[Paper Review] Damping of inhomogeneities in neutralino dark matter

Dominik J. Schwarz, Hofmann, Stefan+1 more|arXiv (Cornell University)|Oct 29, 2001

Dark Matter and Cosmic Phenomena12 references3 citations

TL;DR

This paper investigates damping mechanisms—collisional damping during kinetic decoupling and free streaming after last scattering—that suppress primordial density inhomogeneities in neutralino cold dark matter (CDM). It shows these processes impose a sharp cut-off in the power spectrum, setting a minimal halo mass of ~10⁻⁶ M☉ for the first gravitationally bound CDM structures, challenging prior estimates that underestimated the cut-off by assuming chemical and kinetic decoupling occurred simultaneously.

ABSTRACT

The lightest supersymmetric particle, most likely the neutralino, might account for a large fraction of dark matter in the Universe. We show that the primordial spectrum of density fluctuations in neutralino cold dark matter (CDM) has a sharp cut-off due to two damping mechanisms: collisional damping during the kinetic decoupling of the neutralinos at O(10 MeV) and free streaming after last scattering of neutralinos. The cut-off in the primordial spectrum defines a minimal mass for CDM objects in hierarchical structure formation. For typical neutralino and sfermion masses the first gravitationally bound neutralino clouds have masses above 10^(-6) M_\odot.

Motivation & Objective

• To determine the smallest mass scale for gravitationally bound neutralino dark matter structures.
• To analyze the combined effects of collisional damping during kinetic decoupling and free streaming after last scattering on primordial density perturbations.
• To correct prior overestimations of the free streaming cut-off by accounting for the correct timing of kinetic decoupling relative to chemical decoupling.
• To quantify the minimal halo mass in neutralino CDM models using kinetic theory and transport coefficients.

Proposed method

• Modeling neutralino CDM as an imperfect fluid with bulk and shear viscosity to describe collisional damping during kinetic decoupling at ~40 MeV.
• Calculating the relaxation time τ from elastic scattering cross-sections involving slepton exchange to determine kinetic decoupling temperature.
• Using linearized kinetic theory to derive the exponential damping of density perturbations due to viscosity, with a cut-off scale M_d ∝ (Tτ/M_χ)^{3/2}.
• Analyzing free streaming damping post-decoupling using the free streaming length and scale factor evolution, with damping proportional to exp[−(M_fs/M)^{2/3}].
• Deriving the ratio M_fs/M_d = [√(5/3) ln(a/a_kd)]³ to compare dominance of free streaming over collisional damping after kinetic decoupling.
• Evaluating the free streaming mass at matter-radiation equality using T_kd = 40 MeV and (Ω_cdm + Ω_b)h² = 0.15 to obtain M_fs(a_eq) ≈ 5×10⁻⁶ M☉ for M_χ = 150 GeV.

Experimental results

Research questions

• RQ1 What is the minimal mass scale for the first gravitationally bound neutralino dark matter structures?
• RQ2 How do collisional damping and free streaming jointly affect the primordial power spectrum of CDM density perturbations?
• RQ3 Why do prior estimates of the free streaming cut-off mass differ significantly from the actual value?
• RQ4 At what point does free streaming dominate over collisional damping in damping small-scale inhomogeneities?
• RQ5 How does the timing of kinetic decoupling relative to chemical decoupling influence the final cut-off scale?

Key findings

• The primordial power spectrum of neutralino CDM exhibits a sharp cut-off due to collisional damping and free streaming, suppressing structure formation below ~10⁻⁶ M☉.
• For typical neutralino and sfermion masses (M_χ ≈ 150 GeV, M_sleptons ≈ 250 GeV), the minimal halo mass is approximately 5×10⁻⁶ M☉ at matter-radiation equality.
• The free streaming mass at equality, M_fs(a_eq), is about 1.3×10⁴ times larger than the collisional damping mass M_d, indicating free streaming dominates the cut-off.
• The ratio M_fs/M_d exceeds unity when the scale factor doubles after kinetic decoupling, confirming that free streaming becomes the dominant damping mechanism after this point.
• The study corrects prior literature estimates that assumed simultaneous chemical and kinetic decoupling, which led to an overestimation of the cut-off scale by a factor of ~10⁷.
• The results are robust across typical supersymmetric parameter ranges, indicating the minimal halo mass is insensitive to detailed model parameters.