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Searches for stochastic gravitational-wave backgrounds using pulsar timing arrays look for correlations in the timing residuals induced by the background across the pulsars in the array.
Pergamon Press, Oxford, United Kingdom, 1968
C. W. Helstrom, Statistical Theory of Signal Detection · 1968
Earlier work this paper cites.
R. A. Hulse and J. H. Taylor, “Discovery of a pulsar in a binary system,” Astrophys. J
1975
Earlier work this paper cites.
F. B. Estabrook and H. D. Wahlquist, “Response of Doppler spacecraft tracking to gravitational radiation,” General Relativity and Gravitation
1975
Earlier work this paper cites.
M. V. Sazhin, “Opportunities for detecting ultralong gravitational waves,” Soviet Ast
1978
Earlier work this paper cites.
S. Detweiler, “Pulsar timing measurements and the search for gravitational waves,” Astrophys. J
1979
Earlier work this paper cites.
R. W. Hellings and G. S. Downs, “Upper limits on the istotropic gravitational radiation background from pulsar timing analysis,” Astrophys. J
1983
Earlier work this paper cites.
R. S. Foster and D. C. Backer, “Constructing a pulsar timing array,” Astrophys. J
1990
Cited alongside, same era.
I. H. Stairs, “Testing General Relativity with Pulsar Timing,” Living Reviews in Relativity
2003
Cited alongside, same era.
Cambridge University Press, Cambridge, UK, Dec. 2004
D. R. Lorimer and M. Kramer, Handbook of Pulsar Astronomy · 2004
Cited alongside, same era.
John Wiley & Sons, Inc., Hoboken, NJ, 2006
M. L. Boas, Mathematical methods in the physical sciences · 2006
Cited alongside, same era.
D. R. Lorimer, “Binary and Millisecond Pulsars,” Living Reviews in Relativity
2008
Cited alongside, same era.
K. J. Lee, F. A. Jenet, and R. H. Price, “Pulsar Timing as a Probe of Non-Einsteinian Polarizations of Gravitational Waves,” Astrophys. J
2008
M. Anholm, S. Ballmer, J. D. E. Creighton, L. R. Price, and X. Siemens, “Optimal strategies for gravitational wave stochastic background searches in pulsar timing data,” Phys. Rev. D
2009
Later among the works it cites.
J. M. Weisberg, D. J. Nice, and J. H. Taylor, “Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16,” Astrophys. J
2010
Later among the works it cites.
C. M. F. Mingarelli, T. Sidery, I. Mandel, and A. Vecchio, “Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays,” Phys. Rev. D
2013
Later among the works it cites.
S. R. Taylor and J. R. Gair, “Searching for anisotropic gravitational-wave backgrounds using pulsar timing arrays,” Phys. Rev. D
2013
Later among the works it cites.
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A pulsar timing model predicts the arrival times of the pulses given values for the pulsar’s spin frequency, frequency derivative, location on the sky, proper motion with respect to the solar system barycenter, its orbital parameters if the pulsar is in a binary, etc. [ 2 ] The values of these parameters are typically determined by an iterative least-squares fitting procedure, which minimizes the root-mean-squared (rms) deviation of the resultant timing residuals. Systematic errors in the timing model parameters can usually be identified by this iterative procedure, but unmodelled processes in the timing model will lead to errors in the timing residuals that cannot easily be removed
Cited in the paper.
We are assuming here that the two pulsars—even for the case ζ = 0 \zeta=0 —are distinct (i.e., they do not occupy the same physical location in space). If we consider the same pulsar, as would be the case for an autocorrelation calculation, then the right-hand-side of ( 1
Cited in the paper.
This statement is a generalization (to fields) of the mathematical result that the Fourier transform of the probability distribution p ( x ) p(x) for a random variable x x (i.e., the so-called characteristic function
Cited in the paper.
Recall: ∇ 2 = ( ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 + ∂ 2 ∂ z 2 ) \nabla^{2}=\left(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial y^{2}}+\frac{\partial^{2}}{\partial z^{2}}\right) in Cartesian coordinates ( x , y , z ) (x,y,z)
Cited in the paper.
The field might actually be a tensor field, like the gravitational-wave field h a b ( t , 𝐱 ) h_{ab}(t,\mathbf{x}) , and hence should have tensor indices in general. But for simplicity, we will ignore that complication here
Cited in the paper.
Hint: Work in the coordinate system shown in Fig. 3
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2013
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J. Gair, J. D. Romano, S. Taylor, and C. M. F. Mingarelli, “Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays,” Phys. Rev. D
2014
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