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 $M \leq 30 Msun$. 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 ($Imerg$) by taking the inspiral part into account from $IMR$ up to the merger frequency (fmerg). We first calculate the {\it true} statistical uncertainties using $IMR$ signals and $IMR$ templates. Next, using $IMR$ signals and $Imerg$ templates, we calculate fitting factors and systematic biases, and compare the biases with the {\it true} statistical uncertainties. We find that the valid criteria of the bank of $Imerg$ templates are obtained as $Mcrit \sim 24 Msun$ for detection (if $M>Mcrit$, the fitting factor is smaller than $0.97$), and $Mcrit \sim 26 Msun$ for parameter estimation (if $M>Mcrit$, the systematic bias is larger than the {\it 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 $Iisco$ which is terminated at the innermost-stable-circular-orbit frequency ($fisco<fmerg$). We find that the valid criteria of the bank of $Iisco$ templates are obtained as $Mcrit \sim 15 Msun$ and $\sim 17 Msun$ 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 {\it 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".