nuclear equation of state for high density matterstate of matter in core-collapse supernovae phase...
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Matthias Hempel, Basel University NuPECC meeting Basel, 12.06.2015
Nuclear Equation of State for High Density Matter
RX J1856-3754, Chandra
Crab nebula, Hubble Space Telescope
Equation of State for Compact Stars
Matthias Hempel Basel, 12.6.2015
core-collapse supernova explosionsneutron stars
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progenitor star at onset of collapse
neutron star mergersLi
eben
dörfe
r
Ruf
fert
and
Jank
a
Wik
imed
ia
MH
Matthias Hempel Basel, 12.6.2015
„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
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• „supernova“ EOS: general-purpose EOS, at present only ~30 available • challenge of the „supernova“ EOS:
– finite temperature, T = 0 – 100 MeV – no weak equilibrium, fixed isospin, resp. electron fraction, Ye = 0 – 0.6 – huge range in density, ρ = 104 – 1015 g/cm3
– EOS in tabular form, ~1 million configurations (T, Ye, ρ)
Matthias Hempel Basel, 12.6.2015
10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 10010−1
100
101
102
Baryon density, nB [fm−3]
Tem
pera
ture
, T [M
eV]
Ye
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.56 7 8 9 10 11 12 13 14 15
Baryon density, log10(ρ [g/cm3])
State of matter in core-collapse supernovae
phase coexistence
region
based on: [Fischer et al., ApJS 2010]
• without Coulomb, „bulk“: first order liquid-gas phase transition
• with finite size effects: → non-uniform nuclear matter, formation of nuclei
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•ρ ~109 – 1012 g/cm³: crucial for supernova explosion mechanism
a model for the nuclear interactions and an approach for formation of nuclei/clusters is needed
Matthias Hempel Basel, 12.6.2015
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, ...
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n, p
A1,Z1
A2,Z2
A3,Z3
A5,Z5
A4,Z4
A6,Z6
MH, J. Schaffner-Bielich; NPA 837 (2010) (HS)
• limit at low densities: statistical ensemble of ideal gas of nuclei
• supersaturation densities: only RMF • smooth and continuous change of composition and thermodynamic quantities
Matthias Hempel Basel, 12.6.2015
MB = 0.6 Msun
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Nuclei in a supernova
Matthias Hempel Basel, 12.6.2015 7
Neutron star mass-radius relations
• commonly used EOSs of Lattimer & Swesty 1991, Shen et al. 1998 (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)]
• 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
Symmetry energy
Matthias Hempel Basel, 12.6.2015 8
based on: [Danielewicz & Lee; NPA922 (2014)]
[Lattimer & Lim; ApJ771 (2013)]
Matthias Hempel Basel, 12.6.2015
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
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Bulk Properties and Correlations
........
An event of central collision of Xe + Sn at 50 MeV/nucleon (AMD calculation)
Bulk properties and dynamicse.g. EOS E(ρ)
⇓
⇐⇒interplay
Correlationse.g. clusters and fragments
⇓Isospin dynamics, Symmetry energy
ρn − ρp, n/p, t/3He,. . .
A. Ono (Tohoku U) Light cluster production in antisymmetrized molecular dynamics ECT* SSNHIC 2014 2 / 29
Akira Ono
• 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)
Matthias Hempel Basel, 12.6.2015
Qin et al. 2012 – density and temperature• density extraction: thermal coalescence model of Mekjian
• temperature: double isotope yield ratios
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• systematic differences between matter in heavy-ion collisions and supernovae:
• Coulomb interactions • limited number of participating nucleons • isospin asymmetry
• conditions similar as in core-collapse supernovae, „femtonova“
• ideal to constrain cluster formation in supernova matter
Matthias Hempel Basel, 12.6.2015
Constraining cluster formation in SN EOS
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[MH, Hagel, Natowitz, Röpke, Typel, PRC 91, 045805 (2015)]
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)
104
105
106
107
108
109
1010
1011K c[](fm
9 )
4 5 6 7 8 9 10 11 12 13 14T (MeV)
Exp. (Qin et al. 2012)ideal gasHS(DD2), no CS, A 4SFHo, no CS, A 4LS220, HIC mod., cor. BSTOS, HIC mod.SHT(NL3)SHO(FSU2.1)gRDFQS
• ideal gas behavior ruled out
Matthias Hempel Basel, 12.6.2015
Application of new EOS in CCSN simulations• two-dimensional core-collapse 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
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[Kuo-Chuan Pan et al., arXiv:1505.02513 (2015)]
800 km
color: entropy
Matthias Hempel Basel, 12.6.2015
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? – …
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Matthias Hempel, Basel University NuPECC meeting Basel, 12.06.2015
Nuclear Equation of State for High Density Matter