Probing the Extreme-Mass-Ratio Inspirals Population Constraints with TianQin

TL;DR

This paper explores how the TianQin gravitational wave detector can constrain the population characteristics of extreme-mass-ratio inspirals, providing initial parameter estimates and demonstrating potential for future astrophysical insights.

Contribution

It introduces a parametrization method for EMRI population modeling and assesses TianQin's capability to accurately recover hyper-parameters from gravitational wave data.

Findings

TianQin can recover hyper-parameters within 1σ confidence.

Mass distribution parameters can be measured with up to 46.4% accuracy.

Redshift distribution parameters can be measured with about 15-21% accuracy.

Abstract

Extreme-mass-ratio inspirals (EMRIs), consisting of a massive black hole and a stellar compact object, are one of the most important sources for space-borne gravitational wave detectors like TianQin. Their population study can be used to constrain astrophysical models that interpret the EMRI formation mechanisms. In this paper, as an initial attempt, we employ a parametrization method to describe the EMRI population model in the loss cone formation channel. This approach, however, can be extended to other models such as the accretion disc driven formation channel. We present the phenomenological characteristic of the MBH mass, spin, and redshift distributions. Then, we investigate the posterior distribution of the hyper-parameters that describe this population model. The optimistic results show that TianQin could recover almost all the posterior of the hyper-parameters within $1\sigma$ confidence interval. The hyper-parameters $\alpha_1, \alpha_2, b$, which describe the MBH mass distribution, could be measured with an accuracy of $46.4\%$, $12.6\%$, and $3\%$, respectively. The hyper-parameters $\mu_z$, and $\sigma_z$, which describe the redshift distribution, could be measured with an accuracy of $15.4\%$ and $21.1\%$. With this estimation accuracy, the EMRI population characteristics can be effectively demonstrated, potentially serving as evidence for EMRI formation in the future studies. Furthermore, with an increasing number of detectable events, the parameter estimation for the hyper-parameters will improve and the confidence intervals will be narrowed.