The Rotating Core-Collapse Supernova Dynamics and Neutrino Distributions by Full Boltzmann Neutrino Transport Akira Harada (University of Tokyo) Collaborators: W. Iwakami, H. Okawa、S. Yamada (Waseda) H. Nagakura (Princeton), K. Sumiyoshi (Numazu), H. Matsuhuru (KEK) High Energy Astrophysics 2018 2018/9/6@Hongo campus, University of Tokyo
→Stalled shock Core-Collapse Supernovae Fe Si O,Ne,Mg C,O He H PNS Shock ? • Gravitational Collapse→Core Bounce • Neutrino Heating Mechanism？
•Explosion failed in 1D ← confirmed by the Boltzmann transport •The Boltzmann transport is also required for multi-D simulations. Boltzmann Neutrino Transport Sumiyoshi+ (2005) Liebendoerfer+ (2001)
•Results of multi-D Boltzmann simulations Multi-D Boltzmann Simulation •Collapse of the 11.2 M ⦿ (Woosley+ 2002) Nagakura+ (2018) progenitor •Comparison of the equations of state is shown LS - entropy FS - entropy 16 12 8 4 0 LS - |V| FS - |V| x 10 9 (cm/s) 3 2 1 500 km 0
•Progenitor: 11.2 M ⦿ (Woosley+ 2002) •EOS: Furusawa EOS (multi-nuclear species、 Relativistic Mean Field theory) •ν-reactions: Standard set of Bruenn (1985) +GSI electron capture、Bremsstrahlung •Rotational velocity: Sheller rotation •Grid number: Setup
Entropy (rotating) •Evolution until ~ 200 ms after bounce
Nagakura+ (2018) Entropy (non-rotating) •Evolution until ~ 200 ms after bounce
Time evolutions of shock radii •Evolution until ~ 200 ms after bounce •Comparison between rotating and non-rotating models. 400 350 shock radius r sh [km] 300 250 200 150 100 rotating 50 non-rotating 0 0 0.05 0.1 0.15 0.2 time after bounce t pb [s]
•Evolution until ~ 200 ms after bounce Trajectory of the PNS center •Comparison between rotating and non-rotating models. o ff set of PNS center d PNS [km] 2 1 0 rotating non-rotating -1 0 0.05 0.1 0.15 0.2 time after bounce t pb [s]
Neutrino Distributions •Neutrino Distribution functions at ~ 10 ms after bounce. ~60 km ~170 km 1 MeV 4 MeV 19 MeV e r e r e φ e φ e θ e θ
~170 km 1 MeV 4 MeV 19 MeV Neutrino Distributions •Neutrino Distribution functions at ~ 10 ms after bounce. e r e φ e θ
Neutrino fluxes •φ-component of the neutrino flux at ~ 10 ms after bounce Lab. Fl. rest •The Ray-by-Ray approximation can not capture this feature. laboratory frame. •The sign of the flux is different between in the fluid-rest-frame and in the 10 44 number flux in fluid rest frame [ × 10 40 cm − 2 s − 1 ] number flux in laboratory frame [cm − 2 s − 1 ] 4 10 43 2 10 42 10 41 0 10 40 -2 10 39 -4 10 38 0 100 200 0 100 200 x [km]
Eddington Tensor •Evaluating M1-closure method-Eddington tensor
Eddington tensor •Eddington tensor at ~ 10 ms after bounce Boltzmann M1-closure Boltzmann M1-closure Boltzmann M1-closure 0.8 0.4 0.4 0.7 0.3 0.3 0.6 0.2 0.2 0.5 0.1 0.1 0.4 0 0 0.3 -0.1 -0.1 0.2 -0.2 -0.2 0.1 -0.3 -0.3 0 -0.4 -0.4 r θ -component × 10 r φ -component × 10 rr -component Boltzmann M1-closure Boltzmann M1-closure Boltzmann M1-closure 0.4 0.8 0.6 0.3 0.7 0.4 0.2 0.6 0.2 0.1 0.5 0 0.4 0 -0.1 0.3 -0.2 -0.2 0.2 -0.4 -0.3 0.1 -0.4 0 -0.6 r θ -component × 10 θθ -component θφ -component × 100 Boltzmann M1-closure Boltzmann M1-closure Boltzmann M1-closure 0.4 0.6 0.8 0.3 0.7 0.4 0.2 0.6 0.2 0.1 0.5 0 0 0.4 -0.1 0.3 -0.2 -0.2 0.2 -0.4 -0.3 0.1 -0.4 -0.6 0 r φ -component × 10 θφ -component × 100 φφ -component
Eddington tensor •Eddington tensor at ~ 10 ms after bounce •Tensors calculated by the distribution functions and the M1-closure Boltzmann M1-closure Boltzmann M1-closure 0.8 0.4 0.7 0.3 0.6 0.2 0.5 0.1 0.4 0 0.3 -0.1 0.2 -0.2 0.1 -0.3 0 -0.4 rr -component r φ -component × 10
Eddington tensor •Radial profiles of eigenvalues •~20% errors in M1-closure method •Eddington tensor at ~ 10 ms after bounce 0.8 Boltzmann r sh 0.7 M1 0.6 eigenvalue Eddington factor 0.5 North-East 0.4 0.3 lateral 1 0.2 lateral 2 0.2 error 0 -0.2 50 0 50 100 150 0 5 radius r [km]
Eddington tensor for M1 •The Eddington factor does not necessarily increase with the flux factor increasing. 0.8 Boltzmann r sh 0.7 M1 0.6 eigenvalue Eddington factor 0.5 North-East 0.4 0.3 lateral 1 0.2 lateral 2 0.2 error 0 -0.2 50 0 50 100 150 0 5 radius r [km]
Near to the shock Far from the shock Eddington tensor •The Eddington factor does not necessarily increase with the flux factor increasing. •Comparison of distribution functions e r e θ e φ
Eddington tensor •The flux factor •The Eddington factor •The distribution function at decreases with getting closer to the shock→The flux factor increases and the Eddington factor decreases. Near to the shock Far from the shock e r e r e θ e φ
Eddington factor outer inner •Prolateness of distribution •M1: prolateness is estimated from deviation of distribution actual M1
Boltzmann-Radiation-Hydro code. approximate methods are discovered. evaluated. Summary ~60 km ~170 km • Collapse of rotating progenitor is simulated by • Features which can not be reproduced by • The accuracy of the M1-closure method is e r e r e φ e φ e θ e θ
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