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

◮ Elab = 0.1 − 2 AGeV originates matter with ρ = 2 − 3ρ0 ◮ increasing Elab ∼ 10 AGeV attain densities up to ∼ 8ρ0 ◮ Density attained is extracted from transport calculations ◮ transport models do not include temperature effects and differ

• n 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

• f outer crust of NS

Transverse and elliptical flow

Danielewicz et al Sience 298 (2002)

◮ Boltzmann equation with mean field

U = (aρ + bρν)/[1 + (0.4ρ/ρ9)ν−] + δUp

◮ a, b, ν: fitted to binging energy, saturation density and K ◮ momentum dependence: effective mass m∗ = 0.7m ◮ no isospin/temperature dependence ◮ lower bound does not describe MB1913+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

0.8 1.0 1.2 1.4 1.6

Elab [GeV]

1 2 3 4 5 6 7 (MK+/A)Au+Au / (MK+/A)C+C 0.8 1.0 1.2 1.4 1.6

Elab [GeV]

1 2 3 4 5 6 7 (MK+/A)Au+Au / (MK+/A)C+C

results from different groups

soft EOS, pot ChPT hard EOS, pot ChPT soft EOS, IQMD, pot RMF hard EOS, IQMD, pot RMF KaoS soft EOS, IQMD, Giessen cs hard EOS, IQMD, Giessen cs

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)

◮ Tc = 17.9 ± 0.4 MeV, ρc = 0.06 ± 0.01fm−3, Pc = 0.31 ± 0.03 MeV/fm3 ◮ 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 < K0 < 315 MeV: analysis of up-to-date data on ISGMR (Stone 2013)

Hypernuclei

◮ scattering evetns: → not enough to constrain interactions

◮ for ΛN and Σ N ∼ 850 spin-averaged, ◮ for ΞN 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

(Gal et al (2016))

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

YN interaction

Ξ-hypernuclei

−40 −20 −60 20 −80

<d2σ/dΩdE> (nb/sr 2 MeV) <d2σ/dΩdE> (nb/sr 2 MeV)

counts / 2 MeV counts / 2 MeV Excitation Energy (MeV)

ΛΛBe 12 ΛBe + Λ 11 11Β + Ξ− ΛΛBe 12 ΛBe + Λ 11 11Β + Ξ−

θΚ+ < 14ο θΚ+ < 8ο

10 20 30 10 20 30 40 50 5 10 15 20 25 10 20 30 40 50 20 18 16 14 QF 12 20 16 14 QF 18 12

(Khaustov et al 2000))

◮

12C(K −, K +)12 Ξ Be (E885 Col.)

◮ attractive Ξ-nucleus interactions,

∼ 14 MeV.

◮ recently deeply bound state of

Ξ −14 N, EB = 4.38 ± 0.25 MeV (Nakazawa et al 2015)

ΛΛ-hypernuclei

◮ Necessary to produce a Ξ− followed by

Ξ− + p → Λ + Λ + 28.5MeV

◮ ΛΛ binding from double and single Λ-hypernuclei

∆BΛΛ = BΛΛ(A

ΛΛZ) − 2BΛΛ(A−1 Λ

Z)

◮ Unambiguous measurement 6 ΛΛHe by KEK (2001)

∆BΛΛ = 1.01 ± 0.2+0.18

−0.11MeV ◮ Recent revised to (change in the Ξ− mass)

∆BΛΛ = 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)

LTΛ = ¯ ψΛ fωΛ 2MΛ σµν∂νωµ ψΛ ,

◮ vector meson ω and φ -hyperon: SU(6) symmetry

Rω = 2/3, Rφ = √ 2/3, Ri = gΛi/gNi

◮ ρ-meson does not couple to Λ

Hyperonic stars

Fortin et al arXiv:1701.06373

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4

RφΛ

1.6 1.7 1.8 1.9 2.0 2.1 2.2

Mmax [M ⊙]

TM1-b TM1-a TM1-a TM1-b no hyperons

• nly Λ

UΣ (n0) =0, UΞ (n0) =−14 UΣ (n0) =30, UΞ (n0) =−14 UΣ (n0) =30, UΞ (2/3n0) =−14 UΣ (n0) =0, UΞ (2/3n0) =−14

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4

RφΛ

2.0 2.1 2.2 2.3 2.4 2.5

Mmax [M ⊙]

DDME2D-b DDME2D-a DDME2D-b DDME2D-a no hyperons

• nly Λ

UΣ (n0) =0, UΞ (n0) =−14 UΣ (n0) =30, UΞ (n0) =−14 UΣ (n0) =30, UΞ (2/3n0) =−14 UΣ (n0) =0, UΞ (2/3n0) =−14

◮ Vector meson couplings

choice a: SU(6) symmetry for ω, varying φ -hyperon choice b: gY ω = gNω, varying φ -hyperon ρ-meson: gρΞ = 1

2gρΣ = gρN

◮ Σ-σ coupling: UN

Σ (n0) = 0, +30 MeV

◮ Ξ-σ coupling: UN

Ξ (n0) = −14 MeV and UN Ξ (2n0/3) = −14 MeV

◮ see also van Dale, Colucci, Sedrakian (2013)

ΛN-potential

Fortin et al arXiv:1701.06373

Model RωΛ RσΛ UN

Λ (n0)

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

◮ UN Λ (n0) ≃ −30 MeV in agreement with the binding

energy of single Λ-hypernuclei in the s- and p-shells

◮ RσΛ ∼ 0.62 for SU(6) value for gωΛ, independent of the

model considered.

◮ YN potential

UN

Y (n0) = −

gσY + g′

σY ρs

σ0 + gωY + g′

ωY n0

ω0,

ΛΛ-potential

Fortin et al arXiv:1701.06373

Model ∆BΛΛ = 0.50 ∆BΛΛ = 0.84 RφΛ Rσ∗Λ UΛ

Λ(n0)

Rσ∗Λ UΛ

Λ(n0)

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 < UΛ

Λ(n0) < +9 MeV

in literature taken between −1 or −5 MeV

Kaon condensation

Glendenning & Schaffner-Bielich 1999

500 1000 1500

Energy density [MeV fm

−3]

100 200 300

Pressure [MeV fm

−3]

normal phase kaon phase mixed phase

UK=−100 MeV UK=−120 MeV UK=−140 MeV UK=−80 MeV

◮ Coupled channel calculations based on chiral dynamics (Ramos et

al 2000, Tolos et al 2006): UK −(n0) ≃ −50 MeV

◮ Uexp K −(n0) 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

QCD I

◮ Lattice QCD: presently is the only ab initio calculation that

solves QCD numerically (at µB = 0 or close)

◮ QCD transition from hadrons to a quark-gluon plasma:

smooth crossover at µ = 0, Tc(χ) = 151(3)(3) MeV

Lattice QCD calculation, Aoki et al (2006))

◮ Still no evidence of a critical end point (CEP) ◮ If CEP exists: three families of compact stars

◮ families are distinguished by the radius ◮ Drago et al 2014: hadronic stars (small radii and masses) and

quark stars (large radii and masses)

◮ Benic et al 2015: twin stars, same mass, hadronic and hybrid

stars distinguished by the radius

◮ If CEP exists: other manifestations

◮ If a phase transition happens in a SN, its should be observable

as a second peak in the neutrino signal (Sagert et al PRL 2009)

QCD II

1 10 100 1000 Quark Chemical Potential µ − µ

iron

/3 (MeV) 1e−06 0.001 1 1000 Pressure (MeV fm

−3

) inner

• uter

matter neutron crust crust

pQCD matter

?

SB limit

Central µ in maximally massive stars Maximal limiting µ

(Kurkela ApJ 789, 2014)

◮ T = 0 high density perturbative QCD (pQCD)

◮ state-of-that-art (Kurkela et al PRD81 2010): perturbative calculation

to order O(α2

s) with a massive strange quark.

◮ EOS converges reasonably well for µB > 2.6 GeV

QCD III

Hybrid stars: matching the hadron and quark EOS

How to match the hadronic and quark EOS?

◮ Deconfinement

◮ Impose that deconfinement and chiral symmetry restoration

coincide (Pagliara & Schaffner-Bielich 2007, Klähn et al 2016, Pereira et al 2016)

◮ If quarkyonic phase exists, ρdec > ρχ (Bonanno & Sedrakian 2011, Logoteta et al 2013)

How to match the hadronic and quark EOS?

Hybrid stars

100 200 300 1000 1250 1500 p [MeV/fm3] µB [MeV] RKH 100 200 300 1000 1250 1500 p [MeV/fm3] µB [MeV] HK

Mu,d = 365 MeV Mu,d = 335 MeV

Rehberg, Klevansky, Hüfner 1996 Hatsuda & Kunihiro 1994

◮ Matching the chemical potential

◮ constituent mass of the non-strange quarks in vacuum controls

the beginning of the hadron–quark phase transition (Buballa et al

PLB 2004) ◮ impose µH

B = µQ B at p = 0 (Hoyos et al PRL2016)

◮ ǫ = −p + µBρB ◮ Hugenholtz-von Hove theorem: if p = 0 → µB = ǫ/ρB

Constraints from observations

Neutron star masses

massive neutron stars

1 2 3 10 12 14 16 18 M (M⊙) R (km)

LS180 LS220 LS375 STOS FYSS HS(TM1) HS(DD2) HS(TMA) SFHo SFHx HS(FSU) HS(IUFSU) HS(NL3) SHT(NL3) SHO(FSU) SHO(FSU2.1) SKa

Oertel et al arxiv:1610.03361

◮ PSR J0348+0432 (2.01 (4)M⊙ (Antoniadis et al, 2013), advance of

periastron)

◮ PSR J1614−2230 (1.928(17)M⊙ (Demorest et al 2010, Fonseca et al. 2016),

Shapiro delay)

◮ PSR J1946+3417 (1.828(22) M⊙) (Barr et al, MNRAS 2017), Shapiro

delay and advance of periastron)

Imposing 2M⊙

Fortin et al PRC 94,035804

(Fortin et al 2016) (Fortin et al 2016)

◮ All EoS are causal and predict M > 2.M⊙

◮ range of radii spanned:3km (1M⊙) and 4km (2M⊙)

◮ imposing lab and theoretical constraints:only 4 models remain

◮ range of radii spanned:1km (1M⊙) and 2km (2M⊙) ◮ large high mass uncertainty: lack of constraints on high density

EoS!

Constraining the EOS from NS I

Low mass neutron stars

◮ Smallest NS detected:

◮ J0453+1559: 1.174(4)M⊙ (Martinez et al 2015) ◮ PSR J1918−0642: 1.18+0.10

−0.09 (Fonseca et al 2016)

◮ MNS ∼ 1M⊙: stellar matter up to ∼ ρ0 ◮ Sotani et al 2014: simultaneous observation of mass and radius of low

mass stars puts constraints on the EoS

50 100 150 200 10 100

! (MeV) R (km)

OI 180 OI 230 OI 280 OI 360 Shen Miyatsu FPS SLy4 BSk19 BSk20 BSk21

"c = 2.0"0 "c = 1.0"0 "c = 1.5"0

◮ M and R of low mass

stars in terms of the central density ρc and the parameter η = (K0L2)1/3

◮ simultaneous measurment

• f R and M could

determine η and set constraints on the EoS.

Constraining the EOS from NS

Empirical PR−1/4 relation

◮ empirical result PR−1/4 = C, n0 < n < 2 − 3n0 (Lattimer & Prakash

2001)

◮ Pressure: P = ρ0x2

3

K0

3 (x − 1) + Q0 18 (x − 1)2 + L0δ2

, x = ρ/ρ0

◮ Can we constrain the nucleonic high density EOS from

NS?

Constraining the EOS from NS

M0 + αL0, Alam et al PRC 94, 052801)

0.6 0.8 1 C(RX , b)

K0 L0 K0+αL0

0.6 0.8 1 1.2 1.4 1.6 1.8

MNS (MO)

0.4 0.6 0.8 1 C(RX , b)

M0 L0 M0+βL0

b {

{

b

.

10.5 11 11.5 12 12.5 13 13.5 R1.4 (km) 1000 2000 3000 M0 (MeV) L0 = 40 MeV L0 = 60 MeV L0 = 80 MeV

◮ correlation with 18 RMF EoS+ 24 Skyrme EoS, unified EoS, all

describe 2M⊙ stars

◮ Pearson’s correlation coefficient C(a, b) =

σab √σaaσbb

◮ P = ρ0x2

3

• K0(x − 1)

1 − 2x

3

• + M0

18 (x − 1)2 + L0δ2

., M0 = Q0 + 12K0, x = ρ/ρ0

◮ From De et al 2015: M0(n0) = 1800 − 2400MeV from

energies ISMGR

◮ Prediction:R1.4 = 11.09 − 12.86 km

Constraining the EOS from NS

Steiner, Lattimer & Brown 2015

◮ Statisitical methods were used (Bayesian inference) imposing

several constraints

◮ pure neutron matter calculation near n0 ◮ causality at high density ◮ the largest NS mass measured ◮ general relativity is the correct theory of gravity ◮ several priors were tested ◮ astrophysical observations from photospheric radius expansion

bursts or quiescent low-mass X-ray binaries

◮ R1.4 > 10 km

Neutron star radii

talks C. Heinke, S. Guillot

8 9 10 11 12 13 14 15 16 R1.4 [km] PN14 SL13 GO13 B13 GS13 GS13m GR14

(Fortin et al 2015, Oertel et al 2016)

sources of systematic error: composition of atmosphere, magnetic field intensity, distance of source, residual accretion in binaries, brightness variation over surface, etc ◮ Quiescent X-Ray transients in low mass X-ray binaries

◮ SL13 (Steiner et al 2103) ◮ GS13, GS13m- excluding NGC 6397 (Guillot et al 2013) ◮ GR14 (Guillot & Rutledge 2014)

◮ Bursting NSs - photospheric radius expansion bursts

◮ PN14 (Poutanen et al 2014) ◮ GO13 (Güver & Özel 2013) ◮ SL13 (Steiner et al 2103)

◮ Rotation powered milisecond pulsars: from shape of X-ray pulses

◮ B13: J047-4715 (Bogdanov 2103 )

Direct Urca process

Fortin et al PRC 94,035804

0.0 0.2 0.4 0.6 0.8 1.0

nDU (fm−3 )

40 60 80 100 120 140

L (MeV)

0.5 1.0 1.5 2.0 2.5

MDU (M ⊙)

(Fortin et al 2016) define LDU ∼ 70 MeV

◮ if L > LDU: DUrca for M < 1.5M⊙ ◮ if L < LDU: DUrca for M < 1.5M⊙ ◮ If hyperons are included MDU smaller

MDU 1.5M⊙

◮ Direct Urca process n → p + e− + ¯ νe p + e− → n + νe ◮ this process only operates if pFn ≤ pFp + pFe, ◮ in pure nucleonic stars this implies

Y min

p

= 1 1 +

• 1 + x1/3

e

3 , xe = ne/ (ne + nµ)

Direct Urca process

◮ Horowitz & Piekarewicz PRC66

◮ correlation between MDUrca and the

neutron skin Rn − Rp of 208Pb

0.20 0.22 0.24 0.26 0.28

Rn-Rp (fm)

0.80 1.00 1.20 1.40

MURCA/Msun NL3 S271 Z271v Z271s

◮ Beznogov & Yakovlev (MNRAS 2015)

◮ Typical masses of INSs < MD and of accreting neutron stars MD

(need to explain fast cooling of SAX J1808.4–3658

◮ Statistical study of the thermal evolution of INs and accreting

neutron stars → MDUrca ∼ 1.6 − 1.8M⊙)

◮ ρD: broadened and shifted from ρD0 accounts for effects on cooling

such as superfluidity and/or magnetic fields, possible effects of nuclear physics)

Conclusions

◮ We need more conclusive results from HIC, there is a need to

confront different transport models and confirm that the analysis of data give consistent results by all transport models

◮ More data in YN and YY scattering and hipernuclei are

needed

◮ From QCD: lattice QCD and other theoretical methods are

still not able to set constraints for densities and temperatures as occur in NS, but this may change; it is not clear whether a CEP exists but this may change soon with NICA, FAIR, ALICE

◮ The 2M⊙ pulsars are already constraining the EOS, but the

measurement of other properties such as the radius will certainly give important information at high density.