This note describes fitting formulae for the gravitational waveforms generated by a rapidly rotating neutron star (e.g., newly-formed in the core collapse of a supernova) as it evolves from an initial axisymmetric configuration toward a triaxial ellipsoid (Maclaurin spheroid ⇒ Dedekind ellipsoid). This evolution is driven by the gravitational radiation reaction (a special case of the CFS instability). The details and numerical results can found in [Lai & Shapiro, 1995, ApJ, 442, 259; Here referred as LS].I will use the units such that G = c = 1.The waveform (including the polarization) is given by Eq. (3.6) of LS. Since the waveform is quasi-periodic, I will give fitting formulae for the wave amplitude h (Eq. [3.7] of LS) and the quantity (dN/d ln f ) (Eq. [3.8] of LS; related to the frequency sweeping rate), from which the waveform h + (t) and h × (t) can be easily generated in a straightforward manner.Wave Amplitude: The waveform is parametrized by three numbers: f max is the maximum wave frequency in Hertz, M 1.4 = M/(1.4M ⊙ ) is the NS mass in units of 1.4M ⊙ , R 10 = R/(10 km) is the NS radius in units of 10 km. (Of course, the distance D enters the expression trivially.) It is convenient to express the dependence of h on t through f (the 1 This note was written in 1996. It was not intended for publication. Since I have been getting requests from people interested in GW data analysis about the waveform information, I thought it might be useful to put this note on gr-qc, so that I don't have to spend time looking for the TeX file every time I get a request.

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We investigate the equilibrium and stability of supermassive stars of mass M > ∼ 10 5 M in binary systems. We find that corotating binaries are secularly unstable for close, circular orbits with r < ∼ 4R(M/10 6 M ) 1/6 where r is the orbital separation and R the stellar radius. We also show that corotation cannot be achieved for distant orbits with r > ∼ 12R(M/10 6 M ) −11/24 , since the timescale for viscous angular momentum transfer associated with tidal torques is longer than the evolution timescale due to emission of thermal radiation. These facts suggest that the allowed mass range and orbital separation for corotating supermassive binary stars is severely restricted. In particular, for supermassive binary stars of large mass M > ∼ 6 × 10 6 M , corotation cannot be achieved, as viscosity is not adequate to mediate the transfer between orbital and spin angular momentum. One possible outcome for binary supermassive stars is the onset of quasi-radial, relativistic instability which drives each star to collapse prior to merger: We discuss alternative outcomes of collapse and possible spin states of the resulting black holes. We estimate the frequency and amplitude of gravitational waves emitted during several inspiral and collapse scenarios.

We construct numerical models of the newly discovered binary pulsar J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium code that handles arbitrary spins and in the relativistic, slow-rotation approximation. We compare results for a representative sample of viable nuclear equations of state (EOS) that span three, qualitatively different, classes of models for the description of nuclear matter. A future dynamical measurement of the neutron star's moment of inertia from pulsar timing data will impose significant constraints on the nuclear EOS. Even a moderately accurate measurement ( 10%) may be able to rule out some of these competing classes. Using the measured mass, spin and moment of inertia to identify the optimal model computed from different EOSs, one can determine the pulsar's radius.

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