Prospects for detecting proto-neutron star rotation and spindown using supernova neutrinos

After a successful supernova, a proto-neutron star (PNS) cools by emitting neutrinos on $\sim 1-100$ s timescales. Provided that there are neutrino emission `hot-spots' or `cold-spots' on the surface of the rotating PNS, we can expect a periodic modulation in the number of neutrinos observable by detectors. We show that Fourier transform techniques can be used to determine the frequency of rotation of the PNS from the neutrino arrival times. Provided there is no spindown, a 1-parameter Discrete Fourier Transform (DFT) is sufficient to determine the spin period of the PNS. If the PNS is born as a magnetar with polar magnetic field strength $B_0 \gtrsim 10^{15}$ G and is `slowly' rotating with an initial spin period $\gtrsim 100$ ms, then it can spin down to periods of the order of seconds during the cooling phase. We propose a modified DFT technique with three parameters to detect spindown. Due to lack of neutrino data from a nearby supernova except the $\sim20$ neutrinos detected from SN1987A, we use toy models and one physically motivated modulating function to generate neutrino arrival times. We use the false alarm rate (FAR) to quantify the significance of the Fourier power spectrum peaks. We show that PNS rotation and spindown are detected with $\rm FAR<2\%$ ($2\sigma$) for periodic signal content $\rm M\gtrsim 13-15\%$ if $5\times 10^{3}$ neutrinos are detected in 3 s and with $\rm FAR<1\%$ for $\rm M\geq 5\%$ if $5\times 10^{4}$ neutrinos are detected in 3 s. Since we can expect $\sim 10^{4}-10^{5}$ neutrino detections from a supernova at 10 kpc, detection of PNS rotation and spindown is possible using the neutrinos from the next Galactic supernova.Comment: 18 pages, 16 figure

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

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 $P_{\star0}=50-500$ 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 Alfv\'en 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 $B_0\gtrsim5\times10^{14}$ G, the spindown timescale can be shorter than than the Kelvin-Helmholtz timescale. For $B_0\gtrsim10^{15}$ G, it is of order seconds in early phases. We compute the spin evolution for cooling proto-magnetars as a function of $B_0$, $P_{\star0}$, and mass ($M$). Proto-magnetars born with $B_0$ greater than $\simeq1.3\times10^{15}\,{\rm\,G}\,(P_{\star0}/{400\,\rm\,ms})^{-1.4}(M/1.4\,{\rm M}_\odot)^{2.2}$ 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 $P_{\star0}$. 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.Comment: 16 pages, 10 figure

The early evolution of magnetar rotation -- II. Rapidly rotating magnetars: Implications for Gamma-Ray Bursts and Super Luminous Supernovae

Rapidly rotating magnetars have been associated with gamma-ray bursts (GRBs) and super-luminous supernovae (SLSNe). Using a suite of 2D magnetohydrodynamic simulations at fixed neutrino luminosity and a couple of evolutionary models with evolving neutrino luminosity and magnetar spin period, we show that magnetars are viable central engines for powering GRBs and SLSNe. We also present analytic estimates of the energy outflow rate from the proto-neutron star (PNS) as a function of polar magnetic field strength $B_0$, PNS angular velocity $\Omega_{\star}$, PNS radius $R_{\star}$ and mass outflow rate $\dot{M}$. We show that rapidly rotating magnetars with spin periods $P_{\star}\lesssim 4$ ms and polar magnetic field strength $B_0\gtrsim 10^{15}$ G can release $10^{50}-5\times 10^{51}$ ergs of energy during the first $\sim2$ s of the cooling phase. Based on this result, it is plausible that sustained energy injection by magnetars through the relativistic wind phase can power GRBs. We also show that magnetars with moderate field strengths of $B_0\lesssim 5\times 10^{14}$ G do not release a large fraction of their rotational kinetic energy during the cooling phase and hence, are not likely to power GRBs. Although we cannot simulate to times greater than $\sim 3-5$ s after a supernova, we can hypothesize that moderate field strength magnetars can brighten the supernova light curves by releasing their rotational kinetic energy via magnetic dipole radiation on timescales of days to weeks, since these do not expend most of their rotational kinetic energy during the early cooling phase.Comment: 15 pages, 13 Figure