[Paper Review] Solar System Dark Matter

Stephen L. Adler|ArXiv.org|Mar 27, 2009

Dark Matter and Cosmic Phenomena3 references3 citations

TL;DR

This paper investigates the possibility of Earth- and planet-bound dark matter, proposing that such dark matter could explain anomalous velocity changes in spacecraft flybys. Using orbital tracking data from LAGEOS, lunar orbiters, and lunar laser ranging, the author derives a tight upper bound on Earth-bound dark matter mass, suggesting it could be as dense as ~6×10¹⁰ GeV/c²cm³, and explores its potential role in flyby anomalies via elastic and inelastic scattering with spacecraft nuclei.

ABSTRACT

I review constraints on solar system-bound dark matter, and discuss the possibility that dark matter could be gravitationally bound to the earth and other planets. I briefly survey various empirical constraints on such planet-bound dark matter, and discuss effects it could produce if present, including anomalous planetary heating and flyby velocity changes.

Motivation & Objective

• To assess the feasibility of dark matter gravitationally bound to Earth and other planets.
• To derive observational constraints on Earth-bound dark matter using precise satellite and lunar tracking data.
• To investigate whether dark matter scattering could explain unexplained velocity changes in planetary flybys.
• To model dark matter distributions and scattering dynamics that could produce measurable effects on spacecraft trajectories.

Proposed method

• Uses LAGEOS satellite tracking and lunar laser ranging to measure the combined gravitational parameter GM_combined, isolating the contribution from Earth-bound dark matter.
• Applies the relation GM_dm ≈ GM_combined - GM_⊕ - GM_⊕/R_⊕/m to bound the mass of dark matter between Earth and Moon.
• Models dark matter as a truncated spherical shell at radius r and angle χ relative to Earth's rotation axis, with two velocity components per point.
• Calculates cross-section-averaged velocity changes from elastic and inelastic scattering between dark matter particles and spacecraft nucleons.
• Integrates work increments over the spacecraft orbit to compute net energy and velocity changes.
• Performs a parameter space search over dark matter mass, cross section, and orbital configuration to fit flyby anomaly data.

Experimental results

Research questions

• RQ1 What upper bound can be placed on the mass of dark matter gravitationally bound to Earth using current orbital tracking data?
• RQ2 Could Earth-bound dark matter explain the anomalous velocity changes observed in spacecraft flybys?
• RQ3 What properties must dark matter possess to produce both velocity decreases and increases in flybys via scattering with spacecraft nuclei?
• RQ4 How do the orbital dynamics and velocity distributions of dark matter in a spherical shell affect the net momentum transfer to a spacecraft?
• RQ5 Can a two-species dark matter model with elastic and inelastic scattering reproduce the observed flyby anomalies?

Key findings

• The upper bound on Earth-bound dark matter mass is GM_dm ≈ (0.3 ± 4) × 10⁻⁹ GM_⊕, implying a maximum density of ~6×10¹⁰ GeV/c²cm³ if uniformly distributed.
• The derived bound is significantly higher than galactic halo dark matter density and the upper limit for sun-bound dark matter.
• Earth-bound dark matter could produce velocity changes in flybys if it has a mass much less than 1 GeV and a nucleon scattering cross section of 10⁻³³ to 10⁻²⁷ cm².
• Velocity decreases arise from elastic scattering, while velocity increases result from exothermic inelastic scattering into lighter dark matter states.
• The required dark matter must be non-self-annihilating and stable in the absence of nucleons, differing from standard weakly interacting massive particle (WIMP) models.
• A two-species dark matter model with distinct elastic and inelastic scattering components is proposed to fit the Anderson group's flyby anomaly data.