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

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 $M⩽30M_{\odot }.$ 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 $M_{crit}\sim 24M_{\odot }$ for detection (if $M>M_{crit},$ the fitting factor is smaller than 0.97), and $M_{crit}\sim 26M_{\odot }$ 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 $M_{crit}\sim 15M_{\odot }$ and $\sim 17M_{\odot }$ 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 ($\chi =0.5$) 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. (paper)