COMPARING MODELS OF RAPIDLY ROTATING RELATIVISTIC STARS CONSTRUCTED BY 2 NUMERICAL-METHODS

We present the first direct comparison of codes based on two different numerical methods for constructing rapidly rotating relativistic star s. A code based on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989), written by Stergioulas, is compared to the Butterworth-I sper code (BI), as modified by Friedman, Ipser, and Parker. We compare models obtained by each method and evaluate the accuracy and efficien cy of the two codes. The agreement is surprisingly good, and error bar s in the published numbers for maximum frequencies based on BI are dom inated not by the code inaccuracy but by the number of models used to approximate a continuous sequence of stars. The BI code is faster per iteration, and it converges more rapidly at low density, while KEH con verges more rapidly at high density; KEH also converges in regions whe re BI does not, allowing one to compute some models unstable against c ollapse that are inaccessible to the BI code. A relatively large discr epancy recently reported (Eriguchi et al. 1994) for models based on th e Friedman-Pandharipande equation of state is found to arise from the use of two different versions of the equation of state. For two repres entative equations of state, the two-dimensional space of equilibrium configurations is displayed as a surface in a three-dimensional space of angular momentum, mass, and central density. We find, for a given e quation of state, that equilibrium models with maximum values of mass, baryon mass, and angular momentum are (generically) either all unstab le to collapse or are al stable. In the first case, the stable model w ith maximum angular velocity is also the model with maximum mass, bary on mass, and angular momentum. In the second case, the stable models w ith maximum values of these quantities are all distinct. Our implement ation of the KEH method will be available as a public domain program f or interested users.