Interaction of supernova neutrinos with stochastic gravitational waves

We examine the propagation and flavor oscillations of neutrinos under the influence of gravitational waves (GWs) with an arbitrary polarization. We rederive the effective Hamiltonian for the system of three neutrino flavors using the perturbative approach. Then, using this result, we consider the evolution of neutrino flavors in stochastic GWs with a general energy density spectrum. The equation for the density matrix is obtained and solved analytically in the case of three neutrino flavors. As an application, we study the evolution of the flavor content of a neutrino beam emitted in a core-collapsing supernova. We obtain the analytical expressions for the contributions of GWs to the neutrino fluxes and for the damping decrement, which describes the attenuation of the fluxes to their asymptotic values. We find that the contribution to the evolution of neutrino fluxes from GWs, emitted by merging supermassive black holes, dominates over that from black holes with stellar masses. The implication of the obtained results for the measurement of astrophysical neutrinos with neutrino telescopes is discussed.

Figure 1

(a) The parameter $\mathrm{\Gamma }$ versus the neutrino beam propagation length $x=\tau L$; (b)–(d) the corrections the neutrino fluxes $\mathrm{\Delta }{F}_{{\nu }_{\lambda }}\propto \mathrm{\Delta }{P}_{\lambda }$ owing to the neutrino interaction with stochastic GWs. The parameters of the system are [22, 24, 29] $\mathrm{\Delta }{m}_{21}^2=7.5\times {10}^{-5}{\mathrm{eV}}^2$ and $E=10\mathrm{MeV}$ ($L_{21}=3.3\times {10}^2\mathrm{km}$), ${\theta }_{12}=0.6$, ${\theta }_{23}=0.85$, ${\theta }_{13}=0.15$, ${\delta }_{CP}=3.77$, $L=10\mathrm{kpc}$, ${\mathrm{\Omega }}_0={10}^{-9}$, and $f_{\min }={10}^{-10}\mathrm{Hz}$. The normal neutrino mass ordering is adopted.

Figure 2

The SN neutrino fluxes for different post bounce times $\mathrm{\Delta }t$. The parameters of the neutrino system and GWs are the same as in Fig. 1; $K\mathrm{\Delta }t=1$ corresponds to $t=0.1\mathrm{s}$ after the core bounce. (a) The fluxes $(F_{{\nu }_{\lambda }}{)}_{\mathrm{S}}$ at a source. The blue and green lines overlap since the fluxes of ${\nu }_{\mu }$ and ${\nu }_{\tau }$ coincide [see Eq. (3.8)]. (b) The maximal values of the deviations of the fluxes $(\mathrm{\Delta }{F}_{{\nu }_{\lambda }}^{(\max )}{)}_{\oplus }$ in a detector, owing to the interaction of SN neutrinos with stochastic GWs.