Preliminary study on parameter estimation accuracy of supermassive black hole binary inspirals for TianQin

Abstract

We use the Fisher information matrix method to calculate the parameter estimation accuracy of inspiraling supermassive black holes binaries for TianQin, a proposed space-borne laser interferometric detector aimed at detecting gravitational waves in the millihertz frequency band. The ``restricted'' post-Newtonian waveform in which third order post-Newtonian (3PN) phase including spin effects (spin-orbit $\ensuremath{\beta}$ and spin-spin $\ensuremath{\sigma}$) and first-order eccentricity contribution is employed. Monte Carlo simulations using $1{0}^{3}$ binaries for mass pairs with component masses in the range of $(1{0}^{5},1{0}^{7})\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and cosmological redshift $z=0.5$ show that the medians of the root-mean-square error distributions for the chirp mass ${M}_{c}$ and symmetric mass ratio $\ensuremath{\eta}$ are in the range of $\ensuremath{\sim}0.02%--0.7%$ and $\ensuremath{\sim}4%--8%$, respectively. The luminosity distance ${D}_{L}$ can be determined to be $\ensuremath{\sim}1%--3%$, and the angular resolution of source $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Omega}}$ is better than $12\text{ }\text{ }{\mathrm{deg}}^{2}$. The corresponding results for $z=1.0$ and 2.0, which are deteriorated with the decreasing of the signal-to-noise ratio, have also been given. We show that adding spin parameters degrades measurement accuracy of the mass parameters (${M}_{c}$, $\ensuremath{\eta}$), and the time and the orbital phase of coalescence (${t}_{c}$, ${\ensuremath{\phi}}_{c}$); the inclusion of the first-order eccentricity correction to the phase worsens the estimation accuracy comparing with the circular cases. We also show the effects of post-Newtonian order on parameter estimation accuracy by comparing the results based on second order and third order post-Newtonian phases. Moreover, we calculate the horizon distance of supermassive black hole binaries for TianQin.