Influence of Dark Matter on Light Propagation in Solar System

Abstract

We investigated the influence of dark matter on light propagation in the solar system. We assumed the spherical symmetry of spacetime and derived the approximate solution of the Einstein equation, which consists of the gravitational attractions caused by the central celestial body, i.e. the Sun, and the dark matter surrounding it. We expressed the dark matter density in the solar system in the following simple power-law form, $\varrho (t,r)=\rho (t)(\ell /r{)}^k$, where $t$ is the coordinate time; $r$, the radius from the central body; $\ell$, the normalizing factor; $k$, the exponent characterizing $r$-dependence of dark matter density; and $\rho (t)$, the arbitrary function of time $t$. On the basis of the derived approximate solution, we focused on light propagation and obtained the additional corrections of the gravitational time delay and the relative frequency shift caused by the dark matter. As an application of our results, we considered the secular increase in the astronomical unit reported by Krasinsky and Brumberg (2004) and found that it was difficult to provide an explanation for the observed $d\mathrm{AU}/dt=15\pm 4[m/century]$.

18 pages, 4 figures, accepted for publication in Advances in Space Research

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Cited by in corpus (9)

• Gravitational Anomalies in the Solar System?
• Testing Theories of Gravity with Planetary Ephemerides
• Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law
• An Empirical Explanation of the Anomalous Increases in the Astronomical Unit and the Lunar Eccentricity
• 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
• Effect of Sun and Planet-Bound Dark Matter on Planet and Satellite Dynamics in the Solar System
• The Flyby Anomaly and the Effect of a Topological Torsion Current
• Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit
• Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit