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

A coherent method for the detection and 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 the ground-based efforts (e.g., LIGO, Virgo) at high frequencies ($\sim 10 -10^3$ 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 are individual supermassive black hole binaries that are expected to form in galactic mergers. In this paper, a likelihood based method for detection and 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 estimation problem without invoking some of the approximations that have been used in earlier studies.Comment: 33 pages, 10 figures, submitted to Ap

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

Supermassive black hole binaries are one of the primary targets for gravitational wave searches using pulsar timing arrays. Gravitational wave signals from such systems are well represented by parametrized 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 pulsar timing arrays: 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 gravitational wave searches, where the so-called pulsar phase parameters are maximized numerically, was addressed in an earlier paper (Wang et al. 2014). 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 pulsar timing array. 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, 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.Comment: 30 pages, 11 figures, revised version, published in Ap

The Arecibo Observatory as an Instrument for Investigating Orbital Debris: Legacy and Next Generation Performance

In this paper, we investigate the ability of the Arecibo Observatory to characterize the orbital debris environment and compare it to the primary instrument used by NASA\u27s Orbital Debris Program Office, the Haystack Ultra-Wideband Satellite Imaging Radar (HUSIR). Arecibo\u27s location (183 N) increases the percentage of observable orbits (relative to HUSIR) by 27%, which gives Arecibo access to a much larger and previously unmeasured portion of the environment. Due to the recent collapse of the Arecibo dish, in addition to exploring historic capabilities of the Legacy Arecibo Telescope, estimates of the performance of the proposed Next Generation Arecibo Telescope (NGAT) are explored. We show that the current NGAT design could have a sensitivity comparable to the Goldstone Orbital Debris Radar, currently NASA\u27s most sensitive orbital debris radar. Additionally, design suggestions are presented that would significantly improve the capabilities of the NGAT for orbital debris investigations. We show that, with appropriate hardware upgrades, it would be possible to achieve a minimum-detectable debris size as small as 1 mm. These capabilities would allow data from Arecibo to significantly improve short-term debris environment models, which are used to inform spacecraft design and operations, particularly for orbital debris smaller than 3 mm, which pose the highest penetration risk to most spacecraft

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

The intrinsic intensity modulation of PSR B1937+21 at 1410 MHz

The single-pulse properties of the millisecond radio pulsar PSR B1937+21 are studied in the 1410 MHz radio band. Aside from occasional ``giant pulses'' occurring in restricted regions of pulse phase, the emission appears to be remarkably stable, showing no pulse-to-pulse fluctuations other then those induced by propagation through the interstellar medium. This type of behavior has not been seen in any other pulsar although it was seen in previous 430 MHz observations of this source. The stability of PSR B1937+21 can be understood in the context of the sparking gap model of radio pulsar emission. Given the emission properties of this source at 430 MHz, this model predicts that the emission at all higher frequencies will be just as stable. Since the stability depends on the outflow velocity of the emitting plasma, an upper bound may be placed on its Lorentz factor.Comment: submitted to ApJ

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.