[Paper Review] Comments on recent work on dark-matter capture in the Solar System

Joakim Edsjö, Annika H. G. Peter|arXiv (Cornell University)|Apr 29, 2010

Dark Matter and Cosmic Phenomena6 citations

TL;DR

This paper challenges recent claims of massive dark-matter enhancements in the Solar System by demonstrating that neglecting gravitational ejection of dark matter particles leads to gross overestimations. By applying detailed balance and including both capture and ejection processes, the authors show that the equilibrium dark-matter density bound to the Solar System is only modestly higher than the local Galactic halo density, not orders of magnitude greater as previously claimed.

ABSTRACT

Recently, several papers have appeared that examine the process of capturing dark-matter particles from the Galactic halo to orbits bound to the Solar System. The authors of these papers predict large enhancements to the local dark-matter density via gravitational three-body interactions with planets. However, these conclusions are wrong; these papers do not include the inverse process to capture, namely the ejection of dark-matter particles by three-body gravitational encounters. We emphasize previous work that shows that by including both capture and ejection of dark matter from the Solar System, the density of dark matter bound to the Solar System is small compared to the local Galactic dark-matter density.

Motivation & Objective

• To challenge recent claims of large dark-matter density enhancements in the Solar System due to gravitational three-body interactions.
• To highlight the critical omission of ejection processes in recent studies that overestimate bound dark-matter populations.
• To reaffirm that detailed balance between capture and ejection limits the equilibrium dark-matter density in the Solar System to levels comparable to the local Galactic halo density.
• To demonstrate that numerical and analytical models including both processes yield significantly lower bound dark-matter densities than those reported in Xu & Siegel, Khriplovich & Shepelyansky, and Khriplovich.

Proposed method

• Apply detailed balance arguments to show that equilibrium phase-space density of bound dark matter matches the Galactic halo distribution when velocity is transformed from heliocentric to local rest frame.
• Use the analytical framework of Gould (1991) to model gravitational three-body interactions between dark-matter particles, planets, and the Sun.
• Incorporate numerical simulations from Lundberg & Edsjö (2004) and Peter (2009) to validate the equilibrium behavior of dark-matter populations.
• Analyze the timescales for equilibrium to be reached, showing that for many phase-space regions, equilibrium is achieved within the age of the Solar System.
• Compare the results of models that include ejection with those that neglect it, showing the latter overestimate bound dark-matter densities by orders of magnitude.
• Assess the role of weak interactions (e.g., with solar nuclei) as a potential mechanism for extended particle lifetimes, but find such effects insufficient to significantly boost the bound population.

Experimental results

Research questions

• RQ1 What is the true equilibrium density of dark-matter particles bound to the Solar System when both capture and ejection are included?
• RQ2 Why do recent studies claiming large dark-matter enhancements fail to account for the inverse process of ejection?
• RQ3 How do the timescales for equilibrium in the bound dark-matter population compare to the age of the Solar System?
• RQ4 To what extent can weak interactions with solar or planetary matter prolong the lifetime of captured dark-matter particles and enhance their density?
• RQ5 What is the quantitative difference between models that include ejection and those that do not in predicting the bound dark-matter density?

Key findings

• The equilibrium phase-space density of dark-matter particles bound to the Solar System is approximately equal to the corresponding phase-space density in the Galactic halo, when velocities are transformed between the heliocentric and local rest frames.
• The inclusion of ejection processes reduces the predicted bound dark-matter density by many orders of magnitude compared to models that neglect ejection.
• For most regions of phase space, equilibrium is reached on timescales shorter than the age of the Solar System, meaning the bound population stabilizes at a low level.
• Numerical simulations confirm that detailed balance holds, and the bound dark-matter density remains small compared to the local Galactic halo density.
• Even with weak interactions in the Sun, the resulting population of long-lived bound dark-matter particles remains small, with no significant enhancement of the overall bound density.
• The observed short lifetimes of small bodies in the Solar System (e.g., comets and planetesimals on Myr timescales) provide a strong analogy for why dark-matter particles cannot accumulate indefinitely without ejection.