Using entropy to discriminate annihilation channels in neutralinos making up galactic halos

Abstract

Applying the microcanonical definition of entropy to a weakly interacting and self-gravitating neutralino gas, we evaluate the change in the local entropy per particle of this gas between the freeze out era and present day virialized halo structures. An "entropy consistency" criterion emerges by comparing theoretical and empirical estimates of this entropy. We apply this criterion to the cases when neutralinos are mostly B-inos and mostly Higgsinos, in conjunction with the usual "abundance" criterion requiring that present neutralino relic density complies with 0.2 < Ωχ1 0 < 0.4 for h ≃ 0.65. The joint application of both criteria reveals that a much better fitting occurs for the B-ino than for the Higgsino channels, so that the former seems to be a favored channel along the mass range of 155 GeV < mχ1 0 < 230 GeV. These results are consistent with neutralino annihilation patterns that emerge from recent theoretical analysis on cosmic ray positron excess data reported by the HEAT collaboration. The suggested methodology can be applied to test other annihilation channels of the neutralino, as well as other particle candidates of thermal WIMP gas relics.

Constraining the mSUGRA (minimal supergravity) parameter space using the entropy of dark matter halos

“…However, the valid assumptions made for the freeze-out era are no longer valid for such final states, because in galactic halos, neutralinos are mainly subject to longrange interactions, related to non-extensive forms of energy and entropy. Following the guidelines given in [7], a more general approach can be applied instead, it uses the microcanonical ensemble in the "mean field" approximation. This approach is actually valid at both, the initial and final stages.…”

“…The extra parameter α in Eq. (7), which is the proportionality factor between the escape and dispersion velocities at the halo center has a major role in our work. It is very important for the EC that we are able to give values to α in an independent way.…”

“…Computing the entropy per particle for each one of these states, we can use an "entropy consistency" criterion (EC), based on the comparison of theoretical and empirical estimates for this entropy, to obtain an alternative expression for the relic density of neutralinos Ω χ , functionally dependent of the mSUGRA parameters. This idea was originally introduced by some of us in [7].…”

Entropy considerations in constraining the mSUGRA parameter space

“…Such an approach is valid at both the initial ("freeze-out" era, f ) and final (virialized halo structures, h) states that we wish to compare. Under these conditions, the change in the entropy per particle (s) between these two states is given by [10]:…”

“…where x = m χ /T , T is the temperature of the gas. A region that fits with the conditions associated with the intermediate scale is the central region of halos ( 10pc 3 within the halo core); evaluating the thermodynamical quantities at this region, using equation (2) and some assumptions more, it is possible to construct a theoretical estimate for s h that depends on the nature of neutralinos (m χ and σ v ), initial conditions (given by x f ), cosmological parameters (Ω χ , the Hubble parameter, h) and structural parameters of the virialized halo (central values for temperature and density); for details of these and the following, see section IV of [10]. An alternative estimate for s h can be made based on empirical quantities for observed structures in the present Universe using the microcanonical entropy definition in terms of phase space volume, but restricting this volume to the actual range of velocities accessible to the central particles, that is, up to a maximal escape velocity v e (0) which is related to the central velocity dispersion of the halo (σ h ) by an intrinsic parameter α: v 2 e (0) ∼ ασ 2 h (0).…”