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The NINJA project

A real NINJA

The NINJA (Numerical INJection Analysis) project is aimed to bring numerical relativists and gravitational-wave (GW) data analysts together. The goal of the project is to test data-analysis codes on gravitational waveforms that are as close to nature as we have them: those predicted by numerical relativity (NR). Where only a few years ago the world of NR was completely disconnected from that of data analysis (DA), breakthroughs in NR have overcome that gap, and numerical waveforms can now actually be used in data analysis.

Several numerical-relativity groups around the world computed realistic waveforms of compact binary inspirals of their choice. Since it takes weeks to compute only a few orbits of an inspiral with a NR code, it was decided to only calculate waveforms for the inspiral, merger and ringdown of fairly massive binaries. These waveforms were injected coherently into Gaussian noise with the characterisation of the LIGO and Virgo gravitational-wave interferometers. These signals, buried in synthetic detector noise, were provided to a number of data-analysis groups. These groups used the data to test their different techniques, such as searches (a number of them using the LIGO-Virgo detection pipeline), ringdown analysis, model selection and parameter estimation. While the injection parameters were known to the DA groups, the clean (noise-less) data was not provided.

We used the first round of the NINJA project (summer/fall 2008) to test our Markov-chain Monte-Carlo (MCMC) code SPINSPIRAL on these realistic injections. SPINSPIRAL uses a 1.5-pN template, which includes the inspiral part of the signal, but not the merger and ringdown. As we had expected, this limitation of our waveform has a strong effect on the behaviour of our MCMC. Surprisingly, the MCMC works fairly well, but the algorithm tries to fit the inspiral of our waveform template to the merger and ringdown of the signal. The reason for this is that the high masses of the binary inspirals which were computed by the NR groups have an innermost stable orbit (ISCO) frequency of several tens of Hertz, right in the sweet spot of the detector sensitivity bands, so that the merger and ringdown of these injections would completely dominate the signal-to-noise ratio (SNR). When our Markov chains would lock on to the signal, it would either underestimate the chirp mass or overestimate the magnitude of the spin, in order to account for the strong signal al high frequencies.

However, SPINSPIRAL produced reasonable results when we limited ourselves to the lowest-mass binaries (around 36Mo) and take into account that the fact that we only fit the inspiral part of the waveform reduces the SNR to about 8. When we fixed the spin magnitude in our code to prevent the overestimation mentioned above, we retrieve the injected values of e.g. the masses and distance well. It is especially interesting that despite the 'mismatch' in waveform, the ability of SPINSPIRAL to localise the source in the sky is very good. It seems likely that parameters like sky position and binary orientation are more sensitive to timing and the projection of the waveform on the detectors.

Our results are summarised in a short text which is part of a larger publication that describes the results of the first round of the NINJA project (Aylott et al., 2009). We are looking forward to the next rounds of the NINJA project. In particular, we hope that hybrid waveforms (a post-Newtonian approximation for the low-frequency part of the inspiral and numerical relativity for the high frequency part of the inspiral, the merger and the ringdown) will be used to allow injections of binary inspirals with masses in the range of 10-20Mo or perhaps even lower, which will give us the possibility to use a larger part of the (SNR of) the signal, and hence produce a more realistic accuracy of our parameter estimation.