AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES
A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω [subscript a] excites a pair of secondary waves of frequency ω [subscript b] +...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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IOP Publishing
2014
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| Online Access: | http://hdl.handle.net/1721.1/88583 https://orcid.org/0000-0001-9194-2084 |
| _version_ | 1826189044988510208 |
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| author | Weinberg, Nevin N. Arras, Phil Burkart, Joshua |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Weinberg, Nevin N. Arras, Phil Burkart, Joshua |
| author_sort | Weinberg, Nevin N. |
| collection | MIT |
| description | A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω [subscript a] excites a pair of secondary waves of frequency ω [subscript b] + ω [subscript c] [~ over bar] ω [subscript a]. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ω [subscript b] + ω [subscript c] >> ω [subscript a]. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f [subscript gw] [> over ~] 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δφ [> over ~] 1 radian) that accumulate primarily at low frequencies (f [subscript gw] [< over ~] 50 Hz) and (2) heat the neutron star core to a temperature of T ~ 10[superscript 10] K. Since there are at least ~100 unstable p-g daughter pairs, Δφ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously thought. |
| first_indexed | 2024-09-23T08:09:00Z |
| format | Article |
| id | mit-1721.1/88583 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:09:00Z |
| publishDate | 2014 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/885832022-09-23T11:12:01Z AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES Weinberg, Nevin N. Arras, Phil Burkart, Joshua Massachusetts Institute of Technology. Department of Physics Weinberg, Nevin N. A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω [subscript a] excites a pair of secondary waves of frequency ω [subscript b] + ω [subscript c] [~ over bar] ω [subscript a]. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ω [subscript b] + ω [subscript c] >> ω [subscript a]. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f [subscript gw] [> over ~] 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δφ [> over ~] 1 radian) that accumulate primarily at low frequencies (f [subscript gw] [< over ~] 50 Hz) and (2) heat the neutron star core to a temperature of T ~ 10[superscript 10] K. Since there are at least ~100 unstable p-g daughter pairs, Δφ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously thought. National Science Foundation (U.S.) (AST-0908873) United States. National Aeronautics and Space Administration (NNX09AF98G) 2014-08-07T16:09:30Z 2014-08-07T16:09:30Z 2013-05 2013-02 Article http://purl.org/eprint/type/JournalArticle 0004-637X 1538-4357 http://hdl.handle.net/1721.1/88583 Weinberg, Nevin N., Phil Arras, and Joshua Burkart. “AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES.” The Astrophysical Journal 769, no. 2 (June 1, 2013): 121. https://orcid.org/0000-0001-9194-2084 en_US http://dx.doi.org/10.1088/0004-637x/769/2/121 The Astrophysical Journal Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IOP Publishing arXiv |
| spellingShingle | Weinberg, Nevin N. Arras, Phil Burkart, Joshua AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES |
| title | AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES |
| title_full | AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES |
| title_fullStr | AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES |
| title_full_unstemmed | AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES |
| title_short | AN INSTABILITY DUE TO THE NONLINEAR COUPLING OF p-MODES TO g-MODES: IMPLICATIONS FOR COALESCING NEUTRON STAR BINARIES |
| title_sort | instability due to the nonlinear coupling of p modes to g modes implications for coalescing neutron star binaries |
| url | http://hdl.handle.net/1721.1/88583 https://orcid.org/0000-0001-9194-2084 |
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