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

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 ΔM/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)

LaTex2e, 17 pages, no figures, 7 tables, 61 references. Small problem with a reference fixed. To appear in Journal of Cosmology and Astroparticle Physics (JCAP)

References in corpus (20)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Clumps and streams in the local dark matter distribution
• Distant future of the Sun and Earth revisited
• Dark matter vs. modifications of the gravitational inverse-square law. Results from planetary motion in the solar system
• ASTROD and ASTROD I -- Overview and Progress
• Dark matter in the solar system I: The distribution function of WIMPs at the Earth from solar capture
• Dark matter in the solar system II: WIMP annihilation rates in the Sun
• The Zero Age Main Sequence of WIMP burners
• Dark matter in the solar system III: The distribution function of WIMPs at the Earth from gravitational capture
• Can the flyby anomaly be attributed to earth-bound dark matter?
• Bound on the Dark Matter Density in the Solar System from Planetary Motions
• Uranus's anomalously low excess heat constrains strongly interacting dark matter
• Solar System planetary orbital motions and dark matter
• Planet-bound dark matter and the internal heat of Uranus, Neptune, and hot-Jupiter exoplanets
• Placing direct limits on the mass of earth-bound dark matter
• Capture of dark matter by the Solar System
• Density of dark matter in Solar system and perihelion precession of planets
• Influence of Dark Matter on Light Propagation in Solar System
• Local dark matter searches with LISA
• Classical and relativistic orbital motions around a mass-varying body

Cited by in corpus (15)

• Relativistic effects and dark matter in the Solar system from observations of planets and spacecraft
• Constraints on Dark Matter in the Solar System
• Dark-matter admixed white dwarfs
• Equilibrium Structure and Radial Oscillations of Dark Matter Admixed Neutron Stars
• On the anomalous secular increase of the eccentricity of the orbit of the Moon
• Solar System constraints on local dark matter density
• Orbital effects of non-isotropic mass depletion of the atmospheres of evaporating hot Jupiters in extrasolar systems
• Exact expressions for the pericenter precession caused by some Dark Matter distributions and constraints on them from orbital motions in the Solar System, in the double pulsar and in the Galactic center
• Accretion-Induced Collapse of Dark Matter Admixed White Dwarfs -- I: Formation of Low-mass Neutron Stars
• Brane matter, hidden or mirror matter, their various avatars and mixings: many faces of the same physics
• A halo of trapped interstellar matter surrounding the solar system
• Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl gravity
• Constraining dark matter sub-structure with the dynamics of astrophysical systems
• Re-Examination of Globally Flat Space-Time
• Capture rate of weakly interacting massive particles (WIMPs) in binary star systems