Upper mass limits for stable rotating white dwarfs

Models of nonmagnetic axisymmetric differentially rotating zero-temperature white dwarfs are constructed and tested for stability. Upper mass limits, beyond which models become secularly and dynamically unstable to growth of nonaxisymmetric perturbations, are found at 2.5 solar masses and 4.6 solar masses, respectively. The upper mass limit for secular stability is practically the same for the two angular momentum distributions considered. Crude growth rates due to gravitational radiation and degenerate-electron viscosity are calculated for the secularly unstable models. Except for a narrow parameter range, gravitational radiation is the dominant destabilizing mechanism. For masses between 3.5 and 4.6 solar masses, the secular instability grows on a time scale of about 10 to 1000 years; for masses exceeding about 4.6 solar masses, the dynamic instability grows on a time scale of seconds. Implications of these results for mass-transfer binary star systems and degenerate stellar cores are discussed.