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

Numerical simulations predict that the spin-down rate of a single rotation-powered neutron star depends on the angle \(\alpha\) 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, \(\mu\) is its magnetic moment, while \(k_0 \sim k_1 \sim 1\). Here we describe a simple observational test for this prediction based on the comparison of spin-down rates of 50 nearly orthogonal (with \(\alpha\) close to 90 deg) and 27 nearly aligned (with \(\alpha\) 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 \(\sim 0.15..0.2\) dex. Also, as a by-product of the analysis, we provide yet another constraint on the average braking index of radio pulsars as \(1 \le n \le 4\) with formal significance not worse than 99\%.