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

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

1998-05-22

arxiv.org/abs/astro-ph/9805297v1

Astron.Astrophys.341:110,1999

Astronomy and Astrophysics

Astrophysics

7 pages, 2 figures

Scientific paper

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 $l=m=2$ 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 formaulae enables a quick check of such effects on the development of the instability.

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