Nuclear Equation of State for High Density Matter. Matthias Hempel, Basel University NuPECC meeting Basel,

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1 Nuclear Equation of State for High Density Matter, Basel University NuPECC meeting Basel,

2 Equation of State for Compact Stars neutron stars core-collapse supernova explosions 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 supernova EOS: general-purpose EOS, at present only ~30 available 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 State of matter in core-collapse supernovae 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] 4

5 EOS model: excluded volume NSE with interactions chemical mixture of nuclei and interacting nucleons in nuclear statistical equilibrium (NSE) nucleon interactions: relativistic mean-field (RMF) description of nuclei and medium effects: experimentally measured binding energies and nuclear mass tables, Coulomb screening, excited states, excluded volume,... limit at low densities: statistical ensemble of ideal gas of nuclei supersaturation densities: only RMF smooth and continuous change of composition and thermodynamic quantities A1,Z1 A4,Z4 A3,Z3 n, p A5,Z5 MH, J. Schaffner-Bielich; NPA 837 (2010) (HS) A2,Z2 A6,Z6 5

6 Nuclei in a supernova MB = 0.6 Msun 6

7 Neutron star mass-radius relations commonly used EOSs of Lattimer & Swesty 1991, Shen et al (STOS) eight HS/SFH models, based on relativistic mean-field (RMF) interactions BHB models: DD2 RMF & inclusion of lambda hyperon [T. Fischer, MH, et al.; EPJA50 (2014)] [S. Banik, MH, D. Bandyophadyay; APJS214 (2014)] 7

8 Symmetry energy based on: [Danielewicz & Lee; NPA922 (2014)] [Lattimer & Lim; ApJ771 (2013)] derived from binding energies of isobaric analog states STOS(TM1) and LS in disagreement DD2: matches well SFHo and SFHx (fitted to small NS radii) also in good agreement 8

9 Constraining cluster formation by heavy-ion collisions Qin et al. PRL108 (2012): measured charged particle yields at Texas A&M with low-energy heavy ion collisions primary observable used: equilibrium constant defined by particle yields or number densities advantages of using equilibrium constants: deviations from ideal-gas behavior clearly visible reduces some systematic uncertainties (theory and experiment). Akira Ono An event of central collision of Xe + Sn at 50 MeV/nucleon (AMD calculation) 9

10 Qin et al density and temperature density extraction: thermal coalescence model of Mekjian temperature: double isotope yield ratios conditions similar as in corecollapse supernovae, femtonova ideal to constrain cluster formation in supernova matter systematic differences between matter in heavy-ion collisions and supernovae: Coulomb interactions limited number of participating nucleons isospin asymmetry 10

11 Constraining cluster formation in SN EOS [MH, Hagel, Natowitz, Röpke, Typel, PRC 91, (2015)] K c [ ] (fm 9 ) 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 ideal gas behavior ruled out necessary for agreement: inclusion of all relevant particle degrees of freedom mean-field interactions of nucleons suppression mechanism of nuclei at high densities (e.g. Pauli-blocking/ excluded volume) T (MeV) 11

12 Application of new EOS in CCSN simulations two-dimensional corecollapse supernova simulation with IDSA neutrino transport for 15 Msun progenitor by Kuo-Chuan Pan (Basel) first application of more realistic HS(DD2) EOS in multi-dimensional simulations stronger explosions detailed EOS study in preparation 800 km [Kuo-Chuan Pan et al., arxiv: (2015)] color: entropy 12

13 Summary and conclusions multi-purpose (supernova) EOS has to cover a huge parameter space cluster formation is an essential aspect many aspects of the EOS can be constrained by experiments, theory and astrophysical observations significant uncertainty at highest densities exotic degrees of freedom? quark matter? relevant for many astrophysical questions: how do massive stars explode? which stars end their lives as black holes, which as neutron stars? what is the production site of the neutron-rich heavy elements? 13

14 Nuclear Equation of State for High Density Matter, Basel University NuPECC meeting Basel,