Gravitational instability of the primordial plasma: Anisotropic evolution of structure seeds

Abstract

We study how the presence of a background magnetic field, of intensity compatible with current observation constraints, affects the linear evolution of cosmological density perturbations at scales below the Hubble radius. The magnetic field provides an additional pressure that can prevent the growth of a given perturbation; however, the magnetic pressure is confined only to the plane orthogonal the field. As a result, the "Jeans length" of the system not only depends on the wavelength of the fluctuation but also on its direction, and the perturbative evolution is anisotropic. We derive this result analytically and back it up with direct numerical integration of the relevant ideal magnetohydrodynamics equations during the matter-dominated era. Before recombination, the kinetic pressure dominates and the perturbations evolve in the standard way, whereas after that time magnetic pressure dominates and we observe the anisotropic evolution. We quantify this effect by estimating the eccentricity epsilon of a Gaussian perturbation in the coordinate space that was spherically symmetric at recombination. For a perturbations at the sub-galactic scale, we find that epsilon = 0.7 at z = 10 taking the background magnetic field of order 10^(-9) gauss

Linear perturbations of an anisotropic Bianchi I model with a uniform magnetic field

“…with x i given by (97) with Λ S = 0, or equivalently by (102). If we compare our result with [5], we identify the anisotropic behaviour and we obtain the correct Newtonian limit of [24]. However, our solutions are different and we are unable to explain such discrepancy: we can argue they may have found some sort of average effect, however this is not clear, given the strong anisotropy of the model: the magnetic Jeans wavenumber is present only in one direction, the one with µ = 0.…”

“…While formally the best solution to this problem would be using a two fluid model, with a different equation of state for perturbations, here we will simply drop the relation between v 2 S and w and assume that the perturbed fluid follows a different equation of state with respect to the background fluid. This is correct in the Newtonian approximation and it's in fact the standard way of handling things [39,24], while putting v 2 S = 0 at the end will recover the full covariant value of our calculations for studying pure magnetic effects.…”

“…Condition (103) is the standard Jeans condition [39]: using (89) and (26), eq. (103) translates in [24] k…”

“…The first one means that, in any direction but orthogonal to the background magnetic field, the only necessary condition is the standard one. The second one is an additional condition that must hold for perturbations propagating orthogonally to the background magnetic field, and using (89) and (26) it reads [24] k…”

“…while at perturbative level every dependence on CDM disappears, except from background quantities. We choosed to study the same scales of [24], i.e. k ≈ (17, 1.7, 0.37) Mpc −1 normalized at present time, corresponding to baryonic masses of M ≈ (1.5 × 10 8 , 1.5 × 10 11 , 1.5 × 10 13 ) M and roughly equivalent respectively to a dwarf galaxy, a galaxy and a galaxy cluster.…”