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Tobias Fischer “Dense Phases of Matter” – University of Wrocław, Poland INT Workshop, Seattle WA, July 2016 Wrocław - Google Maps 7/22/16 8:39 PM

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Tobias Fischer “Dense Phases of Matter” – University of Wrocław, Poland INT Workshop, Seattle WA, July 2016 Wrocław - Google Maps 7/22/16 8:39 PM Probing the Equation of State with Neutrinos from Core-collapse Supernovae (?) Tobias Fischer “Dense Phases of Matter” – University of Wrocław, Poland INT Workshop, Seattle WA, July 2016 Wrocław - Google Maps 7/22/16 8:39 PM !"#$!%& !"#$!%&'()#*%+, Wrocław: 3rd largest city in Poland, located in the heart of Europe https://www.google.com/maps/place/Wrocław,+Poland/@50.9889726,…z/data=!4m2!3m1!1s0x470fe9c2d4b58abf:0xb70956aec205e0f5?hl=en Page 1 of 2 Wrocław - Google Maps 7/22/16 8:39 PM !"#$!%& !"#$!%&'()#*%+, 100 miles . at the south-west end of Poland https://www.google.com/maps/place/Wrocław,+Poland/@51.7026291,…z/data=!4m2!3m1!1s0x470fe9c2d4b58abf:0xb70956aec205e0f5?hl=en Page 1 of 2 Wrocław - Google Maps 7/22/16 8:37 PM !"#$!%& !"#$!%&'()#*%+, ~600 000 people living here. https://www.google.com/maps/place/Wrocław,+Poland/@51.1270778,…z/data=!4m2!3m1!1s0x470fe9c2d4b58abf:0xb70956aec205e0f5?hl=en Page 1 of 2 7 Nobel Prize winners: 1. Theodor Mommsen (1817-1903) 1902 (literature) 2. Phillip Lénàrd (1862-1947) 1905 (physics) 3. Eduard Buchner (1860-1917) 1907 (chemistry) 4. Paul Ehrlich (1854-1915) 1908 (medicine) 5. Gerhart Hauptmann (1862-1946) 1912 (literature) 6. Fritz Haber (1868-1934) 1918 (chemistry) 7. Max Born (1882-1970) 1954 (physics) Probing the Equation of State with Neutrinos from Core-collapse Supernovae (?) Contents: • Motivation • Modeling core collapse supernovae • Supernova phenomenology • Equation of state dependence of the neutrino signal • Summary Constraints (?) A neutron stars is born in a core-collapse supernova explosion as hot & lepton-rich protoneutron star (PNS) ⌫¯e PNSs develop (deleptonize & cool) towards neutron stars via the emission of neutrinos of all flavors for about 10–30 s Some insights from SN1987A: ⌫¯e 51 53 Eexpl ~ 10 erg , Ev ~ 3 x 10 erg All current supernova models (that include “accurate” neutrino transport !!!) are in agreement with SN1987A ⌫¯e Blum & Kushnir (2016) ApJ ⌫¯e SN1987A (Feb. 23rd, 1987) Neutrino detection – current and future Supernova equation of state Conditions: 2 T 10− 50 MeV ' − Y ⇢ 0 2 n0 e ' − ⇥ Y 0.01 0.6 NSE e ' − (Nuclear Statistical Equilibrium) (charge fraction/density) µ(A,Z) = Zµp +(A Z) µn − Extends beyond a “simple” relation between pressure and energy [MeV] 2 3 T Nuclear clustering; H, H, 3He, 4He T =0.5 MeV Mott-transition to non-NSE homogeneous phase n (time-dependent nuclear processes) 0 Nuclear medium modifies nucleon properties/nuclear masses (binding energy 3 ⇢ [g cm− ] shifts) TF. et al.,(2011) ApJS 194, 39 Modeling core-collapse supernovae General picture massive stars Core-collapse supernova (& 9M ) (proto)neutron stars (strong gravity) converts iron-core of massive star into proto- neutron star B i n d i n g e n e r g y g a i n available in form of neutrinos of all flavors (weak gravity) Strong gravity of PNS E 3 6 1053 erg (⌫ , ⌫¯ ,⌫ , ⌫¯ ) requires general relativity 4 G ' − ⇥ ! e e µ/⌧ µ/⌧ R G = R g =8T (Einstein equation) µ⌫ µ⌫ − 2 µ⌫ µ⌫ r (t, a) 2 ds2 = ↵(t, a)2dt2 + 0 da2 + r(t, a)2d⌦ − Γ(t, a) ✓ ◆ matter microphysics T tt = ρ(1 + e + J) T ta = T at = ρH T aa = p + ρK Misner & Sharp (1964) PhyRev.136, 571 T θθ = T ⇥⇥ = p + 1 ρ(J K) 2 − Lindquist (1966) AnnPhys.37, 487 Neutrino transport . Lindquist (1966) AnnPhys.37, 487 Neutrinos are light-like geodesics in curved spacetime; massless ultra-relativistic particles. f (t, a, µ, E) F (t, ~x,~v) F (t, a, µ = cos ✓,E)= ⌫ ⌫ ! ⌫ ⇢ 2 dN⌫ = F⌫ (t, a, µ, E) E dE dµ da @F µ @ propagation of the neutrinos along (µ, E)= 4⇡r2↵⇢F ↵@t −↵ @a geodesics with changing local angle µ 1 1 @↵ @ Γ 1 µ2 F − r − ↵ @r @µ − ✓ ◆ @ ln ⇢ 3u @ ⇥ ⇤ Doppler shift and the angular + µ 1 µ2 F aberration between adjacent − ↵@t r @µ − ✓ ◆ comoving observers for µ≠0 1 @↵ 1 @ ⇥ ⇤ + µΓ E3F ↵ @r E2 @E @ ln ⇢ 3u u 1 @ red/blueshift spectra µ2 + E3F − ↵@t r − r E2 @E ✓ ◆ @F + (µ, E) ↵@t coll Liebendörfer et al.,(2004) ApJS 150, 263 Mezzacappa & Bruenn (1993) ApJ 405, 669 Collision integral Mezzacappa & Bruenn (1993) ApJ 410, 740 @F 1 1 (µ, E) = j(E) F (µ, E) F (µ, E) ↵@t ⇢ − − λ(E) collision ✓ ◆ 2 2 emissivity1 E opacity/absorptivity 1 E F (µ, E) + dµ0R⌫N(µ0,µ,E) F (µ0,E) dµ0R⌫N(µ0,µ,E) c (hc)3 − c (hc)3 Z Z 2 1 E 1 2 IN + F (µ, E) dµ0 dE0 E0 R (µ, µ0,E,E0) F (µ0,E0) c (hc)3 ⇢ − ⌫e± ✓ ◆ Z 2 1 E 2 OUT 1 F (µ, E) dµ0 dE0 E0 R (µ, µ0,E,E0) F (µ0,E0) − c (hc)3 ⌫e± ⇢ − Z ✓ ◆ Charged current + e− + p ⌧ n + ⌫e e− + e ⌦ ⌫ +¯⌫ e− + A, Z ⌧ A, Z 1 + ⌫e 8 h i h − i > N + N ⌦ N + N + ⌫ +¯⌫ (N = n, p, ) Juodagalvis et al. (2010), NPA 848, 454 > Hannestadt & Raffelt, (1998), ApJ 507, 339 pair reactions > + > e + n ⌧ p +¯⌫e <> ⌫e +¯⌫e ⌦ ⌫µ/⌧ +¯⌫µ/⌧ > ⌫ + N ⌦ ⌫ + N (N = n, p) > A, Z ⇤ A, Z + ⌫ +¯⌫ > h i h i > 8 :> Fuller & Meyer (1991) ApJ 376, 701 scattering > ⌫ + A, Z ⌦ ⌫ + A, Z TF. et al. (2013), PRC 88, 065804 > h i h i <> ⌫ + e± ⌦ ⌫ + e± > > :> Mezzacappa & Bruenn (1993) ApJ 405, 669 Collision integral Mezzacappa & Bruenn (1993) ApJ 410, 740 @F 1 1 (µ, E) = j(E) F (µ, E) F (µ, E) ↵@t ⇢ − − λ(E) collision ✓ ◆ 2 2 1 E 1 E F (µ, E) + dµ0R⌫N(µ0,µ,E) F (µ0,E) dµ0R⌫N(µ0,µ,E) c (hc)3 − c (hc)3 Z Z 2 1 E 1 2 IN + F (µ, E) dµ0 dE0 E0 R (µ, µ0,E,E0) F (µ0,E0) c (hc)3 ⇢ − ⌫e± ✓ ◆ Z 2 1 E 2 OUT 1 F (µ, E) dµ0 dE0 E0 R (µ, µ0,E,E0) F (µ0,E0) − c (hc)3 ⌫e± ⇢ − Z ✓ ◆ Charged current + e− + p ⌧ n + ⌫e e− + e ⌦ ⌫ +¯⌫ e− + A, Z ⌧ A, Z 1 + ⌫e 8 h i h − i > N + N ⌦ N + N + ⌫ +¯⌫ (N = n, p, ) Juodagalvis et al. (2010), NPA 848, 454 > Hannestadt & Raffelt, (1998), ApJ 507, 339 pair reactions > + > e + n ⌧ p +¯⌫e <> ⌫e +¯⌫e ⌦ ⌫µ/⌧ +¯⌫µ/⌧ > ⌫ + N ⌦ ⌫ + N (N = n, p) > A, Z ⇤ A, Z + ⌫ +¯⌫ > h i h i > 8 :> Fuller & Meyer (1991) ApJ 376, 701 scattering > ⌫ + A, Z ⌦ ⌫ + A, Z TF. et al. (2013), PRC 88, 065804 > h i h i <> ⌫ + e± ⌦ ⌫ + e± > > :> Neutrino opacity and EoS Reddy et al.,(1998) PRD 58, 013009 Here: SV = SA S(q0,q) Charged-current absorption; ⌫e + n e− + p ⌘ ! (density and spin response functions) nucleons are not free gas G2 V 2 d3p 1/λ(E )= F ud (g2 +3g2 ) e (1 F (E )) S(q ,q) ⌫e ⇡ c V A (2⇡ c)3 − e e 0 Lowest order medium ~ Z ~ modification of the weak q = E E ,q= p p 0 ⌫ − e ⌫ − e rate; depends on the EoS (symmetry energy): 3 d pn S(q0,q)=4⇡ δ(q0 + En Ep)fn(En)(1 fp(Ep)) 7 3 10 (2⇡~c) − − νe 6 Ee = E⌫ +(Un Up) Z 10 − e − 5 2 F 10 pn Un Up S (T,ρ) 4 En = + mn⇤ + Un 10 − / ] 1 2 m − n⇤ 3 [s 10 λ 1/ 2 10 DD2− (U − U = 9.4 MeV) 1 10 13n p 3 ρ =2 DD210 (U − Ug = cm 5.3 MeV)− n p 0 ⇥ 10 DD2+ (U − U = 3.7 MeV) T =5MeVn,Ype =0.2 7 10 2 ν¯e 10 20 30 40 50 6 + pp 10 Ee = E⌫¯e (Un Up) E = + m⇤ + U − − p p p 5 2 mp⇤ 10 4 10 ] 1 − 3 [s 10 λ 1/ 2 10 DD2− : U U =9.4MeV 1 n p 10 − DD2 : Un Up =5.3MeV 0 − 10 DD2+ : U U =3.7MeV Roberts et al., (2012) PRC 86, 065803 n − p Horowitz et al., (2012) PRC 86, 065806 0 10 20 30 40 50 60 Martinez-Pinedo & TF et al., (2012) PRL109, 251104 Eν [MeV ] Core-collapse supernova phenomenology Stellar core collapse Implosion of the stellar core due to pressure loss; triggered from e– (Ye = np/nB) 2 captures on protons bound in Ye nuclei (Ye < 0.5 : neutron excess ) Mcore >MCh 1.44 M ' 0.5 56 56 ✓ ◆ e− + Mn Fe + ⌫e ! (Y > 0.5 : neutron defficient ) 56 56 e e− + Fe Co + ⌫e 9 56 ! 56 > e− + Co Ni + ⌫ = ! e ...... > Neutrinolosses ;> 0.50Ye Density Ye e− + A, Z A, Z 1 + ⌫e 14 70 h i!h − i log [g/cm3]=11.97 60 T=1.95MeV Ye =0.349 ]) 0.45 13 50 3 − 40 12 Z log (X ) 0.40 30 10 N,Z 0 -2 [g cm 20 -4 -6 ⇢ 11 -8 ( 10 0.35 -10 10 0 10 0102030405060708090100110120 N log (Hempel & TF et al.,(2012) ApJ 748, 27) 0.30 9 Collapsing stellar core neutronizes; electron fraction drops; collapse 8 0.25 -400 -200 0 200 400 proceeds adiabatically/ super- (x-y) Plane [km] Ye sonically Stellar core collapse Implosion of the stellar core due to pressure loss; triggered from e– (Ye = np/nB) 2 captures on protons bound in Ye nuclei (Ye < 0.5 : neutron excess ) Mcore >MCh 1.44 M ' 0.5 56 56 ✓ ◆ e− + Mn Fe + ⌫e ! (Y > 0.5 : neutron defficient ) 56 56 e e− + Fe Co + ⌫e 9 56 ! 56 > e− + Co Ni + ⌫ = ! e ...... > Neutrinolosses ;> 0.50Ye Density Ye e− + A, Z A, Z 1 + ⌫e 14 70 h i!h − i log [g/cm3]=11.97 60 T=1.95MeV Ye =0.349 ]) 0.45 13 50 3 − 40 12 Z log (X ) 0.40 30 10 N,Z 0 -2 [g cm 20 -4 -6 ⇢ 11 -8 ( 10 0.35 -10 10 0 10 0102030405060708090100110120 N log (Hempel & TF et al.,(2012) ApJ 748, 27) 0.30 9 Collapsing stellar core neutronizes; electron fraction drops; collapse 8 0.25 -400 -200 0 200 400 proceeds adiabatically/ super- (x-y) Plane [km] Ye sonically Neutrino signal – infall phase 50 5 νe ν¯e nuclear de-excitations νµ/τ 10 4 A, Z ⇤ A, Z + ⌫ +¯⌫ ] 1 h i ! h i − ve –burst Fuller & Meyer (1991), ApJ 376, 701 3 1 TF et al.,(2013) PRC 88, 065804 erg s ⌫ e 52 + 1i 2 [10 − ν A, Z L 0.1 h + A, Z i! 1 S u p e r n o v a s h o c k e− h propagation across the stellar collapse 0.01 0 sphere of last inelastic 19 −νe100 −50 0 50 100 150 19 ν¯e scattering (v–sphere) 18 νµ/τ 18 17 17 16 16 ve–deleptonization burst is 15 15generic feature 14 14 [MeV] 13 13 charged current reactions 〉 ν 12 12 e− + p ⌧ n + ⌫e E 11 11 〈 10 10 + e + n p +¯⌫e 9 9 ⌧ 8 8 7 7 6 6 −150 −100 −50 0 50 100 150 t − t [ms] bounce Supernova evolution in a nutshell Entropy per baryon [kB] Collapse halts at saturation density where the core bounces back with the formation of shock wave core collapse post bounce evolution Rapid shock acceleration to radii 4He bounce of about 100–200 km Still gravitationally unstable outer 12C layers of the stellar core; stellar collapse continues 16O infalling heavy nuclei Shock stalling due to energy losses – no prompt explosions 28Si, 32S Later evolution determined from shock energy-balance due to: accretion Radius[km] R⌫ e (n, p, 4He, e±) (a) ram pressure from mass
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