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

TL;DR

This paper derives exact formulas for the pericenter precession caused by dark matter distributions and uses them to set constraints based on orbital data from the Solar System, double pulsar, and Galactic center.

Contribution

It provides exact analytical expressions for dark matter-induced precession without simplifying assumptions, enabling precise constraints in various astrophysical contexts.

Findings

Constraints on dark matter density profiles in the Solar System.

Limits on dark matter around the double pulsar system.

Bounds on dark matter near the Galactic center.

Abstract

We analytically calculate the secular precession of the pericenter of a test particle orbiting a central body surrounded by a continuous distribution of Dark Matter (DM) by using some commonly adopted density profiles for it. We obtain exact expressions without resorting to a-priori simplifying assumptions on the orbital geometry of the test particle. Our formulas allow us to put constraints on the parameters of the DM distributions considered in several local astronomical and astrophysical scenarios, such as the Sun's planetary system, the double pulsar, and the stellar system around the supermassive black hole in Sgr A$^{\ast}$, all characterized by a wide variety of orbital configurations.