Nuclear neutrino energy spectra in high temperature astrophysical environments

Astrophysical environments that reach temperatures greater than $\sim 100$ keV can have significant neutrino energy loss via both plasma processes and nuclear weak interactions. We find that nuclear processes likely produce the highest-energy neutrinos. The important weak nuclear interactions include both charged current channels (electron capture and emission and positron capture and emission) and neutral current channels (deexcitation of nuclei via neutrino pair emission). We show that, in order to make a realistic prediction of the nuclear neutrino spectrum, one must take nuclear structure into account; in some cases, the most important transitions may involve excited states, possibly in both parent and daughter nuclei. We find that the standard technique of producing a neutrino energy spectrum by using a single transition with a $Q$ value and matrix element chosen to fit published neutrino production rates and energy losses will not accurately capture important spectral features.

Figure 1

Electron capture on a nucleus of mass number $A$, proton number $Z$, and excitation energy $E$, producing a nucleus of mass number $A$, proton number $Z-1$, and excitation energy $E^{\prime }$. The electron and neutrino may be exchanged in this diagram for their antiparticles, yielding a final nucleus with proton number $Z+1$.

Figure 2

Neutral current neutrino pair emission from a nucleus of mass number $A$ with initial excitation energy $E$ and final excitation $E^{\prime }$.

Figure 3

Electron decay from a nucleus of mass number $A$, proton number $Z$, and excitation energy $E$ to a nucleus of mass number $A$, proton number $Z+1$, and excitation energy $E^{\prime }$. The electron and antineutrino may be exchanged in this diagram for their antiparticles, yielding a final nucleus with proton number $Z-1$.

Figure 4

Neutral current neutrino scattering from a nucleus of mass number $A$ with initial excitation energy $E$ and final excitation $E^{\prime }$.

Figure 5

${}^{27}\mathrm{Si}$ charged current process neutrino spectrum. The black lines are totals for the nucleus, and the colored lines correspond to the indicated initial parent states.

Figure 6

${}^{31}\mathrm{S}$ charged current process neutrino spectrum. The black lines are totals for the nucleus, and the colored lines correspond to the indicated initial parent states.

Figure 7

${}^{30}\mathrm{P}$ charged current process neutrino spectrum. The black lines are totals for the nucleus, and the colored lines correspond to the indicated initial parent states.

Figure 8

${}^{32}\mathrm{P}$ charged current process antineutrino spectrum. The black lines are totals for the nucleus, and the colored lines correspond to the indicated initial parent states.

Figure 9

${}^{28}\mathrm{Al}$ charged current process neutrino spectrum. The black lines are totals for the nucleus, and the colored lines correspond to the indicated initial parent states.

Figure 10

Normalized energy emission rate in neutrino pairs via deexcitation to a final state with energy $E_f$ for a general nucleus as a function of the ratio of transition energy $\mathrm{\Delta }E$ to temperature $T$. This provides a qualitative guide to compare the emission rates of various nuclei at a given temperature.

Figure 11

Neutrino pair emissivities for a variety of $sd$-shell nuclei. The odd nuclei stay tightly grouped over the entire range of temperature. At low temperature, ${}^{28}\mathrm{Si}$ has low emissivity due to a lack of low-lying states.

Figure 12

There are two allowed deexcitations from low-lying excited states in ${}^{21}\mathrm{Ne}$. Figure 11 shows that each of these transitions becomes important at different temperatures.

Figure 13

Energy-loss rates from neutral current deexcitation of ${}^{27}\mathrm{Al}$ and other major neutrino processes. For electron-positron pair annihilation and the photoprocess, the black (upper) lines are for $\rho ={10}^7{\mathrm{g}/\mathrm{cm}}^3$, the red (middle) lines are for $3\times {10}^7{\mathrm{g}/\mathrm{cm}}^3$, and the green (lower) lines are for ${10}^8{\mathrm{g}/\mathrm{cm}}^3$. The lower panel emphasizes the temperature range appropriate for core O-Ne-Mg burning.

Figure 14

Energy-loss rates from neutral current deexcitation of ${}^{27}\mathrm{Al}$ and electron capture on ${}^{28}\mathrm{Si}$. The product of density and electron fraction $\rho Y_e$ is in ${\mathrm{g}/\mathrm{cm}}^3$.

Figure 15

${}^{27}\mathrm{Al}$ (top) and ${}^{28}\mathrm{Si}$ (bottom) neutral current neutrino spectra. Antineutrino spectra are identical. Notably, the spectra above 10 MeV are similar.

Figure 16

${}^{56}\mathrm{Fe}$ charged current process neutrino spectra computed from the FFN prescription. The $E_i=11.44$ MeV line corresponds to the isobaric analog of the ${}^{56}\mathrm{Mn}$ ground state. In the upper panel, the electron chemical potential is less than the Gamow–Teller resonance energy, while in the lower panel, it is greater than the GT resonance energy. Because of this, the peak in the lower panel is more than four orders of magnitude greater, despite the comparatively small increase in temperature.

Figure 17

${}^{56}\mathrm{Fe}$ charged current process neutrino spectra computed from the FFN prescription at various points during collapse. The enormous jump in neutrino production between the lowest two temperatures is due to the chemical potential in the higher temperature point being greater than the Gamow–Teller resonance energy.

Figure 18

${}^{27}\mathrm{Al}$ thermal strength at temperature $T=0.43$ MeV. The upper panel shows the thermal strengths in the left (forward) and right (reverse) sides of Eq. (17); these are only the thermal strengths and do not include the exponential factors. The lower panel shows the imbalance between the right- and left-hand sides of Eq. (17) (detailed imbalance, solid line) and the imbalance of the thermal strengths (dashed line).