Parameter estimation for space-based gravitational wave detectors with ringdown signals

Unlike ground-based gravitational wave detectors, space-based gravitational wave detectors can detect the ringdown signals from massive black hole binary mergers with large signal-to-noise ratio, and help to extract the source parameters and localize the source. To reduce the computation time in Fisher information matrix, we derive the analytical formulas of frequency-domain ringdown signals for heliocentric detectors and geocentric detectors by considering the effect of the harmonic phases, the rotation period of the geocentric detector, and the detector arm length. We explore the median errors of parameter estimation and source localization with ringdown singals from binaries with different masses and different redshifts. Using a binary source with the total mass $M=10^7 M_odot$ at the redshift $z=1$, we analyze the dependence of these errors on the sky position. We find that the network of space-based gravitational wave detectors can significantly improve the source localization at the ringdown stage.