On the time-dependent density of quadratically coupled dark matter around ordinary matter objects

TL;DR

This paper investigates how quadratic couplings of wave-like dark matter to ordinary matter influence the time-dependent density around objects like planets and stars, affecting detection sensitivity and force interactions.

Contribution

It analyzes the time evolution of dark matter density around spherical objects and clarifies when stationary solutions are valid for experimental detection.

Findings

Determines the time-scale for dark matter fields to reach stationary states.

Clarifies the conditions under which stationary solutions are applicable.

Provides a method to eliminate infinities in energy and force calculations.

Abstract

Wave-like dark matter may feature quadratic couplings to ordinary matter. This carries profound consequences for the phenomenologies of such models. It changes the dark matter density around dense objects made from ordinary matter such as planets and stars, thereby changing the sensitivity of direct detection experiments on Earth as well as implying forces on other ordinary matter objects in the vicinity. In this note we study the time dependence of the dark matter field around spherical objects of ordinary matter. This work indicates the time-scale on which accelerating objects settle into a stationary state and delineates the applicability of stationary solutions for experimental dark matter tests. We also use this to understand (and effectively eliminate) the infinities in energies, forces, and pressures that appear when naively comparing the total energy around objects with different size but the same total number of ordinary matter particles.