Most calculations of the gravitational wave signal from merging compact binaries limit attention to the leading-order quadrupole when constructing models for detection or parameter estimation. Some studies have claimed that if additional "higher harmonics" are included consistently in the gravitational wave signal and search model, binary parameters can be measured much more precisely. Using the lalinference Markov-chain Monte Carlo parameter estimation code, we construct posterior parameter constraints associated with two distinct nonprecessing black hole-neutron star (BH-NS) binaries, each with and without higher-order harmonics. All simulations place a plausible signal into a three-detector network with Gaussian noise. Our simulations suggest that higher harmonics provide little information, principally allowing us to measure a previously unconstrained angle associated with the source geometry well but otherwise improving knowledge of all other parameters by a few percent for our loud fiducial signal (ρ = 20). Even at this optimistic signal amplitude, different noise realizations have a more significant impact on parameter accuracy than higher harmonics. We compare our results with the "effective Fisher matrix" introduced previously as a method to obtain robust analytic predictions for complicated signals with multiple significant harmonics. We find generally good agreement with these predictions; confirm that intrinsic parameter measurement accuracy is nearly independent of detector network geometry; and show that uncertainties in extrinsic and intrinsic parameters can to a good approximation be separated. For our fiducial example, the individual masses can be determined to lie between 7.11 − 11.48M and 1.77 − 1.276M at greater than 99% confidence, accounting for unknown BH spin. Assuming comparable control over waveform systematics, measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions. Using analytic arguments to guide extrapolation, we anticipate higher harmonics should provide little new information about nonprecessing BH-NS binaries, for the signal amplitudes expected for the first few detections. Though our study focused on one particular example -higher harmomics -any study of subdominant degrees of freedom in gravitational wave astronomy can adopt the tools presented here (V /Vprior and DKL) to assess whether new physics is accessible (e.g., modifications of gravity; spin-orbit misalignment) and if so precisely what information those new parameters provide.

The Fisher matrix (FM) has been generally used to predict the accuracy of the gravitational wave parameter estimation. Although the limitation of the FM has been well known, it is still mainly used due to its very low computational cost compared to the Monte Carlo simulations. Recently, Rodriguez et al. [Phys. Rev. D 88, 084013 (2013)] performed Markov chain Monte Carlo (MCMC) simulations using a frequency domain inspiral waveform model (TaylorF2) for nonspinning binary systems with total masses M ≤ 20M ⊙ , they found systematic differences between the predictions from FM and MCMC for M > 10M ⊙ . On the other hand, an effective Fisher matrix (eFM) was recently introduced by Cho et al. [Phys. Rev. D 87, 24004 (2013)]. The eFM is a semi-analytic approach to the standard FM, in which the derivative is taken of a quadratic function fitted to the local overlap surface. In this work, we apply the eFM method to the TaylorF2 waveform for nonspinning binary systems with a moderately high signal to noise ratio (SNR ∼ 15) and find that the eFM can well reproduce the MCMC error bounds in Rodriguez et al. even for high masses. By comparing the eFM standard deviation directly with the 1-σ confidence interval of the marginalized overlap that approximates the MCMC posterior distribution, we show that the eFM can be acceptable in all mass regions for the estimation of the MCMC error bounds. We also investigate the dependence on the signal strength.

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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.

The phenomenological gravitational waveform models, which we refer to as PhenomA, PhenomB and PhenomC, generate full inspiral-merger-ringdown waveforms of coalescing binary back holes (BBHs). These models are defined in the Fourier domain, thus can be used for fast matched filtering in the gravitational wave search. PhenomA has been developed for nonspinning BBH waveforms, while PhenomB and PhenomC were designed to model the waveforms of BBH systems with nonprecessing (aligned) spins, but can also be used for nonspinning systems. In this work, we study the validity of the phenomenological models for nonspinning BBH searches at low masses, m 1,2 ≥ 4M and m 1 + m 2 ≡ M ≤ 30M , with Advanced LIGO. As our complete signal waveform model, we adopt EOBNRv2 that is a time-domain inspiral-merger-ringdown waveform model. To investigate the search efficiency of the phenomenological template models, we calculate fitting factors by exploring overlap surfaces. We find that only PhenomC is valid to obtain the fitting factors better than 0.97 in the mass range of M < 15M . Above 15M , PhenomA is most efficient in symmetric mass region, PhenomB is most efficient in highly asymmetric mass region, and PhenomC is most efficient in the intermediate region. Specifically, we propose an effective phenomenological template family that can be constructed by employing the phenomenological models in four subregions individually. We find that fitting factors of the effective templates are better than 0.97 in our entire mass region and mostly greater than 0.99.