Imprint of magnetic obliquity in apparent spin-down of radio pulsars

Abstract

ABSTRACT Numerical simulations predict that the spin-down rate of a single rotation-powered neutron star depends on the angle α between its spin and magnetic axes as $P\dot{P} \propto \mu ^2 (k_0 + k_1\sin ^2\alpha)$, where P is the star spin period, μ is its magnetic moment, while k0 ∼ k1 ∼ 1. Here, we describe a simple observational test for this prediction based on the comparison of spin-down rates of 50 nearly orthogonal (with α close to 90 deg) and 27 nearly aligned (with α close to 0 deg) pulsars. We found, that the apparent pulsar spin-down is consistent with the theory if assumed, that magnetic moments of orthogonal rotators are systematically larger than those of aligned ones for ∼0.15...0.2 dex. Also, as a by-product of the analysis, we provide yet another constraint on the average braking index of radio pulsars as 1 ≤ n ≤ 4 with formal significance not worse than 99 per cent.