An updated model of neutrino emission from proto-neutron stars

The gist: This updated parametric model for neutrino emission from proto-neutron stars connects neutrino luminosity and average energy directly to stellar properties during emission, showing that neutrino mass ordering plays a crucial role in constraining astrophysical parameters through simulated data analysis.

Model Components

The model incorporates two critical physical processes: convection within the proto-neutron star and the evolution of the neutrinosphere radius during the early emission phase. The neutrino emission is divided into three phases: neutronization burst, accretion phase, and final cooling phase.

Cooling Phase Modeling

The cooling phase is described by a parametric formula for neutrino luminosity as Lν(t) = C t−α exp [−(t/τ) n], where t is the time since core bounce, C is a normalization factor, α describes the power-law behavior during the early cooling phase, τ sets the characteristic cooling timescale, and n controls the steepness of the late-time exponential decline. The neutrino energy distribution follows a Fermi-Dirac thermal spectrum gν(t, Eν, Tc(t)) = πc (hc) 3 E2 ν 1 + exp(Eν/Tc(t)), which depends on the temperature evolution embedded in the function Tc(t). The time evolution of the cooling temperature is modified to account for convection within the PNS mantle, described by Tc(t) = (T0 + δT [1 − exp(−t/τTc)] t ≤ t¯; T1 t −αc exp[−(t/τc) nc] t > τ, where τ¯ marks the onset of convection in the PNS mantle during neutrino cooling, T0 is the initial temperature, δT sets the amplitude of the temperature increase in the first branch, and τTc is the characteristic timescale of that increase.

Accretion Phase Modeling

During the accretion phase, electron neutrinos and antineutrinos are copiously emitted through electron and positron capture on free nucleons in the stellar plasma below the shock front. The electron antineutrino flux produced by positron capture on neutrons is modeled as Φa(t, Eν) = [1 − exp (−t/τr)]Nn(t)σe+n(Eν)ge+ (Ee+, Ta(t)). The quantity Nn(t) represents the number of neutrons available in the accreting region between the shock front and the PNS before the SN explosion and is parametrized as Nn(t) = Yn mn Ma TaTa(t) exp[−(t/τa)2] 1 + t/(0.5 s), where Ma is the accreting mass, expressed in solar masses, and the neutron fraction is fixed at Yn = 0.6. The total νe flux emitted by the SN is given by the sum of the accretion and cooling contributions: Φ0νe(t, Eν) = Φa(t, Eν) + [1 − exp(−(t/τa)2)] Φc(t, Eν), where the factor [1 − exp(−(t/τa)2)] provides a smooth transition from accretion-dominated to cooling-dominated emission on a timescale set by τa.

Flavor Conversions and Observational Sensitivity

Flavor conversions during propagation through the dense stellar environment must be taken into account, using the standard neutrino oscillation framework considering only the Mikheyev-Smirnov-Wolfenstein (MSW) matter effect during propagation through the SN envelope. The electron antineutrino flux at the detector is given by Φνe(t, Eν) = 1/4πD2 (PeeΦ0νe(t, Eν) + (1 − Pee)Φ0νx(t, Eν)), where Pee describes the electron survival probability. For IO mass ordering, only the cooling component contributes for the ν¯e flux at the detector, resulting in Φν¯e(t, Eν) ∼ Φ0νx(t, Eν) = Φc(t, Eν). In contrast, in NO mass ordering, the ν¯e flux at the detector contains the imprint of both the accretion and cooling phases.

Validation and Results

The model was tested against recent 3D FORNAX simulations performed with the FORNAX code. The analysis utilized a Bayesian framework by sampling the posterior distribution defined by the likelihood in Eq. (20). The results show that for IO, the detected signal is sensitive only to the cooling component, allowing inference of time-dependent properties of the νx neutrinosphere. For NO, accretion dominates the signal during the first ∼ 0.5 s after core bounce. The best-fit value of αc and the value of nc are consistent with the EoS adopted in the simulations (SFHo [26]).

Conclusion

The model successfully tests the SN neutrino cooling model against 3D simulations, extending it to earlier times by introducing parametric descriptions of temperature and radius evolution, and including the accretion phase. This approach allows for determining PNS properties through simulated data analysis, providing insights into the EoS through neutrino observations of a future SN. The model demonstrates that in IO, the detected signal is sensitive only to the cooling component, while in NO, accretion dominates during the first ∼ 0.5 s after core bounce.

How it works

The model incorporates two critical physical processes: convection within the proto-neutron star and the evolution of the neutrinosphere radius during the early emission phase. The fitting formula for neutrino luminosity parametrizes effects seen in numerical simulations, incorporating a parametric description of convection and muons within the hot PNS. The time evolution of the cooling temperature is modified to account for convection within the PNS mantle during neutrino cooling. The effective neutrinosphere radius is parametrized as Rc(t) = Rf [1 + δR exp(−t/τR)], where Rf is the asymptotic neutrinosphere radius, which serves as a proxy for the late-time PNS radius. The analysis is performed within a Bayesian framework by sampling the posterior distribution defined by the likelihood in Eq. (20). The temporal evolution of the neutrinosphere radius Rc(t) qualitatively reproduces the expected behavior and serves as a useful proxy for the evolution of the PNS radius, particularly at later times.

Summary of Key Findings

The model accurately describes neutrino luminosity and average energy obtained from numerical simulations for different progenitors. The fitting of Lνx allows us to constrain the effective neutrinosphere radius, used here as a proxy for the PNS radius. Fitting Lν¯e provides information on the accreting mass Ma. The inferred Rc should not be interpreted as a direct measurement of the geometrical PNS radius, but it qualitatively reproduces expected behavior. The sign of the best-fit value of αc and the value of nc are consistent with the EoS adopted in the simulations (SFHo [26]). The analysis shows that for IO, the detected signal is sensitive only to the cooling component, allowing inference of time-dependent properties of the νx neutrinosphere. For NO, accretion dominates the signal during the first ∼ 0.5 s after core bounce. The model provides a quantitative approach to probing the EoS through neutrino observations of a future SN. The model is validated against 3D FORNAX simulations, confirming its ability to describe the neutrino emission from different progenitors.

1. The improved AI system can perform parameter estimation for core-collapse supernovae by assessing the sensitivity to astrophysical properties in the event of a future detection, specifically determining if the neutrino mass ordering plays a crucial role in determining which parameters can be constrained by the observed neutrino data.

2. The system can accurately reconstruct the time evolution of the neutrinosphere radius, as demonstrated by fitting Eq. (8) to posterior distributions, allowing it to infer the time-dependent properties of the νx neutrinosphere and link them to the early-time evolution of PNS oscillations.

3. The system can distinguish between neutrino mass orderings based on the resulting constraints: for IO, it can infer the time-dependent properties of the νx neutrinosphere, whereas for NO, it can determine that accretion dominates the signal during the first ∼ 0.5 s after core bounce.

4. The system can test and validate complex physical models by comparing them against high-fidelity simulations, such as using recent 3D simulations of PNS neutrino emission performed with the FORNAX code to see if they accurately describe the neutrino luminosity and average energy obtained from numerical simulations for different progenitors.