From supernovae to neutron stars Yudai Suwa Yukawa Institute for - PowerPoint PPT Presentation

From supernovae to neutron stars Yudai Suwa Yukawa Institute for Theoretical Physics, Kyoto University

Contents Supernova Neutrino transfer Equation of state for supernova simulations From supernovae to neutron stars 2 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

A supernova (c)ASAS-SN project

Supernovae are made by neutron star formation Baade & Zwicky 1934 4 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Fe Standard scenario of core-collapse supernovae Final phase of stellar Neutron star formation Neutrinosphere formation evolution (core bounce ） （ neutrino trapping ） Neutron Fe Neutrinosphere Star Si O,Ne,Mg C+O HeH ρ c ~10 14 g cm -3 ρ c ~10 11 g cm -3 ρ c ~10 9 g cm -3 shock stall shock revival Supernova! HOW? NS Si O,Ne,Mg C+O HeH 5 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Current paradigm: neutrino-heating mechanism heating region shock cooling region absorption neutron staremission A CCSN emits O (10 58 ) of neutrinos with O (10) MeV. Neutrinos transfer energy Most of them are just escaping from the system (cooling) Part of them are absorbed in outer layer (heating) Heating overwhelms cooling in heating ( gain ) region 6 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

What do simulations solve? Numerical Simulations Hydrodynamics equations Neutrino Boltzmann d ρ equation dt + ρ ∇ · v = 0 , 1 − µ 2 � ∂ f � � d ln ρ � � � cdt + µ ∂ f df + 3 v + 1 Solve ρ d v ∂ r + µ cdt cr r ∂ µ simultaneously dt = −∇ P − ρ ∇ Φ , � � d ln ρ � � + 3 v − v E ∂ f µ 2 + cdt cr cr ∂ E de ∗ e ∗ + P �� � � dt + ∇ · = − ρ v · ∇ Φ + Q E , E 2 v = j (1 − f ) − χ f + c ( hc ) 3 dY e � � � � Rf ′ dµ ′ − f dt = Q N , � 1 − f ′ � dµ ′ (1 − f ) R . × △ Φ = 4 π G ρ , ρ : density , v : velocity , P : pressure , Φ : grav. f : neut. dist. func, µ : cos θ , E : neut. energy, potential, e * : total energy, Y e : elect. frac., j : emissivity, χ : absorptivity, R : scatt. Q : neutrino terms kernel 7 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Neutrino-driven explosion in multi-D simulation Exploding models driven by neutrino heating with 2D/3D simulations Takiwaki+ PASJ, 62 , L49 (2010) see also, e.g., see also, e.g., ApJ, 749 , 98 (2012) Suwa+ (2D) Marek & Janka (2009), Müller+ ApJ, 738 , 165 (2011) (3D) Hanke+ (2013), Lentz+ (2015), (2012), Bruenn+ (2013), Pan+ ApJ, 786 , 83 (2014) ApJ, 764 , 99 (2013) Melson+ (2015), Müller (2015) (2016), O’Connor & Couch MNRAS, 461 , L112 (2016) PASJ, 66 , L1 (2014) (2015) MNRAS, 454 , 3073 (2015) ApJ, 816 , 43 (2016) 8 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Contents Supernova Neutrino transfer Equation of state for supernova simulations From supernovae to neutron stars 9 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Why is neutrino transfer so important? Numerical Simulations Hydrodynamics equations Neutrino Boltzmann d ρ equation dt + ρ ∇ · v = 0 , 1 − µ 2 � ∂ f � � d ln ρ � � � cdt + µ ∂ f df + 3 v + 1 Solve ρ d v ∂ r + µ cdt cr r ∂ µ simultaneously dt = −∇ P − ρ ∇ Φ , � � d ln ρ � � + 3 v − v E ∂ f µ 2 + cdt cr cr ∂ E de ∗ e ∗ + P �� � � dt + ∇ · = − ρ v · ∇ Φ + Q E , E 2 v = j (1 − f ) − χ f + c ( hc ) 3 dY e � � � � Rf ′ dµ ′ − f dt = Q N , � 1 − f ′ � dµ ′ (1 − f ) R . × △ Φ = 4 π G ρ , ρ : density , v : velocity , P : pressure , Φ : grav. f : neut. dist. func, µ : cos θ , E : neut. energy, potential, e * : total energy, Y e : elect. frac., j : emissivity, χ : absorptivity, R : scatt. Q : neutrino terms kernel 10 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Boltzmann equation Sumiyoshi & Yamada (2012); in inertial frame � ∂ f in 1 − µ 2 1 + µ ν ν cos φ ν ∂ ∂ ∂ r ( r 2 f in ) + ∂θ (sin θ f in ) r 2 c ∂ t r sin θ � ∂ f in 1 − µ 2 ν sin φ ν ∂φ + 1 ∂ 1 − µ 2 f in � �� � + ν r sin θ r ∂ µ ν � δ f in 1 − µ 2 � 1 � cos θ ∂ ν (sin φ ν f in ) = − r sin θ ∂φ ν c δ t collision (5) � 1 � δ f = − R abs ( ε , Ω ) f ( ε , Ω ) c δ t emis - abs f in ( r, θ , φ , t ; µ ν , φ ν , ε in ) . + R emis ( ε , Ω )[1 − f ( ε , Ω )] . � d ε ′ ε ′ 2 3D 3D � 1 � δ f � d Ω ′ R scat ( ε , Ω ; ε ′ , Ω ′ ) f ( ε , Ω ) = − (2 π ) 3 c δ t in real space in momentum space scat � d ε ′ ε ′ 2 � × [1 − f ( ε ′ , Ω ′ )] + d Ω ′ R scat ( ε ′ , Ω ′ ; ε , Ω ) (2 π ) 3 7D in total × f ( ε ′ , Ω ′ )[1 − f ( ε , Ω )] , (9) � d ε ′ ε ′ 2 � 1 � � δ f d Ω ′ R pair - anni ( ε , Ω ; ε ′ , Ω ′ ) = − (2 π ) 3 c δ t pair � d ε ′ ε ′ 2 � 7D integro-di fg rential eq. × f ( ε , Ω ) f ( ε ′ , Ω ′ ) + d Ω ′ R pair - emis ( ε , Ω ; ε ′ , Ω ′ ) (2 π ) 3 × [1 − f ( ε , Ω )][1 − f ( ε ′ , Ω ′ )] , (11) so complex… 11 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Methods to solve Boltzmann eq. Direct integration of Boltzmann eq. with discrete-ordinate method => S N method It’s too costly, though. By taking angular moments of radiation fj elds � { E, F i , P ij } ∝ d Ω f { 1 , � i , � i � j } Moment equations; ∂ t E + ∂ i F i = S 0 ∂ t F i + ∂ j P ij = S 1 · · · To close the system, we need additional equation 
 (the same as equation of state in hydrodynamics equation) 12 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Methods to solve Boltzmann eq. (cont.) The simplest way; only cooling terms are taken into account => leakage scheme (no transport; ∂ t e matter = - ∂ t E ) Next is di fg usion assumption, F ∝∇ E , but is wrong in optically thin regime. To take into account both optically thick and thin regime, modi fj cation is needed => Flux limited di fg usion (FLD) F is given by E and ∇ E Isotropic di fg usion source approximation (IDSA) F is given by the distance from last-scattering surface Higher moment ( P ) is helpful to obtain more precise solution. => M 1 closure P is given by E and F Variable Eddington factor (VE) P is given by solving simpler Boltzmann eq. S N > VE > M 1 > FLD, IDSA > leakage approximate ab initio lower cost higher cost 13 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Comparison of methods Yamada+ (1999) FLD (dashed lines) fm ux factor ( | F |/ E ) Monte-Carlo ( ▲ ) S N (solid line) Comparison of IDSA and S N is given in Liebendörfer+ (2009) and Berninger+ (2013) 14 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Methods to solve Boltzmann eq. (cont.) Methods used in supernova community S N Ott+ (2008) ; Sumiyoshi & Yamada (2012) ; Nagakura+ (2017) VE Buras+ (2006) ; Müller+ (2010) ; Hanke+ (2013) M 1 Obergaulinger+ (2014) ; O’Connor & Couch (2015) ; Skinner+ (2016) FLD Burrows+ (2006) ; Bruenn+ (2013) IDSA Suwa+ (2010) ; Takiwaki+ (2012) ; Pan+ (2016) and many others 15 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Questions How is nuclear physics related to supernova explosion? How can we investigate nuclear physics via supernova observations? 16 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP

Contents Supernova Neutrino transfer Equation of state for supernova simulations From supernovae to neutron stars 17 /28 20/2/2017 Yudai Suwa, Quarks and Compact Stars @ YITP