Constraints on Neutron Star Properties from KaoS Heavy-Ion Data

Transcription

1 Constraints on Neutron Star Properties from KaoS Heavy-Ion Data Jürgen Schaffner-Bielich Institute for Theoretical Physics and Heidelberg Graduate School for Fundamental Physics and ExtreMe Matter Institute EMMI EMMI Workshop on Dense Baronic Matter in the Cosmos and the Laboratory, Tübingen, Germany, October 11-12, 2012 p.1

2 Work done in collaboration with: Irina Sagert, Laura Tolos, Debarati Chatterjee, and Christian Sturm e-print: arxiv: [astro-ph.sr], PRC in press p.2

3 Outline Introduction: Neutron Star Masses Nuclear EoS from kaon production in heavy-ion collisions Implications for neutron stars: Neutron star radii for light neutron stars Maximum possible neutron star mass Summary p.3

4 Phase Diagram of Quantum Chromodynamics QCD T T c early universe RHIC, LHC Quark Gluon Plasma FAIR Hadrons nuclei Color Superconductivity neutron stars m / 3 Early universe at zero density and high temperature N µ c µ neutron star matter at small temperature and high density first order phase transition at high density (not deconfinement!) probed by heavy-ion collisions at GSI, Darmstadt (FAIR) p.4

5 Nuclear Equation of State as Input in Astrophysics supernovae simulations: T = 1 50 MeV, n = n 0 proto-neutron star: T = 1 50 MeV, n = n 0 global properties of neutron stars: T = 0, n = n 0 neutron star mergers: T = MeV, n = n 0 p.5

6 Neutron Stars produced in core collapse supernova explosions compact, massive objects: radius 10 km, mass 1 2M extreme densities, several times nuclear density: n n 0 = g/cm 3 in the middle of the crab nebula: a pulsar, a rotating neutron star! p.6

7 The Pulsar Diagram the diagram for pulsars: period versus period change (P-Ṗ) dipole model for pulsars: characteristic age: τ = P/(2P) and magnetic field B = (P P) 1/2 Gauss anomalous x-ray pulsars: AXP, soft-gamma ray repeaters: SGR, young pulsars in supernova remnants: SNR (ATNF pulsar catalog) rapidly rotating pulsars (millisecond pulsars): mostly in binary systems (old recycled pulsars!) p.7

8 Masses of Pulsars (Lattimer and Prakash 2011) nearly 2000 pulsars known with 140 binary pulsars best determined mass: M = (1.4414±0.0002)M Hulse-Taylor pulsar (Weisberg and Taylor, 2004) very high mass of M = (2.74±0.21)M for PSR B (statistical analysis in inclination angle) (Freire et al. 2007) p.8

9 Mass measurement of pulsar PSR J (Freire 2009) s. ω r r ω. s measure post-keplerian parameters from pulsar timing Shapiro delay parameters r and s alone constrain M = (1.67±0.11)M combined with periastron advance ω: M = (1.67±0.01)M rotation of the companion star could influence ω (follow-up observation with Hubble planned) p.9

10 Mass measurement of pulsar PSR J (Demorest et al. 2010) Inclination Angle (deg) Timing residual (µs) Orbital Phase (turns) Probability Density extremely strong signal for Shapiro delay Shapiro delay parameters r and s alone give M = (1.97±0.04)M - new record! by far the highest precisely measured pulsar mass! considerable constraints on neutron star matter properties! Companion Mass (solar) Pulsar Mass (solar) p.10

11 Mass (solar) GR P < rotation Constraints on the Mass Radius Relation (Lattimer and Prakash 2004) J causality AP3 ENG AP4 SQM3 J FSU SQM1 J PAL6 GM3 GS1 Double NS Systems MPA1 MS1 PAL1 MS2 MS Nucleons Nucleons+Exotic Strange Quark Matter Radius (km) spin rate from PSR B of 641 Hz: R < 15.5 km for M = 1.4M Schwarzschild limit (GR): R > 2GM = R s causality limit for EoS: R > 3GM mass limit from PSR J (red band): M = (1.97±0.04)M p.11

12 Kaon Subthreshold Production in Heavy-Ion Collisions p.12

13 Input to transport models: the nucleon potential E/A [MeV] DBHF Bonn A BHF AV 18 BHF AV BF var AV 18 +δv var AV 18 +δv+3-bf Skyrme (K=380) Skyrme (K=200) Skyrme BHF DBHF var ρ/ρ 0 (Fuchs 2006) crucial input to control the amount of compression: the nucleon potential study two extreme cases using the Skyrme model hard EoS: stiffness parameter K = 380 MeV, soft EoS: K = 200 MeV p.13

14 Heavy-ion collisions: density range probed with kaons (Hartnack, Oeschler, Leifels, Bratkovskaya, Aichelin 2012) kaon production by associated production: NN NΛK, NN NNKK produced in a baryon-rich medium at densities of 2n 0 up to 3n 0 long mean-free path of kaons: escape from the high-density region p.14

15 Kaon production in heavy-ion collisions (M K+ /A) Au+Au / (M K+ /A) C+C E/A [MeV] soft EOS hard EOS KaoS ρ/ρ E lab [GeV] nuclear matter is compressed up to 2 3n 0! long mean-free path of kaons: kaons can escape high density matter clear trend indicating high compression a soft EoS Sturm et al. (KaoS collaboration), PRL 2001 Fuchs, Faessler, Zabrodin, Zheng, PRL 2001 p.15

16 Confirmed KaoS data analysis: the nuclear EoS is soft! (M Au A -1 Au )/(M C A-1 C ) E beam = 0.8 AGeV IQMD with KN pot. IQMD w/o KN pot. E beam = 1.0 AGeV IQMD with KN pot. IQMD w/o KN pot. data range data range K N [MeV] Forster et al. (KaoS collaboration) 2007 Hartnack, Oeschler, Aichelin, 2006 kaon production (K + ) far below threshold double ratio: multiplicity per mass number for C+C collisions and Au+Au collisions at 0.8 AGeV and 1.0 AGeV only calculations with a compression modulus of K N 200 MeV and smaller can describe the data = the nuclear equation of state is SOFT! p.16

17 Implication I: Neutron Star Radii and the Asymmetry Potential p.17

18 Probing the EoS: Empirical Nucleon-Nucleon Interaction Ansatz for the energy per particle with u = n/n 0 (Prakash et al. 1988): ǫ/n = m N +E kin 0 + A 2 u+ B σ +1 uσ +S 0 u γ ( nn n p corresponds to the nucleon Skyrme potential used in transport codes parameters A, B, σ fixed by nuclear matter properties n 0, E/A, and compression modulus K 0 asymmetry energy S 0 fixed at n 0, density dependence γ can vary between 0.5 and 1.1 pressure determined by the thermodynamic relation P = n 2 d ( ǫ ) dn n n ) 2 p.18

19 Maximum neutron star mass and compression modulus PL-Z PL-40 NL1 NL-Z NL-SH NL3 K = 300 MeV K = 275 MeV K = 250 MeV K = 225 MeV K = 200 MeV 2.6 M max / M solar TM1 GM1 GM3 2 PSR J m * N / m N (Weissenborn, Chatterjee, JSB 2011) relativistic mean-field model: stiffness of EoS controlled by m /m not the compression modulus K 0 change in maximum mass for different compressibilities: at most 0.1M adopt stiffness parameter K from KaoS data analysis as a constraint on high density EoS only! p.19

20 Low-Mass Neutron Star Radii and the Asymmetry Potential (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) radii for different stiffness parameter (KaoS: K < 200 MeV) central density in a 1.25M neutron star: around 3n 0 radius mostly sensitive to density dependence γ of asymmetry energy (Lattimer and Prakash (2001), Carriere, Horowitz, Piekarewicz (2003), Bao-An Li et al.... ) p.20

21 Neutron Star Radii and the Asymmetry Potential (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) radii for different masses and asymmetry potentials moderate change with mass, stronger dependence on density dependence γ of asymmetry energy constraint from KaoS data analysis reduces uncertainty in isospin independent part of the nuclear EoS p.21

22 A potential measure of the isospin potential 3 π - /π + 2,8 2,6 2,4 2,2 2 1,8 1,6 1,5 DDF NL NLρ NLρδ NLDDρ K 0 /K + 1,4 1,3 1,2 1,1 0,6 0,8 1 1,2 1,4 1,6 1,8 2 E beam (AGeV) (Ferini, Gaitanos, Colonna, Di Toro, Wolter 2006) use different nucleon potentials with different asymmetry potentials particle ratios of kaons (pions) with different isospin: sensitive to different nuclear models p.22

23 Implication II: Constraint on the Maximum Possible Neutron Star Mass p.23

24 Maximum central density of a compact stars (Lattimer and Prakash 2011) maximally compact EoS: p = s(ǫ ǫ c ) with s = 1 stiffest possible EoS (Zeldovich 1961) gives upper limit on compact star mass: M max = 4.1M (ǫ sat. /ǫ f ) 1/2 (Rhoades and Ruffini 1974, Hartle 1978, Kalogera and Baym 1996, Akmal, Pandharipande, Ravenhall 1998, Lattimer and Prakash 2011) p.24

25 Maximum Mass from Causality Argument (Kalogera and Baym 1996) use EoS from Wiringa, Fiks, Fabrocini 1988 (Argonne V 14 potential) probed only up to normal nuclear matter density (at most) maximum possible mass due to causality: M max = 4.1M at ǫ f = ǫ saturation p.25

26 Constraint from heavy-ion data: nucleon potential at 2 3n 0 (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) input to transport simulations: nucleon potential kaon production is sensitive to densities of n = 2 3n 0 (n 0 = 0.17 fm 3 ) constraint: nucleon potential must be below the curve for the Skyrme model with K = 200 MeV at a fiducial density of n f = 2...3n 0 p.26

27 Maximum Masses of Neutron Stars Causality Skyrme Bsk8 n crit =2.5 n 0 n crit =2 n 0 n crit =3 n M [M solar ] R [km] (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) Skyrme parameter set BSK8: fitted to masses of all known nuclei above a fiducial density (determined from the analysis of the KaoS heavy-ion data) transition to stiffest possible EoS causality argument: p = ǫ ǫ c above the fiducial density ǫ f Rhoades, Ruffini (1974), Kalogera, Baym (1996): M max = 4.2M (ǫ 0 /ǫ f ) 1/2 p.27

28 Maximum Masses of Neutron Stars Causality Skyrme SLy4 n crit =2.5 n 0 n crit =2 n 0 n crit =3 n M [M solar ] R [km] (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) Skyrme parameter set Sly4: fitted to properties of spherical nuclei above a fiducial density (determined from the analysis of the KaoS heavy-ion data) transition to stiffest possible EoS causality argument: p = ǫ ǫ c above the fiducial density ǫ f Rhoades, Ruffini (1974), Kalogera, Baym (1996): M max = 4.2M (ǫ 0 /ǫ f ) 1/2 p.27

29 Maximum Masses of Neutron Stars Causality RMF TM1 n crit =2.5 n 0 n crit =2 n 0 n crit =3 n M [M solar ] R [km] (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) RMF parameter set TM1: fitted to properties of spherical nuclei above a fiducial density (determined from the analysis of the KaoS heavy-ion data) transition to stiffest possible EoS causality argument: p = ǫ ǫ c above the fiducial density ǫ f Rhoades, Ruffini (1974), Kalogera, Baym (1996): M max = 4.2M (ǫ 0 /ǫ f ) 1/2 p.27

30 Constraint for neutron stars: causality plus heavy-ion data (Sagert, Tolos, Chatterjee, JSB, Sturm 2012) maximum mass for neutron stars versus the fiducial density same trend for various allowed nuclear models (NL3 is too stiff!) main difference: the density dependence of the asymmetry energy overall upper limit of a maximum mass of M max = 3M for n f = 2n 0 p.28

31 Summary: analysis of kaon production provides a constraint on the nuclear EoS (nucleon potential) at 2 3n 0 implications for neutron stars: radii of light neutron stars: only controlled by asymmetry potential maximum mass of neutron stars: lower than 3M due to causality arguments strong interplay between heavy-ion physics and astrophysics p.29

32 The Future: and NICA P [MeV fm -3 ] DBHF η D = 0.92, η V = 0.0 η D = 1.00, η V = 0.5 η D = 1.02, η V = 0.5 η D = 1.03, η V = 0.5 NICA fixed target flow constraint Danielewicz et al. FAIR NICA collider mode n [fm -3 ] M [M sun ] Causality limit 4U DBHF η D = 0.92, η V = 0.0 η D = 1.00, η V = 0.5 η D = 1.02, η V = 0.5 η D = 1.03, η V = 0.5 RX J1856 PSR J R [km] (Klähn, Blaschke, Weber 2011) left: equation of state and flow constraints, right: compatible mass-radius relations and astrophysical constraints higher baryon densities achieved at higher bombarding energy probing densities beyond 2 3n 0 p.30

33 X-Ray burster binary systems of a neutron star with an ordinary star accreting material on the neutron star ignites nuclear burning red shifted spectral lines measured! (z = 0.35 M/M = 1.5 (R/10 km)) (Cottam, Paerels, Mendez (2002)) Cottam et al. (2008): not confirmed with burst data from 2003 p.31

34 Fits to X-Ray Burster Spectra M / M GR 8 causality F Edd = const A = const T Edd, = const R [km] Neutron star mass M / M O causality SQM3 PAL6 AP4 MS1 GM3 MS0 H solar 619 Hz 500 Hz He Neutron star radius R [km] (Suleimanov, Poutanen, Revnivtsev, Werner 2011) x-ray burster with photospheric radius expansion assume (color-corrected) black-body emission and Eddington flux at touch-down (Özel 2006): simple model fit fails above a certain distance! large correction from model atmosphere composition p.32

35 Mass-Radius Constraints from X-Ray Burster and Binaries r ph >>R M (M ) M (M ) r ph >>R R (km) R (km) (Steiner, Lattimer, Brown 2011) fit to three x-ray burster data with photospheric radius expansion and three quiescent x-ray binaries (from previous analysis) relax constraint at touch-down to be on the surface (r ph R) strong constraint on radius relation (left: combined fit, right: separate fits) p.33

36 Mass-Radius Constraints from Isolated Neutron Stars (Hambaryan, Suleimanov, Schwope, Neuhäuser, Werner, Potekhin 2011) isolated neutron star, pulses in x-rays phase space resolved x-ray spectroscopy fit to geometry of hot spot etc. including redshift z resulting compactness: (M/M )/(R/km) = 0.087±0.004 indication for a stiff equation of state p.34

37 RXJ 1856: Neutron Star or Quark Star? (Trümper et al. (2003), Ho et al. (2007)) VLT/FORS1 HST/STIS CXO/LETG XMM/RGS EUVE VLT/FORS2 HST/WFPC2 F λ (ergs s 1 cm 2 A 1 ) XMM/RGS CXO/LETG EUVE HST/STIS VLT/FORS Wavelength (A) two-component blackbody: small soft temperature, so as not to spoil the x-ray this implies a rather LARGE radius so that the optical flux is right! lower limit for radiation radius: R = R/ 1 2GM/R = 17 km (d/140 pc) from parallax measurement: distance d = 123(+11, 15)pc (Walter, Eisenbeiss, Lattimer, Kim, Hambaryan, Neuhäuser 2011) p.35

38 Neutron Star Radii from Neutron Star Mergers 3.5 f peak [khz] R [km] max (Bauswein and Janka, 2012) neutron star merger simulation with 3D smoothed particle hydro code using conformal flatness approximation strong correlation with peak frequency in gravitational waves and neutron star radius rather insensitive to masses of neutron stars measurable with advanced LIGO in a few years p.36

39 Effect of kaon potentials on double ratio (M K+ /A) Au+Au / (M K+ /A) C+C soft EOS, w/o kaon pot hard EOS, w/o kaon pot soft EOS, with kaon pot hard EOS, with kaon pot E lab [GeV] (Fuchs, Faessler, Zabrodin, Zheng 2001) study double ratio: compare kaon multiplicity in C+C with Au+Au collisions kaon potential is repulsive in dense matter effect is (nearly) linear in density cancels in double ratio p.37

40 Kaon Production: Sensitivity to Different Models (M K+ /A) Au+Au / (M K+ /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 E lab [GeV] (Fuchs 2006) study different transport models and cross sections excitation function for kaon production ratio rather insensitive main difference originates from the underlying EoS! p.38