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

We present an analytic description of the r-mode in- stability 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 for- mulae 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 in- stability. 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.