Present status of modeling the supernova EOS. Matthias Hempel, Basel University Numazu Workshop,

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1 Present status of modeling the supernova EOS, Basel University Numazu Workshop,

2 The general purpose supernova EOS neutron stars core-collapse supernovae MH Liebendörfer Crab nebula, Hubble Space Telescope RX J , Chandra Ruffert and Janka progenitor star at onset of collapse Wikimedia neutron star mergers 2

3 Supernova EOS Introduction EOS provides the crucial nuclear physics input for astrophysical simulations: thermodynamic quantities and nuclear composition plenty of EOSs for cold neutron stars, limited number of supernova EOSs challenge of the supernova EOS: finite temperature, T = MeV no weak equilibrium, fixed isospin, resp. electron fraction, Ye = huge range in density, ρ = g/cm 3 EOS in tabular form, ~1 million configurations (T, Ye, ρ) 3

4 Complete list of currently available SN EOS (17+15) Model Nuclear DOF M max R 1.4M Ξ publ.avail. Refs. Interaction (M ) (km) H&W SKa n, p, α, {(A i,z i )} n El Eid and Hillebrandt (1980); Hillebrandt et al. (1984) LS180 LS180 n,p,α, (A, Z) y Lattimer and Swesty (1991) LS220 LS220 n,p,α, (A, Z) y Lattimer and Swesty (1991) LS375 LS375 n,p,α, (A, Z) y Lattimer and Swesty (1991) STOS TM1 n,p,α, (A, Z) y Shen et al. (1998); Shen et al. (1998, 2011) FYSS TM1 n, p, d, t, h, α, {(A i,z i )} n Furusawa et al. (2013) HS(TM1) TM1 n, p, d, t, h, α, {(A i,z i )} y Hempel and Schaffner-Bielich (2010); Hempel et al. (2012) HS(TMA) TMA n, p, d, t, h, α, {(A i,z i )} y Hempel and Schaffner-Bielich (2010) HS(FSUgold) FSUgold n, p, d, t, h, α, {(A i,z i )} y Hempel and Schaffner-Bielich (2010); Hempel et al. (2012) HS(NL3) NL3 n, p, d, t, h, α, {(A i,z i )} y Hempel and Schaffner-Bielich (2010); Fischer et al. (2014a) HS(DD2) DD2 n, p, d, t, h, α, {(A i,z i )} y Hempel and Schaffner-Bielich (2010); Fischer et al. (2014a) HS(IUFSU) IUFSU n, p, d, t, h, α, {(A i,z i )} y Hempel and Schaffner-Bielich (2010); Fischer et al. (2014a) SFHo SFHo n, p, d, t, h, α, {(A i,z i )} y Steiner et al. (2013) SFHx SFHx n, p, d, t, h, α, {(A i,z i )} y Steiner et al. (2013) SHT(NL3) NL3 n, p, α, {(A i,z i )} y Shen et al. (2011b) SHO(FSU1.7) FSUgold n, p, α, {(A i,z i )} y Shen et al. (2011a) SHO(FSU2.1) FSUgold2.1 n, p, α, {(A i,z i )} y Shen et al. (2011a) LS220Λ LS220 n,p,α, (A, Z), Λ y Oertel et al. (2012); Gulminelli et al. (2013) LS220π LS220 n,p,α, (A, Z), π n Oertel et al. (2012); Peres et al. (2013) BHBΛ DD2 n, p, d, t, h, α, {(A i,z i )}, Λ y Banik et al. (2014) BHBΛφ DD2 n, p, d, t, h, α, {(A i,z i )}, Λ y Banik et al. (2014) STOSΛ TM1 n,p,α, (A, Z), Λ y Shen et al. (2011) STOSY TM1 n,p,α, (A, Z),Y y Ishizuka et al. (2008) STOSYπ TM1 n,p,α, (A, Z),Y,π y Ishizuka et al. (2008) STOSπ TM1 n,p,α, (A, Z), π n Nakazato et al. (2008) STOSπQ TM1 n,p,α, (A, Z), π, q n Nakazato et al. (2008) STOSQ TM1 n,p,α, (A, Z),q n Nakazato et al. (2008) STOSB139 TM1 n,p,α, (A, Z),q y Fischer et al. (2014b) STOSB145 TM1 n,p,α, (A, Z),q y Sagert et al. (2012) STOSB155 TM1 n,p,α, (A, Z),q y Fischer et al. (2011) STOSB162 TM1 n,p,α, (A, Z),q y Sagert et al. (2009) STOSB165 TM1 n,p,α, (A, Z),q y Sagert et al. (2009) [Oertel, MH, Klähn, Typel, submitted to Rev. Mod. Phys.] and many more in preparation/covering parts of the parameter space

5 State of matter in core-collapse supernovae I Temperature, T [MeV] Baryon density, log 10 (ρ [g/cm 3 ]) a model for the nuclear interactions 0.1 and an approach for phase coexistence formation region of nuclei/clusters 0.05 is needed without Coulomb, bulk : first order liquid-gas phase transition with finite size effects: non-uniform nuclear matter, formation of nuclei ρ ~ g/cm³: crucial for supernova explosion mechanism Baryon density, n [fm 3 ] B Y e based on: [Fischer et al., ApJS 2010] 5

6 State of matter in core-collapse supernovae II multi-fragmentation reactions: heavy-ion collisions from several 10 to 100 MeV/A (Sumiyoshi) [Buyukcizmeci et al., NPA (2013)] 6

7 General composition of matter in SN photons (trivial) neutrons and protons light and heavy nuclei, thermal ensemble hyperons, quark matter, baryon resonances, mesons, (not considered as standard) electrons, positrons, (muons) neutrinos: all flavors trapped in the core, degenerate Fermi-Dirac gas free streaming in outer layers not part of the EOS, but of (Boltzmann) transport 7

8 nucleonic EOS 8

9 Interactions and nuclear matter properties of the SN EOSs 9

10 EOS constraints neutron matter from ab-initio calculations E/A (MeV) AFQMC (AV + TBF) AFQMC (2NF) AFQMC (2NF + 3NF) APR Friedman-Pandharipande Hebeler et al. (2010) χpt, Fiorilla et al. (2012) BHF (AV + TBF) agreement between various theoretical abinitio calculations major uncertainty: threebody forces n B (fm -3 ) [Oertel et al., in preparation] talk by J. Holt 10

11 EOS constraints neutron matter E/N-m n [MeV] Chiral EFT N 3 LO DD2 density-dependent NL3 TM1 standard non-linear TMA SFHo additional couplings SFHx FSUgold ω-ρ-coupling IUFSU LS180 non-rel LS220 T. Fischer, MH, et al.; Eur. Phys. J. A 50, 46 (2014) SKa (H&W EOS) not included standard non-linear RMF (NL3, TM1, TMA) in disagreement LS EOS extremely soft, even negative pressure good agreement for DD2 SFHo and FSUgold still acceptable n n [fm -3 ] Chiral EFT: [Hebeler & Schwenk, PRC82 (2010)] [Krüger et al., PRC88 (2013)] 11

12 Symmetry energy expansion around the saturation point of nuclear matter binding energy B0, incompressibility K,... symmetry energy J (S0), slope parameter L,... Esym determines asymmetry β: β = µe / 4Esym L contributes to pressure at saturation: P = β 2 nb L / 3 +Pe(nB β) neutron star radii strongly dependent on symmetry energy 12

13 Constraining the symmetry energy convergence of observational, experimental and theoretical constraints [Lattimer & Steiner, EPJA 50, 40 (2014)] G: Gandolfi et al. 2012: quantum Monte-Carlo H: Hebeler et al. 2010: Chiral EFT 13

14 Constraining the symmetry energy STOS (TM1) in strong disagreement FSUgold, IUFSU, SFHo, and DD2 compatible L (MeV) SKa LS NL3 TM1 TMA DD2 FSUgold IUFSU SFHo SFHx J (MeV) [Oertel et al., in preparation] 14

15 Flow constraint from heavy-ion collisions [Oertel et al., in preparation, based on Danielewicz et al. 2002] note: neutron matter is only extrapolation analysis dependent on transport code used 15

16 Neutron star mass-radius relations [Oertel et al., in preparation] radii range from 11.9 to 14.9 km, but radius constraints not conclusive 16

17 EOS effects in simulations clean and easy: failed SNe, time until black hole formation (hot) maximum mass dynamics of regular CCSNe more delicate, see, e.g.: Sumiyoshi et al. (2005), Marek et al. (2009), Scheidegger et al. (2010), O Connor et al. (2012), Hempel et al. (2012), Steiner et al. (2013), Suwa et al. (2013), Fischer et al. (2014), Togashi et al. (2014), Mirizzi et al. (2015), Pan et al. (2015), well studied: LS vs. STOS one general conclusion: a more compact PNS is favorable for explosions, due to neutrinos with higher fluxes and energies effects of single nuclear matter properties not very pronounced [Janka 2012] talk by T. Takiwaki 17 [Suwa et al. 2013]

18 Comparing LS(220) and HS(DD2) two-dimensional core-collapse supernova simulation with FLASH and IDSA neutrino transport for 15 Msun progenitor by Kuo-Chuan Pan (Basel) first application of HS(DD2) EOS in multi-dimensional simulations [Kuo-Chuan Pan et al., arxiv: (2015)] stronger explosions than for LS220 Si/O interface hits the shock earlier, generating prompt convection detailed study in preparation 800 km 18

19 cluster formation 19

20 Light cluster in supernova matter cluster formation is an essential aspect of warm and dense matter light clusters can be more abundant than protons (cf. Sumiyoshi & Röpke 2008) 250 ms post-bounce 5 s post-bounce E ν [MeV] E ν [MeV] log 10 (ρ [g cm 3 ]) Xi n p ρ T He Y e A 2 H 3 H Radius [km] ν e spheres T [MeV] Ye log 10 (ρ [g cm 3 ]) Xi n p Y e ν e spheres ρ T A 4 He 3 H 2 H Radius [km] T [MeV] Ye [Fischer et al. EPJA 2014] 20

21 Light cluster in supernova matter modify cooling of proto-neutron star relevant for nucleosynthesis in neutrino-driven winds (Arcones et al. 2008) supernova dynamics (?) see: O Connor et al. 2007, Sumiyoshi and Röpke 2008, Arcones et al. 2008, Hempel et al. 2012, Furusawa et a. 2013, EOS: various different theoretical approaches cluster formation can be probed in the lab, femtonova, see e.g. Kowalski et al. 2007, Natowitz et al. 2010, Typel et al

22 Original work of Qin et al. Qin et al. PRL108 (2012): measured charged particle and neutron yields at Texas A&M with low-energy heavy ion collisions. Akira Ono An event of central collision of Xe + Sn at 50 MeV/nucleon (AMD calculation) density extraction: thermal coalescence model of Mekjian temperature: double isotope yield ratios conditions similar as in corecollapse supernovae talk by A. Ono 22

23 Basic aspects of equilibrium constants primary observable used by Qin et al.: equilibrium constant defined by particle yields or number densities ideal gas: using nuclear statistical equilibrium Kc id only a function of temperature, e.g.: thus also composition independent (Qin et al. 2012) not true for an non-ideal (i.e. interacting) system 23

24 Qin et al measurement of equilibrium constants big spread at low densities (!?) different results for HS EOS HS: [MH, J. Schaffner- Bielich; NPA 837 (2010)] origin not clear: table interpolation? misunderstanding of definitions? Qin et al K c [ ] (fm 9 ) this work Exp. (Qin et al. 2012) ideal gas HS(NL3) n B (fm -3 ) systematic differences between matter in heavy-ion collisions and supernovae: Coulomb interactions limited number of participating nucleons isospin asymmetry 24

25 Comparison of all models more consistent at low T (a) (b) Kα: QS, grdf, HS(DD2), SFHO, STOS in agreement Kd, Kt, Kh: cannot be explained by LS, STOS, SHT, SHO K c [ ] (fm 9 ) T (MeV) K c [d] (fm 3 ) T (MeV) QS, grdf, HS(DD2), SFHO, FYSS compatible with experimental data K c [h] (fm 6 ) (c). Exp. (Qin et al. 2012) ideal gas HS(DD2), no CS, A 4 SFHo, no CS, A 4 LS220, HIC mod., cor. B STOS, HIC mod. SHT(NL3) SHO(FSU2.1) grdf QS FYSS, no CS, A 4 K c [t] (fm 6 ) (d) T (MeV) T (MeV) 25

26 Conclusions from the comparison systematic differences of matter in heavy-ion collisions and supernovae are important three components seem to be necessary to explain the experimental data inclusion of all relevant particle degrees of freedom mean-field interactions of nucleons suppression mechanism of nuclei at high densities experimental data not accurate enough to discriminate details, e.g., Pauliblocking vs. excluded volume 26

27 Medium modifications of heavy nuclei [Buyukcizmeci et al., NPA (2013)] comparison of HS(TM1), FYSS (older version) and SMSM (Mishustin, Botvina, Buyukcizmeci), focusing on heavy nuclei overall similar trends each model has its own limitations not yet a consistent prediction for the detailed nuclear composition, especially at high densities and asymmetries 27

28 additional DOFs 28

29 Neutron star mass-radius relations either hyperons have to be included, or their absence has to be explained [Oertel et al., in preparation] 29

30 CCSN explosions by the QCD phase transition [Sagert, et al. PRL 2009] t pb = ms t pb = ms t pb = ms t pb = ms t pb = ms t pb = ms phase transition induces collapse of the proto-neutron star once pure quark matter is reached, collapse halts formation of a second shock higher temperatures, increased neutrino heating positive velocities shock merges with standing accretion shock explosion 30

31 Neutrino signal Luminosity [10 53 erg/s] Luminosity [10 53 erg/s] rms Energy [MeV] e Neutrino e Antineutrino Time After Bounce [s] µ/τ Neutrino µ/τ Antineutrino Time After Bounce [s] e Neutrino e Antineutrino µ/τ Neutrinos Time After Bounce [s] colored lines with phase transition, black without second neutrino burst due to quark matter peak and height determine density and strength of the phase transition measurable with present day neutrino detectors [DasGupta et al. 2009] 31

32 Mass-radius relation of hybrid EOS and SN explosions Mass [solar mass] B 1/4 =155 MeV, α s =0.3 B 1/4 =162 MeV B 1/4 =165 MeV B 1/4 =139 MeV, α s =0.7 B 1/4 =145 MeV, α s =0.7 TM Radius [km] explosions in spherical symmetry (T. Fischer et al. ApJS 2011) PSR J PSR J PSR B no explosions for sufficiently high maximum mass weak phase transition quark matter behaves similarly as hadronic matter masquerade cf.: Fischer, Blaschke, et al. 2012: PNJL hybrid EOS only few models tested, mechanism still possible for others? 32

33 Inverted convection in proto-hybrid stars higher specific heat in the quark phase temperature decrease for isentropes consequence: positive entropy gradients are convectively unstable inverted convection: cool matter is transported outwards [Yudin, MH, et al. arxiv: ] 33

34 Inverted convection in proto-hybrid stars Ledoux criterion for convection: ( ) ( ) ϵ ds ϵ S dr + dy Y dr > 0. P,Y P,S let s ignore composition changes, keep YL=0.4=const. dε/ds determines convection, usually negative 34

35 Inverted convection in proto-hybrid stars positive values are convectively unstable for positive entropy gradients consequences in supernovae? [Yudin, MH, et al. arxiv: ] 35

36 Summary and conclusions many valuable constraints available none of the existing SN EOSs is directly compatible with all constraints, but some perform reasonably well modeling of light and heavy nuclei in coexistence with nucleons mostly on a phenomenological level more microscopic but still practical approaches? EOS at highest densities still very uncertain imposing only nucleons at highest densities is not sufficient additional DOFs can lead to interesting effects in CCSNe 36