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Astron. Astrophys. 341, 110-116 (1999)

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Analytic description of the r-mode instability in uniform density stars

K.D. Kokkotas 1 and N. Stergioulas 2

1 Department of Physics, Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece (e-mail: kokkotas@astro.auth.gr)
2 Max-Planck-Institute for Gravitational Physics, The Albert Einstein Institute, D-14473 Potsdam, Germany
(e-mail: niksterg@aei-potsdam.mpg.de)

Received 28 May 1998 / Accepted 29 September 1998


We present an analytic description of the r-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitational-wave emission, for both current and mass multipole radiation and for the damping timescale, due to viscosity. The [FORMULA] current-multipole radiation dominates the timescale of the instability. We estimate the deviation of the second order accurate results from the lowest order approximation and show that the uncertainty in the equation of state has only a small effect on the onset of the r-mode instability. The viscosity coefficients and the cooling process in newly-born neutron stars are, at present, uncertain and our analytic formulae enable a quick check of such effects on the development of the instability.

Key words: gravitational waves – instabilities – stars: neutron – stars: oscillations

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© European Southern Observatory (ESO) 1999

Online publication: November 26, 1998