Parameter Estimation Precision with Geocentric Gravitational Wave Interferometers: Monochromatic Signals

We present a Fisher information matrix study of the parameter estimation precision achievable by a class of future space-based, “mid-band”, gravitational wave interferometers observing monochromatic signals. The mid-band is the frequency region between that accessible by the Laser Interferometer Space Antenna (LISA) and ground-based interferometers. We analyze monochromatic signals observed by the TianQin mission, gLISA (a LISA-like interferometer in a geosynchronous orbit) and a descoped gLISA mission, gLISA_d, characterized by an acceleration noise level that is three orders of magnitude worse than that of gLISA. We find that all three missions achieve their best angular source reconstruction precision in the higher part of their accessible frequency band, with an error box better than ${10}^{-10}$ sr in the frequency band [${10}^{-1},10$] Hz when observing a monochromatic gravitational wave signal of amplitude $h_0={10}^{-21}$ that is incoming from a given direction. In terms of their reconstructed frequencies and amplitudes, TianQin achieves its best precision values in both quantities in the frequency band [${10}^{-2},4\times {10}^{-1}$] Hz, with a frequency precision ${\sigma }_{f_{gw}}=2\times {10}^{-11}$ Hz and an amplitude precision ${\sigma }_{h_0}=2\times {10}^{-24}$. gLISA matches these precisions in a frequency band slightly higher than that of TianQin, [$3\times {10}^{-2},1$] Hz, as a consequence of its smaller arm length. gLISA_d, on the other hand, matches the performance of gLISA only over the narrower frequency region, [$7\times {10}^{-1},1$] Hz, as a consequence of its higher acceleration noise at lower frequencies. The angular, frequency, and amplitude precisions as functions of the source sky location are then derived by assuming an average signal-to-noise ratio of 10 at a selected number of gravitational wave frequencies covering the operational bandwidth of TianQin and gLISA. Similar precision functions are then derived for gLISA_d by using the amplitudes resulting in the gLISA average SNR being equal to 10 at the selected frequencies. We find that, for any given source location, all three missions display a marked precision improvement in the three reconstructed parameters at higher gravitational wave frequencies.