Abstract
Pulsar timing arrays (PTAs) are designed to detect gravitational waves with periods from several months to several years, e.g. those produced by wide supermassive black-hole binaries in the centers of distant galaxies. Here we show that PTAs are also sensitive to mergers of supermassive black holes. While these mergers occur on a timescale too short to be resolvable by a PTA, they generate a change of metric due to non-linear gravitational-wave memory which persists for the duration of the experiment and could be detected. We develop the theory of the single-source detection by PTAs, and derive the sensitivity of PTAs to the gravitational-wave memory jumps. We show that mergers of black holes are-detectable (in a direction, polarisation, and time-dependent way) out to co-moving distances of billion light years. Modern predictions for black-hole merger rates imply marginal to modest chance of an individual jump detection by currently developed PTAs. The sensitivity is expected to be somewhat higher for futuristic PTA experiments with the Square Kilometre Array (SKA).
The world is full of obvious things which nobody by any chance ever observes.
Sherlock Holmes(Sir Arthur Conan Doyle)
This chapter is adapted from: R. van Haasteren and Y. Levin Gravitational-wave memory and Pulsar Timing Arrays MNRAS (2010) 401(4): 2372–2378 By permission of Oxford University Press on behalf of the Royal Astronomical Society.
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- 1.
It is always possible to represent the signal this way.
- 2.
For an array of 20 pulsars, there is a significant chance that a pulsar would have a strong alignment with the burst source, in which case 2 oppositely directed frequency jumps could be observed for this pulsar. However, since this would be for one pulsar at most, and since one of the two jumps is then indistinguishable from a glitch, we can safely ignore this fact.
- 3.
This is always possible by e.g. the Gramm–Schmidt procedure.
- 4.
A useful identity:
$$\begin{aligned} \frac{\partial [(t-t_0)\Theta (t-t_0)]}{\partial t_0}=-\Theta (t-t_0). \end{aligned}$$(3.37)
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van Haasteren, R. (2014). Gravitational-Wave Memory and Pulsar Timing Arrays. In: Gravitational Wave Detection and Data Analysis for Pulsar Timing Arrays. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39599-4_3
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DOI: https://doi.org/10.1007/978-3-642-39599-4_3
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