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 (GW) interferometers observing monochromatic signals. The mid-band is the frequency region between that accessible by LISA and ground-based interferometers. We analyze monochromatic signals from TianQin, gLISA, and gLISA$_d$, a descoped gLISA which has acceleration noise three orders of magnitude worse than 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 GW 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 derived assuming an average SNR of 10 at selected GW frequencies within TianQin and gLISA's bands. The same is done for gLISA$_d$ using amplitudes yielding an SNR of 10 for gLISA. We find that, for any given source location, all three missions display a marked precision improvement in the three reconstructed parameters at higher GW frequencies.