The Early Evolution of Magnetar Rotation I: Slowly Rotating "Normal" Magnetars

Abstract

In the seconds following their formation in core-collapse supernovae, "proto"-magnetars drive neutrino-heated magneto-centrifugal winds. Using a suite of two-dimensional axisymmetric MHD simulations, we show that relatively slowly rotating magnetars with initial spin periods of $P_{\star 0}=50-500$ 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 super-luminous supernovae. Since the flow is non-relativistic at early times, and because the Alfvén radius is much larger than the proto-magnetar radius, spindown is millions of times more efficient than the typically-used dipole formula. Quasi-periodic plasmoid ejections from the closed zone enhance spindown. For polar magnetic field strengths $B_0\gtrsim 5\times 10^{14}$ G, the spindown timescale can be shorter than than the Kelvin-Helmholtz timescale. For $B_0\gtrsim 10^{15}$ G, it is of order seconds in early phases. We compute the spin evolution for cooling proto-magnetars as a function of $B_0$, $P_{\star 0}$, and mass ($M$). Proto-magnetars born with $B_0$ greater than $\simeq 1.3\times 10^{15}\mathrm{G}(P_{\star 0}/400\mathrm{ms}{)}^{-1.4}(M/1.4{\mathrm{M}}_{\odot }{)}^{2.2}$ 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 spindown. Spindown is more efficient for lower $M$ and for larger $P_{\star 0}$. 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.

16 pages, 10 figures

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