Accuracy of parameter estimations with a spaceborne gravitational wave observatory

Abstract

Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and Laser Interferometer Space Antenna (LISA) for monochromatic gravitational waves. With the long-wavelength approximation, we derive analytical formulas for the parameter estimation errors. We separately analyze the effects of the amplitude modulation due to the changing orientation of the detector plane and the Doppler modulation due to the translational motion of the center of the detector around the Sun. We disclose that in the low-frequency regime there exist different patterns in angular resolutions and estimation errors of sources' parameters between LISA and TianQin, the angular resolution falls off as ${S}_{n}(f)/{f}^{2}$ for TianQin but ${S}_{n}(f)$ for LISA, and the estimation errors of the other parameters fall off as $\sqrt{{S}_{n}(f)}/f$ for TianQin but $\sqrt{{S}_{n}(f)}$ for LISA. In the medium-frequency regime, we observe the same pattern where the angular resolution falls off as ${S}_{n}(f)/{f}^{2}$ and the estimation errors of the other parameters fall off as $\sqrt{{S}_{n}(f)}$ for both TianQin and LISA. In the high-frequency regime, the long-wavelength approximation fails; we numerically calculate the parameter estimation errors for LISA and TianQin and find that the parameter estimation errors measured by TianQin are smaller than those by LISA.