Stochastic effects on observation of ultralight bosonic dark matter

TL;DR

This paper develops a comprehensive method to account for stochastic effects in detecting ultralight bosonic dark matter signals, improving the accuracy of coupling constant constraints across various measurement durations and dark matter velocities.

Contribution

It extends previous formulations to arbitrary measurement times and includes velocity-dependent signals, providing a generic approach to analyze stochastic effects in ultralight bosonic DM detection.

Findings

Accurately estimates upper bounds on coupling constants using numerical simulations.

Shows stochastic effects significantly impact small mass region constraints.

Provides semi-analytic estimates for future experimental bounds.

Abstract

Ultralight bosonic particles are fascinating candidates of dark matter (DM). It behaves as classical waves in our Galaxy due to its large number density. There have been various methods proposed to search for the wave-like DM, such as methods utilizing interferometric gravitational-wave detectors. Understanding the characteristics of DM signals is crucial to extract the properties of DM from data. While the DM signal is nearly monochromatic with the angular frequency of its mass, the amplitude and phase are gradually changing due to the velocity dispersion of DMs in our Galaxy halo. The stochastic amplitude and phase should be properly taken into account to accurately constrain the coupling constant of DM from data. Previous works formulated a method to obtain the upper bound on the coupling constant incorporating the stochastic effects. One of these works compared the upper bound with and without the stochastic effect in a measurement time that is much shorter than the variation time scale of the amplitude and phase. In this paper, we extend their formulation to arbitrary measurement time and evaluate the stochastic effects. Moreover, we investigate the velocity-dependent signal for dark photon DM including an uncertainly of the velocity. We demonstrate that our method accurately estimates the upper bound on the coupling constant with numerical simulations. We also estimate the expected upper bound of the coupling constant of axion DM and dark photon DM from future experiments in a semi-analytic way. The stochasticity especially affects constraints on a small mass region. Our formulation offers a generic treatment of the ultralight bosonic DM signal with the stochastic effect.