Differential rotation of the unstable nonlinear r-modes
Abstract
At second order in perturbation theory, the r-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r-mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.
Additional Information
© 2016 American Physical Society. (Received 8 April 2015; published 13 January 2016) We thank Andrey Chugunov for helpful comments on an earlier draft of this manuscript; Luciano Rezzolla and Chugunov for discussions of magnetic-field evolution; and the referee for a careful reading, useful suggestions, and insight into the likely role of nonlinear saturation in the evolution of the r-mode's magnetic field. J. F. thanks Shin'ichirou Yoshida for corrections and contributions to an early set of notes. L. L. thanks the Leonard E. Parker Center for Gravitation, Cosmology and Astrophysics, University of Wisconsin at Milwaukee, for their hospitality during several visits during which much of the research presented here was performed. L. L. was supported at Caltech in part by a grant from the Sherman Fairchild Foundation and by Grants No. DMS-1065438 and No. PHY-1404569 from the National Science Foundation. J. F. was supported in part by Grant No. PHY-1001515 from the National Science Foundation.Attached Files
Published - PhysRevD.93.024023.pdf
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Additional details
- Eprint ID
- 64246
- Resolver ID
- CaltechAUTHORS:20160204-151121620
- Sherman Fairchild Foundation
- DMS-1065438
- NSF
- PHY-1404569
- NSF
- PHY-1001515
- NSF
- Created
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2016-02-04Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field