Sky localization of space-based gravitational wave detectors

Localizing the sky position of the gravitational wave source is a key scientific goal for gravitational wave observations. Employing the Fisher information matrix approximation, we compute the angular resolutions of LISA and TianQin, two planned space-based gravitational wave detectors and examine how detectors' configuration properties, such as the orientation change of the detector plane, heliocentric or geocentric motion and the arm length etc. affect the accuracy of source localization. We find that the amplitude modulation due to the annual changing orientation of the detector plane helps LISA get better accuracy in the sky localization and better sky coverage at frequencies below several mHz, and its effect on TianQin is negligible although the orientation of TianQin's detector plane is fixed. At frequencies above roughly 30mHz, TianQin's ability in the sky localization is better than LISA. Further we explore potential space detector networks for fast and accurate localization of the gravitational wave sources. The LISA-TianQin network has better ability in sky localization for sources with frequencies in the range 1-100 mHz and the network has larger sky coverage for the angular resolution than the individual detector.