[Paper Review] Thermal transport of the solar captured dark matter and its impact on the indirect dark matter search

Chian-Shu Chen, Guey-Lin Lin+1 more|arXiv (Cornell University)|Aug 21, 2015

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper investigates thermal energy transport in solar-captured self-interacting dark matter (SIDM), showing that DM temperature can exceed the solar core temperature when DM-nucleon scattering is weak. The key result is that using the correct DM temperature—higher than solar core temperature—can enhance indirect detection signals by up to a factor of 3.5 in certain scenarios, significantly improving annihilation rate predictions beyond standard assumptions of thermal equilibrium with the Sun.

ABSTRACT

We study the thermal transport occurring in the system of solar captured dark matter (DM) and explore its impact on the DM indirect search signal. We particularly focus on the scenario of self-interacting DM (SIDM). The flows of energies in and out of the system are caused by solar captures via DM-nucleon and DM-DM scatterings, the energy dissipation via DM annihilation, and the heat exchange between DM and solar nuclei. We examine the DM temperature evolution and demonstrate that the DM temperature can be higher than the core temperature of the Sun if the DM-nucleon cross section is sufficiently small such that the energy flow due to DM self-interaction becomes relatively important. We argue that the correct DM temperature should be used for accurately predicting the DM annihilation rate, which is relevant to the DM indirect detection.

Motivation & Objective

• To investigate how thermal energy transport affects the temperature of dark matter (DM) trapped in the Sun, particularly in the self-interacting DM (SIDM) scenario.
• To determine whether the DM temperature deviates from the solar core temperature due to suppressed DM-nucleon scattering and enhanced DM self-interactions.
• To assess the impact of accurate DM temperature on indirect dark matter detection rates, especially annihilation signals.
• To derive and solve the thermal transport equation for trapped DM, accounting for energy flows from capture, self-interaction, and heat exchange with solar nuclei.

Proposed method

• The authors model the time evolution of trapped DM number and energy using coupled differential equations for DM number density and kinetic energy, incorporating capture, self-interaction, and annihilation rates.
• They derive thermal transport coefficients $ J_c, J_s, J_χ, J_a $ corresponding to DM-nucleon scattering, DM self-interaction, heat exchange with nuclei, and annihilation, respectively.
• The system is analyzed under the condition $ C_s^2 \gg 4C_cC_a $, where self-interaction dominates, allowing simplification of the energy evolution equation.
• The DM temperature $ T_\chi $ is computed by solving $ \frac{dE_\chi}{dt} \approx J_\chi + J_s - C_s E_\chi $, with $ J_\chi \propto (T_\chi - T_c)/m_\chi $, showing that $ T_\chi $ can exceed $ T_c $ for heavy DM.
• Numerical solutions are performed for varying $ \sigma_{\chi p} $, $ \sigma_{\chi\chi} $, and $ m_\chi $, with initial conditions tested for robustness.
• The annihilation rate $ \Gamma_A \propto C_a N_\chi^2 $ is compared under $ T_\chi = T_c $ and $ T_\chi > T_c $, revealing signal enhancements when $ T_\chi $ is correctly modeled.

Experimental results

Research questions

• RQ1 Can the temperature of self-interacting dark matter trapped in the Sun exceed the solar core temperature due to suppressed DM-nucleon scattering?
• RQ2 How does DM self-interaction influence the thermal equilibrium between trapped DM and solar nuclei?
• RQ3 What is the impact of using the true DM temperature on the predicted indirect detection signal from DM annihilation in the Sun?
• RQ4 Does the enhancement in the annihilation rate depend on the DM mass and self-interaction cross section?
• RQ5 How robust is the final DM temperature to uncertainties in the initial thermalization timescale?

Key findings

• The DM temperature $ T_\chi $ can exceed the solar core temperature $ T_c $, reaching up to $ T_\chi / T_c \sim 3.5 $ for $ \sigma_{\chi\chi} = 10^{-23}~{\rm cm^2} $ and $ m_\chi = 50~{\rm GeV} $, when $ \sigma_{\chi p} $ is small.
• For $ \sigma_{\chi p} = 10^{-47}~{\rm cm^2} $, the DM temperature reaches $ T_\chi \sim 3.5 T_c $, significantly increasing the annihilation rate compared to assuming $ T_\chi = T_c $.
• The annihilation rate $ \Gamma_A $ is enhanced when $ T_\chi > T_c $, because the increase in $ N_\chi $ from reduced annihilation rates at higher $ T_\chi $ can outweigh the suppression in $ C_a \propto T_\chi^{-3/2} $.
• When $ \sigma_{\chi\chi} = 10^{-24}~{\rm cm^2} $, $ N_\chi $ continues to grow linearly, and $ \Gamma_A(T_\chi) < \Gamma_A(T_c) $, showing signal suppression under certain parameter choices.
• The final DM temperature $ T_\chi(t_\odot) $ is independent of initial conditions, converging to a stable fixed point determined by $ \sigma_{\chi\chi} $, $ \sigma_{\chi p} $, and $ m_\chi $, confirming robustness of the result.
• The thermal equilibrium time scale $ \tau^{\rm eq}_\chi $ does not affect the final $ T_\chi $, as long as the system reaches steady state, validating the model's consistency.