[Paper Review] Detailed Solar System dynamics as a probe of the Dark Matter hypothesis

X. Hernández|arXiv (Cornell University)|Jan 29, 2019

Advanced Thermodynamics and Statistical Mechanics1 references4 citations

TL;DR

This paper argues that the Sun's gravitational interaction with a hypothetical dark matter halo should produce a trailing dynamical friction wake, inducing measurable orbital perturbations in the Solar System. However, precise radio ranging data show no such deviations—ruling out the wake’s existence and strongly disfavoring the dark matter hypothesis as an explanation for galactic dynamics.

ABSTRACT

Within the dark matter paradigm, explaining observed orbital dynamics at galactic level through the inclusion of a dominant dark halo, implies also the necessary appearance of dynamical friction effects. Satellite galaxies, globular clusters and even stars orbiting within these galactic halos, will perturb the equilibrium orbits of dark matter particles encountered, to produce a resulting trailing wake of slightly enhanced dark matter density associated with any perturber in the halo. The principal effect of this gravitational interaction between an orbiting body and the dark matter particles composing it, is the appearance of a frictional drag force slowly removing energy and angular momentum from the perturber. Whilst this effect might be relevant to help bring about the actual merger of the components of interacting forming galaxies, at smaller stellar scales, it becomes negligible. However, the trailing wake will still be present. In this letter I show that the corresponding dark matter wake associated to the Sun, will constitute a small but resonant perturbation on solar system dynamics which can be ruled out, as current laser and radio ranging measurements are now over an order of magnitude more precise than the amplitude of the orbital perturbations which said wake implies. The absence of any such detection implies the nonexistence of the dynamical friction trailing wake on the sun, which in turn strongly disfavours dark matter as an explanation for the observed gravitational anomalies at galactic scales.

Motivation & Objective

• To test the viability of the dark matter hypothesis by examining its dynamical consequences on Solar System orbits.
• To investigate whether the dynamical friction wake trailing the Sun due to dark matter interactions would produce detectable orbital perturbations.
• To use high-precision radio ranging data to constrain the existence of such a wake and thereby test the consistency of the dark matter paradigm.
• To derive upper limits on local dark matter density based on the non-detection of expected perturbations.
• To evaluate whether extended gravity models are more consistent with Solar System observations than dark matter scenarios involving dynamical friction.

Proposed method

• Modeling the Sun's motion through a dark matter halo as a perturber generating a trailing wake via dynamical friction.
• Calculating the radial acceleration perturbation induced by the wake using a quasi-resonant response model derived from gravitational potential gradients.
• Applying the derived perturbation amplitude to planetary orbits (Mars and Saturn) using orbital dynamics equations.
• Comparing predicted perturbations to residuals from the latest INPOP17a ephemerides, which are accurate to ~3.6 m (Mars) and ~31.6 m (Saturn).
• Using statistical significance to assess the probability of observing such perturbations if the dark matter wake were present.
• Deriving upper bounds on local dark matter density by requiring predicted perturbations to lie within observational confidence intervals.

Experimental results

Research questions

• RQ1 Would the dynamical friction wake trailing the Sun due to dark matter interactions produce measurable orbital perturbations in the Solar System?
• RQ2 How do the predicted amplitudes of these perturbations compare to current observational residuals from radio ranging data?
• RQ3 What upper limits on local dark matter density can be derived from the non-detection of such perturbations?
• RQ4 How does the statistical significance of the non-detection challenge the consistency of the dark matter paradigm with Solar System dynamics?
• RQ5 To what extent do extended gravity models remain viable compared to dark matter models that predict such wakes?

Key findings

• The expected radial perturbation amplitude due to the Sun’s dark matter wake is 11.26 meters for Mars and 252 meters for Saturn.
• These predicted perturbations exceed the observational residuals (3.6 m for Mars and 31.6 m for Saturn) by factors of 3.13 and 7.85, respectively.
• The probability of observing such perturbations if the dark matter wake existed is only 0.17% for Mars and 5.7×10⁻¹⁵ for Saturn.
• The non-detection implies an upper limit on local dark matter density below 3.13 times the preferred value of 0.01 M☉ pc⁻³ for Mars, and below 6.8 times for Saturn.
• The results are inconsistent with the standard dark matter halo density of 0.01 M☉ pc⁻³, which is tightly constrained by galactic rotation curves.
• The analysis suggests that extended gravity models are more consistent with Solar System observations than dark matter models producing a dynamical friction wake.