2013/12/3 MMCOCOS@Fukuoka University 3D Simulations of Core-collapse Supernovae Tomoya Takiwaki(NAOJ) Kei Kotake(Fukuoka U) Yudai Suwa(YITP) Tomohide Wada(vis) And many collaborators
Plan 1. Brief summary of SN explosion mechanism 2. Development of Neutrino Transport in our code 3. Result 4. Toward observations
200km
Iron Core Free escaping region Neutrino Sphere Proto Neutron Star Diffusion region
Detail of Neutrino Heating Mechanism Janka 01 -Cooling term -Heating term If we assume hydrostatic profile with pressure of radiation dominant. Above gain radius, the heating is dominant.
Solvers of Radiation Hydrodynamics Ab initio, no assumption=> Boltzmann equation, 6D differential equation Sn method directly solve the equation 3 space 3 phase space(momentum or velocity space) Sumiyoshi & Yamada 2012 Computation cost is extra-ordinary high
Solvers of Radiation Hydrodynamics To omit computational cost, integrate out phase space <- 4 dimensional equations Fundamental problem If we solve equation for E and F, how P is determined?
Many solvers Two moment One moment FLD: F is assumed by E and E Variable Eddington factor: P is computed by the simplified Boltzmann equation IDSA: F is assumed from the neutrino sphere No transport system M1-Closure: P is assumed from the E and F Method: Sn > VE > M1 > FLD, IDSA > Leakage ab initio high cost Leakage: source term is only considered as the cooling term approximation low cost
IDSA: trapped part f(x,y,z,e,theta,phi) 6 dimensional variable Divided to trapped part and streaming part Trapped Particle Angular and energy integration Determine temperature and chemical potential for Fermi-Dirac distribution by Y and Z 1 st order term of (v/c) is fully included) Diffusion source term is calculated in each energy and transported to free streaming part
IDSA: Freestreaming part f(x,y,z,e,theta,phi) 6 dimensional variable Divided to trapped part and streaming part Free streaming Particle v/c term is ignored Spectral Transport Ray-by-Ray manner
Numerical cost for implicit scheme Not proportional to product of the grid, Nr Nt Np Ne Ntn Npn Nr Nt Np :space Ne Ntn Npn : phase space Neutrino reactions are usually solved implicitly. matrix inversion and iteration is necessary. Guess X Correct X is found! X: neutrino distribution function Cost of matrix inversion: N^3 or N^2 *O(10) For example: Sumiyoshi 2005 (N_r N_e N_tn)^3
Numerical cost of Neutrino spectral transport In IDSA, neutrino is explicitly calculated and for optically thick region, Beta-equilibrium is assumed. Numerical cost is Liner product of each grids. Nr Nt Np Ne Very economic scheme! In our Finest case 384(r)x128(θ)x256(φ)x20(energy), ~2 month is used with 16,768 core of K-computer
Luminosity[10^51erg/s] Average Energy[MeV] Comparison of Method Time Liebendoerfer et al 2005 Sn andve General relativistic simulation Time Our newest version of IDSA ecp,aecp,eca,csc,nsc,pap,nes,nbr Newtonian Gravity For simple spherical computation, the result is rather consistent.
Dimensionality
Radius 1D spherical simulations 2000-2005 Assume spherical symmetry and solve sophisticated neutrino transport Sumiyoshi+ 05 Spherically symmetric grid Neutrino is going from the center and head outer layor <=the shock stalls Time =>Why it fails? Gives motivation for MD study
A example of failed explosion 1D-spherical symmetry Entropy is visualized Supernova fails
Radius 2D axi-symmetric simulations 2005-2010 Assume axi-symmetry and investigate effect of the convection Rotational axsis Marek & Janka 2009 convection entropy The shock revives Time Convection enhances neutrino heating rate and found successful explosion. Dimensionality is quite important!
Two important process Neutrino Driven Convection Standing Accretion shock instability
Neutrino driven convection Takiwaki+12 plumes Gain region Negative entropy gradient makes Rayleigh Taylor instability at the gain region. The growing time scale is ~10ms
Standing Accretion Shock Instability(SASI) Pressure Wave Scheck+ 2008 Advective-acoustic cycle Foglizzo Vorticity Wave
SASI, 3D pressure rot v Red: high pressure Blue low pressure Red: clockwise vorticity Blue: anticlock wise vorticity Takiwaki+1
Now we ll start to show my result answering these questions (1) Does the shock revives? (2) How energetic does the shock expand? (3) What shape the expanding shock forms?
3D model of s11.2 progenitor Explode! progenitor:s11.2 EoS:LS-K220 resolution: 384(r)x128(θ)x256(φ) The finest grid Neutrino Trasport: Ray-by-Ray:IDSA +Leakage Hydro: HLLE, 2 nd order
Convergence of the resolution The evolution of the averaged shock radius in 3D is converged with the two resolutions.
2D vs 3D 2D simulation overestimate the anisotropy of the shock. The averaged shock radius of 2D is also larger than that of 3D.
SASI in 3D The amplitude of SASI in 3D is smaller than 2D. 3D 2D Iwakami+2008
2D vs 3D SASI in 3D is small => 2D > 3D Small scale turbulence => 3D > 2D? =>3D is larger =>3D is larger 2D is larger<= 2D is larger<= Takiwaki+ submitted to ApJ Dolence+ 2013 Open Question: Does the small scale turbulence affect the evolution of the shock? Yes(Dolence+2013), No (Couch 2013)
Progenitor dependence and Effect of rotations Initial angular velocity s11.2 N13 s27 0 rad/s performed performed Performed 0.3rad/s Performed 0.5ras/s - performed 1.0rad/s Performed Performed performed 2.0rad/s Performed performed Performed Compare these 11 models
Investigate Progenitor dependence and Effect of rotations Initial angular velocity s11.2 N13 s27 0 rad/s performed performed Performed 0.3rad/s Performed 0.5ras/s - performed 1.0rad/s Performed Performed performed 2.0rad/s Performed performed Performed Compare these 11 models
N13 Ω=0rad/s Explode! progenitor:n13.0 EoS:LS-K220 resolution: 384(r)x64(θ)x128(φ) The finest grid Neutrino Trasport: Ray-by-Ray:IDSA +Leakage Hydro: HLLE, 2 nd order
s27 Ω=0rad/s Failed progenitor:s27.0 EoS:LS-K220 resolution: 384(r)x64(θ)x128(φ) The finest grid Neutrino Trasport: Ray-by-Ray:IDSA +Leakage Hydro: HLLE, 2 nd order
Progenitor dependence and Effect of rotations Initial angular velocity s11.2 N13 s27 0 rad/s performed performed Performed 0.3rad/s Performed 0.5ras/s - performed 1.0rad/s Performed Performed performed 2.0rad/s Performed performed Performed Compare these 11 models
N13 Ω=2.0rad/s Explode! progenitor:n13 EoS:LS-K220 resolution: 384(r)x64(θ)x128(φ) The finest grid Neutrino Trasport: Ray-by-Ray:IDSA +Leakage Hydro: HLLE, 2 nd order
s27 Ω=2.0rad/s Explode! progenitor:s27 EoS:LS-K220 resolution: 384(r)x64(θ)x128(φ) The finest grid Neutrino Trasport: Ray-by-Ray:IDSA +Leakage Hydro: HLLE, 2 nd order
Growth of anisotropy of the shock N13 Spiral mode Sloshing mode Blondon+2007 m=1 spiral mode is dominant. It might be Spiral SASI ( should be confirmed).
Does rotation affect the shock revival? Rapid rotation s11.2 N13 s27.0 Rapid rotation For 11.2M_s, light progenitor, it does not.for 13 M_s it does. Rapid rotation makes the shock oblate and the shock expansion begins from the eqator.
Q1 Does the shock revives? s11.2 N13 s27 0 rad/s O O X 0.3rad/s - O - 0.5ras/s - O - 1.0rad/s O O X 2.0rad/s O O O Compare these 11 models
How energetic that is? s11.2 Rapid rotation N13 s27.0 Observe 0.1-0.4 10^51erg. For 11.2M_s and 13 M_s, Rapid rotation weaken the Eexp because luminosity becomes smaller in that model.
How energetic does the shock expand? s11.2 N13 s27 0 rad/s 0.08 0.3 X 0.3rad/s - 0.1-0.5ras/s - 0.08-1.0rad/s 0.06 0.08 X 2.0rad/s 0.06 0.15 0.4 Compare these 11 models
s11.2 =0.0rad/s Large convective bubble characteriz es the shape.
s27.0 =2.0rad/s Rather oblate?
N13 Ω=2.0rad/s Initially expand oblately, Finally Expand, prolately Because Neutrino heating at pole is enhanecd.
Summary -IDSA scheme is very economic scheme, that can capture the feature of neutrino emission in more sophisticated scheme. -With this advantage, we perform several (11+3) 3D simulations to investigate dependence of the progenitor and effect of rotation. -We find the shock revival in self-consistent 3D model(keeping in mind our model is easier explode compare to the MPA group due to lack of a few kind of neutrino interactions). -It is easier to revive the shock in the lighter progenitor compared to heavier progenitor. -Rapid rotation helps the shock revival, but does not promote energetic explosions. -We find many kinds shock morphology(bubbly prolate oblate), depending on the rotation and the progenitor.
Prospect to the observation
Neutrino oscilation Dasgputa+2012
Neutrino oscilation
Appendix
Luminosity[10^52erg/s] Luminosity[10^52erg/s] Luminosity[10^52erg/s] 2D vs 3D study with Light bulb Method Nordhaus+ 2010 Hanke+ 2012 Mass accretion rate[m_s/s] Couch+ 2012 Mass accretion rate[m_s/s] 3D > 2D Nordhaus+2010, Dolence+2013 2D > 3D Hanke+2012, Couch+2012 Mass accretion rate[m_s/s]
Viscosity as the hidden parameter HLL 2D HLL 1D ATV ATV 3D HLL ATV