## Abstract

Rotating, self-gravitating mass of incompressible ideal fluid possesses an axially symmetric equilibrium configuration known as the Maclaurin spheroid. Fluid viscosity causes dissipation-induced instability of this equilibrium [1,2]. Chandrasekhar [3] discovered that radiation reaction force due to emission of gravitational waves could lead to a radiative instability of the Maclaurin spheroids. In the presence of both viscosity and resistivity the ratio of these two dissipative forces plays a crucial role [4], determining the instability window for the Chandrasekhar-Friedman-Schutz (CFS) instability. The CFS instability is commonly accepted nowadays as one of the main triggers of gravitational radiation from single neutron stars that is the next goal for the existing (LIGO, Virgo) and planned (LISA) detectors of gravitational waves [5,6]. Perturbation theory for eigenvalues in combination with numerical methods was proposed for calculation of instability windows of the CFS instability already in [3,4,7]. We are extending this approach to the multiple-parameter case by adopting the methodology of [8,9] to get better approximations and to put the CFS to the general context of the dissipation-induced instability theory.

[1] Chandrasekhar, S.: On stars, their evolution and their stability. Science 226(4674), 497–505 (1984)

[2] Roberts, R. H., Stewartson, K.: On the stability of a Maclaurin spheroid of small viscosity. Astrophys. J. 137, 777–790 (1963)

[3] Chandrasekhar, S.: Solutions of two problems in the theory of gravitational radiation. Phys. Rev. Lett. 24(11), 611–615 (1970)

[4] Lindblom, L., Detweiler, S. L.: On the secular instabilities of the Maclaurin spheroids. Astrophys. J. 211, 565–567 (1977)

[5] Ho, W. C. G.: Gravitational waves from neutron stars and asteroseismology. Phil. Trans. R. Soc. A 376, 20170285 (2018)

[6] Schutz B. F.: Gravitational-wave astronomy: delivering on the promises. Phil. Trans. R. Soc. A 376, 20170279 (2018)

[7] Schutz, B. F.: Perturbations and stability of rotating stars-III. Perturbation theory for eigenvalues. Mon. Not. R. astr. Soc. 190, 21–31 (1980)

[8] Kirillov, O. N., Verhulst, F.: Paradoxes of dissipation-induced instability or who opened Whitney’s umbrella? Z. angew. Math. Mech. 90, 462–488 (2010)

[9] Kirillov, O. N.: Singular diffusionless limits of double-diffusive instabilities in magneto-hydrodynamics. Proc. R. Soc. A 473(2205), 20170344 (2017)

[1] Chandrasekhar, S.: On stars, their evolution and their stability. Science 226(4674), 497–505 (1984)

[2] Roberts, R. H., Stewartson, K.: On the stability of a Maclaurin spheroid of small viscosity. Astrophys. J. 137, 777–790 (1963)

[3] Chandrasekhar, S.: Solutions of two problems in the theory of gravitational radiation. Phys. Rev. Lett. 24(11), 611–615 (1970)

[4] Lindblom, L., Detweiler, S. L.: On the secular instabilities of the Maclaurin spheroids. Astrophys. J. 211, 565–567 (1977)

[5] Ho, W. C. G.: Gravitational waves from neutron stars and asteroseismology. Phil. Trans. R. Soc. A 376, 20170285 (2018)

[6] Schutz B. F.: Gravitational-wave astronomy: delivering on the promises. Phil. Trans. R. Soc. A 376, 20170279 (2018)

[7] Schutz, B. F.: Perturbations and stability of rotating stars-III. Perturbation theory for eigenvalues. Mon. Not. R. astr. Soc. 190, 21–31 (1980)

[8] Kirillov, O. N., Verhulst, F.: Paradoxes of dissipation-induced instability or who opened Whitney’s umbrella? Z. angew. Math. Mech. 90, 462–488 (2010)

[9] Kirillov, O. N.: Singular diffusionless limits of double-diffusive instabilities in magneto-hydrodynamics. Proc. R. Soc. A 473(2205), 20170344 (2017)

Original language | English |
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Pages | 8 |

Number of pages | 1 |

Publication status | Published - 19 Jun 2019 |

Event | Instabilities and Turbulence in Strato-Rotational Flows - International Center of Academic Exchange of Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany Duration: 19 Jun 2019 → 20 Jun 2019 https://www.b-tu.de/fg-aerodynamik-stroemungslehre/aktuelles/tagungen/istrof-2019 |

### Conference

Conference | Instabilities and Turbulence in Strato-Rotational Flows |
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Abbreviated title | ISTROF 2019 |

Country/Territory | Germany |

City | Cottbus |

Period | 19/06/19 → 20/06/19 |

Internet address |