A pulsar timing array and the nHz-GW sky

A variety of sources is expected to emit GWs in the frequency range detectable by pulsar timing. Each of these sources will typically have a different spectrum that allows us in principle to distinguish between the sources. In general, one can expect a random superposition of a GW emission from a large number of independent sources, leading to a stochastic GW background. The effect of such a GW background is such that the Earth is modified in a manner that is the same for all sources being timed. In other words, a displacement of the Earth causes the pulses from all pulsars in a particular sky direction to arrive early, while signals from sources in the opposite direction would come late. Pulse arrival times from pulsars in perpendicular directions would be unaffected. The consequence is the existence of a correlation between the timing residuals of an ensemble of timed pulsars in the PTA. A stochastic GW background manifests itself as a distinct trend in the correlation between these timing residuals as a function of pulsar angular separation on the sky – a quadrupole signature in this correlation, to be more precise (see Figure 2).

Gravity waves are sent out due to the coalescence of black holes at the centres of two merging galaxies. These gravity waves propagate through space until they arrive at the Milky Way, where they modulate the signals from pulsars, such that the apparent pulsar period is alternately red-shifted and blue-shifted as the wave passes over the pulsar and the Earth (John Rowe Animation/Australia Telescope National Facility, CSIRO).

The most prominent contributor to a stochastic GW background is the population of supermassive binary black holes which are expected to have merged during the evolution of galaxies in the early Universe. In fact, a detection of such a signal would have direct consequences on cosmological models and their predictions for the expected merger rate (e.g. Jaffe & Backer 2003, ApJ, 584, 616; Jenet et al. 2006, ApJ, 653, 1571). However, more exotic GW sources also exist, and other contributions to a stochastic GW background include cosmological sources such as inflation and phase transitions (e.g. Maggiore, 2000, Phys. Rep. 331, 283), relic gravitational waves (Battye & Shellard, 1997, Classical Quantum Gravity, 13, A239; Grishuk 2005, Physics-Uspekhi, 38, 1235) or cosmic strings (e.g. Damour & Vilenkin, 2005, Phys. Rev. D, 71, 063510). It is also possible to detect single sources of GW emission, such as the periodic GW signal of a binary super-massive black hole in the centre of a nearby Galaxy (e.g. Jenet et al. 2004, ApJ, 606, 799) or a transient GW burst (e.g. Lommen 2002, in WE-Hereaus Seminar on “Neutron Stars, Pulsars, and Supernova Remnants”, ed. Becker, Lesch & Trümper, MPE-Garching, 114). In this case, however, a sufficiently good timing precision must be matched with a fortuitous relative geometrical alignment and an appropriately dense data span. It is possible but unlikely that such signals can be detected before the Square-Kilometre Array (SKA) may become operational at the end of the next decade (cf. Kramer et al. 2004, New Astronomy Reviews, 48, 993).

Hopefully it has been made sufficiently clear that the direct detection of GWs is crucial for a number of reasons. The most important and fundamental of these implications is the goal of eventually determining whether GR is the correct theory of gravity, or simply the best we have at the moment. If it is the latter, we can hope to answer the question that asks when, and under what circumstances, will GR break down. It can also allow us to explore the question of whether there are other current or heretofore unimagined theories that supercede it in describing everything from the evoution of our Milky Way and other galaxies to the formation and unfolding over time of our Universe. Pulsar timing array science is being performed by three major collaborations around the world: the EPTA in Europe, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), and the Parkes Pulsar Timing Array (PPTA) in Australia. This endeavour has begun to prove itself as an important – and possibly the first – method towards direct gravitational wave detection.