Comparison of Neutrino Transport Approximations in Core-Collapse Supernova Simulations

Transcription

1 Comparison of Neutrino Transport Approximations in Core-Collapse Supernova Simulations Sherwood Richers 1 Evan O Connor 2 Christian Ott 1 1 TAPIR, California Institute of Technology 2 CITA, University of Toronto November 9, 12 Sherwood Richers Neutrino Transport Approximations November 9, 12 1/13

2 Outline Introduction: What are core-collapse supernovae? Methods: How are neutrinos approximated? Results: How do the resulting explosions differ? Conclusions: Which method is right? Sherwood Richers Neutrino Transport Approximations November 9, 12 2/13

3 Core-Collapse Supernovae Star collapses and core rebounds. Shock propagates out through infalling star. Neutrinos emitted from core heat, pressurize, and leptonize the gain region. Sherwood Richers Neutrino Transport Approximations November 9, 12 3/13

4 Core Collapse Supernovae Dominant Neutrino Processes in the core: electron capture e + p ν e + n positron capture e + + n ν e + p scattering ν l + l ν l + l in the gain region: neutrino capture ν e + n e + p anti-neutrino capture ν e + p e + + n scattering ν l + l ν l + l Neutrinos carry away energy and lepton number. Neutrinos heat, pressurize, and leptonize the gain region. Sherwood Richers Neutrino Transport Approximations November 9, 12 4/13

5 Neutrino Approximations 3-D Boltzmann Equation 1 I c t + Ω I = C(I) Neutrino Intensity Distribution I(x, Ω, ɛ, t) Full Boltzmann transport is prohibitively expensive. Study effects of individual parameters. 1-D simulations can be used to: better understand approximation effects before doing 3-D simulations. assess the predictive power of an approximation. Sherwood Richers Neutrino Transport Approximations November 9, 12 5/13

6 Neutrino Approximations Lightbulb Fixed neutrino properties Lνe = Lν e = erg/s Tνe = Tν e = 4 MeV Analytic heating, cooling, and electron fraction h i H Lνe r 2 Tν2e erg g s h i erg 6 C T g s Ye = Ye (ρ) only consider νe and ν e Sherwood Richers Neutrino Transport Approximations November 9, 12 6/13

7 Neutrino Approximations Leakage Calculate optical depth τ (r) neutrino energy and number loss rate Energy-averaged neutrino heating based on above net neutrino luminosity and neutrinosphere temperature. Considers νe, ν e, and νx Sherwood Richers Neutrino Transport Approximations November 9, 12 7/13

8 Neutrino Approximations Two-Moment Evolves the 0th (energy) and 1st (flux) moments of the neutrino distribution function with an analytic closure relation. 24 energy bins for each species νe, ν e, and νx. Currently no dependence on fluid velocity or coupling between energy groups. Sherwood Richers Neutrino Transport Approximations November 9, 12 8/13

9 Results - Neutrino Energies Eνe [MeV] E νe [MeV] Eνx [MeV] Two-Moment GR 10 Leakage Newtonian 5 Lightbulb t t bounce [ms] Lightbulb scheme does not emit ν x and assumes constant energy. Leakage energies are unreliable due to different definition of energy. Sherwood Richers Neutrino Transport Approximations November 9, 12 9/13

10 Results - Neutrino Luminosities Newt. ν-luminosity [ B s ] GR ν-luminosity [B s ] Two-Moment Leakage Lightbulb ν e ν e ν x t t bounce [ms] Lightbulb scheme does not emit ν x. Lightbulb scheme heating can be unphysical. Sherwood Richers Neutrino Transport Approximations November 9, 12 10/13

11 Results - Supernova Structure Ye T [MeV] log 10 ( ρ g cm 3 ) Two-Moment Leakage Lightbulb Radius [km] GR Newtonian Lightbulb scheme temperature differs within PNS. Lightbulb scheme electron fraction large due to Y e (ρ) prescription. Density profiles remain similar. Sherwood Richers Neutrino Transport Approximations November 9, 12 11/13

12 Results - Shock and PNS Radius R ρ=10 11 g/cm 3 [km] R shock [km] Two-Moment Leakage Lightbulb GR Newtonian t t bounce [ms] Constant input luminosity causes lightbulb scheme s shock to be larger. Lightbulb scheme s PNS is large because Y e (ρ) prescription keeps core pressure high. Sherwood Richers Neutrino Transport Approximations November 9, 12 12/13

13 Conclusions There are clear qualitative differences between the schemes. The two-moment scheme makes the fewest approximations. The leakage scheme appears to fit qualitatively with the two-moment results, but differs quantitatively. The lightbulb scheme differs qualitatively from more sophisticated schemes in many areas. Must compare to full Boltzmann or Monte Carlo transport. Sherwood Richers Neutrino Transport Approximations November 9, 12 13/13