Pulsar Timing Arrays: Gravitational-wave detectors as big as the Galaxy

Rutger van Haasteren

[Rutger van Haasteren is the recipient of the 2011 GWIC (Gravitational Wave International Committee) Thesis Prize for his PhD thesis “Gravitational Wave detection and data analysis for Pulsar Timing Arrays” (PDF). -- 2Physics.com]

Author: Rutger van Haasteren 

Affiliation: 
Currently at Albert-Einstein-Institute (Max-Plack Institute for Gravitational Physics) in Hannover, Germany;
PhD research done at Leiden Observatory, Leiden University, The Netherlands.

Pulsars, rapidly rotating neutron stars that send an electromagnetic pulse towards the Earth with each revolution, are intimately connected to gravitational research and testing of Einstein's general theory of relativity. Besides the fact that neutron stars have very strong gravitational fields -- which is interesting from a general relativity point of view, their use as accurate clocks allows for a whole range of new gravitational experiments. Especially millisecond pulsars, recycled pulsars that have been spun-up by a companion star (see this video by John Rowe Animation/Australia Telescope National Facility, CSIRO, Australia), are very stable rotators due to their high spin frequency, relatively low magnetic field, and high mass. This makes millisecond pulsars most suitable as nearly-perfect Einstein clocks.

2Physics articles by past winners of the GWIC Thesis Prize:

Haixing Miao (2010): "Exploring Macroscopic Quantum Mechanics with Gravitational-wave Detectors"
Holger J. Pletsch (2009): "Deepest All-Sky Surveys for Continuous Gravitational Waves"
Henning Vahlbruch (2008): "Squeezed Light – the first real application starts now"
Keisuke Goda (2007): "Beating the Quantum Limit in Gravitational Wave Detectors"
Yoichi Aso (2006): "Novel Low-Frequency Vibration Isolation Technique for Interferometric Gravitational Wave Detectors"
Rana Adhikari (2003-5)*: "Interferometric Detection of Gravitational Waves : 5 Needed Breakthroughs"
*Note, the gravitational wave thesis prize was started initially by LIGO as a biannual prize, limited to students of the LIGO Scientific Collaboration (LSC). The first award covered the period from 1 July 2003 to 30 June 2005. In 2006, the thesis prize was adopted by GWIC, renamed, converted to an annual prize, and opened to the broader international community.

We can accurately track a pulsar's trajectory with respect to the Earth by monitoring the arrival times of their pulses; given that for the most well-timed millisecond pulsars we can determine the time of arrival of a single averaged pulse up to 50 nanoseconds, we are effectively sensitive to variations in the Earth-pulsar distance up to only several dozens of meters. This is because light can only travel about one foot in a nanosecond. Because some pulsars are in very tight binary systems, such an accurate measurement of the orbit of a pulsar around a companion can be used to verify/falsify the predictions of general relativity. This was first done with the binary pulsar, PSR J1915+1606, also called the Hulse-Taylor binary, which was discovered in 1974 [1]. This system is a double neutron star system of which one of the two bodies is a pulsar. The two stars are close together: a full orbital period only takes 7.75 hours. For two such massive bodies in such a tight orbit general relativity predicts that the emission of gravitational waves is significant, which would cause a decrease in the orbital period due to loss of energy of the system (see see this video by John Rowe Animation/Australia Telescope National Facility, CSIRO, Australia). By closely tracking the dynamics of the Hulse-Taylor binary, this decrease in the orbital period was confirmed exactly (figure 1), confirming the existence of gravitational waves. This has resulted in Hulse and Taylor been awarded the Nobel prize in physics in 1993 [2].

Figure 1: Decreasing period of rotation of binary pulsar PSR J1915+1606

The confirmation of the existence of gravitational waves with the Hulse-Taylor binary is considered an indirect detection of gravitational waves, because it has been shown that the energy loss of a system is consistent with gravitational-wave emission. A direct detection would have to consist of evidence that the gravitational waves are present elsewhere than at the point of emission: by using a gravitational-wave detector.

Generally speaking, two approaches exist to directly detect gravitational waves:
1) A large body of mass is used as a resonator, where the gravitational waves are expected to excite the resonant frequencies of such a so-called resonant-mass detector.
2) A signal is sent from one place to another, where the gravitational waves are expected to perturb the propagation of the signal such that its arrival time slightly changes. In laser interferometry detectors (e.g. LIGO) this results in a changing interference pattern at the point of recombination of two laser beams.

Figure 2: Concept of a pulsar timing array [Image credit: David J. Champion]

As it turns out, millisecond pulsars can be used to 'construct' a gravitational-wave detector of the second kind, where the pulse propagation from the pulsar to the Earth is perturbed by astrophysical gravitational waves [3]. The very regular arrival times of a millisecond pulsar will arrive slightly early or late due to gravitational waves that pass through the Earth-pulsar system, which in principle makes the gravitational waves detectable. Because the typically observed millisecond pulsars for these purposes are several kpc away, a pulsar timing array is basically a gravitational wave detector of galactic scale (figure 2; Also see this video by John Rowe Animation/Australia Telescope National Facility, CSIRO, Australia)).

A pulsar timing array is sensitive to gravitational waves with frequencies of a few dozen to a few hundred nHz [4], which is the frequency range where tight supermassive black-hole binaries (SMBHB) are expected to be the dominant sources of continuous gravitational waves. A canonical SMBHB system that would contribute to the gravitational-wave signal would consist of two supermassive black holes with masses of close to one billion solar masses at a distance of a Gpc, with an orbital period of several months to years. Many such systems are expected to exist in the universe, which would results in an isotropic superposition usually called a stochastic background of gravitational waves [5]. Large-scale computer simulations of the evolution of the universe suggest that some of the individual sources might be eventually uniquely detectable, but the bulk of the signal would consist of such an isotropic stochastic background of gravitational waves [6]. Because the evolution of the universe is intimately connected to the SMBHB gravitational-wave signal, it is thought that measuring the stochastic gravitational-wave background and possibly single SMBHB sources would contribute greatly to our understanding of cosmology. This is a frequency band that is unreachable for any other type of gravitational-wave detector, which makes pulsar timing arrays a unique and complementary tool next to the other gravitational-wave detection programmes like the ground-based gravitational observatories.

Pulsar timing array science is still relatively new, and a new international pulsar timing array (IPTA, [7]) collaboration has only recently been formed as an alliance between three ongoing pulsar timing array efforts: the European Pulsar Timing Array (EPTA, [8]), the North American Nanohertz Observatory for Gravitational waves (NANOGrav, [10]), and the Australian Parkes Pulsar Timing Array (PPTA, [9]). The PPTA uses a single radio telescope based in Parkes, Australia, with a 64m dish. NANOGrav uses the worlds two largest single-dish radio telescope: the 100m Green Bank Telescope, and the 305m Arecibo Observatory. The EPTA uses five radio telescopes spread throughout Europe: the Westerbork synthesis radio telescope in the Netherlands, the Lovell telescope in the UK, the Effelsberg telescope in Germany, the Nancay radio telescope in France, and the Sardinia radio telescope in Italy. These five European radio telescopes are currently being linked together to coherently combine their signals, effectively forming one big phased array called the Large European Array for Pulsars (LEAP, [8]). This improvement should boost sensitivity for pulsar timing array purposes.

The Effelsberg Radio Telescope near Effelsberg, Germany. This is the worlds second-largest fully steerable radio telescope, with a diameter of 100 meters. [Image credit: Gemma Janssen]

Between the ground-based gravitational-wave detectors and pulsar timing arrays, it is basically a scientific race focused on who will make the first detection, with both projects having good chances of being the first. Pulsar timing arrays have the advantage that the signal rms is expected to increase sharply with time. Even if pulsar timing arrays cannot reduce their noise with their always ongoing efforts, sensitivity will still gradually increase over time, making a detection possible. However, the theoretical predictions about the stochastic background amplitude and the event rates of single sources are less certain than for ground-based detectors. The big ground-based detectors are currently upgrading their instruments, which are expected to become operational somewhere in 2015.

The Parkes Radio Telescope near Parkes, Australia. This radio telescope with a diameter of 64 meters is the worlds leading radio telescope in discovery of radio pulsars. [Image credit: Aristeidis Noutsos]

Even without upgrading instruments, sensitivity of both types of gravitational-wave detectors can be increased with better data analysis methods which would allow more information to be extracted from the data. In order to do that, a Bayesian data analysis method for pulsar timing arrays has been developed that can theoretically extract all information of the signal that is present in the data. General relativity describes the gravitational-wave signal of the stochastic background as a both time correlated and spatially correlated signal between all the pulsars, which means that the data of the different pulsars cannot be treated individually. Extracting such a signal from the data is non-trivial, especially for non-uniformly sampled data with ill-understood noise like that of millisecond pulsars. The Bayesian analysis is suitable for such an analysis, and has been shown to work well for both stochastic background signals [11], and single sources like the gravitational-wave memory effect [12]. The developed Bayesian analysis has resulted in the most stringent upper-limit on the stochastic gravitational-wave background to date [11].

The Westerbork Synthesis Radio Telescope near Westerbork, The Netherlands. This radio telescope is composed of 14 dishes with a diameter of 25 meter, which combine into a radio telescope of similar sensitivity to that of the Effelsberg Radio Telescope. [Image credit: Cees Bassa]

In the coming years, the Chinese five hundred meter aperture spherical telescope (FAST, [13]), and the planned Square Kilometre Array (SKA, [14]) will provide a major leap in sensitivity. Especially the SKA, built by a collaboration of 20 countries, will dramatically change pulsar timing array science. It will be a phased array of many dishes located across South Africa, Australia and New Zealand [15]. With its vast collecting area of one million square meter it is expected to find nearly all the pulsars in the Galaxy. With all those pulsars a very sensitive gravitational-wave detector with possibly up to one hundred arms can be constructed. This should open up a new window to observe the universe, and provide unique insights into cosmology.

References:
[1] R.A. Hulse, J.H. Taylor, "Discovery of a pulsar in a binary system", The Astrophysical Journal, 195, L51 (1975). Full text.
[2] http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/
[3] Frank B. Estabrook and Hugo D. Wahlquist, "Response of Doppler spacecraft tracking to gravitational radiation", General Relativity and Gravitation, 6, 439 (1975). Abstract.
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[9] G. Hobbs, D. Miller, R. N. Manchester, J. Dempsey, J. M. Chapman, J. Khoo, J. Applegate, M. Bailes, N. D. R. Bhat, R. Bridle, A. Borg, A. Brown, C. Burnett, F. Camilo, C. Cattalini, A. Chaudhary, R. Chen, N. D’Amico, L. Kedziora-Chudczer, T. Cornwell, R. George, G. Hampson, M. Hepburn, A. Jameson, M. Keith, T. Kelly, A. Kosmynin, E. Lenc, D. Lorimer, C. Love, A. Lyne, V. McIntyre, J. Morrissey, M. Pienaar, J. Reynolds, G. Ryder, J. Sarkissian, A. Stevenson, A. Treloar, W. van Straten, M. Whiting and G. Wilson, "The Parkes Observatory Pulsar Data Archive", Publications of the Astronomical Society of Australia, 26, 103 (2009). Full Text.
[10] P. B. Demorest, R. D. Ferdman, M. E. Gonzalez, D. Nice, S. Ransom, I. H. Stairs, Z. Arzoumanian, A. Brazier, S. Burke-Spolaor, S. J. Chamberlin, J. M. Cordes, J. Ellis, L. S. Finn, P. Freire, S. Giampanis, F. Jenet, V. M. Kaspi, J. Lazio, A. N. Lommen, M. McLaughlin, N. Palliyaguru, D. Perrodin, R. M. Shannon, X. Siemens, D. Stinebring, J. Swiggum, W. W. Zhu, "Limits on the Stochastic Gravitational Wave Background from the North American Nanohertz Observatory for Gravitational Waves", eprint arXiv:1201.6641 (2012)
[11] R. van Haasteren, Y. Levin, G. H. Janssen, K. Lazaridis, M. Kramer, B. W. Stappers, G. Desvignes, M. B. Purver, A. G. Lyne, R. D. Ferdman, A. Jessner, I. Cognard, G. Theureau, N. D’Amico, A. Possenti, M. Burgay, A. Corongiu, J. W. T. Hessels, R. Smits and J. P. W. Verbiest, "Placing limits on the stochastic gravitational-wave background using European Pulsar Timing Array data", Monthly Notices of the Royal Astronomical Society, 414, 3117 (2011). Abstract.
[12] Rutger van Haasteren and Yuri Levin, "Gravitational-wave memory and pulsar timing arrays", Monthly Notices of the Royal Astronomical Society, 401, 2372 (2010). Abstract.
[13] R. Smits, M. Kramer, B. Stappers, D.R. Lorimer, J. Cordes, and A. Faulkner, "Pulsar searches and timing with the square kilometre array", Astronomy & Astrophysics, 505, 919 (2009). Abstract.
[14] T. Joseph W. Lazio, "The Square Kilometre Array", in Panoramic Radio Astronomy: Wide-field 1-2 GHz Research on Galaxy Evolution (2009). Full Text.
[15] http://www.skatelescope.org/news/dual-site-agreed-square-kilometre-array-telescope/