Comment on “ Instabilities in Close Neutron Star Binaries ”

In a recent Physical Review Letter, Wilson and Mathews [1] presented some interesting numerical calculations of a system of two equally massive neutron stars in strong-field gravity. In particular they estimated the innermost stable circular orbit in their system. Here we point out a possibly important consequence of their results: Their calculated configurations have total angular momentum J and total mass M too large to form any Kerr black hole: J > M. For a compact binary system in general relativity, the concept of the innermost stable orbit is not really well defined, because the orbit shrinks due to gravitational radiation reaction. However, because the orbit shrinks slowly, an approximate definition can be given, see [2–5] for discussion. Figure 1 displays various calculations for the innermost stable orbit in the (J,M) plane; previous results [2–5] give J < ∼ M. In contrast, Wilson and Mathews [1] find J/M ≈ 1.31 (point 1), well outside the allowed region of final states (J < M) for Kerr black holes (see Black Hole Limit curve). 1 The Wilson-Mathews results therefore imply that the system 1 must radiate substantial amounts of J after loss of orbital stability, during merger. The concomitant loss of M is governed by the relation ∆M = πf∆J where f is the gravity wave frequency [6] (assuming quadrupole emission). One expects that f will substantially exceed the final orbital frequency (about 410 Hz in [1]), since the holes ought to plunge quickly together after loss of orbital stability. In Fig. 1, conjectural evolutions are shown as dotted arrows, labeled by conjectured frequency f? in Hz, normalized to M0 = 2.90M⊙. This additional radiation could be of considerable importance for the detection and characterization of these sources by LIGO and VIRGO [6]. An often-discussed possibility could be realized here, namely the formation of an excited, nearly extremal Kerr black hole, radiating copiously at its rigid rotation frequency f = Ω+/π = 1/(2πM). Note however that this frequency is “too high”: the excess J cannot be primarily lost in this way, since such an excited hole would evolve parallel to the Black Hole Limit in Fig. 1, rather than across it.