Probing the population of extreme-mass-ratio inspirals with TianQin

Extreme-mass-ratio inspirals (EMRIs), consisting of a massive black hole (MBH) and a stellar compact object, are one of the most important sources for spaceborne 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 hyperparameters that describe this population model. The optimistic results show that TianQin could recover almost all the posterior of the hyperparameters within a $1\ensuremath{\sigma}$ confidence interval. The hyperparameters ${\ensuremath{\alpha}}_{1}$, ${\ensuremath{\alpha}}_{2}$, and $b$, which describe the MBH mass distribution, could be measured with an accuracy of 46.4%, 12.6%, and 3%, respectively. The hyperparameters ${\ensuremath{\mu}}_{z}$ and ${\ensuremath{\sigma}}_{z}$, 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 hyperparameters will improve and the confidence intervals will be narrowed.