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⋆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 B0 ≳ 5 × 1014 G, the spindown timescale can be shorter than than the Kelvin-Helmholtz timescale. For B0 ≳ 1015 G, it is of order 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 spindown. Spindown 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.

Three-dimensional General-relativistic Simulations of Neutrino-driven Winds from Magnetized Proto–Neutron Stars

“…Following this trend to later times than the duration of our simulation, we conclude that a moderate fraction of the timeaveraged wind material could well attain values of η that surpass the second and potentially also third r-process peaks. Though due to numerical limitations we cannot follow the multiple cycles of trapped-zone inflation and mass ejection seen by Thompson & ud-Doula (2018) and Prasanna et al (2022), our results are in broad agreement with the findings of these authors.…”

“…The presence of a magnetic field can significantly impact the dynamics of the PNS wind in regions where the magnetic pressure P B = B 2 /8π greatly exceeds the fluid pressure P f (Thompson 2003;Thompson & ud-Doula 2018;Prasanna et al 2022). In the gain region just above the PNS surface, where neutrino heating begins to exceed neutrino cooling, the radiation pressure of photons and electron/positrons dominates over the gas pressure and hence P f ; P rad = (11/12)aT 4 , where a is the radiation constant.…”

“…By contrast, outflowing material in the equatorial regions of the wind are initially trapped by the nonradial magnetic field at lower latitudes (Figures 5, 6, and 13), with the magnetosphere in this region maintaining a dipole field structure well above the PNS surface (Figure 3). Neutrino heating raises the thermal pressure of the trapped fluid in the equatorial region until it obeys P f > P B (Thompson 2003;Prasanna et al 2022), at which point fluid begins to escape and the closed zone begins to shrink from the outside inwards. Energy input from αparticle formation appears to aid the ejection of matter from the equatorial regions, and by the end of the simulation the isotropic-equivalent mass-loss rate even slightly overshoots that of the otherwise equivalent unmagnetized wind (Figure 5).…”

“…These authors also found that a small fraction of the ejecta reaches large values of η  10 10 , sufficient for a second-or even third-peak r-process, due to the transient ejection of high-entropy matter from the closed zone. Although the evolution of our hi-B model indeed resembles a single episode of closed-zone inflation and eruption, our simulations unfortunately cannot be run as long as those by Thompson & ud-Doula (2018) and Prasanna et al (2022) due to the higher computational cost of our 3D GRMHD simulations that aim to resolve the neutrinosphere marginally, versus axisymmetric 2D simulations.…”

“…Likewise, Prasanna et al (2022) performed similar simulations but covering a wider parameter space of the neutrino-driven winds from slowly rotating magnetars, focusing on the effects that neutrino-driven mass loss has in opening magnetic field lines and enhancing the star's spin-down rate relative to the magnetic dipole rate. Our goal here is to explore a similar setup using 3D GRMHD simulations including neutrino transport via an M0 scheme, thus paving the way for future simulations within this numerical setup that include both magnetic fields and rapid rotation together.…”