Parameter estimation on gravitational waves from neutron-star binaries with spinning components



As we enter the advanced-detector era of ground-based gravitational-wave (GW) astronomy, it is critical that we understand the abilities and limitations of the analyses we are prepared to conduct. Of the many predicted sources of GWs, binary neutron-star (BNS) coalescences are paramount; their progenitors have been directly observed (Lorimer 2008), and the advanced detectors will be sensitive to their GW emission up to \(\sim 400~\mathrm{Mpc}\) away (Abbott et al., 2016).

When analyzing a GW signal from a circularized compact binary merger, strong degeneracies exist between parameters describing the binary (e.g., distance and inclination). To properly estimate any particular parameter(s) of interest, the marginal distribution is estimated by integrating the joint posterior probability density function (PDF) over all other parameters. In this work, we sample the posterior PDF using software implemented in the LALInference library (Veitch et al., 2015). Specifically we use results from LALInfernce_nest (Veitch et al., 2010), a nest sampling algorithm (Skilling, 2006), and LALInference_MCMC (Christensen et al., 2004; Röver et al., 2006; van der Sluys et al., 2008), a Markov-chain Monte Carlo algorithm (chapter 12 Gregory, 2005).

Previous studies of BNS signals have largely assessed parameter constraints assuming negligible neutron-star (NS) spin, restricting models to nine parameters. This simplification has largely been due to computational constraints, but the slow spin of NSs in short-period BNS systems observed to date (e.g., Mandel et al., 2010) has also been used as justification. However, proper characterization of compact binary sources must account for the possibility of non-negligible spin; otherwise parameter estimates will be biased (Buonanno et al., 2009; Berry et al., 2015). This bias can potentially lead to incorrect conclusions about source properties and even misidentification of source classes.

Numerous studies have looked at the BNS parameter estimation abilities of ground-based GW detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO; Aasi et al., 2015) and Advanced Virgo (AdV; Acernese et al., 2015) detectors. Nissanke et al. (2010); Nissanke et al. (2011) assessed localization abilities on a simulated non-spinning BNS population. Veitch et al. (2012) looked at several potential advanced-detector networks and quantified the parameter-estimation abilities of each network for a signal from a fiducial BNS with non-spinning NSs. Aasi et al. (2013) demonstrated the ability to characterize signals from non-spinning BNS sources with waveform models for spinning sources using Bayesian stochastic samplers in the LALInference library (Veitch et al., 2015). Hannam et al. (2013) used approximate methods to quantify the degeneracy between spin and mass estimates, assuming the compact objects’ spins are aligned with the orbital angular momentum of the binary (but see Haster et al., 2015). Rodriguez et al. (2014) simulated a collection of loud signals from non-spinning BNS sources in several mass bins and quantified parameter estimation capabilities in the advanced-detector era using non-spinning models. Chatziioannou et al. (2015) introduced precession from spin–orbit coupling and found that the additional richness encoded in the waveform could reduce the mass–spin degeneracy, helping BNSs to be distinguished from NS–black hole (BH) binaries. Littenberg et al. (2015) conducted a similar analysis of a large catalog of sources and found that it is difficult to infer the presence of a mass gap between NSs and BHs (Özel et al., 2010; Farr et al., 2011; Kreidberg et al., 2012), although, this may still be possible using a population of a few tens of detections (Mandel et al., 2015). Finally, Singer et al. (2014) and the follow-on Berry et al. (2015) represent an (almost) complete end-to-end simulation of BNS detection and characterization during the first \(1\)\(2\) years of the advanced-detector era. These studies simulated GWs from an astrophysically motivated BNS population, then detected and characterized sources using the search and follow-up tools that are used for LIGO–Virgo data analysis (Aasi et al., 2014; Abbott et al., 2016a). The final stage of the analysis missing from these studies is the computationally expensive characterization of sources while accounting for the compact objects’ spins and their degeneracies with other parameters. The present work is the final step of BNS characterization for the Singer et al. (2014) simulations using waveforms that account for the effects of NS spin.

We begin with a brief introduction to the source catalog used for this study and Singer et al. (2014) in section \ref{sec:sources}. Then, in section \ref{sec:spin} we describe the results of parameter estimation from a full analysis that includes spin. In section \ref{sec:mass} we look at mass estimates in more detail and spin-magnitude estimates in section \ref{sec:spin-magnitudes}. In section \ref{sec:extrinsic} we consider the estimation of extrinsic parameters: sky position (section \ref{sec:sky}) and distance (section \ref{sec:distance}), which we do not expect to be significantly affected by the inclusion of spin in the analysis templates. We summarize our findings in section \ref{sec:conclusions}. A comparison of computational costs for spinning and non-spinning parameter estimation is given in appendix \ref{ap:CPU}.

Source Simulation and Selection


We have restricted our study to the first year of the advanced-detector era, using the same \(250\) simulations that Singer et al. (2014) analysed with non-spinning parameter estimation. For these, Gaussian noise was generated using the ‘early’ 2015 aLIGO noise curve found in Barsotti et al. (2012). Approximately \(50,000\) BNS sources were simulated, using the SpinTaylorT4 waveform model (Buonanno et al., 2003; Buonanno et al., 2009), a post-Newtonian inspiral model that includes the effects of precession, to generate the GW signals. Component masses were uniformly distributed between \(1.2~\mathrm{M}_\odot\) and \(1.6~\mathrm{M}_\odot\), which reflects the range of observed BNS masses (Özel et al., 2012). Component spins were isotropically oriented, with magnitudes \(\chi_{1,\,2} = c |\boldsymbol{S}_{1,\,2}|/G m_{1,\,2}^2\) drawn uniformly between \(0\) and \(0.05\); here, \(|\boldsymbol{S}_{1,\,2}|\) are the NSs’ spin angular momenta and \(m_{1,\,2}\) are their masses (the indices \(1\) and \(2\) correspond to the more and less massive components of the binary, respectively). The range of simulated spin magnitudes was chosen to be consistent with the observed population of short-period BNS systems, currently bounded by PSR J0737\(-\)3039A (Burgay et al., 2003;