Effect of Sun and Planet-Bound Dark Matter on Planet and Satellite Dynamics in the Solar System

TL;DR

This paper investigates how Sun and planet-bound Dark Matter accretion affects orbital dynamics in the solar system, suggesting observable secular changes in planetary orbits and implications for planetary evolution over billions of years.

Contribution

It introduces a model linking Dark Matter accretion to orbital variations, providing new estimates consistent with observational data and exploring long-term planetary evolution.

Findings

Earth's orbit increases by 0.02-0.05 m/yr, matching observed AU secular increase.

Planetary orbits could have shifted by 10^-2 to 10^1 au over 4.5 Gyr due to Dark Matter.

Upper bounds on Sun's gravitational parameter variation are consistent with Dark Matter accretion rates.

Abstract

We apply our recent results on orbital dynamics around a mass-varying central body to the phenomenon of accretion of Dark Matter-assumed not self-annihilating-on the Sun and the major bodies of the solar system due to its motion throughout the Milky Way halo. We inspect its consequences on the orbits of the planets and their satellites over timescales of the order of the age of the solar system. It turns out that a solar Dark Matter accretion rate of \approx 10^-12 yr^-1, inferred from the upper limit \Delta M/M= 0.02-0.05 on the Sun's Dark Matter content, assumed somehow accumulated during last 4.5 Gyr, would have displaced the planets faraway by about 10^-2-10^1 au 4.5 Gyr ago. Another consequence is that the semimajor axis of the Earth's orbit, approximately equal to the Astronomical Unit, would undergo a secular increase of 0.02-0.05 m yr^-1, in agreement with the latest observational determinations of the Astronomical Unit secular increase of 0.07 +/- 0.02 m yr^-1 and 0.05 m yr^-1. By assuming that the Sun will continue to accrete Dark Matter in the next billions year at the same rate as in the past, the orbits of its planets will shrink by about 10^-1-10^1 au (\approx 0.2-0.5 au for the Earth), with consequences for their fate, especially of the inner planets. On the other hand, lunar and planetary ephemerides set upper bounds on the secular variation of the Sun's gravitational parameter GM which are one one order of magnitude smaller than 10^-12 yr^-1. Dark Matter accretion on planets has, instead, less relevant consequences for their satellites. Indeed, 4.5 Gyr ago their orbits would have been just 10^-2-10^1 km wider than now. (Abridged)