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

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

Single Pulse Characteristics of the Millisecond Radio Pulsar PSR B1937+21 at 430 MHz

The single-pulse characteristics of the millisecond pulsar PSR B1937+21 are studied using the recently installed Caltech baseband recorder at the Arecibo Radio Observatory in Puerto Rico. This is the first such analysis of this object that includes both average intensity pulses as well as "giant pulses." Pulse ensemble-averaging techniques are developed in order to study the characteristics of PSR B1937+21's single pulses since the high time resolution signal-to-noise ratio is less than unity. This analysis reveals that the non-giant pulse radio emission is extremely stable. All observed fluctuations are consistent with diffractive interstellar scattering. Such intrinsic stability has yet to be observed in other radio pulsars

Using the Intensity Modulation Index to Test Pulsar Radio Emission Models

This letter explores the possibility of testing pulsar radio emission models by observing pulse-to-pulse intensity modulation. It is shown that a relationship between a pulsar's period, period derivative, and intensity modulation is a natural consequence of at least one theoretical model of radio pulsar emission. It is proposed that other models may also predict a similar correlation. The exact form of the relationship will depend on the model in question. Hence, observations of intensity modulation should be able to determine the validity of the various emission models. In an attempt to search for the predicted dependencies, the modulation properties of a set of 12 pulsars are studied. These data are suggestive, but they are unable to differentiate between three possibilities for the emission process. Future observations will be able to confirm these results and determine whether or not specific emission models are viable.Comment: Accepted by ApJ Letters for the October 20th issu

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

Gravitational Wave Hotspots: Ranking Potential Locations of Single-Source Gravitational Wave Emission

The steadily improving sensitivity of pulsar timing arrays (PTAs) suggests that gravitational waves (GWs) from supermassive black hole binary (SMBHB) systems in the nearby universe will be de- tectable sometime during the next decade. Currently, PTAs assume an equal probability of detection from every sky position, but as evidence grows for a non-isotropic distribution of sources, is there a most likely sky position for a detectable single source of GWs? In this paper, a collection of galactic catalogs is used to calculate various metrics related to the detectability of a single GW source resolv- able above a GW background, assuming that every galaxy has the same probability of containing a SMBHB. Our analyses of these data reveal small probabilities that one of these sources is currently in the PTA band, but as sensitivity is improved regions of consistent probability density are found in predictable locations, specifically around local galaxy clusters.Comment: 9 pages, 9 figures, accepted for submission in Ap