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

Abstract

We investigate the gravitational waves (GWs) at low frequencies produced by neutrinos that are emitted anisotropically from the proto-neutron star (PNS) during its cooling phase that lasts about a minute. We are particularly interested in the deci-Hz range, to which some satelliteborne detectors are expected to have good sensitivities. We first give a formulation based on the spherical-harmonic expansion of the neutrino luminosity to obtain the gravitational waveform as well as the characteristic strain. In the absence of multi-dimensional simulations of PNS cooling, from which we can extract reliable data on the neutrino luminosities as a function of solid angle, we construct them by hand. In the first model, the time evolution is approximated by piece-wise exponential functions (PEFs); in the second model we employ the time evolution obtained in a 1D cooling simulation for all harmonic components for simplicity; In both cases, we consider not only axisymmetric components but also non-axisymmetric ones; for the latter, in particular, we consider as the third model axisymetric neutrino emissions that are misaligned with the rotation axis and, as a result, rotate with the PNS. We find from the first model that the decay times in PEF at late phases can be inferred from the positions of bumps and dips in the characteristic strain of the GW in the case of a slow cooling, whereas it may be obtained by identifying the positions of slope change in the case of rapid cooling, which may be induced by convections in PNS. We confirm the former result also in the second model. The results of the third model show that the gravitational waves emitted by the neutrinos are circularly polarized in contrast to the first two models, in which only linear polarizations occur, and give oscillatory features in the waveform with the frequencies of integral multiples of the rotation frequency, which are also clearly reflected in the characteristic strain. Finally we compare the GW signals thus obtained with the sensitivity curves of some GW detectors that are expected to be sensitive to GWs in the deci-Herz range. The results tell us that they, DECIGO in particular, will be able to detect the GW signals as we consider them in this paper if they are emitted from within our Galaxy.