We investigate the gravitational waves (GWs) at low frequencies produced by neutrinos that are emitted anisotropically from the protoneutron star (PNS) during its cooling phase that lasts for about a minute. We are particularly interested in the deci-Hz range, in which some satellite-borne 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 multidimensional simulations of PNS cooling, from which we can extract reliable data on the neutrino luminosities as a function of a solid angle, we construct them by hand. In the first model, the time evolution is approximated by piecewise exponential functions. In the second model we employ the time profile obtained in a 1D cooling simulation for all harmonic components for simplicity. In both cases, we consider not only axisymmetric components but also nonaxisymmetric ones. In the third model, we consider axisymmetric neutrino emissions, the axis of which is misaligned with the rotation axis and, as a result, rotates with the PNS. We find from the first model that the decay times in piecewise exponential function 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 they may be obtained by identifying the positions of slope change in the case of rapid cooling, which may be induced by convection 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 contain circularly-polarized components 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 planned GW detectors that are expected to be sensitive to GWs in the deci-Hz range. If these admittedly crude models are any guide, these detectors, DECIGO in particular, will have a fair chance of detecting the GW signals as we consider them in this paper if they are emitted from within our Galaxy.

• Received 30 January 2022
• Revised 2 June 2022
• Accepted 5 June 2022

DOI:https://doi.org/10.1103/PhysRevD.105.123028