CaltechAUTHORS
  A Caltech Library Service

Differential rotation of the unstable nonlinear r-modes

Friedman, John L. and Lindblom, Lee and Lockitch, Keith H. (2016) Differential rotation of the unstable nonlinear r-modes. Physical Review D, 93 (2). Art. No. 024023. ISSN 2470-0010. http://resolver.caltech.edu/CaltechAUTHORS:20160204-151121620

[img] PDF - Published Version
See Usage Policy.

645Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20160204-151121620

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevD.93.024023DOIArticle
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.93.024023PublisherArticle
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.
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSFDMS-1065438
NSFPHY-1404569
NSFPHY-1001515
Record Number:CaltechAUTHORS:20160204-151121620
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160204-151121620
Official Citation:Differential rotation of the unstable nonlinear r-modes John L. Friedman, Lee Lindblom, and Keith H. Lockitch Phys. Rev. D 93, 024023 – Published 13 January 2016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64246
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Feb 2016 23:26
Last Modified:04 Feb 2016 23:26

Repository Staff Only: item control page