High density EoS for (core-collapse) supernovae and neutron stars

Transcription

1 High density EoS for (core-collapse) supernovae and neutron stars Micaela Oertel Laboratoire Univers et Théories (LUTH) CNRS / Observatoire de Paris/ Université Paris Diderot Trento workshop on nuclear structure and astrophysical applications, Trento, July 8-12, 23 Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 1 / 28

2 Outline 1 Introduction 2 Neutron star equations of state 3 Standard equations of state for core-collapse supernovae 4 Developments in the supra-saturation regime 5 Summary and Outlook Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 2 / 28

3 Outline 1 Introduction 2 Neutron star equations of state 3 Standard equations of state for core-collapse supernovae 4 Developments in the supra-saturation regime 5 Summary and Outlook Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 2 / 28

4 Outline 1 Introduction 2 Neutron star equations of state 3 Standard equations of state for core-collapse supernovae 4 Developments in the supra-saturation regime 5 Summary and Outlook Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 2 / 28

5 Outline 1 Introduction 2 Neutron star equations of state 3 Standard equations of state for core-collapse supernovae 4 Developments in the supra-saturation regime 5 Summary and Outlook Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 2 / 28

6 Outline 1 Introduction 2 Neutron star equations of state 3 Standard equations of state for core-collapse supernovae 4 Developments in the supra-saturation regime 5 Summary and Outlook Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 2 / 28

7 Let us start with a nice picture Crab nebula (credit : ESO) Crab nebula : remnant of the supernova of 154 (observed by chinese and arab astronomers) A millisecond pulsar (neutron star) is located near the center of the nebula Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 3 / 28

8 R [km] R ~ 3 Fe R [km] formation ~ 1 R [km] R s ~ 2 R g ~ 1 R ν ~ 5 Fe, Ni.5 1. νe Si M(r) [M ] Si burning shell Si ν e Fe, Ni.5 1. M(r) [M ] nuclear matter ( > nuclei Si burning shell δ PNS δ < free n, p νe 1.3 gain layer 1.5 cooling layer p n Si M(r) [M ] R [km] ~ 1 R [km] R s ~ 1 km position of shock formation R [km] R ns ~ 1 R ν PNS.5 heavy nuclei α,n n, p c Fe, Ni Fe 11 free n, p 11 Ni α r process? α,n, 12 C, seed Si M(r) [M ] Si burning shell Si M(r) [M ] Si burning shell Ni Si He O 3 M(r) [M ] Matter composition and equation of state Matter composition changes dramatically through core collapse and NS formation Starting point : onion like structure with iron/nickel core+ degenerate electrons Upon compression (+deleptonisation) : heavier and more neutron rich nuclei For n B > n /2 : nuclei disappear in favor of free nucleons Composition of matter above n and at T > 1 MeV relatively unknown NS matter cold (T < 1 MeV on a timescale of minutes) Different stages of a supernova R Fe shock radius of Initial Phase of Collapse (t ~ ) ο ) δ ~ M Ch Bounce and Shock Formation (t ~.11s, c 2 o) δ Shock Stagnation and ν Heating, Explosion (t ~.2s) ν e ν e ν e ν e,µ,τ,ν e,µ,τ ν e ν e ν e,µ,τ,ν e,µ,τ R Fe R Fe R ν Neutrino Trapping M hc Shock Propagation and ν e Burst (t ~.12s) nuclear matter nuclei (Janka et al. 7) (t ~.1s, ~1¹² g/cm³) δ Neutrino Cooling and Neutrino Driven Wind (t ~ 1s) 9 Be, ν e ν e ν e ν e ν e ν e ν e ν e ν e,µ,τ,ν e,µ,τ ν e,µ,τ,ν e,µ,τ Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 4 / 28

9 Matter composition and equation of state Matter composition changes dramatically through core collapse and NS formation Starting point : onion like structure with iron/nickel core+ degenerate electrons Upon compression (+deleptonisation) : heavier and more neutron rich nuclei For n B > n /2 : nuclei disappear in favor of free nucleons Composition of matter above n and at T > 1 MeV relatively unknown NS matter cold (T < 1 MeV on a timescale of minutes) Z (Proton Number) Z (Proton Number) Nuclear abundancies at different stages T= 9. GK, ρ= 6.8e+9 g/cm 3, Y e =..433 Log (Mass Fraction) N (Neutron Number) T= GK, ρ= 3.39e+11 g/cm 3, Y e =..379 Log (Mass Fraction) N (Neutron Number) (Janka et al. 7) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 5 / 28

10 Matter composition and the equation of state Matter composition changes dramatically through core collapse and NS formation Starting point : onion like structure with iron/nickel core+ degenerate electrons Upon compression (+deleptonisation) : heavier and more neutron rich nuclei For n B > n /2 : nuclei disappear in favor of free nucleons Composition of matter above n and at T > 1 MeV relatively unknown NS matter cold (T < 1 MeV on a timescale of minutes) Phase diagram of bulk nuclear matter (RMF/TMA) T [MeV] Y p =.5 Y p =.3 Y p = n B [fm -3 ] (Hempel & Schaffner-Bielich 9) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 6 / 28

11 Construction of an equation of state The equation of state (EOS) thermodynamically relates different quantities to close the system of hydrodynamic equations. For a cold neutron star in β-equilibrium : equations depend on baryon number density and pressure EOS is P (nb) (or equivalent) For core collapse : equations depend on baryon number density, lepton number density (no β-equilibrium), temperature, and pressure EOS is P (n B, T, Y L) (or equivalent) Use thermodynamic principles to obtain thermodynamically consistent EOS (e.g. s = f/ T ni ) Here : concentrate on the high density (supra-saturation) and high temperature part (see talk by S. Typel for the sub-saturation regime) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 7 / 28

12 Neutron star EOS Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 8 / 28

13 Constraints on the (high density) EOS 1. Constraints related to neutron star observations (see talk by N. Chamel, too) Main present constraint on the supra-saturation part : neutron star masses Observed masses in binary systems (NS-NS, NS-WD, X-ray binaries) with most precise measurements from double neutron star systems. All NS-NS systems give masses close to 1.4M Recently two precise mass measurements in NS-WD binaries M = 1.97 ±.4M (PSR J , (Demorest et al, Nature 2) M = 2. ±.4M (PSR J , (Antoniadis et al, Science 23) (Lattimer & Prakash, astro-ph/61244) Without exotica : no problem with a two solar mass NS (but 2M probably not the end of the story) Additional particles add d.o.f. softening of the EOS lower maximum mass Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 9 / 28

14 Constraints on the (high density) EOS 2. Constraints related to nuclear experiments and theoretical developments Extracting parameters of symmetric nuclear matter around saturation (n, E B, K, S, L) Data from heavy ion collisions (flow constraint, meson production,...) (cf previous talks) Data on nucleon-nucleon interaction fixing startpoint of many-body calculations Experimental data from hyperon-nucleon (YN) diffusion + data on hypernuclei scarce no standard values U ΛN (n B = n ) 3 MeV commonly accepted Low density neutron matter : Monte-Carlo simulations and EFT approaches Lattice QCD simulations (but not possible for high densities) Λ single partical potential U Λ (p=) [MeV] 5-5 NSC97a -1 NSC97c NSC97f NSC89 J4 χeft ρ B [ρ ] Σ single particle potential U Σ -(p=) [MeV] 35 NSC97a 3 NSC97c NSC97f 25 NSC89 J4 χeft ρ B [ρ ] (Djapo, Schaefer, Wambach PRC 8) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 1 / 28

15 Why wondering about hyperons in the NS core? They can appear in the core of neutron stars if their chemical potential becomes large enough to make the conversion of N into Y energetically favorable. The order in which the different hyperons appear depends on the interaction Most models predict that they appear at n B 2 3n Similar result for different types of models Phenomenological mean field models (RMF or Skyrme type, Glendenning ApJ 85, Balberg & Gal NPA 98,...) Microscopic many body calculations (BHF or RG, Baldo et al. PRC 98, Vidaña et al. PRC, Djapo et al. PRC 8...) abundances abundances e - p n µ Σ Λ p e - n MC1-H/NY FG µ Ξ Λ Ξ ρ[fm -3 ] Σ MC1-HF/NY (Massot, Margueron & Chanfray, 21) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

16 Mass-radius relation for EOS containing hyperons Mass-radius relation Classical result : maximum neutron star mass 1.4M for stars with hyperons (Glendenning ApJ 85, Baldo et al. PRC, Vidaña et al. PRC,...) Big contradiction with recent observations! (Baldo et al. PRC ) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

17 Solution of the hyperon problem I 1. Modify the interaction Need short-range repulsion to stiffen the EOS In phenomenological models not difficult (Bednarek et al. A& A 22, Bonanno & SedrakianA& A 22,Weissenborn et al. PRC 22, NPA 22, M.O. et al. PRC 22,...) : High density repulsion mainly via Y Y interaction (φ-meson in RMF models) Two solar mass neutron stars containing hyperons can be accomodated In microscopic models (BHF) this seems to be a problem (Vidaña et al., EPJL 11, Schulze & Rijken PRC 11) No (precise) data on Y Y -interaction and hyperonic three-body (Y Y Y, Y NN, Y NN) forces availible difficult to include Adding phenonmenological TBF (Vidaña et al., 2) does not seem to help However, not really possible to make hyperons disappear M max / M solar PL-Z PL-4 NL-SH NL1 NL3 NL-Z PSR J TM1 GM1 nucleons z =. z =.1 z =.2 z =.3 SU(6) z =.5 z =.6 z =.7 z =.8 GM m N * / m N (Weissenborn et al. PRC 12). 2.5 Gravitational Mass [M ] PSR J Radius R [km] 1 3 PSR J Hulse-Taylor (Vidaña et al., EPJL 11) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

18 Solution of the hyperon problem II 2. Let quarks appear early enough In quark matter, the phenomenological models can be supplemented easily with the necessary repulsion (Weissenborn et al., 21, Alford et al. 27,...) Gives constraints on the allowed parameter range Mass M [M ] Hybrid, mixed (CFL+APR) Quark star (QCD O(α s 2 )) Neutron star (DBHF) 2σ EXO Hybrid (2SC+DBHF) Hybrid (2SC+HHJ) Radius R [km] 1σ (Alford et al., 27) Early enough means that quarks appear at sufficiently low densities to prevent hyperons from softening the EOS too much Strong repulsion compatible with lattice data? (Steinheimer & Schramm PLB 11) Problem of reconfinement (very stiff QM EOS becomes again disfavored with respect to hadronic one at very high densities) (Haensel& Zdunik 12) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

19 Core-collapse supernova EOS Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

20 The standard core-collapse EOS Two EOS mainly used in simulations : Lattimer-Swesty (NPA 1991) : Non-relativistic nuclear liquid drop model including surface effects and Coulomb effects Thermodynamically consistent (minimisation of the free energy) H. Shen et al. (NPA 1998) : Relativistic mean field model with TM1 parameter set Finite size effects via Thomas-Fermi approximation Same limiting assumptions for particle content : free nucleons, α particles + one (average) heavy nucleus, electrons/positrons, photons Some simulations employ the Hillebrandt & Wolff EOS (A & A 1984) : Nuclear statistical equilibrium (NSE) model at low densities Hartree-Fock single nucleus approximation for the intermediate density region Homogneous matter treated by Skyrme non-relativistic model For recent developments in the sub-saturation regime see talk by S. Typel Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

21 Is the classical picture adequate? Can we trust the existing EOS in the high density/high temperature region? Example : profiles for a 4M progenitor at, 5, 68 ms after bounce Example : density and temperature range for a 4M progenitor ρ [1 14 g/cm 3 ] T [MeV] Y e radius [km] radius [km] radius [km] (Sumiyoshi et al. 9) (T. Fischer, Ladek Zdroj 9) Extreme conditions : ρ = 1 6 g/cm g/cm 3 T =.2MeV 15 MeV Y e =.5.5 The temperatures and densities reached suggest that additional particles (hyperons, mesons, quarks,...) should be added (as conjectured for neutron stars and measured in heavy ion collisions)! Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

22 Quark matter in supernovae? (Sagert et al. PRL 29, Meixner et al, arxiv ,...) Lattice QCD : T c of roughly 15-2 MeV at vanishing baryon number density Quantitative location of the other borders not very well known Discussed as possibly occuring in the center of neutron stars (for many years!) Could lead to a second shock wave in supernova events (Sagert et al. PRL 9, Fischer et al. 21) helping to produce a succesful explosion Phase transition between hadronic matter and the QGP Supernovæ Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

23 Quark matter in supernovae? (Sagert et al. PRL 29, Meixner et al, arxiv ,...) Lattice QCD : T c of roughly 15-2 MeV at vanishing baryon number density Quantitative location of the other borders not very well known Discussed as possibly occuring in the center of neutron stars (for many years!) Could lead to a second shock wave in supernova events (Sagert et al. PRL 29, Fischer et al. 21) helping to produce a succesful explosion Imprint of the second shock wave on neutrino spectra from Sagert et al. (PRL 29) Luminosity [1 53 erg/s] Luminosity [1 53 erg/s] rms Energy [MeV] (a) e Neutrino e Antineutrino Time (b) After Bounce [s] µ/τ Neutrino µ/τ Antineutrino Time (c) After Bounce [s] e Neutrino e Antineutrino µ/τ Neutrinos Time After Bounce [s] Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

24 Hyperons in supernova EOS (Nakazato et al. ApJ 22, Sumiyoshi et al. ApJL 29, Ishizuka et al. J. Phys. G 28, H. Shen et al. ApJ 21, M.O. et al. PRC 22, F. Gulminelli et al. arxiv 13.39,...) Extended H. Shen type RMF models with hyperons for the moment not compatible with two solar mass neutron star Here : local potential model by Balberg and Gal (Balberg & Gal 97) similar to LS EOS for nuclear part (LS+ EOS) Choose values of the parameters compatible with hyperonic data and PSR J Thermal effects increase hyperon fractions Effect on thermodynamic quantities not negligeable Different hyperon fractions as function of T for n B =.3 and.15 fm 3, Ye =.1 (M.O. et al. PRC 22) x Λ x Σ - x Ξ BG 22BG 22g2.8 22g3 22pm (a) (c) HShen+L.2.2 (e) (f) T [MeV] T [MeV].4 (b) (d) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, 23 2 / 28

25 Hyperons in supernova EOS (Nakazato et al. ApJ 22, Sumiyoshi et al. ApJL 29, Ishizuka et al. J. Phys. G 28, H. Shen et al. ApJ 21, M.O. et al. PRC 22, F. Gulminelli et al. arxiv 13.39,...) Extended H. Shen type RMF models with hyperons for the moment not compatible with two solar mass neutron star Here : local potential model by Balberg and Gal (Balberg & Gal 97) similar to LS EOS for nuclear part (LS+ EOS) Choose values of the parameters compatible with hyperonic data and PSR J Thermal effects increase hyperon fractions Effect on thermodynamic quantities not negligeable Thermodynamic quantities as function of T for n B =.3 and.15 fm 3, Ye =.1 (M.O. et al. PRC 22) p [MeV/fm 3 ] ε [MeV/fm 3 ] c s BG 22BG 22g2.8 22g3 22pm (a) (c) LS, K = 22 MeV LS, K = 18 MeV HShen+L HShen.1 (e).5 (f) T [MeV] T [MeV].15.1 (b) (d) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

26 Strangeness driven phase transition in star matter? The BG-model presents a (first order) phase transition from nuclear to hypernuclear matter. For star matter (µ S = ) this transition is strangeness drive, i.e. the order parameter is given essentially by n S. The existence of a such a phase transition depends stronlgy on the (not well known) Y Y - and NY -interaction. It has been seen e.g. in the RMF model by Schaffner-Bielich et al. (Schaffner-Bielich et al. PRL 22, Gal & Schafnner-Bielich PRC 2) Phase diagram of the nλ-system in the BG model ) -3 (fm Λ ρ III II I T= T=5 MeV T=1 MeV T=2 MeV (F.Gulminelli, A. Raduta, M.O., PRC 22) ρ (fm n ) Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

27 ) The npλ-system Three density variables : n n, n p, n Λ or equivalently n B, n C, n s related to conserved charges (baryon number, charge and strangeness) coexistence borders become surfaces in 3D space At µ s = two phase transitions For ns = at subsaturation (n B < n =.16fm 3 ) the nuclear liquid-gas transition is recovered For supra-saturation density (n B > 2n ) the strangeness-driven phase transition of the nλ-system is recovered Projection of the coexistence domains in the n B, n C -plane for µs = (star matter) (F.Gulminelli et al ) -3 (fm ρ C.25 npλ T= LG µ = S ρ (fm ) B S Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

28 ) The npλ-system with electrons Adding electrons means that total charge neutrality has to be fulfilled n p = n e charge density no longer good degree of freedom Study the system as function of n B, n S, n L The LG phase transition triggered by n B = n n + n p n p fixed by charge neutrality and huge electron incompressibility strong quenching of the phase transition Projection of the coexistence domains in the n B, n L -plane for µs = (star matter) (F.Gulminelli et al ) -3 (fm ρ Lepton.14 npλ+e µ = S At suprasaturation density phase transition triggered by n s only loose correlation with n C almost no quenching T= LG ρ (fm ) B S Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

29 And in a simulation... Simulations are 1D GR (CoCoNuT-code) with a neutrino leakage scheme (B. Peres et al. PRD 23), progenitors have 4M ZAMS (Woosley, Heger, Weaver Rev. Mod. Phys. 22, Woosley & Weaver ApJ 1995) Phase transition density only reached for progenitor with high mass accretion rate (low metallicity) Phase transition induces a mini-collapse followed by pronounced oscillations ( 7 Hz) No second shock wave as in simulations with phase transition to QGP (Sagert et al. PRL 29) (Preliminary) 2D results show a considerable softening of the phase transition Central density as a function of postbounce time, progenitor with low metallicity (B. Peres et al. PRD 23) ρ c [1 14 g.cm -3 ] Λ EoS AH time t [ms] Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

30 And in a simulation... Simulations are 1D GR (CoCoNuT-code) with a neutrino leakage scheme (B. Peres et al. PRD 23), progenitors have 4M ZAMS (Woosley, Heger, Weaver Rev. Mod. Phys. 22, Woosley & Weaver ApJ 1995) Phase transition density only reached for progenitor with high mass accretion rate (low metallicity) Phase transition induces a mini-collapse followed by pronounced oscillations ( 7 Hz) No second shock wave as in simulations with phase transition to QGP (Sagert et al. PRL 29) (Preliminary) 2D results show a considerable softening of the phase transition Central density as a function of postbounce time, progenitor with low metallicity (B. Peres et al. PRD 23) ρ c [1 14 g.cm -3 ] t [ms] Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

31 Comparison between LS and LS+ EOS Strong reduction of time until black-hole collapse by including Λ-hyperons in the EOS for both progenitor models Confirms qualitatively Shen+ hyperons results (Nakazato et al. ApJ 22, Sumiyoshi et al. ApJL 29), but much stronger effect (softer nuclear part of LS) Central density as a function of postbounce time, progenitor with solar metallicity (B. Peres et al. PRD 23) ρ c [1 14 g.cm -3 ] t [ms] LS22+π EoS LS22 EoS LS22+Λ EoS AH time Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28

32 Summary and Outlook 1. Neutron star (cold) EOS Hyperon puzzle not solved, actually two main directions proposed Additional short range repulsion essentially via Y Y -interaction (works well in phenomenological models!) Early transition to quark matter avoiding hyperons Personal take home message : need more hyperonic data as input to microscopic calculations! 2. EOS in core-collapse suparnovae High temperature favors appearance of additional particles (hyperons, quarks,...) EOS availible with additional particles compatible with a two solar mass neutron star Strong effect on the simulations due to strong softening of the EOS in the PNS, e.g. collapse time to a black hole Interesting effects of possible phase transition (second shock wave explosion?) Personal take home message : additional particles cannot be neglected for core-collapse dynamics! Micaela Oertel (LUTH) CC Supernova and NS EOS Trento, July 11, / 28