The early evolution of magnetar rotation – I. Slowly rotating ‘normal’ magnetars

Abstract

ABSTRACT In the seconds following their formation in core-collapse supernovae, ‘proto’-magnetars drive neutrino-heated magnetocentrifugal winds. Using a suite of two-dimensional axisymmetric magnetohydrodynamic simulations, we show that relatively slowly rotating magnetars with initial spin periods of P⋆0 = 50–500 ms spin down rapidly during the neutrino Kelvin–Helmholtz cooling epoch. These initial spin periods are representative of those inferred for normal Galactic pulsars, and much slower than those invoked for gamma-ray bursts and superluminous supernovae. Since the flow is non-relativistic at early times, and because the Alfvén radius is much larger than the proto-magnetar radius, spin-down is millions of times more efficient than the typically used dipole formula. Quasi-periodic plasmoid ejections from the closed zone enhance spin-down. For polar magnetic field strengths B0 ≳ 5 × 1014 G, the spin-down time-scale can be shorter than the Kelvin–Helmholtz time-scale. For B0 ≳ 1015 G, it is of the order of seconds in early phases. We compute the spin evolution for cooling proto-magnetars as a function of B0, P⋆0, and mass (M). Proto-magnetars born with B0 greater than $\simeq 1.3\times 10^{15}\, {\rm \, G}\, (P_{\star 0}/{400\, \rm \, ms})^{-1.4}(M/1.4\, {\rm M}_\odot)^{2.2}$ spin down to periods >1 s in just the first few seconds of evolution, well before the end of the cooling epoch and the onset of classic dipole spin-down. Spin-down is more efficient for lower M and for larger P⋆0. We discuss the implications for observed magnetars, including the discrepancy between their characteristic ages and supernova remnant ages. Finally, we speculate on the origin of 1E 161348−5055 in the remnant RCW 103, and the potential for other ultra-slowly rotating magnetars.