Pulsar Timing Arrays: No longer a Blunt Instrument for Gravitational Wave Detection

📝 Abstract

Pulsar timing now has a rich history in placing limits on the stochastic background of gravitational waves, and we plan soon to reach the sensitivity where we can detect, not just place limits on, the stochastic background. However, the capability of pulsar timing goes beyond the detection of a background. Herein I review efforts that include single source detection, localization, waveform recovery, a clever use of a “time-machine” effect, alternate theories of gravity, and finally studies of the noise in our “detector” that will allow us to tune and optimize the experiment. Pulsar timing arrays are no longer “blunt” instruments for gravitational-wave detection limited to only detecting an amplitude of the background. Rather they are shrewd and tunable detectors, capable of a rich and dynamic variety of astrophysical measurements.

💡 Analysis

Pulsar timing now has a rich history in placing limits on the stochastic background of gravitational waves, and we plan soon to reach the sensitivity where we can detect, not just place limits on, the stochastic background. However, the capability of pulsar timing goes beyond the detection of a background. Herein I review efforts that include single source detection, localization, waveform recovery, a clever use of a “time-machine” effect, alternate theories of gravity, and finally studies of the noise in our “detector” that will allow us to tune and optimize the experiment. Pulsar timing arrays are no longer “blunt” instruments for gravitational-wave detection limited to only detecting an amplitude of the background. Rather they are shrewd and tunable detectors, capable of a rich and dynamic variety of astrophysical measurements.

📄 Content

arXiv:1112.2158v2 [astro-ph.HE] 21 Dec 2011 Pulsar Timing Arrays: No longer a Blunt Instrument for Gravitational Wave Detection Andrea N. Lommen Franklin and Marshall College, 415 Harrisburg Pike, Lancaster, PA 17604 E-mail: andrea.lommen@fandm.edu Abstract. Pulsar timing now has a rich history in placing limits on the stochastic background of gravitational waves, and we plan soon to reach the sensitivity where we can detect, not just place limits on, the stochastic background. However, the capability of pulsar timing goes beyond the detection of a background. Herein I review efforts that include single source detection, localization, waveform recovery, a clever use of a “time-machine” effect, alternate theories of gravity, and finally studies of the noise in our “detector” that will allow us to tune and optimize the experiment. Pulsar timing arrays are no longer “blunt” instruments for gravitational-wave detection limited to only detecting an amplitude of the background. Rather they are shrewd and tunable detectors, capable of a rich and dynamic variety of astrophysical measurements.

1. Introduction Pulsars are basically celestial clocks, and as such, can be used to construct a Galactic-scale gravitational wave detector using the same concept as ground-based interferometric detectors, i.e. one looks for phase changes in the arrival of the signal at the vertex station, in this case, earth. The length scales of our detector ‘arms’ (1000 light years) as compared to the length of ground- based arms (4km) allow us to probe a different gravitational-wave frequency regime (nHz), a complement to the ground-based kHz regime (Yardley et al. 2010). For almost 30 years pulsar timers have been putting limits on the energy density of the stochastic background using pulsar timing (Romani & Taylor 1983; Stinebring et al. 1990; Kaspi, Taylor, & Ryba 1994; Lommen 2001; Jenet et al. 2006; van Haasteren et al. 2011; Yardley et al. 2011). They point out that at some moment in the future, we will detect rather than limit the stochastic background. This moment is predicted to be sometime within this decade (Demorest et al. 2009; Verbiest et al. 2009). In the last 10 years the field of gravitational-wave detection using pulsars has matured, and we are now considering much more than just the background of gravitational waves. We are demonstrating that very precise work on specific sources can be done, and that we need to ‘tune’ this detector in order to maximize our sensitivity to these sources. This manuscript briefly reviews these efforts, and is organized as follows. In §2 I give some more details about the concept and current thought behind using pulsar timing arrays (PTAs) to detect gravitational waves. In the subsequent sections I review the work that shows that PTAs can be (§3) directional detectors, (§4) used to recover the gravitational waveform, (§5) used to recover information about the source at some time in past, (§6) used to measure luminosity distance to gravitational-wave sources, (§7) used to test alternate theories of gravity, and (§8) characterized as a formal ‘detector’ using measurements of their noise. Finally, in §9 I summarize the ways in which a PTA is no longer a ‘blunt’ instrument for gravitational-wave detection, but rather a tunable, pointable, and adjustable detector that can be used to gain very specific astrophysical information about the gravitational-wave source being detected.
2. An overview of the concept of gravitational-wave detection using pulsars. Figure 1. (Adapted from NASA) Schematic of a gravitational wave from a black hole binary impinging on a 2-pulsar pulsar timing array. When proper length scales are used the gravitational waves are nearly planar on the scale of the earth-pulsar systems, but §6 discusses the possibility of measuring their curvature. Assume a gravitational wave is propagating through space in direction ˆk apparently due to some distant source such as a supermassive binary black hole (see figure 1). The gravitational wave changes the curvature of the space-time along which the electromagnetic wave is traveling, and as such induces a change in the time that the pulse arrives at earth. The size of the change at time t for a pulse from pulsar j, τGW(ˆk, t)j, is given by τGW(ˆk, t)j = F +(ˆk, ˆnj)g+(t, Lj, ˆk · ˆnj) + F ×(ˆk, ˆnj)g×(t, Lj, ˆk · ˆnj), (1) for a TT-gauge gravitational-wave metric perturbation with form h+e+ + h×e×. ˆnj is a unit vector pointing to pulsar j, Lj is the distance to that pulsar. F +/× are geometric functions of ˆk and ˆn which we omit here for brevity but can be found in Burt, Lommen, & Finn (2011). Functions g+ and g× are integrals of h+ and h× as follows (Finn & Lommen 2010): g(+/×)(t, Lj, ˆkj · ˆnj) = Z Lj 0 h+/×  t −(1 + ˆk · ˆnj)(Lj −λ)  dλ. (2) Note that we are using geometrized units where c = G = 1. Following Finn & Lommen (2010) we assume that a function f exists for which df+/×(u)/du = h+/×(u). (3) For a plane wave we can then do the integra

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