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1 @ τ weak 1 σ weak n target v relative sec ( T 10MeV ) 2 ( σ weak 4G2 F h2 c 2 π T 2, n target ρ m u, v relative c ( τ dyn 1 0.4msec Gρ ) 1/2 ρ g/cm 3 ) 1 ρ g/cm 3 (T 10MeV, ρ > g/cm 3 ) τ weak τ dyn ν n ν n γ n e λ ν λ γ, λ e, λ N

2 Energetics E G = ( GM 2 core GM 2 ) core R Fe core R NS E kin O(10 51 )erg (obs.) E rad O(10 49 )erg (obs.) E GW?? O(10 53 )erg E ν O(10 53 )erg ν e 26 M Fe core E νe erg M Fe core E νe m Fe 1.4M 10MeV E ν tot O(10 53 )erg 10% cf. E ν (SNIa) < erg = thermal ν ν e = ν e, ν e, ν µ E νe (collapse) erg E νe (neutronization burst) erg E ν (shocked accreted matter) erg E ν (PNScooling) erg

3 σ νe > σ νe > σ νµ R(ν e sphere) > R( ν e sphere) > R(ν µ sphere) T (ν e sphere) < T ( ν e sphere) < T (ν µ sphere) ω νe < ω νe < ω νµ T < 100MeV, ρ < g/cm 3 : µ ±, τ ± ν (ν e, ν e, ν µ, ν µ, ν τ, ν τ ), ν µ ν x = 1 4 (ν µ + ν µ + ν τ + ν τ ) e p ν e n, e + n ν e p e A(N, Z) ν e A (N + 1, Z 1) e e + ν ν plasmon ν ν NN NN ν ν ( ) Nn Npl ν l, Npl Nnν l (modified URCA) ν e ν e ν x ν x νa νa νn νn νl νl NNν NNν νν νν

4 νeneutronization burst shock stall ν(all) ρ c bounce 14 >10 g/cm 3 Proto Neutron Star shock wave τ(collapse)~o(10 100)ms τ (neutronization burst)<o(10)ms t(stall)=o(100ms) shock revival νwind PNS cooling ν heating Hot Bubble t(core exp.)=o(1)s τ(pns cooling)=o(10)s

5 Supernova Explosion Neutron Star t(sne)=hours day SN1987A

6 (electron capture) e A ν e A, λ ν R core ν trapping (ρ > g/cm 3 ) ν e from e A ν e A and e p ν e n main opacity source: coherent scattering ν e A ν e A ρ λ ν < R core : (neutrinosphere ) σ A 2 ων 2 τ diff = 3Rcore/cλ 2 ν > τ dyn (neutrino trapping) ν e collapse σ E^2 increase opaque ν trapping ν degenerate µ(ν) increase coherent scattering nuclei survive e capture suppress not so n rich Positive feedback (Sato 1975) SN1987A ν e A e A, ν e n e p ( ω νe < 5 6 µ e) ν e A ν e A, ν e N ν e N ( isoenergetic scat.) Y L trap ν e e ν e e (down scattering: ω ν, λ ν )

7 R shock < R νsphere S c O(1), T c O(10)MeV, Y e 0.3 : (PNS: protoneutron star) ν e, ν e, ν x : (µ νe > 100MeV, µ νe = µ νe, µ νx = 0) M i.c M ( YL trap 0.5 ) 2 = M E shock GM 2 i.c. R i.c. Y L 10/3 trap several erg > E SNE (kinetic + radiation) erg R shock < R νsphere neutrinosphere : A np, r(shock) < r(ν sphere): ν e e p nν e (σ(e A) < σ(e p)) trap r(shock) > r(ν sphere): ν e main opacity source = ν e (neutronization burst) τ NB τ < shock propagation 10msec, L νe NB > erg/sec L νe NBdt erg Y e deep trough

8 In the shocked region (S O(10), ) A np, e e + e p ν e n, e e + ν ν e + n ν e p νn νn, νe ± νe ± ν e, ν e, ν x : thermal energy ν e, ν e : ν e, ν x : (n νe,ν x (center) < n νe,ν x (mantle)) M PNS = M i.c. ( 0.7M ) M NS ( 1.4M ) T ν MeV shocked matter (r 100km > R νsphere ) ν e n e p ν e p e + n νe ± νe ± heating = ν ν e e + T MeV hot bubble S > 100, ρ 10 5 g/cm 3 delayed explosion (τ O(1)sec)

9 τ τ diff = O(10)sec τ dyn 1msec: deleptonization hot lepton-rich PNS cold Neutron Star e p ν e n e + n ν e p e e + ν ν NN NN ν ν νn νn νe ± νe ± e + e e + ν x ν x NN NNν x ν x PNS = cool (S O(1)) unshocked inner core + hot (S O(10)) shocked outer mantle PNS cooling = rapid cooling stage of the shocked outer mantle + cooling stage of the inner core ρ(mantle) is not so high large λ ν cooling/deleptonization S(mantle) contraction T (mantle) T : mantle : heat flux( ν e, ν µ ) S(core) t > 10sec: T

11 Neutronization burst. Thompson et al., ApJ 592 (2003) 434 Fig.6 (failed explosion)

12 cooling deleptonization n p ν e p ne + σ νe σ νx ω νe ω νx

13 M inner core 1.457M ( YL trap 0.5 ) 2 = M E shock GM 2 inner core R inner core Y L 10/3 trap several erg Y L,trap ν trapping core ν e ρ < ρ trap Opacity higher e-cap rate, smaller opacity smaller Y L,trap, E shock σ(e p ν e n) > σ(e A ν e A ) X p E shock S(Fe core) X p E shock (bulk/surface)? W sym X p E shock down scattering (νe νe, νa νa ) ω ν, S λ ν Y L,trap, E shock Bruenn 85: p(f 7/2 ) n(f 5/2 ) Gamow-Teller transition N < 40: possible, N 40: impossible shell model /β (LMP: Langanke and Martinez-Pinedo): Brueen (N > 40 ) FFN(Fuller, Fowler and Newman)

14 Ye WW LMP MFe (M ) WW LMP central entropy / baryon (k B ) WW LMP Ye MFe (M ) S (k B ) Star Mass (M ) Star Mass (M ) Star Mass (M ) rate Fe : WW(FFN) LMP G. Martinez-Pinedo et al., astro- Figure 1: weak int. ph/ LMP (A = 45 65, Shell model ): GT strength Y e M Fe core

15 T 10 5 Bruenn LMSH Ye,c, Ylep,c Bruenn LMSH Y e Y lep ρ c (g cm 3 ) sc (kb), Tc (MeV) Bruenn LMSH ρ c (g cm 3 ) s (MeV s 1 baryon 1 ) de dt Eν (MeV) ρ c (g cm 3 ) ρ c (g cm 3 ) Figure 2: 15M G. Martinez-Pinedo et al., astro-ph/ LMS: N > 40 (A = Shell Model Monte Carlo + RPA) LMSH: FFN(A < 45)+LMP(A = )+LMS(A = ), NSE X p Y L trap NSE

16 Juodagalvis, Langanke et al., 2010, FFN/Shell model/shell Model Monte Carlo+RPA Fermi-Dirac parameterization+rpa(z = 28 70, N = ), electron screening Fig. 1. (Color online.) Nuclei included in the calculation of the NSE-averaged rates and spectra. The sd pool is marked by circles, the shell model pool is marked by pluses, the SMMC + RPA pool is marked by crosses, and the FD + RPA pool is marked by diamonds. Fig. 2. (Color online.) A comparison of the electron capture rates on 64,65 Ni calculated from the diagonalization shell model (only allowed contributions) and the hybrid SMMC + RPA model (both allowed and forbidden contributions). Stellar conditions of the 25M trajectory (see Table 1) are used. Fig. 10. (Color online.) Pool-averaged electron capture rates calculated along the stellar trajectories for the 15M and 25M progenitor stars. The rates based on the sum of all pools of nuclei are shown by solid lines. The dashed lines show the average rate when the FD + RPA pool is omitted. The dotted lines show the average rate for the sum of all pools when the screening effects to the rates are neglected. Fig. 11. (Color online.) Pool-averaged emitted neutrino spectra for the 15M and 25M trajectories. The line legend is the same as in Fig. 10. Two stellar conditions are used in each case corresponding to snapshot numbers 10 and 15 of the respective trajectory. For snapshot number 10 in the lower panel the curves no FD and full coincide. electron screening ρ 10 11, g/cm 3

17 Fig. 6. (Color online.) Fraction of nuclei covered by the various pools of nuclei as defined in the text. The fractions have been calculated for the two stellar trajectories given in Table 1. The pools are sd (dotted line), LMP (dashed line), SMMC + RPA (double-dash-dotted line), and FD + RPA (dash-double-dotted line). Solid lines show the summed pool coverage. Thick solid lines show present pool coverage, and thin solid lines show coverage by the LMSH pool. ( i Y i) nuclei is calculated by summing over all nuclei except protons, neutrons and α particles.

18 NSE EOS (Furusawa et al., ApJ738, 2011): Figure 1. Mass fractions in log 10 of nuclei in the (N, Z) plane for ρb = g cm 3, T = 1 MeV, and Yp = 0.3. The cross indicates the representative nucleus for the H. Shen EOS under the same condition. Figure 2. Mass fractions in log 10 of nuclei in the (N, Z) plane for ρb = g cm 3, T = 1 MeV, and Yp = 0.3. The cross indicates the representative nucleus for the H. Shen EOS under the same condition. Figure 5. Average mass number, Ā, of heavy nuclei with Z 6 for our EOS (solid red lines) and Hempel s EOS (dotted green lines) together with the mass number of representative nucleus for H. Shen s EOS (dashed blue liens) as a function of density for T = 1 MeV and Yp = 0.1, 0.3, 0.5. The insets are the close-ups of the high density regimes. Figure 6. Square of mass numbers (top), the standard deviation of mass number, σa = A 2 Ā 2 (middle), and the dispersion normalized by the average mass number squared, σ 2 A /A2 (bottom), of heavy nuclei with Z 6 for T = 1 MeV and Yp = 0.1 (left), 0.3 (middle), and 0.5 (right). In the top panels, the solid and dotted lines show the average mass number squared, A 2, and the square of average mass number, Ā 2, in our EOS, respectively, whereas the dashed lines display the mass number squared of the representative nucleus for the H. Shen EOS. A single nucleus EOS A 2

19 ion screening (Horowitz 1997, Bruenn and Mezzacappa 1997) Coulomb effect ions in correlated states σ(νa νa) decreases when the wave length of neutrinos > ion seperation FIG. 2. The angle-averaged ion screening correction S ion ( ) at the core center for selected central densities, as a function of neutrino energy, for models S15s7b and S25s7b. (Bruenn and Mezzacappa 1997) Y L trap = not so drastic (narrow ω ν window is affected) Y L trap M inner core (2 6%) E shock

20 NN NN ν ν Suzuki and Ishizuka: One Pion Exchange model ν x ν x : ρ > g/cm 3, T 10MeV ν e e + ν x ν x enhance L νx ω νx multiple scattering suppression (Raffelt and Seckel 1991) (Hannestad and Raffelt, Raffelt and Seckel 1998, Shen and Suzuki, Burrows et al. 2000) νn : ρ > g/cm 3, ω ν > 10MeV ES ω νx νnn : νn νn en weak magnetism ( ): σ νe p(20mev) : 15%

21 effective mass, nucleon density/spin fluctuations reduction of opacity L ν (Sawyer 1995, München group , Burrows and Sawyer , Reddy et al , Yamada and Toki ) νn ( ): ρ > g/cm 3 σ L ν (t > 100ms) FIG. 11. Log 10 of the electron neutrino luminosity (L e ) in ergs s 1 versus time after bounce in ms, with and without accretion. For the accretion models, total opacity suppression factors of 0.3, 0.1, and 0.05 were assumed above g cm 3 and of 0.3 and 0.1 were assumed above g cm 3. The fiducial model is dashed, the model without accretion is dot-dashed, the models with correction above g cm 3 are dotted, and those with correction above g cm 3 are solid. On this plot, the models with the largest corrections have the highest luminosities after 2500 ms. The comparisons between the dashed curve and all others are the most germane. Burrows and Sawyer, Phys. Rev. C58 (1998) 554, Fig.11

22 2 H, 3 H, 3 He, 4 He Sumiyoshi and Röpke Xi n 10-5 p d 10-6 t 3He X 4He 10-7 A r [km] FIG. 2: (Color online) Mass fraction X i of light clusters as function of the radius for the post-bounce supernova core shown in Fig. 1. Sumiyoshi and Röpke PRC77 (2008) <σω>/a [10 42 cm 2 MeV] ν CC ν NC ν scatt Tν [MeV] (a) <σω>/a [10 42 cm 2 MeV] ν CC ν NC ν scatt Tν [MeV] (b) <σω>/2a [10 42 cm 2 MeV] 1000 CC H(ν ) d 4He Tν [MeV] <σω>/2a [10 42 cm 2 MeV] 1000 NC He d 4He Tν [MeV] FIG. 3: Thermal average of energy transfer cross sections. The solid and dotted curves in (a) ((b)) show the cross sections for ν e d e pp(νcc) and νd νpn(νnc) ( ν e d e + nn( νcc) and νd νpn( νnc)), respectively. The dot-dashed curve in (a) and (b) shows cross section for the elastic νd scattering. FIG. 4: Averaged energy transfer cross sections in unit of MeV cm 2. The solid, dashed and dash-dotted curves show the νd, ν- 4 He and ν- 3 H (left panel) and ν- 3 He (right panel) cross sections, respectively. (See the main text for the references on A=3, 4 nuclei cross sections.) Nakamura et al., 2009, d ν

23 ν : EOS FIG. 1. Explosion energies vs. time after the start of the simulations (125 ms after bounce) for exploding one-dimensional (dotted lines) and twodimensional models (solid lines). The numbers denote the initial e and e luminosities in ergs s 1. 1D/2.10: no exp. 1D/2.20: exp. (Janka and Müller, ApJ 448 (1995) L109, Fig.1) 10 3 A D 10 3 Newton+O(v/c) Relativistic radius [km] 10 2 B C Radius [km] time after bounce [ms] mistake: σ(νn νn) too small Explosion!. Liebendörfer et al., astro-ph/ v1 Fig Time After Bounce [s] No Explosion!. NH 13M, GR Boltzman, LS EOS+Si burning, S = 103, E = 12, A = 6, 3ν GR compact PNS T L ν, Boltzmann heating rate Liebendörfer et al., Phys.Rev. D63 (2001) (astro-ph/ v2) Fig.6

1 (T 1MeV, ρ > 1 14 g/cm 3 ) τ weak τ dyn ν n ν n γ n e λ ν λ γ, λ e, λ N (neutrinosphere) 3 6 (ν e, ν e,ν µ, ν µ,ν τ, ν τ ) T < O(1MeV) = m µ n e n µ

21.3.12 @KEK H He CO ONeMg Fe Si M>8M '! " # $ % & 1 (T 1MeV, ρ > 1 14 g/cm 3 ) τ weak τ dyn ν n ν n γ n e λ ν λ γ, λ e, λ N (neutrinosphere) 3 6 (ν e, ν e,ν µ, ν µ,ν τ, ν τ ) T < O(1MeV) = m µ n e n µ,