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Wang Y.,University of Texas at Brownsville | Wang Y.,1 West University Boulevard | Mohanty S.D.,University of Texas at Brownsville | Mohanty S.D.,1 West University Boulevard | And 2 more authors.
Astrophysical Journal | Year: 2014

The use of a high precision pulsar timing array is a promising approach to detecting gravitational waves in the very low frequency regime (10-6-10-9 Hz) that is complementary to ground-based efforts (e.g., LIGO, Virgo) at high frequencies (∼10-103 Hz) and space-based ones (e.g., LISA) at low frequencies (10-4-10-1 Hz). One of the target sources for pulsar timing arrays is individual supermassive black hole binaries which are expected to form in galactic mergers. In this paper, a likelihood-based method for detection and parameter estimation is presented for a monochromatic continuous gravitational wave signal emitted by such a source. The so-called pulsar terms in the signal that arise due to the breakdown of the long-wavelength approximation are explicitly taken into account in this method. In addition, the method accounts for equality and inequality constraints involved in the semi-analytical maximization of the likelihood over a subset of the parameters. The remaining parameters are maximized over numerically using Particle Swarm Optimization. Thus, the method presented here solves the monochromatic continuous wave detection and parameter estimation problem without invoking some of the approximations that have been used in earlier studies. © 2014. The American Astronomical Society. All rights reserved. Source

Wang Y.,Huazhong University of Science and Technology | Wang Y.,University of Texas at Brownsville | Wang Y.,1 West University Boulevard | Mohanty S.D.,University of Texas at Brownsville | And 3 more authors.
Astrophysical Journal | Year: 2015

Supermassive black hole binaries are one of the primary targets of gravitational wave (GW) searches using pulsar timing arrays (PTAs). GW signals from such systems are well represented by parameterized models, allowing the standard Generalized Likelihood Ratio Test (GLRT) to be used for their detection and estimation. However, there is a dichotomy in how the GLRT can be implemented for PTAs: there are two possible ways in which one can split the set of signal parameters for semi-analytical and numerical extremization. The straightforward extension of the method used for continuous signals in ground-based GW searches, where the so-called pulsar phase parameters are maximized numerically, was addressed in an earlier paper. In this paper, we report the first study of the performance of the second approach where the pulsar phases are maximized semi-analytically. This approach is scalable since the number of parameters left over for numerical optimization does not depend on the size of the PTA. Our results show that for the same array size (9 pulsars), the new method performs somewhat worse in parameter estimation, but not in detection, than the previous method where the pulsar phases were maximized numerically. The origin of the performance discrepancy is likely to be in the ill-posedness that is intrinsic to any network analysis method. However, the scalability of the new method allows the ill-posedness to be mitigated by simply adding more pulsars to the array. This is shown explicitly by taking a larger array of pulsars. © 2015. The American Astronomical Society. All rights reserved. Source

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