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 (?)

!"#$!%& !"#$!%&'()#*%+,

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 protoneutron 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 =8T (Einstein equation) µ⌫ µ⌫ 2 µ⌫ µ⌫ r (t, a) 2 ds2 = ↵(t, a)2dt2 + 0 da2 + r(t, a)2d⌦ (t, a) ✓ ◆ matter microphysics

T tt = (1 + e + J) T ta = T at = H T aa = p + K Misner & Sharp (1964) PhyRev.136, 571 T = T ⇥⇥ = p + 1 (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 @↵ @ 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 @ ⇥ ⇤ + µ 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 ⇢ (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 ⇢ (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/(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⇡ (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,) 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 =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 decient ) 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

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 decient ) 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

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 in evolution Supernova

Radius [km] -0.2 -0.2 -0.1 0 0.1 0.2 12 4 16 28 He C O Fe - core Si, core collapse core 32 S Entropy per baryon [ baryon per Entropy R t – t infalling heavy nuclei heavy infalling ⌫ e bounce Shock “standing” bounce ⌫ [s] (proto)neutron star (proto)neutron post bounce evolution post bounce ⌫ k B ]

accretion (n, p,e (n, p, ⌫ ⌫ 4 ± He, e ) shock ⌫ ± ) (b) (a) to: due energy-balance from determined evolution Later energy to – losses due stalling Shock continues collapse stellar core; stellar the of layers outer unstable gravitationally Still km 100–200 of about radii to acceleration shock Rapid the shock wave with back saturation at bounces core the where density halts Collapse shock accretion behind deposition (transport) liberation energy of shock ahead material mass infalling from accretion; pressure ram no prompt explosions formation of of formation Neutrino signal – post-bounce

50 5 νe ν¯e νµ/τ 10 4 charged current reactions ]

1 e + p ⌧ n + ⌫e − + 3 e + n ⌧ p +¯⌫e 1 erg s ⌫ e 52 + 1i 2 pair processes

[10 ν A, Z + L 0.1 h e + e ⌧ ⌫ +¯⌫ + A, Z i! 1 e h N + N ⌧ N + N + ⌫ +¯⌫ stellar collapse mass accretion ⌫e +¯⌫e ⌧ ⌫µ/⌧ +¯⌫µ/⌧ 0.01 0 19 −νe100 −50 0 50 100 150 19 ν¯ 18 e ⌫µ/⌧ 18 νµ/τ elastic scattering 17 17 16 16 ⌫ + N ⌫0 + N 15 15 ⌧ 14 14 ⌫¯e inelastic scattering

[MeV] 13 13 〉

ν 12 12 ⌫ + e± ⌧ ⌫0 + e± E 11 11 〈 ⌫e 10 10 9 9 8 8 Neutrino-energy hierarchy 7 7 r e ﬂ e c t s s t r e n g t h o f 6 6 −150 −100 −50 0 50 100 150 coupling to matter t − t [ms] bounce Triggering the explosion onset

(11.2M ) General concept: E n e r g y 0.5 liberation from central s/nB Ye protoneutron star (PNS) to 10 standing shock ]

B 0.4 Continuous energy deposition that 8 e Y drives shock to increasingly larger radii 0.3 (timescale: ~100 milliseconds) 6 Ejection of the stellar mantle; leaves bare PNS behind 0.2 4 Electron Fraction, 0.1 Entropy per Baryon, s2 [k infalling Yam & Leonard (2009) Nature 458 low-entropy A massive hypergiant star as the materialPreliminary progenitor of the supernova SN ( 56Fe, 56Ni ) 0 0.0 2005gl -500 -400 -300 -200 -100 0 100 200 300 400 500 (x-y) Plane [km] “. . . was a single star and that it indeed Neutrino heating (& cooling): Alternative scenarios: vanished following the explosion of SN 53 Magnetic ﬁelds 2005gl . . . On the basis of its luminosity, Ev = 3 – 6 x 10 erg (available) (Le Banc & Wilson (1970) ApJ 161, 542) such a star is likely to be an extreme Eexpl ~ 1050 – 1051 erg Sound waves member of the group of luminous blue (kinetic energy of ejecta) (Burrows et al.,(2006) ApJ 640, 878) variable stars (LBVs), which are thought to be very massive (>50 Msolar) short- (Bethe & Wilson (1985) ApJ 295, 14) High-density phase transition (Sagert & TF et al.,(2009) PRL 102, 081101) lived stars.” Triggering the explosion onset

(11.2M ) General concept: E n e r g y 0.5 liberation from central s/nB Ye protoneutron star (PNS) to 10 standing shock ]

•Müller et al.,(2012) ApJ 756, 22 • Sumiyoshi et al.,(2014) ApJS 216, 37 (2D, energy- and angle- (static ﬁeld, angle- and energy- dependent neutrino transport; dependent Boltzmann-like transport; ray-by-ray approximation) comparison with ray-by-ray (9.6, 11.2, 15, 27 M ) approximation) •Roberts et al.,(2016) astro-ph/arXiv 1604.07848 (27 M ) (full 3D, energy-dependent transport @ 3D Cartesian grid)

• Suwa et al.,(2013) ApJ 764, L6 •Pan et al.,(2016) •Bruenn et al.,(2013) ApJ 767, L6 (2D, energy-dependent isotropic ApJ 817, 33 (2D, energy-dependent multi-group diffusion source approximation) ﬂux-limited diffusion approximation) (2D, energy- (11.2, 13, 15 M ) (12, 13, 15, 20, 25 M ) dependent isotropic diffusion source approximation) (15, 20 M )

Not “complete” story yet – supernova problem not fully solved ! Magnetically-driven supernova explosions

Rapid rotation and amplification of magnetic field (Le Banc & Wilson (1970) ApJ 161, Burrows et al.,(2007) ApJ 669, 585 542) Energetic bi-polar explosions May explain existence of magnetars Caveat: requires very high core spin and/or initial magnetic field of stellar core Perhaps few rare events

Associated with production of r-process elements:

10−2

] −3

⊙ 10

10−4 Winteler et al.,(2013) ApJ 750, L22 10−5

10−6 Ejected Mass [M

10−7 60 80 100 120 140 160 180 200 220 240 Mass Number PNS deleptonization

Beyond supernova explosion onset – once the stellar mantle is ejected . . . The supernova story continues for more than 10 seconds! Mildly independent from details of the supernova explosion mechanism Can be modeled in spherical symmetry

< 10 (> 104 km)

low-mass outﬂow: ! “v-driven wind” 6 (mass ejection from 10 PNS surface) 100 km) (⇠

⌫ + n p + e ! e 10 ! + 10 ⌫¯e + p n + e ! ! neutrino heating at PNS PNS surface ! PNS 14 10 ( 20 30 km) deleptonization 3 ⇠ ⇢ [g cm ] T =5 30 MeV (neutrino diffusion) · E 1053 erg ⌫ ⇠ Pons et al., (1999) ApJ 513, 780 PNS deleptonization

formation of heavy nuclei ?

proton rich (Ye > 0.5) neutron rich (Ye < 0.5) vp process neutron-capture process ! < 10 formation of seed nuclei (> 104 km)

low-mass outﬂow:! ! “v-driven wind” 6 (mass ejection from 10 (↵-rich freeze out) PNS surface) 100 km) (⇠

⌫ + n p + e ! e 10 ! + 10 ⌫¯e + p n + e ! ! neutrino heating at PNS PNS surface ! PNS 14 10 ( 20 30 km) deleptonization 3 ⇠ ⇢ [g cm ] T =5 30 MeV (neutrino diffusion) · E 1053 erg ⌫ ⇠ PNS deleptonization

Nucleosynthesis Deleptonization timescale: is determined at t = 10 30 s v–decoupling formation of heavy nuclei ?

proton rich (Ye > 0.5) neutron rich (Ye < 0.5) vp process neutron-capture process ! < 10 formation of seed nuclei (> 104 km)

low-mass outﬂow:! ! “v-driven wind” 6 (mass ejection from 10 (↵-rich freeze out) PNS surface) 100 km) (⇠

⌫ + n p + e ! e 10 ! + 10 ⌫¯e + p n + e ! ! neutrino heating at PNS PNS surface ! PNS 14 10 ( 20 30 km) deleptonization 3 ⇠ ⇢ [g cm ] T =5 30 MeV (neutrino diffusion) · E 1053 erg ⌫ ⇠ Neutrino signal Qian et al., (1996) ApJ 471, 331

ν −burst mass accretion deleptonization 0 Current models predict small e 7 10 spectral difference; 40 6 2 1

] "⌫¯e 2Q +1.2Q /"⌫¯e 1

− Y 1+ 5 e 2 ' "⌫e 2Q +1.2Q /"⌫e 30 −1 ✓ ◆ 4 10 (similar neutrino luminosities) erg s

52 20 3 & 5 MeV (Ye < 0.5)

[10 neutron rich ν 2 8

L " " 10 ν −2 ⌫¯e ⌫e > e h ih i > 1 ν¯e 10 <> < 5 MeV (Ye > 0.5) νµ/τ proton rich 0 > TF et al.,(2016)et PRDTF (submitted) > −0.02 0 0.02 0.1 0.2 0.3 1 10 40 ": = E2 / E ) h ⌫ i h ⌫ i h ⌫ i t − tbounce [s] Light neutron-capture elements 38

16 νe (gauged to 60Zn) ν¯e HD1222563 ν 4 14 µ/τ 10 standard weak rates +10% ν −spectral differences ν¯µ/τ 3 e 10 12 −10% νe−spectral differences 2 Zn 10

1 [MeV] 10 10 〉

ν 0 Sr 10 Zr

E 8

〈 −1 10 Ba Integrated Abundances −2 6 10 Pb −3 4 10 La Eu −4 10

−0.1 0 0.1 0.2 0.3 1 10 40 al., et TF Martinez-Pinedo& (2014)41,044008 JPG 20 30 40 50 60 70 80 Atomic Number, Z t − tbounce [s] Roberts et al., (2012) PRC 86, 065803 Hüdepohl et al.,(2010) PRL 104, 251101 (integrated nucleosynthesis) Equation of state dependence of the neutrino signal Excluded volume approach S.Typel (2016) EPJA 52,16

Geometric approach; −3 nB [fm ] modifying the available 0.08 0.1 0.12 0.14 0.16 0.18 0.2 volume: 14 HS(DD2−EV) (v = +8.0) Vi = V i HS(DD2) − ref. EOS (v=0) =1 v n 12 HS(DD2−EV) (v = −3.0) i j j j X 1.4 10 stiff Excluded volume

] 1.2 ρ parameter: 3 0 − 1.0

[c] v vn =vp

8 s

c ⌘ 0.8 ref. EOS v v 0.6 (⇢;v)=exp | | (⇢ ⇢ )2 6 2 0 2 3 4 5 6 soft ⇢ P [MeV fm (Gauss-functional) 4

2 T =3MeV DD2 – RMF parameters: Ye =0.3 K = 243 MeV 0 S = 31.67 MeV 1 1.5 2 2.5 3 3.5 L = 55.04 MeV ρ [1014 g cm−3] Excluded volume approach TF (2016) EPJA 52, 54

Geometric approach; (Evolution of central density and temperature) modifying the available volume: 4.5 HS(DD2−EV) (v = +8.0) Vi = V i 4 HS(DD2) − ref. case (v=0) soft HS(DD2−EV) (v = −3.0) =1 v n i j j 3.5 ref. EOS j

] X 3 − Excluded volume 3 stiff parameter:

14 2.5 v vn =vp 20 ⌘ [10 g cm 18 v v 2 2 (⇢;v)=exp | | (⇢ ⇢0) 16 2 central ⇢ ρ 14 1.5 [MeV] (Gauss-functional) 12 central 1 T 10 8 0.5 0 0.1 0.2 0.3 0.4

0 −0.1 0 0.1 0.2 0.3 0.4 0.5 t − tbounce [s] Excluded volume approach TF (2016) EPJA 52, 54

Geometric approach; modifying the available volume: 7 ν HS(DD2−EV) (v = +8.0) Vi = V i e HS(DD2) − ref. case (v=0) 6 =1 v n HS(DD2−EV) (v = −3.0) i j j j 5 X ]

1 Excluded volume − parameter: 4 ν¯e erg s v vn =vp

52 ⌘ 3 v v 2 [10 (⇢;v)=exp | | (⇢ ⇢0) ν 2 L 2 ⇢ νµ/τ (Gauss-functional) 1 A f f e c t s o n l y s u p e r - saturation density EoS; all 0 0.0 0.1 0.20.2 0.30.3 0.40.4 0.5 o t h e r n u c l e a r m a t t e r 17 t – t [s] ν¯µ/τ bounce p r o p e r t i e s r e m a i n 16 unchanged Supernova neutrino signal is insensitive 15 to supra-saturationνµ/τ density EOS 14 13 ν¯e

[MeV] 12 〉

ν 11 E 〈 10 νe 9 8 7 6 0 0.1 0.2 0.3 0.4 0.5 t − tbounce [s] 7 HS(DD2−EV) (v = +8.0) νe 6 HS(DD2) − ref. case (v=0) HS(DD2−EV) (v = −3.0) 5 ] 1 −

4 ν¯e erg s 52 3 [10

ν TF (2016) EPJA 52, 54 ExcludedL 2 volume approach νµ/τ 1 Geometric approach; modifying the available 0 volume: 0.1 0.2 0.3 0.4 17 Vi = V i ν¯µ/τ 16 =1 v n i j j 15 j νµ/τ X 14 Excluded volume 13 parameter: ν¯e v vn =vp [MeV] 12 〉

⌘ ν 11 E v v 2 〈 (⇢;v)=exp | | (⇢ ⇢ ) 10 2 0 νe ⇢ 9 (Gauss-functional) 8 7 A f f e c t s o n l y s u p e r - 6 saturation density EoS; all 0.00 0.1 0.20.2 0.30.3 0.40.4 0.50.5 o t h e r n u c l e a r m a t t e r tt −– ttbouncebounce [s][s] p r o p e r t i e s r e m a i n unchanged Supernova neutrino signal is insensitive to supra-saturation density EOS Quark-hadron phase transition

Sagert & TF et al.,(2009) PRL 102, 081101 14 3 ⇢ [10 g cm14 ]3 TF et al., (2011) ApJS 194, 28 Baryon Density, ρ [10 g/cm ] 11 22 33 44 55 66 7 8 9 1010 1111 1212 13 Quark matter EoS: bag 2 10010 model with ﬁxed bag pressure Extended transition Pure quark- Transition from some ]

] region of 3 matter phase nuclear model (TM1)

–3 1 1010 instability Hadron-quark transition region: extended phase of instability; large latent heat

Pressure [MeV/fm Onset of quark- P [MeV fm [MeV P 0 101 s = 1 k /baryon hadron mixed B s = 2 k /baryon phase B s = 3 k /baryon B s = 4 k /baryon B −1 100.1 0.10.1 0.2 0.30.3 0.4 0.50.5 0.60.6 0.7 0.80.8 Baryon Density, n [fm−3] –3 B nB [fm ] Sagert & TF et al. (2009), PRL Quark-hadron phase transition 102, 081101

deleptonization burst form core bounce 40 νe ν¯ 35 e ν km/s] µ/τ 4 ] 1 − 30 Signal from strong 1st order phase transition

erg s 25 Velocity [10 Velocity 52 at high densities 20 10 100 1000 Radius [km]

15 ]) 3 15 10 13 Luminosity [10 11 5 9

(Density[g/cm

40 10 7 −0.2 0 0.2 0.4 0.6 ν0.8e

log 5 ν¯e 10 100 1000 35 νµ/τ Radius [km]

XQ 30 0.5 1.0 0.4 0.8 25 e 0.6 Y 0.3 0.2 0.4 0.5 0.6 0.2 0.4 time [s] 20 0.1 0.2 0

Mean Energy [MeV] 10 100 1000 15 Radius [km]

al.(2010),et PRC 81 TF Dasgupta& −0.2 0 0.2 0.4 0.6 0.8 Time After Core Bounce [s] Sagert & TF et al. (2009), PRL Quark-hadron phase transition 102, 081101

deleptonization burst form core bounce 40 νe ν¯ 35 e ν km/s] µ/τ 4 ] 1 − 30 Signal from strong 1st order phase transition

erg s 25 Velocity [10 Velocity 52 at high densities 20 10 100 1000 Radius [km]

15 ]) 3 15 10 13 Luminosity [10 11 5 9

(Density[g/cm

40 10 7 −0.2 0 0.2 0.4 0.6 ν0.8e

log 5 ν¯e 10 100 1000 35 νµ/τ Radius [km]

XQ 30 0.5 1.0 0.4 0.8 25 e 0.6 Y 0.3 0.2 0.4 0.5 0.6 0.2 0.4 time [s] 20 0.1 0.2 0

Mean Energy [MeV] 10 100 1000 15 Radius [km]

al.(2010),et PRC 81 TF Dasgupta& −0.2 0 0.2 0.4 0.6 0.8 Time After Core Bounce [s] Summary Summary

Neutrino signal from core-collapse supernovae mildly insensitive to supra-saturation density EoS Great progress in modeling, in particular in view of multi- dimensional nature Summary

−3 10 sim. data −4 Neutrino signal from core-collapse supernovae mildly 10 HD 122563 [28] −5 10 insensitive to supra-saturation density EoS −6 10

−7 10

−8 Great progress in modeling, in particular in view of multi- 10

Elemental abundances −9 dimensional nature 10 −10 10 25 30 35 40 45 50 55 Charge number Z Massive star explosions (canonical) cannot explain galactic 90 enrichment of heavy neutron-capture elements; 38

0.5 50

40 Electron fraction, Y 0.48 Y e 30 (a) Core-collapse supernovae (SNe) (b) Neutron star merger (NSM) Entropy per baryon , S [k S 0.46 20 1 2 3 4 5 6 t − t [s] rate ~10-2 yr-1 rate ~10-5 yr-1 bounce Consistent with metal-poor star observations (HD 122563)

Argast et al., (2004) A&A 416, 997 Yuan et al.,(2016) MNRAS 456, 3253 2 ⌫e H ppe 2 + Summary ⌫¯e H nne 2 ⌫e nn H e 2 + ⌫¯e pp H e Neutrino signal from core-collapse supernovae mildly 3 ⌫e H nppe insensitive to supra-saturation density EoS 3 + ⌫¯e H nnne 3 3 Great progress in modeling, in particular in view of multi- ⌫e H He e 3 3 + ⌫¯e He H e dimensional nature 2 ⌫ H pn⌫ 3 2 2 10 Massive star2 explosions− (canonical) cannot explain galactic ⌫ H H ⌫ νe H→ pp e (a) 3 3 − 3 3 νe H→ He e − ⌫ H H ⌫ enrichment2 → of heavy neutron-capture elements; 38

[10 15 32 ]) σ

3 T 14 30 associated weak processes consistent with EoS ν−spheres ρ 28 −1 13 26 [g/cm 24 10 ρ

( supernova 12 22 10 shock position 20 11 18 TF. et al.,(2016) EPJWC.10906002F 16 3 10 10 14 0 2 + 1 12 10ν¯e H→ nn e 10(b) Nakamura et al.,(2001) PRC63, 034617 9 cooling 10 3 → 3 + 8 Temperature [MeV] ν¯e He He heating 6 3 + 8 “complete “ 2 ν¯e H→ nnn e Furusawa et al.,(2013) ApJ 774, 13 4

10 Baryon Density, log v-trapping + 07 2 ν¯e p → ne Nasu et al.,(2015) ApJ 801, 12 10 1 2 n 10 10 0.5 ] 2 1 −1 p 10 ( /A ) 10 cm i ⌘ 0.4 − 42 −2 4He 0 10 10 2 0.3 [10 H σ −3 10 0.2 −1 Mass Fractions Y 10 e Electron Fraction −4 10 0.1 3H −2 10 −5 10 0 1 10 100 1 2 E [MeV] 10 10 ν Radius [km] Summary

Neutrino signal from core-collapse supernovae mildly insensitive to supra-saturation density EoS Great progress in modeling, in particular in view of multi- dimensional nature Massive star explosions (canonical) cannot explain galactic B1/4 [MeV] enrichment of heavy neutron-capture elements; 38

4 3 T [MeV] 50 3 2 2 1 1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 −3 Klähn & TF (2015) ApJ 810, 8 nB [fm ] Summary n Neutrino signal from core-collapse supernovae mildly io insensitive to supra-saturation density EoS nt Great progress in modeling, in particular in view of multi- e dimensional nature tt Massive star explosions (canonical) cannot explain galactica enrichment of heavy neutron-capture elements; 38

Neutrino detection

Neutrino cross section in a water target detector

(G.G.Raffelt) The end of a massive star (& 9M ) ~1 billion km Implosion of the stellar core due to pressure loss; triggered from e– captures on protons bound in nuclei Jupiter orbit 56 56 e + Mn Fe + ⌫e hydrogen 56 ! 56 e + Fe Co + ⌫e envelope 56 ! 56 e + Co Ni + ⌫ (dilute) ! e ......

e + A, Z A, Z 1 + ⌫ h i!h i e Collapsing stellar core neutronizes; electron fraction drops

(Ye = np/nB)

Ye > 0.5 : neutron rich

Ye > 0.5 : proton rich 9 > > = MCore > MCH Stellarcore > ; > Stellar core collapse

50 5 Entropy per baryon [kB] νe ν¯e νµ/τ 10 4 ] 1 − core collapse post bounce evolution 3 1 erg s 4 bounce nuclear electron captures He 52 e + A, Z A, Z 1 + ⌫e 2

Radius[km] 15 15 (n, p, 4He, e±) 14 14

[MeV] 13 13 〉

ν 12 12

E 11 11 ⌫ ⌫ 〈 ⌫ ⌫ 10 10 ± neutrino free- (n, p, e ) 9 9 Fe - core- Fe 8 8 streaming regime (proto)neutron star 7 7 -0.2 -0.1 0 0.1 0.2 6 6 t – t [s] −-0.15150 − -0.10100 −-0.0550 00 50 100 150 bounce t t– − t t [s][ms] bouncebounce Stellar core collapse

50 5 Entropy per baryon [kB] νe ν¯e νµ/τ 10 4 ] 1 − core collapse post bounce evolution 3 1 erg s 4 bounce nuclear electron captures He 52 e + A, Z A, Z 1 + ⌫e 2

Radius[km] R 15 15 ⌫e (n, p, 4He, e±) 14 14

[MeV] 13 13 〉

ν 12 12

elastic scattering on nuclei E 11 11 ⌫ ⌫ 〈 ⌫ ⌫ 10 10 trapping ⌫e + A, Z ± A, Z + ⌫e neutrino free- (n, p, e ) 9 9 Fe - core- Fe h i!h i (determines neutrino trapping) 8 8 streaming regime (proto)neutron star neutrino 7 7 -0.2 -0.1 0 0.1 0.2 6 6 t – t [s] −-0.15150 − -0.10100 −-0.0550 00 50 100 150 bounce t t– − t t [s][ms] bouncebounce Core bounce and shock formation

50 5 Entropy per baryon [kB] νe ν¯e νµ/τ 10 4 ]

1 ve –burst − core collapse post bounce evolution 3 1 erg s 4 bounce nuclear electron captures He 52 e + A, Z A, Z 1 + ⌫e 2

h i!h i [10 ν 12C nuclear de-excitations L 0.1 1 A, Z ⇤ A, Z + ⌫ +¯⌫ h i ! h i 16O Fuller & Meyer (1991), ApJ 376, 701 stellar collapse TF et al.,(2013) PRC 88, 065804 0.01 0 19 −νe100 −50 0 50 100 150 19 ν¯e 28 32 18 18 Si, S S u p e r n o v a s h o c k νµ/τ 17 17 propagation across the 16 16 sphere of last inelastic Radius[km] 15 15 R⌫e 4 ± scattering(n, p (,v –He,sphere) e ) 14 14

[MeV] 13 13 〉

ve–deleptonization burst ν 12 12

E 11 11 (is⌫ generic⌫ feature) 〈 ⌫ ⌫ 10 10 trapping ± neutrino free- Shock charged(n, p ,current e ) reactions 9 9 Fe - core- Fe 8 8 streaming regime (proto)neutrone + p starn + ⌫e neutrino ⌧ 7 7 + 6 6 -0.2 -0.1 0 e 0.1+ n ⌧ p +¯ 0.2⌫e t – t [s] −-0.15150 − -0.10100 −-0.0550 00 50 100 150 bounce t t– − t t [s][ms] bouncebounce Post bounce mass accretion

50 5 νe Entropy per baryon [kB]ν¯e ⌫e νµ/τ 10 4 ] 1 − ⌫¯e 3 1 post bounce evolution erg s

charged current reactions 52 bounce e + p ⌧ n + ⌫e 2 [10 + ν ⌫µ/⌧ e + n ⌧ p +¯⌫e L 0.1 pair processes 1 + e + e ⌧ ⌫ +¯⌫ mass accretion 0.01 0 N + N ⌧ N + N + ⌫ +¯⌫ 19 −νe100 −50 0 50 100 150 19 ν¯ infalling18 heavye nuclei ⌫µ/⌧ 18 ⌫e +¯⌫e ⌫µ/⌧ +¯⌫µ/⌧ νµ/τ ⌧ 17 17 elastic scattering 16 16 ⌫ + N ⌧ ⌫0 + N 15 15 (n, p, 4He, e±) inelastic scattering R⌫14e ⌫¯ 14 neutrino decoupling e [MeV] 13 13 〉 ⌫ + e± ⌫0 + e± ⌧ ν 12 12

E 11 11 〈 ⌫ ⌫e 10 ⌫ ⌫ ⌫ 10 9 (n, p, e±) 9 Shock 8complete neutrino trapping 8 7 7 (proto)neutron star 6 6 -0.2 -0.1 0 − 150 − 100 0.1 − 50 0.20 0 0.0550 1000.10 1500.15 t − t [ms] t – tbounce [s] bounce t – tbounce [s] vBag approach to quark matter

400 ] -3 300

200

100

M [MeV] P[MeV fm 0

-100 0 100 200 300 400 500 600 700 * µ [MeV] 800 TM1 NJL 600 µ > µχ BM χ B1/4 = 181.6 MeV dc eff 1/4

] BM χ-dc B = 150.0 MeV -3 400 eff

µ = µ 200 dc χ P [MeV fm

µχ -200 0 500 1000 1500 [MeV] µB Neutrino signal in multi-dim’l simulations

] Presence of millisecond variations 1

(⌫e, ⌫¯e, ⌫µ/⌧ ) of the neutrino signal

erg s Induced from convection and

52 associated shock oscillations

[10 Persist even in detection on Earth ⌫ L May allow distinction of strong bi- polar explosions Müller & Janka (2014) ApJ788, 82 MüllerJanka& (2014) [MeV] i ⌫ E h

t t [s] bounce Production of heavy-element

(too late, not frequent Argast et al.(2004) AA416,997 enough) Evolution Core-collapse Neutron star of massive supernovae vs. mergers stars (SN Ib,c II) • slow (s) process (n-capture << decay) Anders & Grevesse (1989) ➡ Stellar evolution

• rapid (r) process neutron (n-capture >> decay) ➡ Explosive - capture environment processes

• neutrino-induced (intermediate mass elements?) Some relevant current equation of state constraints

S . . . nuclear symmetry energy (Astronomy/Astrophysics; neutron stars) L . . . slope of the symmetry energy Each EoS has a unique Mass-Radius relation

Steiner et al., (2010) ApJ 722 (low-mass X-ray binary source analysis)

Demorest et al.,(2010) Nature 09466 Lattimer & Lim (2013) ApJ 771, 14 Antoniadis et al.,(2013) Science 340, 448