Field of Science

Very precise pulsar measurements

A neutron star is made of neutrons, right? Astrophysicists ponder this question and forge theory after theory, but the only thing they conclude with certainty is that a neutron star by any other name would still be made of the densest form of matter know to exist in our Universe. Under certain conditions a star which has exhausted all of its fuel and is sufficiently massive will not be able to support its own weight with pressure support (as in a regular star) or with electron degeneracy support (as in a white dwarf) such that electrons and protons merge to form neutrons because it is a more energetically favorable arrangement of the matter. A neutron star is a sort of massive atomic nucleus, but without charge. The actual composition and detailed properties of neutron star are still theoretically uncertain.
New measurements of the pulsating neutron star and helium-oxygen-carbon white dwarf binary system J1614-2230 reported in a Nature letter are the highest precision determinations of a neutron star's mass to date. The data comes from the massive Green Bank Telescope using the new Green Bank Ultimate Pulsar Processing instrument which accurately records the time of arrival of each radio pulse sent out by the rapidly rotating neutron star (which is a pulsar). The quality of this instrument, having over a tera op of computing power, and the size of the telescope, 100 meters, made this measurement possible. For a quick rundown of this result you can watch these quick movies on the scientific implications and the technology behind the discovery which were created by the NRAO.

The analysis uses a general relativistic effect involving the time delay of light known as the Shapiro delay effect. When a light ray passes a massive object it follows a curved path. General relativity says that curvature of light rays can only take place when the velocity of the propagation of the light rays also varies with position. The Shapiro delay increases the light travel time through the curved space-time near a massive body. The equation to determine the time delay effect is delightfully simple.
The delay depends on the mass, M, of the time delaying body between the source and the observer, the gravitational constant G, the speed of light, c, and the geometry of the system. The geometry is that light has to be passing near the gravitating body before it gets to the observer for the effect to occur at all so the vector that points from the observer to the source, R, and the vector that points from the observer to the gravitating mass are vital. Pulsar J1614-2230 is a nearly edge on, 89 degrees, system meaning that when the white dwarf passes in front of the pulsar during the binary orbit the Shapiro effect will be very strong. I ran a quick calculation of the time delay and found it to be exactly on the order of a few microseconds. The first figure in the paper shows the geometry and the measured effect.
With this data in hand the standard Keplerian orbital parameters are calculated for this clean binary system and the masses of the objects are calculated. The mass of the neutron star was found to be 1.97 +/- 0.04 solar masses which is the most precise measurement of neutron star mass to date. Unfortunately this measurement technique does not provide any information about the radius of the neutron star, but because the mass was so high it already set a limit on the equation of state of the neutron star matter. This means that we can begin to answer what a neutron star is really made of. Different kinds of matter have a different behavior as you add more mass to them which is intuitive if you thought how discrepant with respect to size a planet made out of cotton candy versus rock would be. This result indicates that exotic models of hadronic matter including hyperons, kaon condensates are ruled out. Condensed quark matter is not ruled out, but highly constrained with this data. This is a big deal for particle physicists because this kind of system is an experiment that could never be carried out in a lab, but is necessary to probe fundamental physics.

This cool result on neutron stars glosses over another application of precise pulsar measurements that the authors of this Nature paper regarded as noise. The plot above is very neat and clean, but before the data looks like that a timing analysis must take into account the time delays associated with many more mundane effects. Effects that change the time of arrival of the pulsar include the variations in the Euclidean distance between the Earth and the pulsar resulting from Earth’s orbital motion, the proper motion of the pulsar, and its binary motion, dispersive delays in the interstellar medium, and time dilation of clocks in the observatory and pulsar frames and along the propagation path. The Earth's orbital motion about the solar system barycenter (known as the Roemer delay) is up to 500 seconds and so must be removed from the data. The powerful thing is that the Earth's orbital motion tells us about the mass and orbits of all the bodies in our solar system. A paper published in the Astrophysical Journal states that with ten years of careful observation of 20 pulsars the masses and orbits of solar system bodies could be determined better than with any other method and even undiscovered trans-Neptunian objects could be found.

Precise pulsar measurements are powerful. The first extrasolar planet ever discovered was actually made with pulsar measurements. Pulsars can tell us about the nature of neutron stars, the properties of own solar system, oh and even gravitational waves. If only astronomers had the money to build a pulsar timing array... References

Demorest PB, Pennucci T, Ransom SM, Roberts MS, & Hessels JW (2010). A two-solar-mass neutron star measured using Shapiro delay. Nature, 467 (7319), 1081-3 PMID: 20981094

D. J. Champion, G. B. Hobbs, R. N. Manchester, R. T. Edwards, D. C. Backer, M. Bailes, N. D. R. Bhat, S. Burke-Spolaor, W. Coles, P. B. Demorest, R. D. Ferdman, W. M. Folkner, A. W. Hotan, M. Kramer, A. N. Lommen, D. J. Nice, M. B. Purver, J. M. Sarkissian, I. H. Stairs, W. van Straten, J. P. W. Verbiest, & D. R. B. Yardley (2010). Measuring the mass of solar system planets using pulsar timing ApJ arXiv: 1008.3607v1


  1. This is such a lucid and informative piece of astronomy writing, Alex. I spent the whole day exploring your ideas, and I look forward to interacting with you on Twitter. We seem to be following each other.

    I'm going to read your whole website over the next few days, I think.

  2. Very interesting. I was wondering how they got such accurate measurements. Thanks for taking the time to prepare this. Bob B. , Houston Texas.


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