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The Stability of Tidally Deformed Neutron Stars to Three- and Four-mode Coupling

Venumadhav, Tejaswi and Zimmerman, Aaron and Hirata, Christopher M. (2014) The Stability of Tidally Deformed Neutron Stars to Three- and Four-mode Coupling. Astrophysical Journal, 781 (1). Art. No. 23. ISSN 0004-637X.

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It has recently been suggested that the tidal deformation of a neutron star excites daughter p- and g-modes to large amplitudes via a quasi-static instability. This would remove energy from the tidal bulge, resulting in dissipation and possibly affecting the phase evolution of inspiralling binary neutron stars and hence the extraction of binary parameters from gravitational wave observations. This instability appears to arise because of a large three-mode interaction among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We show that additional four-mode interactions enter into the analysis at the same order as the three-mode terms previously considered. We compute these four-mode couplings by finding a volume-preserving coordinate transformation that relates the energy of a tidally deformed star to that of a radially perturbed spherical star. Using this method, we relate the four-mode coupling to three-mode couplings and show that there is a near-exact cancellation between the destabilizing effect of the three-mode interactions and the stabilizing effect of the four-mode interaction. We then show that the equilibrium tide is stable against the quasi-static decay into daughter p- and g-modes to leading order. The leading deviation from the quasi-static approximation due to orbital motion of the binary is considered; while it may slightly spoil the near-cancellation, any resulting instability timescale is at least of order the gravitational wave inspiral time. We conclude that the p-/g-mode coupling does not lead to a quasi-static instability, and does not impact the phase evolution of gravitational waves from binary neutron stars.

Item Type:Article
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URLURL TypeDescription Paper
Venumadhav, Tejaswi0000-0002-1661-2138
Hirata, Christopher M.0000-0002-2951-4932
Additional Information:© 2014 American Astronomical Society. Received 2013 July 16; accepted 2013 December 4; published 2013 December 31. We thank Yanbei Chen for useful discussions regarding volume-preserving displacements. We thank Samaya Nissanke and Dave Tsang for useful discussions and comments on this manuscript.We also thank Anthony Piro for valuable comments on this manuscript. T.V. was supported by the International Fulbright Science and Technology Award. A.Z. was supported by NSF Grant PHY-1068881, CAREER Grant PHY-0956189, and by the David and Barbara Groce Startup Fund. C.H. was supported by the Simons Foundation, the David & Lucile Packard Foundation, and the US Department of Energy (award DE-SC0006624).
Funding AgencyGrant Number
International Fulbright Science and Technology AwardUNSPECIFIED
David and Barbara Groce Startup FundUNSPECIFIED
Simons FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0006624
Subject Keywords:binaries: close; stars: neutron; stars: oscillations
Issue or Number:1
Record Number:CaltechAUTHORS:20140207-112728673
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Official Citation:The Stability of Tidally Deformed Neutron Stars to Three- and Four-mode Coupling Tejaswi Venumadhav et al. 2014 ApJ 781 23
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43725
Deposited By: Jason Perez
Deposited On:07 Feb 2014 22:49
Last Modified:03 Oct 2019 06:10

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