[Paper Review] Universal gravothermal evolution of isolated self-interacting dark matter halos for velocity-dependent cross sections

Nadav Joseph Outmezguine, Kimberly K. Boddy+3 more|arXiv (Cornell University)|Apr 13, 2022

Advanced Thermodynamics and Statistical Mechanics4 citations

TL;DR

This paper investigates the universal gravothermal evolution of isolated self-interacting dark matter (SIDM) halos with velocity-dependent cross sections, showing that their core collapse dynamics are approximately universal and can be mapped onto constant-cross-section models using a timescale defined at minimum central density. The key result is that collapse time depends primarily on an average cross section at the core's minimum density, with less than 3% variation due to velocity dependence, enabling robust modeling of SIDM halos across diverse particle physics scenarios.

ABSTRACT

We study the evolution of isolated self-interacting dark matter (SIDM) halos using spherically-symmetric gravothermal equations allowing for the scattering cross section to be velocity dependent. We focus our attention on the large class of models where the core is in the long mean free path regime for a substantial time. We find that the temporal evolution exhibits an approximate universality that allows velocity-dependent models to be mapped onto velocity-independent models in a well-defined way using the scattering timescale computed when the halo achieves its minimum central density. We show how this timescale depends on the halo parameters and an average cross section computed at the central velocity dispersion when the central density is minimum. The predicted collapse time is fully defined by the scattering timescale, with negligible variation due to the velocity dependence of the cross section. We derive new self-similar solutions that provide an analytic understanding of the numerical results.

Motivation & Objective

• To understand the universal evolution of isolated SIDM halos under velocity-dependent self-interaction cross sections.
• To determine whether the details of velocity-dependent scattering can be systematically removed via time scaling, enabling mapping to constant-cross-section models.
• To quantify the core collapse timescale in terms of halo parameters and particle physics inputs, especially the average cross section at minimum central density.
• To derive self-similar solutions that explain the inner halo structure and evolution in the long mean free path (LMFP) regime.
• To provide a framework for testing and calibrating analytic SIDM models against N-body simulations using measurable quantities like $V_{\rm max}$ and $r_s$.

Proposed method

• Solving spherically-symmetric gravothermal equations with mass conservation, hydrostatic equilibrium, and energy transport via a heat flux ansatz.
• Incorporating velocity-dependent cross sections through a general parametrization, including Yukawa-type and resonant $s$-wave scattering models.
• Defining a scattering timescale based on the cross section evaluated at the core's minimum central density and corresponding velocity dispersion.
• Deriving self-similar solutions valid in the long mean free path (LMFP) regime to analytically describe core evolution and collapse.
• Calibrating the effective average cross section $\sigma_{c,0}$ and velocity dependence exponent $n$ using numerical results and comparing to N-body simulations.
• Mapping velocity-dependent models onto constant-cross-section models via a rescaling of time using the scattering timescale at minimum central density.

Experimental results

Research questions

• RQ1 Does the gravothermal evolution of SIDM halos with velocity-dependent cross sections exhibit approximate universality, independent of the specific velocity dependence?
• RQ2 Can velocity-dependent models be systematically mapped onto constant-cross-section models using a well-defined timescale?
• RQ3 How does the core collapse timescale depend on halo parameters and the average cross section at minimum central density?
• RQ4 To what extent is the collapse timescale sensitive to the velocity dependence of the cross section?
• RQ5 Can self-similar solutions accurately describe the inner halo structure and evolution in the LMFP regime for generic velocity-dependent cross sections?

Key findings

• The core collapse timescale depends primarily on the average cross section $\sigma_{c,0}$ evaluated at the core's minimum central density and corresponding velocity dispersion, with less than 3% variation due to velocity dependence.
• The halo evolves to a maximal core size $r_{\rm core,0} \simeq 0.45 r_s$ with central density $\rho_{c,0} \simeq 2.4 \rho_s$ and 1D velocity dispersion $v_{c,0} \simeq 0.64 V_{\rm max}$, independent of the velocity dependence of the cross section.
• The temporal evolution is dominated by the long mean free path (LMFP) regime for a large portion of model space, where the effective conductivity depends on an average cross section $\sigma_{c,0}$.
• Self-similar solutions are derived for the LMFP regime and provide a good qualitative explanation for the numerical results, though they slightly overestimate the timescale variation due to velocity dependence.
• The gravothermal evolution is nearly universal: vastly different velocity-dependent cross section models yield the same halo evolution when scaled by the scattering timescale at minimum central density.
• The results enable direct application of analytic SIDM models developed for constant cross sections to velocity-dependent cases by using $\sigma_{c,0}$ and $n$ as input parameters, with $V_{\rm max}$ and $r_s$ as measurable observables.