  Measuring the rotation of core-collapse supernovae (SN) and of their
progenitor stars is extremely challenging. Here it is demonstrated that
neutrinos may potentially be employed as stellar gyroscopes, if phases of
activity by the standing accretion-shock instability (SASI) affect the neutrino
emission prior to the onset of the SN explosion. This is shown by comparing the
neutrino emission properties of self-consistent, three-dimensional (3D) SN
simulations of a 15 M_sun progenitor without rotation as well as slow and fast
rotation compatible with observational constraints. The explosion of the fast
rotating model gives rise to long-lasting, massive polar accretion downflows
with stochastic time-variability, detectable e.g. by the IceCube Neutrino
Observatory for any observer direction. While spectrograms of the neutrino
event rate of non-rotating SNe feature a well-known sharp peak due to SASI for
observers located in the proximity of the SASI plane, the corresponding
spectrograms of rotating models show activity over a wide range of frequencies,
most notably above 200 Hz for rapid rotation. In addition, the Fourier power
spectra of the event rate for rotating models exhibit a SASI peak with lower
power than in non-rotating models. The spectra for the rotating models also
show secondary peaks at higher frequencies with greater relative heights
compared to the main SASI peak than for non-rotating cases. These rotational
imprints will be detectable for SNe at 10 kpc or closer.
