Frequency band of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi></mml:math>-mode Chandrasekhar-Friedman-Schutz instability
Abstract
Rapidly rotating neutron stars can be unstable to the gravitational-wave-driven Chandrasekhar-Friedman-Schutz (CFS) mechanism if they have a neutral point in the spectrum of nonaxisymmetric $f$-modes. We investigate the frequencies of these modes in two sequences of uniformly rotating polytropes using nonlinear simulations in full general relativity, determine the approximate locations of the neutral points, and derive limits on the observable frequency band available to the instability in these sequences. We find that general relativity enhances the detectability of a CFS-unstable neutron star substantially, both by widening the instability window and enlarging the band into the optimal range for interferometric detectors like LIGO, VIRGO, and GEO-600.