Constraints on the equation of state of dense matter from - PowerPoint PPT Presentation

Constraints on the equation of state of dense matter from experiments and observations Constança Providência CFisUC, Universidade de Coimbra, Portugal NewCompStar 2017, 31 March, 2017

Outline Constraints from Heavy ion Collisions Constraints from theory Constraints from observations Constraints at saturation and subsaturation: tallk Typel

Constraints from Heavy ion Collisions

Experimental constraints on NS ◮ EOS from HIC ◮ E lab = 0 . 1 − 2 AGeV originates matter with ρ = 2 − 3 ρ 0 ◮ increasing E lab ∼ 10 AGeV attain densities up to ∼ 8 ρ 0 ◮ Density attained is extracted from transport calculations ◮ transport models do not include temperature effects and differ on the modelling of the collisional term, and the interaction ◮ no real comparison between transport models has been made ◮ Understand baryon-baryon and baryon-meson both in vacuum and as a function of density ◮ more scattering data involving hyperons are needed ◮ important information can be obtained from kaonic-atoms and hypernuclei ◮ Properties of neutron rich nuclei: constraints on the thickness of outer crust of NS

Transverse and elliptical flow Danielewicz et al Sience 298 (2002) ◮ Boltzmann equation with mean field U = ( a ρ + b ρ ν ) / [1 + (0 . 4 ρ/ρ 9 ) ν − ] + δ U p ◮ a , b , ν : fitted to binging energy, saturation density and K ◮ momentum dependence: effective mass m ∗ = 0 . 7 m ◮ no isospin/temperature dependence ◮ lower bound does not describe M B 1913+16 = 1 . 4408 ± 0 . 0003 M ⊙ ( Kähn 2006 ) How much do the results depend on the transport code and parametrization of the mean-field?

HIC II Kaon production in HIC ◮ production of kaons below threshold in NN collisions ◮ requires the collective contribution of several nucleons ◮ the production is more probable during the initial phase when matter is highly compressed ◮ since K + are not absorbed by matter they can be used to tag the EoS (incompressibility of matter) ◮ however, besides the effect of nuclear matter, it is also necessary to consider repulsive interaction K-N ◮ it is not easy to disentangle between both effects

HIC II Kaon production in HIC hard EOS: K=380 MeV soft EOS: K=200 MeV results from different groups 7 7 soft EOS, pot ChPT hard EOS, pot ChPT 6 6 (M K+ /A) Au+Au / (M K+ /A) C+C (M K+ /A) Au+Au / (M K+ /A) C+C soft EOS, IQMD, pot RMF hard EOS, IQMD, pot RMF KaoS 5 5 soft EOS, IQMD, Giessen cs hard EOS, IQMD, Giessen cs 4 4 3 3 2 2 1 1 0.8 0.8 1.0 1.0 1.2 1.2 1.4 1.4 1.6 1.6 E lab [GeV] E lab [GeV] Lynch et al 2009 Fuchs 2006 ◮ Constraint of Lynch et al is “an educated guess” based on available analysis of Fuchs 2006 for C+C, Au+Au), 180 < K < 250 MeV) ◮ FOPI Coll. 2005/2012 - “ no strong constraint on EOS can be derived at this stage” and need of experimental confirmation of the isospin effect. ◮ Le Fèvre et al 2016: “ need consensus in both data and transport codes analysis”.

Nuclear liquid-gas phase transition Buyukcizmeci et al 2013 ◮ blue: coexistence lines with TM1 ( Sugahara & Toki 1994 ) ◮ shaded: typical conditions in multigragmentation reactions ( Botvina & Mishustin 2010 ) ◮ dashed: isentropic lines from Statistical Model for Supernova Matter ( Botvina & Mishustin 2010 ) ◮ dotted: CCSN simulation ( Sumiyoshi et al 2005 )

Nuclear liquid-gas phase transition: Critical temperature Compilation: Odilon et al PRC94(2016) Experimental analysis ( Elliot et al, PRC87, 2013 ) ◮ T c = 17 . 9 ± 0 . 4 MeV, ρ c = 0 . 06 ± 0 . 01fm − 3 , P c = 0 . 31 ± 0 . 03 MeV/fm 3 ◮ analysis of particles yields of six different sets of experimental data using a liquid drop model approach ◮ Theoretical calculations ( Odilon et al, PRC94 (2016) ) ◮ RMF including only σ non-linear terms ◮ 0 . 58 < m ∗ < 0 . 64: spin-orbit splittings within accepted exp. values ◮ 250 < K 0 < 315 MeV: analysis of up-to-date data on ISGMR ( Stone 2013 )

Hypernuclei ◮ scattering evetns: → not enough to constrain interactions ◮ for Λ N and Σ N ∼ 850 spin-averaged, ◮ for Ξ N only a few ◮ no data for YY ◮ Alternative information:hypernuclei ◮ � 40 single Λ-hypernuclei ◮ a few double Λ and single-Ξ ◮ no unambiguous Σ-hypernucleus: most probably Σ-nucleus potential repulsive

Λ-hypernuclei Production mechanisms ◮ ( K − , π − ), strangeness exchange ◮ ( π + , K + ), associated production ◮ ( e , e ′ K + ), electro-production ◮ hypernuclei possibly produced in excited states ◮ γ -ray transitions allow to analyse excited states ◮ small spin-orbit strangth of the ( Gal et al (2016) ) YN interaction

Ξ-hypernuclei 50 θ Κ + < 14 ο < d 2 σ /d Ω dE > (nb/sr 2 MeV) 30 20 40 18 counts / 2 MeV 16 14 20 30 20 12 10 QF 12 C( K − , K + ) 12 ◮ 11 Ξ Be (E885 Col.) Λ Be + Λ 10 12 ΛΛ Be 11 Β + Ξ − ◮ attractive Ξ-nucleus interactions, 25 ∼ 14 MeV. < d 2 σ /d Ω dE > (nb/sr 2 MeV) 50 20 θ Κ + < 8 ο ◮ recently deeply bound state of 18 20 16 40 Ξ − 14 N , E B = 4 . 38 ± 0 . 25 MeV counts / 2 MeV 14 15 30 ( Nakazawa et al 2015 ) 12 10 20 QF 11 5 Λ Be + Λ 10 12 ΛΛ Be 11 Β + Ξ − −80 −60 −40 −20 0 20 Excitation Energy (MeV) ( Khaustov et al 2000) )

ΛΛ-hypernuclei ◮ Necessary to produce a Ξ − followed by Ξ − + p → Λ + Λ + 28 . 5MeV ◮ ΛΛ binding from double and single Λ-hypernuclei ΛΛ Z ) − 2 B ΛΛ ( A − 1 ∆ B ΛΛ = B ΛΛ ( A Z ) Λ ◮ Unambiguous measurement 6 ΛΛ He by KEK (2001) ∆ B ΛΛ = 1 . 01 ± 0 . 2 +0 . 18 − 0 . 11 MeV ◮ Recent revised to (change in the Ξ − mass) ∆ B ΛΛ = 0 . 67 ± 0 . 17MeV

Constraining the density functional with hypernuclei I Shen, Yang and Toki, 2006 ◮ Self-consistent calculation of Λ-hypernuclei within TM1 ◮ single Λ-hypernuclei binding energies: fix the σ -hyperon coupling ◮ double Λ-hypernuclei: fix the σ ∗ -hyperon coupling ◮ a weak Λ-nuclear spin-orbit interaction: tensor term ( Noble 1980 ) f ω Λ L T Λ = ¯ σ µν ∂ ν ω µ ψ Λ , ψ Λ 2 M Λ ◮ vector meson ω and φ -hyperon: SU(6) symmetry √ R ω = 2 / 3 , R φ = 2 / 3 , R i = g Λ i / g Ni ◮ ρ -meson does not couple to Λ

Hyperonic stars Fortin et al arXiv:1701.06373 2.2 2.5 no hyperons no hyperons TM1-b 2.1 DDME2D-b 2.4 only Λ DDME2D-a U Σ ( n 0 ) =0 , U Ξ ( n 0 ) = − 14 TM1-a 2.0 U Σ ( n 0 ) =30 , U Ξ ( n 0 ) = − 14 M max [ M ⊙ ] M max [ M ⊙ ] U Σ ( n 0 ) =30 , U Ξ (2 / 3 n 0 ) = − 14 2.3 U Σ ( n 0 ) =0 , U Ξ (2 / 3 n 0 ) = − 14 1.9 only Λ 2.2 U Σ ( n 0 ) =0 , U Ξ ( n 0 ) = − 14 1.8 TM1-b U Σ ( n 0 ) =30 , U Ξ ( n 0 ) = − 14 U Σ ( n 0 ) =30 , U Ξ (2 / 3 n 0 ) = − 14 TM1-a 2.1 U Σ ( n 0 ) =0 , U Ξ (2 / 3 n 0 ) = − 14 1.7 DDME2D-a DDME2D-b 1.6 2.0 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 R φ Λ R φ Λ ◮ Vector meson couplings choice a : SU(6) symmetry for ω , varying φ -hyperon choice b : g Y ω = g N ω , varying φ -hyperon ρ -meson : g ρ Ξ = 1 2 g ρ Σ = g ρ N ◮ Σ- σ coupling: U N Σ ( n 0 ) = 0 , +30 MeV ◮ Ξ- σ coupling: U N Ξ ( n 0 ) = − 14 MeV and U N Ξ (2 n 0 / 3) = − 14 MeV ◮ see also van Dale, Colucci, Sedrakian (2013)

Λ N -potential Fortin et al arXiv:1701.06373 U N Model Λ ( n 0 ) R ω Λ R σ Λ TM1-a 2/3 0.621 -30 TM1-b 1 0.892 -31 DDME2D-a 2/3 0.621 -32 DDME2D-b 1 0.896 -35 ◮ U N Λ ( n 0 ) ≃ − 30 MeV in agreement with the binding energy of single Λ -hypernuclei in the s- and p-shells ◮ R σ Λ ∼ 0 . 62 for SU(6) value for g ω Λ , independent of the model considered. ◮ YN potential � σ 0 + � ω 0 , U N � g σ Y + g ′ � g ω Y + g ′ Y ( n 0 ) = − σ Y ρ s ω Y n 0

ΛΛ-potential Fortin et al arXiv:1701.06373 Model ∆ B ΛΛ = 0 . 50 ∆ B ΛΛ = 0 . 84 U Λ U Λ R φ Λ R σ ∗ Λ Λ ( n 0 ) R σ ∗ Λ Λ ( n 0 ) √ TM1-a 2 / 3 0.533 -11.2 0.557 -14.2 − √ TM1-b 2 / 2 0.843 2.7 0.864 -1.2 − √ NL3-a − 2 / 3 0.534 -9.9 0.559 -13.2 √ NL3-b − 2 / 2 0.846 9.0 0.868 4.8 √ DDME2D-a 2 / 3 0.535 -11.9 0.555 -11.7 − √ DDME2D-b 2 / 2 0.846 -3.4 0.862 -3.4 − Λ potential in pure Λ matter : − 14 < U Λ Λ ( n 0 ) < +9 MeV in literature taken between − 1 or − 5 MeV

Kaon condensation Glendenning & Schaffner-Bielich 1999 300 normal phase kaon phase mixed phase −3 ] Pressure [MeV fm U K =−80 MeV 200 U K =−100 MeV U K =−120 MeV 100 U K =−140 MeV 0 0 500 1000 1500 −3 ] Energy density [MeV fm ◮ Coupled channel calculations based on chiral dynamics ( Ramos et al 2000, Tolos et al 2006 ): U K − ( n 0 ) ≃ − 50 MeV ◮ U exp K − ( n 0 ) still controversial, more experiments are needed ◮ Probabily kaons do not play a role in NS

Constraints from theory

QCD Phase diagram ( CBM/FAIR ) ◮ Still many questions: ◮ Is there a Critical End Point? ◮ Are chiral symmetry restoration and deconfinement transitions coincident or not? ◮ Is there a quarkionic phase? Talks of Pasztor, Klähn, Vourinen, Blaschke