Astronomers Find Speed Limit for Whirling Pulsars

Reckless pulsars -- spinning searchlights in space -- might tear themselves apart if they whirled too fast, but ripples in the cosmic fabric first predicted by Albert Einstein may set a celestial speed limit.

That limit is still extremely high, about 760 revolutions per second, astronomers said on Wednesday. But scientists figure some of the fastest pulsars could technically go two or three times that speed. Unfortunately, they would inevitably disintegrate if they did.

What stops them is the phenomenon predicted by Einstein's theory of relativity -- the rippling of the fabric of space and time. Known to scientists as gravitational radiation, these ripples are a bit like waves on an ocean and are produced by massive objects in motion. They have never been directly detected.

Pulsars qualify as such massive moving objects, since they contain the mass of the sun packed into a sphere about 10 miles in diameter, scientists said at a briefing at NASA (news - web sites) headquarters. Their findings were published in the journal Nature.

Created when a star explodes, most pulsars start spinning perhaps 30 times a second and slow down over millions of years. But a dense pulsar can waltz in space with a companion star, siphoning material from its companion, which makes it spin much faster, up to hundreds of times a second.

Scientists used NASA's Rossi X-ray Timing Explorer satellite -- designed to observe fast-moving, high-energy objects in space -- to monitor 11 dense pulsars in Earth's cosmic neighborhood. Those pulsars were all several thousand light-years away. A light-year is about 6 trillion miles, the distance light travels in a year.

The satellite kept track of the pulsars' spin rate by watching for thermonuclear explosions on their surfaces. Those blasts last only a few seconds but give off bursts of X-ray light and flicker in a distinctive way that lets astronomers figure out how fast the pulsars are twirling.

None of the 11 spun faster than 619 times per second, Deepto Chakrabarty of the Massachusetts Institute of Technology (news - web sites) said at the briefing. Scientists' statistical analysis of the 11 pulsars led them to conclude their top speed must be below 760 revolutions per second.

The faster a pulsar spins, some scientists believe, the more gravitational radiation it might release, and as that happens, the pulsar's spherical shape is ever so slightly deformed. That deformity might act as a brake on the pulsar's spin rate.

The gravitational waves emitted by the deformed pulsars may eventually be detected by earthly instruments of the Laser Interferometer Gravitational-Wave Observatory, Barry Barish of the California Institute of Technology said at the briefing.

"As the gravitational wave comes to me or my instrument, it actually has the effect of stretching space a little bit in one direction and squashing it in another direction," Barish said. "It goes back and forth between stretching and squashing at the rate of several hundred times a second."

That distortion is extremely small, measuring only a very small fraction of an atom, Barish said.

Further information is available online at http://www.gsfc.nasa.gov/topstory/2003/0702pulsarspeed.html.

Suppose you were watching the Earth--yes, "watching", with a radio telescope--from a distant star. Suppose you were looking in a frequency band where there was a particularly powerful radio station. The station isn't always on; for some reason, it only operates for a few weeks at a time, at odd intervals. Over the years, you'd see the signal go on and off. Superimposed over this signal, you'd see the signal go up and down with a period of 24 hours. This "flicker" is caused by the rotation of the Earth: when the transmitter is on the far side of the Earth, it's harder to hear than when it's pointing at you. In the periods when the blast of radio waves is being sent out, you can measure the rotation of the Earth.

Suppose you are on a distant planet "watching" earth with a radio telescope. You just happened to be tuned to the frequency that the International Space Station transmits a spot beam down to Houston on. You don't see it when it is pointed away from you towards earth, nor do you see it when the earth blocks the signal. In fact, you see it only for a moment as it transits around the limb of earth just before it is blocked by the earth itself. You also see it as it reappears around the other limb before it points away again. Since the ISS orbits about once every 90 minutes, you see the signal twice in each orbit or about once every 45 minutes. You of course, know nothing about the ISS nor the fact that it is in orbit so you assume the observed signal is attached to the surface of the object being observed -- earth in this case. Would you conclude that the earth rotates once every 45 minutes or 32 times a day based on your observations? If so, you would be wrong.

What data fixes the observed thermonuclear "flicker" to the pulsar's surface? Are you sure the gasses being compressed into a thermonuclear explosion aren't "in orbit" around the pulsar as they spiral down towards the pulsar's surface?

Would you conclude that the earth rotates once every 45 minutes or 32 times a day based on your observations? If so, you would be wrong.

Well, you probably wouldn't, because you'd see that every other pulse was doppler-shifted in an opposite direction.

This effect would be far more pronounced in the case of a neutron star, where the velocities are hugely greater, and you may also see the orbits precess. The most telling thing, however, is that radio objects in orbit around a neutron star will have different orbits, and therefore different periods, whereas the observed periodicity of pulsar pulses is stable to one part in 10^8!

I might also point out that these rotational periods are at the limit of what the strong nuclear force can hang onto; the period of an object in free-fall at a larger radius is bound to be much smaller.

I'm not up to speed (so to speak) on pulsars. What, precisely, prevents rotational speeds faster than 760 revolutions per second? Something like tidal forces? And why wouldn't a sufficiently massive pulsar be able to overcome that?

Which leads to my next question: could a black hole revolve faster than 760 rps?

I'm not sure the question has meaning as it applies to a Black Hole; it doesn't have a solid surface, and besides, I don't know how you'd measure it's rotation with the event horizon prevent anything other than Hawking radiation from getting out. In any case, I assume that the "Black Hole has no Hair" theorem includes angular momentum as one of the physical properties that is preserved by a Black Hole,in which case the stuff inside it, as it approaches the singularity at the center, probably approaches light-like speeds, as required by the Law of Conservation of Angular Momentum.

The article says: "What stops them [from disintegrating at faster than 760 rps] is the phenomenon predicted by Einstein's theory of relativity -- the rippling of the fabric of space and time. Known to scientists as gravitational radiation ... " Could someone explain, for a humble layman, what that has to do with the speed of rotation?

The article is poorly written in this reagard; I had the same question you have after reading it. But as best I can figure, the "centrifugal" forces generated by rotation of the pulsar in excess of the predicted 760 rps limit results in the outer layers of the pulsar's surface bulging out asymmetrically, resulting in displacement of the center of mass (and hence center of gravity) of the star away from the axis of rotation. This would cause the pulsar's gravitational field to appear to "wobble" as it's center moves slighty closer and then father away from an observer at approximately right angles to the axis of rotation. This would manifest itself as gravity waves, which would carry away energy from the pulsar. I'm guessing that the magnitude of the gravity waves (and the energy in them) is probably related to the moment of inertia of the asymmetry, which is proportional to r²(I think...); thus as the star rotates faster, the rate of energy loss through gravitational radiation would increase at an exponential rate (as the asymmetry begins to move further and further away from the axis of rotation, increasing it's moment of inertia), which would tend to slow it down. Furthermore, I'm guessing that above the 760 rps limit, the the gravitation of the pulsar is insufficient to "hang on" to the asymmetry, which means it tends to keep moving ever further outward, moving the center of mass and gravity further away from the axis of rotation, vastly increasing the loss of energy (read angular momentum) thru gravity waves.

The analogy might be an automobile tire; there exists some speed above which the tire cannot hold iteself together angainst the centrifugal forces that are trying to fling it apart; when that point is reached, the tire starts to distort not in a nice symmetric fashion, but rather the weakest point starts to deform the most, which unbalances the tire while further increasing the centrifugal forces on the overly deformed part -- which in turn deforms it even more, resulting in imminent catastrophic failure of the tire as a result of the positive feedback loop of deformation => increasing displacement from the axis of rotation => more centrifugal force on the displaced portion of the tire => more deformation => and so on until it fails.

But I'm about as much an expert on this as you are (IOW, the above is my WAG).... so I'll wait for the big dogs to weigh in on this one.

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