Nuclear Equation of State for High Density MatterState of matter in core-collapse supernovae phase...

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


„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)


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


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


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)]


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)


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


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


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


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

Nuclear Equation of State for High Density MatterState of matter in core-collapse supernovae phase...

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