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SPINSPIRAL: parameter estimation for compact binary inspirals with spinning components
Inspiral signals from binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave interferometers (LIGO, Virgo and GEO-600). If such a binary contains a black hole, it is expected to be spinning moderately (Belczynski et al. 2008). A spinning black hole causes the binary orbit to precess, introducing phase and amplitude modulations in the gravitational-wave signal. Accounting for these effects improves the detection efficiency and also improves the accuracy of the parameter estimation on the signal. The accuracy with which the binary parameters can be estimated is of significant astrophysical interest; measuring the black-hole spin and the spin alignment can provide us with valuable information on supernovae and their kicks.
In collaboration with the Compact Binary Coalescence (CBC) group of the LIGO-Virgo Collaboration (LVC), we developed the parameter-estimation code SPINSPIRAL for the follow-up analysis of gravitational-wave signals from compact binary inspirals. We follow a Bayesian approach for the parameter estimation; a Markov-chain Monte-Carlo (MCMC) technique is used to compute the posterior probability-density functions (posterior PDFs), which provide an estimate of the parameter values and their accuracies (van der Sluys et al. 2008a). For the first time, we both estimated the parameters of a binary inspiral source with a spinning, precessing component and determined the accuracy of the parameter estimation, for simulated observations with ground-based gravitational-wave detectors. We demonstrate that we can obtain the distance, sky position, and binary orientation at a higher accuracy than previously suggested in the literature. For an observation of an inspiral with sufficient spin and two or three detectors we find an accuracy in the determination of the sky position of the order of tens of square degrees (van der Sluys et al. 2008b). SPINSPIRAL can be used in the CBC follow-up pipeline, to allow the automatic follow-up of interesting events that come out of the detection pipeline and has been used for parameter estimation in the sixth LIGO and second Virgo science runs (S6/VSR2), with the enhanced detectors.
The output from SPINSPIRAL can be reduced, analysed and presented with a tool called AnalyseMCMC.
We tested SPINSPIRAL on a semi-blind analysis using software injections. A signal is injected in simulated, Gaussian noise. We typically start several serial chains from different, random positions in parameter space. The part of the run between between the start of the chain and the moment where the chain locks on to the true values is called the burn-in. The length of the burn-in, and whether the chains have converged at all, can be determined by combining the data of the serial chains.
The chains typically take a few days to a week to provide first results, and ten days to two weeks to collect sufficient data to do statistical analysis. SPINSPIRAL can do coherent analysis for a network of detectors, where we typically use one, two or three non-colocated detectors (e.g. LIGO H1, LIGO L1 and Virgo). Whereas the accuracy of parameter estimation increases only slightly for the intrinsic parameters like masses and spin when more detectors are added to the network, the determination of the source position and binary orientation (inclination and polarisation angle) become much more accurate in such a case, as is expected.
Apart from running SPINSPIRAL on self-performed software injections into Gaussian noise, we are preparing our code for the analysis of real data. The LSC-Virgo collaboration regularly performs hardware injections, during which a (binary-inspiral) signal is added to the detector data by physically moving the mirrors of the interferometer. These hardware injections form a realistic test for the different data-analysis codes and pipelines.
As a part of the CBC Bayesian follow-up group, we systematically run SPINSPIRAL (and other Bayesian codes) on a number of hardware injections, using the results from the CBC detection pipeline where possible. We describe the results from a selection of those runs in van der Sluys et al. 2009a. We conclude that our code can analyse these realistic cases well, that even the weakest detected GW signals can be followed up by SPINSPIRAL and that we find biases in some of the parameters, which we ascribe to the difference in post-Newtonian order of the injection and the MCMC template.
SPINspiral source code and documentation
The source code for SPINSPIRAL can be found on SourceForge.net. We provide code releases, a git repository, information on dependencies and installation, code documentation and a user manual there. The source code can also be obtained from the LSC Git repository.