Constraints on Compact Dark Matter Population from Micro-lensing Effect of Gravitational Wave for the third-generation gravitational Wave Detector

Abstract

Since the pioneering detection of gravitational wave (GW) from a binary black hole merger by the LIGO-Virgo collaboration, GW has become a powerful probe for astrophysics and cosmology. If compact dark matter (DM) candidates, e.g. primordial black holes, contribute a substantial fraction of the DM component across a broad mass range, they would yield distinctive micro-lensing signatures on GW signals. In this paper, based on the third-generation ground-based GW detector, i.e. Einstein Telescope, we propose to constrain population information of compact DM by simulating micro-lensing GWs and analyzing with the hierarchical Bayesian inference framework. For a population with a power-law mass function, we demonstrate that detections of several micro-lensing GW signals in $10^4$ binary black holes coalescence events would constrain the abundance of compact DM to $\sim10^{-3}$. It suggests that searching for and identifying micro-lensing signatures in future detections could be complementary and helpful in constraining compact DM scenarios.

Figures (3)

• Figure 1: Left: The posterior distribution for one of lensing GW events in 8 detectable micro-lensing GW events. Right: The cross represents the range of values within $2\sigma$ confidence level of luminosity distance for GW sources and redshift mass for lens extracted from the posterior distribution of 8 detectable micro-lensing GW events. And the scattered points represent the true values of these micro-lensing events.
• Figure 2: Left: The proportion of detectable micro-lensing GW events for Eq. (\ref{['eq2-2-8f']}). The blue data points represent simulated values, while the solid red line indicates the corresponding polynomial fit to these data. Right: Solid lines with points represent inferred lens masses of 8 micro-lensing GWs at $95\%$ confidence levels with median value derived from the posterior distribution of redshifted lens mass $p(M_{\rm l}^{z}|d_i)$ and luminosity-distance distribution of GW sources $p(d_{\rm L}(z_{\rm s})|d_i)$ in Figure \ref{['fig1']}. The star points represent the true values of the simulated lens masses.
• Figure 3: The posterior distributions for hyperparameters $[\gamma, \log_{10}(f_{\rm CO})]$ within $2\sigma$ confidence level. The blue solid point represent the truth values for hyperparameters $[\gamma=1, \log_{10}(f_{\rm CO})=-2.5]$ in our simulation.