[Paper Review] Dark matter bound to the Solar System: consequences for annihilation searches

Annika H. G. Peter|ArXiv.org|May 15, 2009

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper re-evaluates dark matter annihilation signals in the Solar System by modeling the orbital evolution of WIMPs bound to the Sun and Earth, showing that gravitational perturbations from planets significantly alter WIMP phase-space densities. It finds that neutrino and near-solar γ-ray fluxes are suppressed by orders of magnitude compared to standard assumptions, challenging prior detection prospects.

ABSTRACT

One method to search for particle dark matter is to hunt down its annihilation products. In the Solar System, three potential types of signals of annihilation have been identified: neutrinos and gamma-rays from the Sun, and neutrinos from the Earth. Each of these signals depends sensitively on the orbital evolution of dark matter once it becomes bound to the Solar System. I will review progress on characterizing these signals based on recent improvements in the determination of the properties of the bound dark matter population.

Motivation & Objective

• To improve estimates of WIMP annihilation signals in the Solar System by accounting for the orbital evolution of bound dark matter.
• To quantify how gravitational perturbations from planets alter the phase-space density of WIMPs captured by the Sun and Earth.
• To assess the detectability of near-solar γ-rays from WIMP annihilation, challenging earlier optimistic predictions.
• To evaluate the impact of non-thermalized WIMP populations on neutrino fluxes from the Sun, particularly for heavy WIMPs.
• To highlight the critical dependence of detection sensitivity on accurate astrophysical modeling of WIMP dynamics

Proposed method

• Simulates the orbital evolution of WIMPs captured by the Sun using Monte Carlo realizations of scattering processes and gravitational perturbations.
• Models WIMP energy loss per scattering using the energy transfer formula $ Q \sim m_A v_{\text{esc}}^2 $, where $ m_A $ is the target nucleus mass.
• Calculates thermalization timescales based on the ratio of orbital energy $ E \sim -m_\chi v_{\text{esc}}^2 (R_\odot / a) $ to energy loss per scatter $ Q $.
• Compares phase-space densities from simulations to the free-space phase density used in earlier studies (e.g., Gould's model).
• Estimates γ-ray fluxes from WIMP annihilation just outside the Sun, incorporating gravitational focusing and orbital decay.
• Evaluates background fluxes from cosmic ray interactions and inverse-Compton scattering to assess detectability of WIMP signals

Experimental results

Research questions

• RQ1 How do planetary gravitational torques affect the phase-space distribution of WIMPs bound to the Solar System?
• RQ2 To what extent is the WIMP annihilation rate in the Sun suppressed due to incomplete thermalization and finite scattering timescales?
• RQ3 What is the true flux of near-solar γ-rays from WIMP annihilation, and how does it compare to astrophysical backgrounds?
• RQ4 How do the results from detailed simulations differ from the standard assumption of free-space phase density in WIMP signal calculations?
• RQ5 Can WIMP annihilation signals in the Solar System be detected with current or planned neutrino and γ-ray telescopes?

Key findings

• For a 100 GeV WIMP with spin-dependent scattering cross section $ \sigma_p^{\text{SD}} \approx 10^{-49}\,\text{cm}^2 $, thermalization in the Sun takes longer than the age of the Solar System.
• For a 10 TeV WIMP, thermalization timescales exceed the age of the Solar System unless $ \sigma_p^{\text{SD}} \approx 10^{-44}\,\text{cm}^2 $, indicating significant non-thermal populations.
• The phase-space density of bound WIMPs is suppressed by up to three orders of magnitude compared to the free-space phase density used in earlier models.
• Near-solar γ-ray fluxes are estimated at $ \sim 10^{-7}\,\text{km}^{-2}\text{yr}^{-1} $ for $ m_\chi = 1\,\text{TeV} $, but are further suppressed by gravitational effects and astrophysical backgrounds.
• Cosmic ray-induced γ-ray fluxes from the Sun (e.g., $ \sim 3 \times 10^{-7}\,\text{cm}^{-2}\text{s}^{-1} $ above 100 MeV) vastly exceed any WIMP-induced signal, making detection nearly impossible.
• Neutrino fluxes from the Sun are reduced by orders of magnitude due to incomplete thermalization, especially for heavy WIMPs, undermining prior constraints based on thermal equilibrium assumptions.