Validity of the Effective Fisher matrix for parameter estimation analysis: Comparing to the analytic Fisher matrix

The effective Fisher matrix method recently introduced by Cho et al. is a semi-analytic approach to the Fisher matrix, in which a local overlap surface is fitted by using a quadratic fitting function. Mathematically, the effective Fisher matrix should be consistent with the analytic one at the infinitesimal fitting scale. In this work, using the frequency-domain waveform (TaylorF2), we give brief comparison results between the effective and analytic Fisher matrices for several non-spinning binaries consisting of binary neutron stars with masses of (1.4, 1.4)M_sun, black hole-neutron star of (1.4, 10)M_sun, and binary black holes of (5, 5) and (10, 10)M_sun for a fixed signal to noise ratio (SNR=20) and show a good consistency between two methods. We also give a comparison result for an aligned-spin black hole-neutron star binary with a black hole spin of \chi=1, where we define new mass parameters (Mc, \eta^-1, \chi^7/2) to find good fitting functions to the overlap surface. The effective Fisher matrix can also be computed by using the time-domain waveforms which are generally more accurate than frequency-domain waveform. We show comparison results between the frequency-domain and time-domain waveforms (TaylorT4) for both the non-spinning aligned-spin binaries.