Basic characteristics of neutrino flavor conversions in the postshock regions of core-collapse supernova

One of the active debates in core-collapse supernova (CCSN) theory is how significantly neutrino flavor conversions induced by neutrino-neutrino self-interactions change the conventional picture of CCSN dynamics. Recent studies have indicated that strong flavor conversions can occur inside neutrino spheres where neutrinos are tightly coupled to matter. These flavor conversions are associated with either collisional instability or fast neutrino-flavor conversion (FFC) or both. The impact of these flavor conversions on CCSN dynamics is, however, still highly uncertain due to the lack of global simulations of quantum kinetic neutrino transport with appropriate microphysical inputs. Given fluid profiles from a recent CCSN model at three different time snapshots in the early postbounce phase, we perform global-quantum kinetic simulations in spherical symmetry with an essential set of microphysics. We find that strong flavor conversions occur in optically thick regions, resulting in a substantial change of neutrino radiation field. The neutrino heating in the gain region is smaller than the case with no flavor conversions, whereas the neutrino cooling in the optically thick region is commonly enhanced. Based on the neutrino data obtained from our multiangle neutrino transport simulations, we also assess some representative classical closure relations by applying them to diagonal components of density matrix of neutrinos. We find that Eddington tensors can be well-approximated by these closure relations except for the region where flavor conversions occur vividly. We also analyze the neutrino signal by carrying out detector simulations for Super-Kamiokande, DUNE, and JUNO. We propose a useful strategy to identify the sign of flavor conversions in neutrino signal, that can be easily implemented in real data analyses of CCSN neutrinos.

Figure 1

Fluid snapshots used in the present study. They are taken from a spherically symmetric CCSN model of 15 solar mass progenitor in [72]. From left to right, we show fluid profiles for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively. In each panel, $\rho$, $Y_e$, and $T$ distributions are displayed, and the colors distinguish these quantities. We note that $Y_e$ distribution is reduced by 10% from the original CCSN model; see the text for more details.

Figure 1

Fluid snapshots used in the present study. They are taken from a spherically symmetric CCSN model of 15 solar mass progenitor in [72]. From left to right, we show fluid profiles for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively. In each panel, $\rho$, $Y_e$, and $T$ distributions are displayed, and the colors distinguish these quantities. We note that $Y_e$ distribution is reduced by 10% from the original CCSN model; see the text for more details.

Figure 2

Color map of ELN distributions, $(f_{ee}-{\overline{f}}_{ee})$, normalized by the sum of all flavors of neutrinos and antineutrinos, as functions of radius and neutrino flight angle. The distributions are taken from classical neutrino transport models ($H=\overline{H}=0$) at the end of each simulation (neutrinos are in quasisteady states). From left to right, we show results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively. In each panel, we also highlight $(f_{ee}={\overline{f}}_{ee})$ by black solid lines.

Figure 2

Color map of ELN distributions, $(f_{ee}-{\overline{f}}_{ee})$, normalized by the sum of all flavors of neutrinos and antineutrinos, as functions of radius and neutrino flight angle. The distributions are taken from classical neutrino transport models ($H=\overline{H}=0$) at the end of each simulation (neutrinos are in quasisteady states). From left to right, we show results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively. In each panel, we also highlight $(f_{ee}={\overline{f}}_{ee})$ by black solid lines.

Figure 3

Radial profiles of the maximum growth rate of flavor conversion as a function of radius. From left to right, we show the result for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively. In this analysis, we take into account the attenuation parameter ($\xi ={10}^{-4}$). Red and blue lines show the result with and without collision terms, respectively, which is useful to see which collisional instability or FFC dominates flavor conversions; see the text for more details.

Figure 3

Radial profiles of the maximum growth rate of flavor conversion as a function of radius. From left to right, we show the result for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively. In this analysis, we take into account the attenuation parameter ($\xi ={10}^{-4}$). Red and blue lines show the result with and without collision terms, respectively, which is useful to see which collisional instability or FFC dominates flavor conversions; see the text for more details.

Figure 4

The same figure as Fig. 3 but for cases with no attenuation of oscillation Hamiltonian, i.e., $\xi =1$.

Figure 4

The same figure as Fig. 3 but for cases with no attenuation of oscillation Hamiltonian, i.e., $\xi =1$.

Figure 5

Same figure as Fig. 2 but for the time-averaged ELN-$\mu \mathrm{LN}$ distributions in quasisteady states, obtained from quantum kinetic neutrino transport simulations.

Figure 5

Same figure as Fig. 2 but for the time-averaged ELN-$\mu \mathrm{LN}$ distributions in quasisteady states, obtained from quantum kinetic neutrino transport simulations.

Figure 6

Radial profiles of some important time-averaged quantities in quantum kinetic neutrino transport simulations. From top to bottom, we show the result of neutrino heating-cooling rate, average energy, and energy flux of all flavors of neutrinos. As a reference, we display their counterparts in cases with classical neutrino transport as black colors (denoted by “Clas”), while the line type distinguishes neutrino flavors. Other colored lines correspond to results of quantum kinetic simulations. From left to right, we show the results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively.

Figure 6

Radial profiles of some important time-averaged quantities in quantum kinetic neutrino transport simulations. From top to bottom, we show the result of neutrino heating-cooling rate, average energy, and energy flux of all flavors of neutrinos. As a reference, we display their counterparts in cases with classical neutrino transport as black colors (denoted by “Clas”), while the line type distinguishes neutrino flavors. Other colored lines correspond to results of quantum kinetic simulations. From left to right, we show the results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively.

Figure 7

Time-averaged energy spectra for neutrino number flux measured at the outer boundary. The line colors and types are the same as those used in Fig. 6. From left to right, we show the results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively.

Figure 7

Time-averaged energy spectra for neutrino number flux measured at the outer boundary. The line colors and types are the same as those used in Fig. 6. From left to right, we show the results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively.

Figure 8

Radial profiles of $k^{rr}$ ($r\text{−}r$ components of energy-integrated Eddington tensor) for diagonal components of density matrix. The top and bottom panels show the result of electron-type and heavy-leptonic neutrinos, respectively. We distinguish neutrinos and antineutrinos by line types, in which the former and latter are denoted by the solid and dashed lines, respectively. The colors distinguish various ways to compute Eddington tensors. Black lines show the Eddington tensors directly computed from full angular distributions (denoted as grqknt). For other colors, we compute Eddington tensor from zeroth and first angular moments (which are obtained from quantum kinetic simulations) with classical closure relations. In this study, we study four closure relations; Minerbo (red), Livermore (blue), Janka (green), and NJ (purple). From left to right, we display results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively.

Figure 8

Radial profiles of $k^{rr}$ ($r\text{−}r$ components of energy-integrated Eddington tensor) for diagonal components of density matrix. The top and bottom panels show the result of electron-type and heavy-leptonic neutrinos, respectively. We distinguish neutrinos and antineutrinos by line types, in which the former and latter are denoted by the solid and dashed lines, respectively. The colors distinguish various ways to compute Eddington tensors. Black lines show the Eddington tensors directly computed from full angular distributions (denoted as grqknt). For other colors, we compute Eddington tensor from zeroth and first angular moments (which are obtained from quantum kinetic simulations) with classical closure relations. In this study, we study four closure relations; Minerbo (red), Livermore (blue), Janka (green), and NJ (purple). From left to right, we display results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms, respectively.

Figure 9

Same as Fig. 8 but for $k^{\theta \theta }(=k^{\varphi \varphi })$.

Figure 9

Same as Fig. 8 but for $k^{\theta \theta }(=k^{\varphi \varphi })$.

Figure 10

Energy—and azimuthally—integrated neutrino angular distributions at 60 km for ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$ model. In each panel, we separate the results of classical neutrino transport (top) and quantum kinetic one (bottom) by a horizontal gray line. In the left top panel, we display the outgoing radial direction by a black arrow. Left and right panels distinguish results of neutrinos and antineutrinos, respectively, while top and bottom ones show results of electron- and $\mu$-type neutrinos, respectively.

Figure 11

Energy spectra of neutrino event rate for the major reaction channel on each detector. From top to bottom, we show the results in SK, DUNE, and JUNO, respectively, while the results for models of ${\mathrm{T}}_{\mathrm{b}}=100\mathrm{ms}$, 200 ms, and 300 ms are displayed from left to right panels. Line type distinguishes the results between quantum (solid) and classical (dashed) simulations. We also take into account the adiabatic MSW neutrino oscillation effect, whose dependence is denoted by color; black (no MSW), red (normal mass hierarchy), and blue (inverted mass hierarchy). See the text for more details.