Description
Rotating, selfgravitating mass of incompressible ideal fluid possesses an axially symmetric equilibrium configuration known as the Maclaurin spheroid. Fluid viscosity causes dissipationinduced 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 ChandrasekharFriedmanSchutz (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 multipleparameter case by adopting the methodology of [8,9] to get better approximations and to put the CFS to the general context of the dissipationinduced 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.: Gravitationalwave astronomy: delivering on the promises. Phil. Trans. R. Soc. A 376, 20170279 (2018)
[7] Schutz, B. F.: Perturbations and stability of rotating starsIII. Perturbation theory for eigenvalues. Mon. Not. R. astr. Soc. 190, 21–31 (1980)
[8] Kirillov, O. N., Verhulst, F.: Paradoxes of dissipationinduced instability or who opened Whitney’s umbrella? Z. angew. Math. Mech. 90, 462–488 (2010)
[9] Kirillov, O. N.: Singular diffusionless limits of doublediffusive instabilities in magnetohydrodynamics. Proc. R. Soc. A 473(2205), 20170344 (2017)
Period  19 Jun 2019 → 20 Jun 2019 

Event title  Instabilities and Turbulence in StratoRotational Flows 
Event type  Conference 
Location  Cottbus, Germany, Brandenburg 
Degree of Recognition  International 
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Research output

Instability windows of ChandrasekharFriedmanSchutz instability
Research output: Contribution to conference › Abstract › peerreview