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Pulsars, Super-Massive Black Holes,
and the Gravitational Wave Background

by John G. Cramer

Alternate View Column AV-213
Keywords: pulsars, black holes, cosmic background, gravitational waves
Published in the July-August-2021 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 03/11/2021 and is copyrighted ©2021 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

About a decade ago (Analog October-2010 issue) I wrote an AV column describing NANOGrav, a new astrophysics collaboration that proposed to use observation of the precise arrival-time variations of pulsars to detect and measure low frequency gravitational waves.  Now, after many detector technical improvements and years of data collection, NANOGrav has presented their first significant results.  In this AV column I want to discuss them, but let's begin by reviewing the characteristics, detection, and possible astrophysical sources of low frequency gravitational waves.

Gravitational waves can be viewed as the spreading ripples of distortion in the gravitational field that are created when a massive object is moved and its gravitational field is disturbed.   Like light waves, gravitational waves travel at the speed of light and obey the inverse-square law [intensity ~ (distance)-2].  Gravitational waves induce a kind of "kneading" distortion in the space through which they move, making local transverse 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 as a long sausage 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 modes of polarization.  Viewed head-on, gravitational waves with the "+" polarization mode alternately compress and expand space top-to-bottom and side-to-side (kneading space with a "+" pattern).  Gravitational waves having the "×" polarization mode compress and expand space along lines 45° to the right of vertical and 45° to the left of vertical (kneading with an "×" pattern).  These two independent polarization modes make gravitational wave detection more difficult, because a given detector is usually sensitive to only one of the two modes and therefore detects only half of the possible signal intensity.

Because gravity is such a weak force, gravitational waves are elusive and very difficult to detect.  The presence of gravitational waves was first deduced by Taylor and Hulze in 1978 from observing radio pulses from the spin-down of a binary pulsar system that was losing energy by emitting gravitational waves.   Gravitational waves were first directly detected by the LIGO Collaboration in 2015, with the observation of waves from the final spin-down of a binary black hole system.

However, interferometer detectors of the LIGO type are primarily sensitive to gravitational waves with frequencies ranging from about 10 Hz to 10 kHz.  The space-based interferometer detector LISA, which is scheduled to launch in about 2034, will be sensitive to gravitational waves with frequencies between 1 Hz and 10-5 Hz.  Both of these detectors are therefore blind to potentially interesting gravitational waves that have frequencies below 10-6 Hz, corresponding to periods of 11.6 days or more.

As discussed in my AV column in the October-2010 issue of Analog, there is also another way of detecting gravitational waves, particularly those of low frequency.  The NanoGrav Collaboration (North American Nanohertz Observatory for Gravitational Waves) uses small variations in arrival times of the precisely timed radio emission pulses from pulsars.  The NANOGrav observations of pulsar timing will be sensitive to gravitational waves with very low frequencies between 10-7 and 10-10 Hz.

Current astrophysical modeling tells us that every galaxy should contain a super-massive black hole at its center.  When a pair of galaxies collide, a pair of co-orbiting super-massive black holes should form, having net mass on the order of 107 solar masses.  (By contrast, LIGO has observed the merger of black hole binary systems with masses up to around 100 solar masses.)  Such ultra-massive systems, during in-spiraling, should produce some of the brightest gravitational waves in the universe. These would be low frequency gravitational waves that fall within the range of sensitivity of NANOGrav observations.

NANOGrav is beginning the search for such ultra-massive black hole gravitational radiation.  At this point, no positive observations of gravitational wave signals from super-massive black hole binaries has been found, but the absence of such observations makes it possible to set limits on galactic binary masses and asymmetries.  NANOGrav has placed constraints on the net masses and mass ratios of the 216 hypothetical binaries in the Milky Way.  For 19 galaxies, only very unequal-mass binaries are allowed, with the mass of the secondary less than 10 percent that of the primary.

The first "multi-messenger" search, using both light and NANOGrav gravitational-wave information, has been performed.  It focused on candidate galaxy 3C66B, a system believed to contain a super-massive black hole binary pair. The apparent 1.05-year orbital period for the binary in 3C66B makes it an excellent candidate for the NANOGrav frequency window. The analysis, using data from 11 years of pulsar data collection, places a limit on the net mass of the candidate super-massive black hole binary in 3C66B to be less than (1.65±0.02) × 109 solar masses.

NANOGrav is also sensitive to low frequency gravitational waves that were produced by another source: the very early universe.  The current LCDM Model of Cosmology hypothesizes that just after the Big Bang there was a period called "inflation" in which the universe initially expanded exponentially, even superluminally (for unknown reasons) and then shifted to a much slower rate of expansions (also for unknown reasons).  The inflation hypothesis, first proposed in the late 1970s by Alan Guth and others, explains several problematic aspects of the early universe (horizon, flatness, uniformity, no magnetic monopoles, …), but the conjecture has its critics.  If the inflation scenario is valid, than during the inflationary period the rapid expansion should have produced intense primordial gravitational waves.  This radiation, Doppler-shifted to low frequencies by the subsequent expansion, should still be present and in principle detectable as low frequency gravitational wave "noise".

We note that such primordial gravitational radiation is not the only possible indicator of inflation.  As reported in my AV column in the October-2014 issue of Analog, there was a swirl of excitement in the astrophysics community in 2014 when the BICEP2 experiment announced that they had detected "B-type swirls" in the linear polarization pattern of the cosmic microwave background that indicated the presence of such primordial gravitational radiation, produced by inflation and structuring the polarization of the microwave background.  This "observation" was taken as positive evidence that inflation in the early universe was a real phenomenon.

Unfortunately, those result turned out to be wrong.  The BICEP2 claim of inflation effects was revealed to be the result of faulty analysis that had not properly taken into account the effects of interstellar dust as they modified the polarization of the microwaves.  The BICEP2 result was ultimately retracted, and no new data or analysis of primordial microwave polarization has so far conclusively shown any indication of the effects of gravitational background radiation.

But now NANOGrav has accumulated 12.5 years of intriguing pulsar data that show possible "first hints" of low-frequency gravitational wave background.  They studied 47 pulsars, 45 of which had data sets of at least three years. These showed a spectral signature, a low-frequency noise feature, that is the same across multiple pulsars. The timing changes NANOGrav studied are so small that the evidence isn't apparent when studying any one pulsar, but in aggregate, they add up to a significant signature.

The important question is whether this signature can be attributed to primordial gravitational waves, and by implication, to inflation.  There is a way of answering this question with analysis of the pulsar data.  If the gravitational radiation was truly created during the inflation period, it should show no characteristics of monopole or dipole radiation, but should show definite signs of a quadrupole radiation pattern.

The data analysis so far confirms the absence of monopole and dipole radiation patterns, but the statistics are insufficient to determine whether or not a statistically significant quadrupole signal is present.  Thus, we are teased by possibility of a confirmation of primordial inflation, but no definite result is possible until more statistics are accumulated.

Our current understanding of the early universe is in turmoil because of the discrepant values of the Hubble constant (see my AV column in the March-April-2020 issue of Analog) and the tentative indications that the early universe might have initially had enough mass density for closure (see my AV column in the May-June-2020 issue of Analog).  The confirmation of inflation would add to the astrophysical turmoil, because the hypothesis is controversial and there are alternatives to inflation (e.g,  recycling and Big Bounce models) that predict no primordial gravitational radiation and would be falsified by observation of a gravitational wave background.  There are also other variant conjectures of the early universe that might take different and distinguishable forms in generating gravitational waves.  Therefore, the resolution of questions about the presence and characteristics of primordial gravitational radiation will have a huge impact on our understanding of the early universe.

Watch this AV column for further developments.

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 is coming soon from Baen Books.

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: .


Gravitational-Wave Background:

Zaven Arzoumanian, et al, "The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background", preprint ArXiv 2009.04496.

Ultra-massive Black Hole Binaries:

Zaven Arzoumanian, et al, "The NANOGrav 11 yr Data Set: Limits on Supermassive Black Hole Binaries in Galaxies within 500 Mpc", preprint ArXiv 2101.02716

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