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Supermassive black hole binaries are one of the primary targets forgravitational wave searches using pulsar timing arrays. Gravitational wavesignals from such systems are well represented by parametrized models, allowingthe standard Generalized Likelihood Ratio Test (GLRT) to be used for theirdetection and estimation. However, there is a dichotomy in how the GLRT can beimplemented for pulsar timing arrays: there are two possible ways in which onecan split the set of signal parameters for semi-analytical and numericalextremization. The straightforward extension of the method used for continuoussignals in ground-based gravitational wave searches, where the so-called pulsarphase parameters are maximized numerically, was addressed in an earlier paper(Wang et al. 2014). In this paper, we report the first study of the performanceof the second approach where the pulsar phases are maximized semi-analytically.This approach is scalable since the number of parameters left over fornumerical optimization does not depend on the size of the pulsar timing array.Our results show that, for the same array size (9 pulsars), the new methodperforms somewhat worse in parameter estimation, but not in detection, than theprevious method where the pulsar phases were maximized numerically. The originof the performance discrepancy is likely to be in the ill-posedness that isintrinsic to any network analysis method. However, scalability of the newmethod allows the ill-posedness to be mitigated by simply adding more pulsarsto the array. This is shown explicitly by taking a larger array of pulsars.

Coherent network analysis for continuous gravitational wave signals in a pulsar timing array: Pulsar phases as extrinsic parameters