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

After a successful supernova, a proto-neutron star (PNS) cools by emitting neutrinos on similar to 1-100 s time-scales. Provided that there are neutrino emission 'hotspots' 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 PNS rotation rate from the neutrino arrival times. Provided there is no spin-down, 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 greater than or similar to 10(15) G and is 'slowly' rotating with an initial spin period greater than or similar to 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 frequency parameters to detect spin-down. Due to lack of neutrino data from a nearby supernova except the similar to 20 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 spin-down are detected with (2 sigma) for periodic signal content if 5 x 10(3) neutrinos are detected in similar to 3 s and with for if 5 x 10(4) neutrinos are detected in similar to 3 s. Since we can expect similar to 10(4)-10(5) neutrino detections from a supernova at 10 kpc, detection of PNS rotation and spin-down is possible using the neutrinos from the next Galactic supernova.