Gravitational waves from the r-modes of rapidly rotating neutron stars

Since the last Amaldi meeting in 1997 we have learned that the r-modes of rapidly rotating neutron stars are unstable to gravitational radiation reaction in astrophysically realistic conditions. Newborn neutron stars rotating more rapidly than about 100 Hz may spin down to that frequency during up to one year after the supernova that gives them birth, emitting gravitational waves which might be detectable by the enhanced LIGO interferometers at a distance which includes several supernovae per year. A cosmological background of these events may be detectable by advanced LIGO. The spins (about 300 Hz) of neutron stars in low-mass x-ray binaries may also be due to the r-mode instability (under different conditions), and some of these systems in our galaxy may also produce detectable gravitational waves—see the review by G. Ushomirsky in this volume. Much work is in progress on developing our understanding of r-mode astrophysics to refine the early, optimistic estimates of the detectability of the gravitational waves. I THE R-MODE INSTABILITY The r-mode instability has been the subject of about thirty papers over the past two years. I will not be able to do them all justice here. Instead I will summarize the most important (as I see them) results with a direct impact on gravitationalwave detection, beginning with the basic model worked out in 1998 and ending with the latest (end of 1999) developments in this rapidly changing field. The reason for the excitement is a version of the CFS instability—named for Chandrasekhar, who discovered it in a special case [2], and for Friedman and Schutz, who investigated it in detail and found that it is generic to rotating perfect fluids [3]. The CFS instability allows some oscillation modes of a fluid body to be driven rather than damped by radiation reaction, essentially due to a disagreement between two frames of reference. The mechanism can be explained heuristically as follows. In a non-rotating star, gravitational waves radiate positive angular momentum from a forward-moving 1) For a recent review with more emphasis on completeness, see Friedman and Lockitch [1]. mode and negative angular momentum from a backward-moving mode, damping both as expected. However, when the star rotates the radiation still lives in a non-rotating frame. If a mode moves backward in the rotating frame but forward in the non-rotating frame, gravitational radiation still removes positive angular momentum—but since the fluid sees the mode as having negative angular momentum, radiation drives the mode rather than damps it. Another example of such an effect due to a disagreement between frames of reference is the well-known KelvinHelmholtz instability, which leads to rough airplane rides over the jet stream and pounding surf on the California coast. Mathematically, the criterion for the CFS instability is