"Cosmic Chords" Support of Einstein's Theory

The strongest gravitational fields ever measured have been recorded by scientists using the Rossi X-Ray Timing Explorer (RXTE) satellite. At the APS/AAPT Joint Spring Meeting in Columbus, Ohio, Frederick Lamb of the University of Illinois described how observed very rapid oscillations in the brightness of xrays emanating from certain neutron stars can be used to deduce their properties, such as mass and size. The data may also represent the first evidence for a unique effect of strongly curved spacetime predicted by Einstein's theory of gravity but never before observed.

Generation of the Sonic-Point Keplerian Frequency QPO: An illustration of how the high frequency X-ray brightness oscillations are thought to be produced.

RXTE was designed to monitor (over microsecond time intervals) the x rays coming from binary star systems in which matter from a conventional star is siphoned off into an accretion disk surrounding a nearby neutron star or black hole. Neutron In about 16 binary-star systems that contain neutron stars, blobs of gas in the disk are thought to spiral in toward the neutron star, picking up speed and approaching the speed of light before they make a final plunge onto the surface. When gas from these clumps collides with the surface of the star, it reaches temperatures of 100 million degrees. The x rays produced in this process become dimmer when the hot gas is on the far side of the star and brighter when the heated gas is on the near side of the star, leading to quasi-periodic oscillations in the x-ray brightness. In fact, some of these neutron stars that produce high frequency x-ray oscillations radiate more energy in a second than the sun radiates in a week, according to Lamb.

The researchers had expected to observe a cacophony of frequencies in the x-ray emission from the stars, similar to the discord produced when one presses keys randomly on a piano. Instead, they discovered that the brightness variations only occur at certain well-defined rates, "pure tones" that have been dubbed "cosmic chords", which correspond to special orbital periods for the gas going around the star. "The clockwork of the universe is much more orderly than we had dreamed," Lamb said. "The pureness of these tones makes it possible to use them to investigate how matter moves in the strongly curved space-time near these neutron stars."

The gravitational fields measured corresponded to a spacetime warping of 30%. By comparison, the proportional curvature of space is only about one part in a million near the sun's surface and one part per billion near the Earth's surface. The spacetime encountered by the gas is so highly warped because the gas is able to skim within a few km of the neutron star, which itself is only about 10 km in diameter.

Flow Inside the Sonic Point: This shows a perspective view of accreting gas swirling around the neutron star.

Lamb and William Zhang of NASA Goddard focused particularly on the binary-star system 4U1820-30, about 20,000 light years from Earth. The neutron star has a mass of 2.3 solar masses and orbits its companion star in only 11 minutes. Close observations of this system confirmed a prediction made by Lamb and his colleagues Coleman Miller and Dimitrios Psaltis that the gas blobs would continue to spiral inward until they reached an "innermost stable orbit," where they would orbit before making the dive for the surface. This is a purely general relativistic (GR) effect; in Newton's mechanics, by contrast, the blob could have gotten arbitrarily close to the surface, providing it were going fast enough.

Lamb and Miller's calculations showed how the x-ray brightness oscillations could be used to determine the masses and dimensions of neutron stars and to look for evidence of the innermost stable orbit. They predicted that the frequency of the x-ray brightness variations should increase as the gas flows onto the neutron star and hence its x-ray power rises, until the clumps of gas producing the oscillations reach the innermost stable orbit, at which point they should become constant as the x-ray power continues to rise. The observations by Zhang and his collaborators confirmed Lamb's prediction of this effect. They found that as its x-ray power rises, the frequency of the brightness oscillations increases until it reaches approximately 1,050 times per second. As the x-ray power increases further, the frequency remains constant, indicating that the innermost stable orbit has been reached.

According to Zhang, this correlation between theory and experiment opens up a new "strong-gravitational field" era in GR studies. "There is a good possibility that the Rossi Explorer has provided the first evidence supporting the predictions of Einstein's theory of gravity about how matter moves in strongly curved space-time," said Lamb. "All previous tests of general relativity have been made in regions where space-time is curved only very, very weakly." The measurements of the gas motion even provide hints as to the nature of the strong nuclear force sustaining the neutron star against further gravitational collapse. The new evidence indicates that the nuclear force is stiffer and more repulsive than has generally been thought.