Equation of State for Neutron Stars with Mass and Radius - PowerPoint PPT Presentation

Equation of State for Neutron Stars with Mass and Radius constraints Laura Tolós Mario Centelles and Angels Ramos Annual NewCompStar Conference 2017 27-31 March 2017 Staszic Palace, Warsaw, Poland

Neutron Stars: Watts et al ‘16 A Cosmic Laboratory for Matter under Extreme Conditions Outline o Motivation o New Calibration of FSU2 model o Hyperons and Magnetic Fields o Summary Astrophys.J. 834 (2017) no.1, 3

Lattimer ‘13 Motivation Mass • > 2000 pulsars known • best determined masses: Hulse-Taylor pulsar M=1.4414 ± 0.0002 M � � Hulse-Taylor Nobel Prize 1994 • PSR J1614-2230 1 M=(1.97 ± 0.04) M � ; PSR J0348+0432 2 M=(2.01 ± 0.04) M � 1 Demorest et al ’10; 2 Antoniadis et al ‘13

Fortin et al ’15: Radius � RP-MSP: Bodganov ‘13 � BNS-1: Nattila et al ‘16 � BNS-2: Guver & Ozel ‘13 analysis of X-ray spectra from � QXT-1: Guillot & Rutledge ‘14 neutron star (NS) atmosphere: � BNS+QXT: Steiner et al ’13 • RP-MSP: X-ray emission from radio millisecond pulsars • BNS: X-burst from accreting NSs • QXT: quiescent thermal emission of accreting NSs theory + pulsar observations: R 1.4M � ~11-13 Km Lattimer and Prakash ’16 Some conclusions: � marginally consistent analyses, favored R < 13 Km (?) � future X-ray telescopes (NICER, eXTP) with precision for M-R of ~ 5% � GW signals from NS mergers with precision for R of ~1 km Bauswein and Janka ’12; Lackey and Wade ‘15 adapted from Fortin’s talk @ NewCompstar Annual Meeting ‘16

EoS: Hyperons EoS: Magnetic fields Magnetar Scarce experimental anomalous X- information: few YN scattering ray pulsar and data, and 40 single and 3 double Λ soft γ -ray hypernuclei repeater with a surface The Hyperon magnetic field Puzzle of ~10 14 -10 15 G Mereghetti ‘08 ; The presence of hyperons induces Rea and Esposito ‘11; Turolla et al. ’15 a strong softening of the EoS that leads to maximum neutron star The presence of strong magnetic masses < 2M � fields inside NSs is a possible source for a stiff EoS that could Solution? sustain masses of 2M � stiffer YN and YY interactions How the EoS is affected by strong � magnetic fields? � hyperonic 3-body forces Chakrabarty et al. ‘97; Bandyopadhyay et al. ‘98 ; � push of Y onset by condensates Broderick et al. ’00 ‘02; Suh and Mathews ‘01; � quark matter below Y onset � Harding and Lai’ 06 ; Chen et al. ‘07; Rabhi et al. ’08 ’10; Sinha et al ’13; Lopes and Menezes ’12; Dexheimer et al ’12; Gomes et al ‘13 … Chatterjee and Vidana ‘16

Some Constraints for Neutron Star EoS - astrophysical observations : 2M � , R<13 km (?)… - atomic nuclei: nuclear ground- state energies, sizes of nuclear charge distributions and 208 Pb Lattimer and Prakash ’04 neutron skin thickness HICs - heavy-ion collisions (HICs) : particle multiplicities and elliptic flow Fuchs et al ‘01 Danielewicz et al ‘02

New calibration of FSU2 model Our model is based on FSU2 model Chen and Piekariewicz ‘12 stiffening of EoS at n>>n 0 : small ζ implies stiff EoS at n>>n 0 modify density dependence of E sym at 1-2n 0 : smal l Λ w implies stiff EoS at n 0

small ζ implies stiff EoS at n>>n 0 small Λ w implies stiff EoS at n 0 NL3 ( ζ = Λ w =0): reproduces properties of atomic nuclei but not HICs FSU ( ζ =0.06; Λ w =0.03): reproduces properties of atomic nuclei while softer than NL3 FSU2 ( ζ = 0.0256; Λ w = 0.0008): - first best-fit model to 2M � - intermediate EoS between NL3 and FSU FSU2R ( ζ = 0.024; Λ w = 0.05): - has FSU2 saturation properties and E sym (n=0.1fm -3 ) while fitting 2 M � - reproduces properties of atomic nuclei and HICs

M max is governed by the stiffness of the EoS at n>>n 0 (small ζ � stiff EoS @ n>> n 0 � large M max ) R 1.5M � dominated by the density dependence of the EoS at 1-2 n 0 ( large Λ w � soft EoS @1-2 n 0 � small R) FSU2R ( ζ = 0.024; Λ w = 0.05): M max = 2.05 M � , R 1.5M � =12.8 Km fulfilling atomic nuclei properties and HICs data

Implications for atomic nuclei Energies Symmetry energy and slope and charge radii E sym = E/A ( n 0 , x p = 0) − E/A ( n 0 , x p = 0 . 5) ✓ ∂ E sym ( n ) ◆ L = 3 n 0 ∂ n n 0 Excellent agreement with recent empirical and theoretical constraints 208 Pb neutron skin thickness Horowitz et al ’12 The differences between Tarbert et al (MAMI) ’14 FSU2R and the experimental energies and radii are at the Roca-Maza et al ’15 level of 1% or smaller Fairly compatible within errors

Hyperons.. Hypernuclear observables Hashimoto and Tamura ‘06; Gal et al. ’16 ( N ) Hyperons soften EoS: U ( n 0 ) = − 28 MeV Λ M max gets reduced by ~15% ( N ) U Σ ( n 0 ) = +30 MeV (M max < 2 M � for FSU2R) ( N ) U ( n 0 ) = − 18 MeV while R insensitive � Ξ ( Λ ) U Λ ( n 0 / 5) = +0 . 67 MeV We tense FSU2 to make EoS stiffer: 2.5 2.5 FSU2H ( ζ = 0.008; Λ w = 0.05), FSU2H FSU2R compatible with atomic nuclei and 2 2 HiCs for neutron matter nuc, B=0 FSU2R FSU2H 1.5 hyp, B=0 1.5 M/M sun M/M sun npeµ M max 2.05M � 2.38M � 1 1 R 1.5M � 12.8 Km 13.2 Km 0.5 0.5 npeµY M max 1.77M � 2.03M � R 1.5M � 12.8 Km 13.2 Km 0 0 10 11 12 13 14 10 11 12 13 14 15 R [km] R [km]

..and Magnetic Fields Chakrabarty et al ‘97 B c ~2x10 18 G, B s ~10 15 G - magnetic fields produce larger M max than B=0 case (EM contribution is crucial) - particle fractions at finite B-field: hyperonic magnetars re-leptonize and de-hyperonize with respect to B=0 stars, while the proton abundance increases substantially. This might facilitate direct Urca processes, drastically altering the cooling evolution of the star. Warning: Need of general relativistic treatment of strongly magnetised NSs Chatterjee et al ‘15

Summary We have obtained a new EoS for the nucleonic and hyperonic inner core of neutron stars that fulfills 2M � and R<13 Km, as well as the saturation properties of nuclear matter, the properties of atomic nuclei together with constraints from HICs: - a new parametrization of FSU2, FSU2R, fulfills 2M � with R<13 Km, while reproducing the energies and charge radii of nuclei, having E sym =30.2 MeV & L=44.3 MeV and producing Δ r np =0.133fm - hyperons soften EoS and FSU2R produces M< 2M � while R is insensitive: a slight modified parametrization, FSU2H, still compatible with the properties of atomic nuclei and HiCs - hyperonic magnetars re-leptonize and de-hyperonize with respect to B=0 stars, while the proton abundance increases substantially. This might facilitate direct Urca processes. Need of general relativistic treatment of strongly magnetised NSs