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Pulsar Timing and Gravitational Wave Detection

by John G. Cramer

Alternate View Column AV-154
Keywords: pulsar, timing, gravitational, wave, detection
Published in the October-2010 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 5/16/2010 and is copyrighted ©2010 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

                The first pulsar was observed in November 28, 1967 by Antony Hewish and his graduate student Jocelyn Bell Burnell of the Cavendish Laboratory at Cambridge University in the UK.  The object they detected with their radio telescope emitted surprisingly regular bursts of radio waves.   They initially called their discovery "LGM-1".  The LGM designation stood for "little green men", an inside joke based on the speculation that they might be receiving radio signals from an alien civilization.   It was subsequently concluded that the radio pulses were the result of a "lighthouse-effect" made by radio waves beamed from the magnetic poles of a spinning neutron star, so that the radio beam swept across the detector making regular pulses as the neutron star rotated.

A neutron star is an ultra-dense stellar remnant left behind by a low-mass supernova.  (High-mass supernovas leave behind black holes.)  A typical neutron star has a mass about 1.4 times that of our Sun, but it has a radius of only about 10 kilometers.  The large mass and small size give it a density comparable to that of atomic nuclei.   Essentially, a neutron star is a giant nucleus consisting almost entirely of neutrons held together by the force of gravity.  Neutron stars have about the same angular momentum that their parent star had before the supernova and typically spin very rapidly, about one rotation every 0.0014 seconds or 42,900 RPM .  They have polar magnetic fields between 104 and 1010 tesla, much larger than any magnetic field that we are able to produce in our puny Earth-bound laboratories.  This huge field, combined with the high spin rate, causes many neutron stars to beam radio pulses (and also visible light and x-ray pulses) as they rotate.

Perhaps the most remarkable thing about neutron-star pulsars, aside from the fact that they exist at all, is that the pulses are so regular in time.   They are not perfectly regular, however, because neutron stars spin down, due mainly to the emission of electromagnetic radiation, and lose spin energy and angular momentum as they age.  Young neutron stars, created within the last 100,000, years have the highest spin-down rates and the most rotational "noise" due to internal star-quakes.  Older systems, with ages up to 100 million years, have rotational periods that are more stable and reliable.

In 1974 Joseph H. Taylor of Princeton University and his graduate student Russell A. Hulse detected radio pulses from one of a pair of neutron stars that were closely orbiting each other.  The timing and Doppler shift of the pulses allowed them to precisely determine the rotation period of the binary system (about 8 hours). They made repeated measurements over several years and found that the rotation period of the binary system was increasing because the two stars were slowly "spinning down", losing a tiny fraction of their rotational energy as they orbited.  They showed that this loss of energy was precisely the amount predicted by Einstein's general theory of relativity as the energy loss due to the production of gravitational waves by the two massive counter-rotating stars.  Thus, in a rather indirect way, gravitational waves have been "observed" though their removal of energy and angular momentum from a binary neutron star.  In 1993 Taylor and Hulse received the Nobel Prize in Physics in recognition of this work.

Some pulsar systems have exceptionally regular pulse rates.  By far the best pulsar systems, from the point of view of pulse regularity, are the millisecond pulsar binary systems (period less than 10 milliseconds).  These are pulsar members of a binary system in which the companion star has a relatively low mass.  Astronomers have identified about 70 of these pulsar systems distributed fairly uniformly around our galaxy.  They have remarkably stable periods.  One of these pulsars with the less-than-memorable name of PSD J037-4715 was determined to have a period of 5.757451924362137 ± 0.000000000000002 milliseconds at midnight, April 6, 2001 , and to have a spin-down rate of 5.79370 ± 0.00002 x 10-20.  This illustrates the remarkable precision with which the pulsar's pulses can be timed.  This precision can be exploited for direct investigation of other phenomena, including gravitational waves.

What are gravitational waves?  A gravitational field, which can be viewed as a distortion of local space, surrounds every massive object.  Gravitational waves can be viewed as spreading ripples in this space distortion which arise when a massive object is moved and its gravitational fields disturbed.   Like light, gravitational waves travel at the speed of light and obey the inverse-square law [intensity is proportional to 1/(distance)2]. Gravitational waves induce a kind of "kneading" distortion in the space through which they move, making local distances alternately larger and smaller.  In one direction, perpendicular to the wave's direction of travel, space is stretched, while in the other direction space is compressed, with the stretch and compression exchanging places after half a period of the wave.  The wave can be visualized a longsausage with its sides alternately pinched in side-to-side and top-to-bottom, with the pinches along the length of the sausage repeating with each wavelength and the entire sausage moving forward at the speed of light.

Gravitational waves have two distinct states of polarization.  Viewed head-on, gravitational waves with the "+" polarization state alternately compress and expand space top-to-bottom and side-to-side (kneading space with a "+" pattern).  Gravitational waves having the "X" polarization state compress and expand space along lines 450 to the right of vertical and to the left of vertical (kneading with an "X" pattern).  These two polarization states make gravitational wave detection more difficult because a given detector is usually sensitive to only one of the two states and therefore detects only half of the possible signals.

Gravitational waves are very difficult to detect directly because they are the wave embodiment of the weakest force of the universe (gravity is 4.3 x 10-40 times weaker than electromagnetism).  The effects of gravitational waves on matter are correspondingly small.  Early detection attempts, using large resonant cylinders as detectors, produced some f\positive reports in the 1970's.  Ultimately, however, resonant-cylinder detectors were shown to be too insensitive to detect gravitational waves at the intensities expected.  At this writing (5/11/2010), despite the construction and operation of major interferometer-based gravitational wave detectors in the USA (LIGO), Germany (Geo 600), Italy (Virgo), and Japan (TAMA 300), gravitational waves have still not been directly detected.

Now there is a clever new approach to the problem of gravitational wave detection.   As gravitational waves travel, they distort the space through which they travel, causing adjacent points to momentarily become farther apart or closer together.  The result of this is that radio waves moving through a gravitational-wave distorted region of space will have a small variation, on the order of a microsecond, in their transit time through the region.  This effect is independent of the polarization of the gravitational wave.

Thus, the precise timing of the radio pulses from millisecond pulsars will be modified as they pass through a region where the gravitational waves are present, and the pulse train will be delayed by microseconds to nanoseconds.  This, at least in principle, permits gravitational-wave detection.  Further, since there are about 70 known millisecond pulsars, a large fraction of which having trains of pulses that could be delayed by same gravitational wave, pairs of pulsar signals can be correlated to focus on the time delay variation present in both signals from the two pulsars, thereby suppressing noise.  These relative strengths of these correlations can also give fairly precise information on the direction and distance of the source that produced the gravitational waves, provided that production was in the right frequency range and of sufficient intensity.

The NANOGrav Collaboration (North American Nanohertz Observatory for Gravitational Waves) is US/Canadian group of radio astronomers who are attempting to use millisecond pulsar timing, combining observations from a number of radio telescopes, to directly detect low frequency gravitational waves.  The work is complementary to that of ground-based gravitational wave detectors (e.g., LIGO, etc.) and to the proposed space-based detector (LISA).  LIGO is sensitive to gravitational waves with frequencies between 50 Hz and 10 kHz.  LISA will be sensitive to gravitational waves with frequencies between 1 Hz and 10-5 Hz.  The NANOGrav observations of pulsar timing will be sensitive to gravitational waves with very low frequencies between 10-7 and 10-10 Hz.

It turns out that significant gravitational wave radiation from two independent mechanisms should exist in the NANOGrav range of frequencies.  In particular, there should be large numbers of super-massive black hole binary systems in the universe.  These systems, usually near galactic centers, should involve pairs of orbiting super-massive black holes with masses on the order of 107 solar masses.  Such systems should produce very intense low frequency gravitational waves that fall within the range of sensitivity of NANOGrav observations.  In addition, it is expected that during the inflationary period of the early universe, primordial gravitational waves of similar intensities and frequencies should have been produced as the universe expanded and should still be present as the gravitational analog of the cosmic microwave background.

The problem for the NANOGrav detection of gravitational waves is that the present precision with which pulsar periods are determined lacks sufficient precision to achieve the needed sensitivity due to sparse data collection and insufficient duration of pulsar detection.  Their goal is to correct these deficiencies by 2015 and to monitor at least 20 pulsars with 100 nanosecond precision and 5 pulsars with 10 nanosecond precision.

This improvement should allow them to observe, identify, and locate many supermassive black hole binaries and probably to detect the gravitational wave background radiation from the Big Bang.

Therefore, this is an exciting time for gravitational wave astronomy.  In the next few years, we can expect the first results from the NANOGrav effort, pinpointing the locations of binary systems of supermassive black holes.  During this period we also expect the observations, at higher frequencies, of gravitational wave detection by the ground-based gravitational wave detectors.  Watch this column and the science press for breaking news of direct gravitational wave detection.

Note:  In this version of this AV column, the term "gravity wave" has been replaced with "gravitational wave" everywhere in the text to conform with standard terminology.  This is because the term  "gravity wave" refers to a type of wave on the surface of the ocean.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


The NANOGrav Collaboration:


Gravity Waves and Pulsar Timing:

"The International Pulsar Timing Array project: using pulsars as a gravitational wave detector", G. Hobbs, et al,, Classical and Quantum Gravity, Volume 27, Issue 8, pp. 084013 (2010); arXiv e-print:0911.5206 .

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