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We investigate the gravitational waves (GWs) at low frequencies produced byneutrinos that are emitted anisotropically from the proto-neutron star (PNS)during its cooling phase that lasts about a minute. We first give a formulationbased on the spherical-harmonic expansion of the neutrino luminosity to obtainthe gravitational waveform as well as the characteristic strain. In the absenceof multi-dimensional simulations of PNS cooling, from which we can extractreliable data on the neutrino luminosities as a function of solid angle, weconstruct them by hand. In the first model, the time evolution is approximatedby piece-wise exponential functions (PEFs); in the second model we employ thetime evolution obtained in a 1D cooling simulation for all harmonic componentsfor simplicity; In both cases, we consider not only axisymmetric components butalso non-axisymmetric ones; for the latter, in particular, we consider as thethird model axisymetric neutrino emissions that are misaligned with therotation axis and, as a result, rotate with the PNS. We find from the firstmodel that the decay times in PEF at late phases can be inferred from thepositions of bumps and dips in the characteristic strain of the GW in the caseof a slow cooling, whereas it may be obtained by identifying the positions ofslope change in the case of rapid cooling, which may be induced by convectionsin PNS. We also find from the first model that the rotation of PNS can bereflected in GW waveforms. Finally, we compared the characteristic strains withsensitivity curves GW detectors, finding that above phenomena are expected tobe detected by DECIGO if the PNS is located at 10kpc.

Gravitational wave signals in the deci-Hz range from neutrinos during the proto-neutron star cooling phase