Stochastic effects on observation of ultralight bosonic dark matter
  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.
