flux between the two species. We derive closed sets of GIC vector and subsequently scalar evolution equations. We then investigate solutions in different regimes of interest. In particular, we study long-wavelength and arbitrary-wavelength Langmuir and ion-acoustic perturbations. The harmonic oscillations are superposed on a Jeans-type instability. We find a generalized Jeans criterion for collapse in a two-temperature plasma, which states that the species with the largest sound velocity determines the Jeans wavelength. Furthermore, we find that within the limit for gravitational collapse, initial perturbations in either the total density or charge density lead to a growth in the initial temperature difference. These results are relevant for the basic understanding of the evolution of inhomogeneities in cosmological models.
Highlights
Plasmas and electromagnetic fields are common in our Universe
From (35a) we find that an initial perturbation in either the total density or the charge density causes a pertur bation o f the expansion, unless the plasma consists o f electrons and positrons with m = 0;
From (40) we find that in an equal temperature plasma the rela tive temperature perturbation only fluctuates with the oscillation in the charge density, but by allowing for a temperature differ ence in the background (|a | > 0 ) the temperature difference grows as a power-law during gravitational collapse
Summary
Plasmas and electromagnetic fields are common in our Universe. They play an important role in a diverse setting of astrophysical and cosmological processes. There are occasions when general relativistic gravity has to be taken into account in conjunction with plasma physics, such as in the close vicinity of the aforementioned rotating black holes. Another prominent example is our Universe, in which the plasma state has over time been more or less prominent. We formulate the set of governing equations for the plasma dynamics on a general relativistic background These equations are analysed by perturbing the two-fluid model around an isotropic and homo geneous background using the covariant gauge invariant approach. Local fluctuations might occur and more importantly we hope to apply the generalized two-fluid equa tions derived in this paper to other two-temperature fluids in fu ture papers, such as dark matter - ordinary matter, decoupled free streaming neutrinos in the early universe and possibly the advection dominated accretion flows onto black holes, where the electrons and protons are thought to be out of thermal equilibrium
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