Parameter estimation using a complete signal and inspiral templates for low-mass binary black holes with Advanced LIGO sensitivity

Abstract

We study the validity of inspiral templates in gravitational wave data analysis with Advanced LIGO sensitivity for low mass binary black holes with total masses of M ≤ 30M . We mainly focus on the nonspinning system. As our complete inspiral-merger-ringdown waveform model (IMR), we assume the phenomenological model, "PhenomA", and define our inspiral template model (I merg ) by taking the inspiral part into account from IMR up to the merger frequency (f merg ). We first calculate the true statistical uncertainties using IMR signals and IMR templates. Next, using IMR signals and I merg templates, we calculate fitting factors and systematic biases, and compare the biases with the true statistical uncertainties. We find that the valid criteria of the bank of I merg templates are obtained as M crit ∼ 24M for detection (if M > M crit , the fitting factor is smaller than 0.97), and M crit ∼ 26M for parameter estimation (if M > M crit , the systematic bias is larger than the true statistical uncertainty where the signal to noise ratio is 20), respectively. In order to see the dependence on the cutoff frequency of the inspiral waveforms, we define another inspiral model I isco which is terminated at the innermost-stable-circular-orbit frequency (f isco < f merg ). We find that the valid criteria of the bank of I isco templates are obtained as M crit ∼ 15M and ∼ 17M for detection and parameter estimation, respectively. We investigate the statistical uncertainties for the inspiral template models considering various signal to noise ratios, and compare those to the true statistical uncertainties. We also consider the aligned-spinning system with fixed mass ratio (m 1 /m 2 = 3) and spin (χ = 0.5) by employing the recent phenomenological model, "PhenomC". In this case, we find that the true statistical uncertainties can be much larger than those for the nonspinning system due to the mass-spin degeneracy. For inspiral PhenomC templates truncated at f merg , the fitting factors can be better but the biases are found to be much larger compared to those for the nonspinning system. In particular, we find significantly asymmetric shapes of the three-dimensional overlaps including bimodal distributions.

Gravitational wave searches for aligned-spin binary neutron stars using nonspinning templates

“…As the efficiency of a template waveform model for the search is evaluated by the fitting factor, its validity for the parameter estimation can be examined by the bias [30][31][32]. We determine the fitting factor and the bias in the following way [20,32,33]. First, we repeat a grid search around λ 0 until we find the crude location of λ rec in the overlap surface.…”

“…The bias corresponds to a systematic error in the GW parameter estimation. As the efficiency of a template waveform model for the search is evaluated by the fitting factor, its validity for the parameter estimation can be examined by the bias [30][31][32].…”

Accuracy in measuring the neutron star mass in the gravitational wave parameter estimation for black hole-neutron star binaries

“…In general, if a binary system has spins, a degeneracy between the components' mass ratio and their spins significantly degrades our ability to measure the individual compo- nent masses [17,18]. Therefore, in the posterior distribution of parameter estimation for an aligned-spin system, the mass parameters are strongly correlated with the spin parameter; thus, the range of error in M NS can be significantly increased compared to that for a nonspinning system (for example, see [29,30]). …”

Efficiency of nonspinning templates in gravitational wave searches for aligned-spin binary black holes

“…In this work, however, we want to remove the effect of discreteness on the fitting factor. To do so, we choose sufficiently fine spacings in the template space defined in the M c − η plane [43,44]. 3 For example, in order to obtain FF eff for one signal, we repeat a grid search around λ 0 until we find the crude location of the peak point in the overlap surface.…”