Practical Methods for Continuous Gravitational Wave Detection using Pulsar Timing Data

Gravitational Waves (GWs) are tiny ripples in the fabric of space-time predicted by Einstein's General Relativity. Pulsar timing arrays (PTAs) are well poised to detect low frequency ($10^{-9}$ -- $10^{-7}$ Hz) GWs in the near future. There has been a significant amount of research into the detection of a stochastic background of GWs from supermassive black hole binaries (SMBHBs). Recent work has shown that single continuous sources standing out above the background may be detectable by PTAs operating at a sensitivity sufficient to detect the stochastic background. The most likely sources of continuous GWs in the pulsar timing frequency band are extremely massive and/or nearby SMBHBs. In this paper we present detection strategies including various forms of matched filtering and power spectral summing. We determine the efficacy and computational cost of such strategies. It is shown that it is computationally infeasible to use an optimal matched filter including the poorly constrained pulsar distances with a grid based method. We show that an Earth-term-matched filter constructed using only the correlated signal terms is both computationally viable and highly sensitive to GW signals. This technique is only a factor of two less sensitive than the computationally unrealizable optimal matched filter and a factor of two more sensitive than a power spectral summing technique. We further show that a pairwise matched filter, taking the pulsar distances into account is comparable to the optimal matched filter for the single template case and comparable to the Earth-term-matched filter for many search templates. Finally, using simulated data optimal quality, we place a theoretical minimum detectable strain amplitude of $h>2\times 10^{-15}$ from continuous GWs at frequencies on the order $\sim1/T_{\rm obs}$.Comment: submitted to Ap

Detection of variable frequency signals using a fast chirp transform

The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of significant interest for the new generation of interferometric gravitational wave detectors such as LIGO. However, this work has significant generality beyond gravitational wave signal detection. We define a Fast Chirp Transform (FCT) analogous to the Fast Fourier Transform (FFT). Use of the FCT provides a simple and powerful formalism for detection of signals with variable frequency just as Fourier transform techniques provide a formalism for the detection of signals of constant frequency. In particular, use of the FCT can alleviate the requirement of generating complicated families of filter functions typically required in the conventional matched filtering process. We briefly discuss the application of the FCT to several signal detection problems of current interest

Constraining the coalescence rate of supermassive black-hole binaries using pulsar timing

Pulsar timing observations are used to place constraints on the rate of coalescence of supermassive black-hole (SMBH) binaries as a function of mass and redshift. In contrast to the indirect constraints obtained from other techniques, pulsar timing observations provide a direct constraint on the black-hole merger rate. This is possible since pulsar timing is sensitive to the gravitational waves (GWs) emitted by these sources in the final stages of their evolution. We find that upper bounds calculated from the recently published Parkes Pulsar Timing Array data are just above theoretical predictions for redshifts below 10. In the future, with improved timing precision and longer data spans, we show that a non-detection of GWs will rule out some of the available parameter space in a particular class of SMBH binary merger models. We also show that if we can time a set of pulsars to 10ns timing accuracy, for example, using the proposed Square Kilometre Array, it should be possible to detect one or more individual SMBH binary systems

Detecting gravitational wave memory with pulsar timing

We compare the detectability of gravitational bursts passing through the solar system with those passing near each millisecond pulsar in an N-pulsar timing array. The sensitivity to Earth-passing bursts can exploit the correlation expected in pulse arrival times while pulsar-passing bursts, though uncorrelated between objects, provide an N-fold increase in overall time baseline that can compensate for the lower sensitivity. Bursts with memory from mergers of supermassive black holes produce step functions in apparent spin frequency that are the easiest to detect in pulsar timing. We show that the burst rate and amplitude distribution, while strongly dependent on inadequately known cosmological evolution, may favor detection in the pulsar terms rather than the Earth timing perturbations. Any contamination of timing data by red spin noise makes burst detection more difficult because both signals grow with the length of the time data span T. Furthermore, the different bursts that could appear in one or more data sets of length T 10yr also affect the detectability of the gravitational wave stochastic background that, like spin noise, has a red power spectrum. A burst with memory is a worthwhile target in the timing of multiple pulsars in a globular cluster because it should produce a correlated signal with a time delay of less than about 10years in some cases. © 2012. The American Astronomical Society. All rights reserved.

Radio Pulse Properties of the Millisecond Pulsar PSR J0437-4715. I. Observations at 20cm

We present a total of 48 minutes of observations of the nearby, bright millisecond pulsar PSR J0437-4715 taken at the Parkes radio observatory in Australia. The data were obtained at a central radio frequency of 1380 MHz using a high-speed tape recorder that permitted coherent Nyquist sampling of 50 MHz of bandwidth in each of two polarizations. Using the high time resolution available from this voltage recording technique, we have studied a variety of single-pulse properties, most for the first time in a millisecond pulsar. We find no evidence for "diffractive" quantization effects in the individual pulse arrival times or amplitudes as have been reported for this pulsar at lower radio frequency using coarser time resolution (Ables et al. 1997). Overall, we find that the single pulse properties of PSR J0437-4715 are similar to those of the common slow-rotating pulsars, even though this pulsar's magnetosphere and surface magnetic field are several orders of magnitude smaller than those of the general population. The pulsar radio emission mechanism must therefore be insensitive to these fundamental neutron star properties.Comment: 24 Postscript pages, 11 eps figures. Accepted for publication in the Astrophysical Journal. Abbreviated abstract follow

Pulsar timing and spacetime curvature

We analyze the effect of weak field gravitational waves on the timing of pulsars, with particular attention to gauge invariance, that is, to the effects that are independent of the choice of coordinates. We find (1) the Doppler shift cannot be separated into gauge invariant gravitational wave and kinetic contributions; (2) a gauge invariant separation can be made for the time derivative of the Doppler shift in which the gravitational wave contribution is directly related to the Riemann tensor, and the kinetic contribution is that for special relativity; (3) the gaugedependent effects in the Doppler shift play no role in the program of gravitational wave detection via pulsar timing. The direct connection shown between pulsar timing and the Riemann tensor of the gravitational waves will be of importance in discussions of gravitational waves from alternative (non-Einsteinian) theories of gravitation

Search for Electromagnetic Counterparts to LIGO-Virgo Candidates: Expanded Very Large Array

This paper summarizes a search for radio wavelength counterparts to candidate gravitational wave events. The identification of an electromagnetic counterpart could provide a more complete understanding of a gravitational wave event, including such characteristics as the location and the nature of the progenitor. We used the Expanded Very Large Array (EVLA) to search six galaxies which were identified as potential hosts for two candidate gravitational wave events. We summarize our procedures and discuss preliminary results.Comment: 4 pages; to appear in the New Horizons in Time Domain Astronomy, Proceedings of IAU Symposium 285, eds. R. E. M. Griffin, R. J. Hanisch & R. Seama

A coherent method for the detection and parameter estimation of continuous gravitational wave signals using a pulsar timing array

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

Electromagnetic Strong Plasma Turbulence

The first large-scale simulations of continuously driven, two-dimensional electromagnetic strong plasma turbulence are performed, for electron thermal speeds 0.01c⩽v⩽0.57c, by integrating the Zakharov equations for coupled Langmuir and transverse (T) waves near the plasma frequency. Turbulence scalings and wave number spectra are calculated, a transition is found from a mix of trapped and free T eigenstates for v⩾0.1c to just free eigenstates for v⩽0.1c, and wave energy densities are observed to undergo slow quasiperiodic oscillations

Pulsar timing as a probe of non-einsteinlan polarizations of gravitational waves

Einstein\u27s theory of gravity predicts waves of the distortion of spacetime with two degrees of polarization; alternative theories predict more polarizations, up to a maximum of six. Although laser interferometric gravity wave detectors can be used to search for at least some of the non-Einsteinian polarizations, their configuration is not optimal for the task. By contrast, the angular distribution of pulsars in the sky makes pulsar timing a flexible tool for detecting all polarizations. We give here an analysis of the sensitivity of pulsar timing to an isotropic stochastic gravitational wave background of waves with non-Einsteinian polarizations and conclude that their detection may be feasible in the near future. In particular, we compute the number of pulsars necessary to detect a stochastic background made up of one type of polarization and to distinguish non-Einsteinian from standard polarizations. We conclude that for biweekly observations made for five years with rms timing accuracy of 100 ns, detecting non-Einsteinian modes will require: 60 pulsars in the case of the longitudinal mode; 60 for the two spin-1 \ shear\ modes; and 40 for the spin-0 \ breathing\ mode. These are targets that should be easily achievable with the proposed Square Kilometer Array project. To discriminate non-Einsteinian modes from Einsteinian modes, we need 40 pulsars for the breathing mode, 100 pulsars for the longitudinal mode, and 500 pulsars for the shear mode. We confirm the previous estimate that 40 pulsars are needed to detect the spin-2 \ transverse\ (Einsteinian) polarizations. Better focused statistical tests may allow improvements in sensitivity for some of these polarizations. © 2008. The American Astronomical Society. All rights reserved