Accuracy of estimation of parameters with space-borne gravitational wave observatory

TL;DR

This paper compares the parameter estimation accuracy of TianQin and LISA gravitational wave observatories across different frequency regimes using Fisher matrix analysis, revealing distinct patterns in angular resolution and error scaling.

Contribution

It provides analytical formulas and numerical results for parameter errors of TianQin and LISA, highlighting differences in their performance across frequency ranges.

Findings

TianQin has better parameter estimation errors at high frequencies.

Angular resolution scales differently for TianQin and LISA in low-frequency regime.

Parameter errors decrease with frequency following specific power laws in different regimes.

Abstract

Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and 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.