The distribution of tilt angles in newly born NSs: Role of interior viscosity and magnetic field

We study how the viscosity of neutron star (NS) matter affects the distribution of tilt angles (X) between the spin and magnetic axes in young pulsars. Under the hypothesis that the NS shape is determined by the magnetically induced deformation, and that the toroidal component of the internal magnetic field exceeds the poloidal one, we show that the dissipation of precessional motions by bulk viscosity can naturally produce a bi-modal distribution of tilt angles, as observed in radio/γ -ray pulsars, with a low probability of achieving X ~ (20°-70°) if the interior B-field is ~(10¹¹-10¹⁵)G and the birth spin period is ~10-300 ms. As a corollary of the model, the idea that the NS shape is solely determined by the poloidal magnetic field, or by the centrifugal deformation of the crust,is found to be inconsistent with the tilt angle distribution in young pulsars. When applied to the Crab pulsar, with X ~ 45°- 70° and birth spin ≥ 20ms,our model implies that:(i)the magnetically induced ellipticity is ϵ_B≥ 3 × 10^-6; and (ii) the measured positive X ~ 3.6 × 10^-12 rad s^-1 requires an additional viscous process, acting on a time-scale ≤ 10⁴ yr. We interpret the latter as crust-core coupling via mutual friction in the superfluid NS interior. One critical implication of our model is a gravitational wave signal at (twice) the spin frequency of the NS. For ϵ_B~ 10^-6, this could be detectable by Advanced LIGO/Virgo operating at design sensitivity.