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After a successful supernova, a proto-neutron star (PNS) cools by emittingneutrinos on $\sim 1-100$ s timescales. Provided that there are neutrinoemission `hot-spots' or `cold-spots' on the surface of the rotating PNS, we canexpect a periodic modulation in the number of neutrinos observable bydetectors. We show that Fourier transform techniques can be used to determinethe frequency of rotation of the PNS from the neutrino arrival times. Providedthere is no spindown, a 1-parameter Discrete Fourier Transform (DFT) issufficient to determine the spin period of the PNS. If the PNS is born as amagnetar 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 canspin down to periods of the order of seconds during the cooling phase. Wepropose a modified DFT technique with three parameters to detect spindown. Dueto lack of neutrino data from a nearby supernova except the $\sim20$ neutrinosdetected from SN1987A, we use toy models and one physically motivatedmodulating function to generate neutrino arrival times. We use the false alarmrate (FAR) to quantify the significance of the Fourier power spectrum peaks. Weshow 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 $\sim10^{4}-10^{5}$ neutrino detections from a supernova at 10 kpc, detection of PNSrotation and spindown is possible using the neutrinos from the next Galacticsupernova.

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