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: A Cosmic Laboratory for Matter under Extreme Conditions

• Motivation
• New Calibration of FSU2 model
• Hyperons and Magnetic Fields
• Summary

Watts et al ‘16

Outline

Astrophys.J. 834 (2017) no.1, 3

• > 2000 pulsars known
• best determined masses:

Hulse-Taylor pulsar M=1.4414 ± 0.0002 M

Hulse-Taylor Nobel Prize 1994

• PSR J1614-22301

M=(1.97 ± 0.04) M; PSR J0348+04322 M=(2.01 ± 0.04) M

1Demorest et al ’10; 2Antoniadis et al ‘13

Mass

Lattimer ‘13

Motivation

Radius

Fortin et al ’15:

RP-MSP: Bodganov ‘13 BNS-1: Nattila et al ‘16 BNS-2: Guver & Ozel ‘13 QXT-1: Guillot & Rutledge ‘14 BNS+QXT: Steiner et al ’13

analysis of X-ray spectra from neutron star (NS) atmosphere:

• RP-MSP: X-ray emission from

radio millisecond pulsars

• BNS: X-burst from accreting NSs
• QXT: quiescent thermal emission
• f accreting NSs

theory + pulsar observations: R1.4M~11-13 Km 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 Lattimer and Prakash ’16 adapted from Fortin’s talk @ NewCompstar Annual Meeting ‘16

EoS: Hyperons

Scarce experimental information: few YN scattering data, and 40 single and 3 double Λ hypernuclei The presence of hyperons induces a strong softening of the EoS that leads to maximum neutron star masses < 2M Solution?

• stiffer YN and YY interactions

hyperonic 3-body forces push of Y onset by condensates quark matter below Y onset

The Hyperon Puzzle

Chatterjee and Vidana ‘16

EoS: Magnetic fields

Magnetar anomalous X- ray pulsar and soft γ-ray repeater with a surface magnetic field

• f ~1014-1015 G

The presence of strong magnetic fields inside NSs is a possible source for a stiff EoS that could sustain masses of 2M How the EoS is affected by strong magnetic fields?

Chakrabarty et al. ‘97; Bandyopadhyay et al. ‘98 ; Broderick et al. ’00 ‘02; Suh and Mathews ‘01; 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 … Mereghetti ‘08 ; Rea and Esposito ‘11; Turolla et al. ’15

Lattimer and Prakash ’04

• astrophysical observations:

2M, R<13 km (?)…

• atomic nuclei: nuclear ground-

state energies, sizes of nuclear charge distributions and 208Pb neutron skin thickness

• heavy-ion collisions (HICs):

particle multiplicities and elliptic flow

Some Constraints for Neutron Star EoS

Fuchs et al ‘01 Danielewicz et al ‘02

HICs

Our model is based on FSU2 model

stiffening of EoS at n>>n0: small ζ implies stiff EoS at n>>n0

Chen and Piekariewicz ‘12

modify density dependence of Esym at 1-2n0: small Λw implies stiff EoS at n0

New calibration of FSU2 model

NL3 (ζ=Λw=0): reproduces properties of atomic nuclei but not HICs FSU (ζ=0.06; Λw=0.03): reproduces properties of atomic nuclei while softer than NL3 FSU2 (ζ= 0.0256; Λw= 0.0008):

• first best-fit model to 2M
• intermediate EoS between NL3

and FSU FSU2R (ζ= 0.024; Λw= 0.05):

• has FSU2 saturation properties and

Esym(n=0.1fm-3) while fitting 2 M

• reproduces properties of atomic nuclei

and HICs small ζ implies stiff EoS at n>>n0 small Λw implies stiff EoS at n0

FSU2R (ζ= 0.024; Λw= 0.05): Mmax= 2.05 M, R1.5M =12.8 Km fulfilling atomic nuclei properties and HICs data Mmax is governed by the stiffness of the EoS at n>>n0 (small ζ stiff EoS @ n>> n0 large Mmax ) R1.5M dominated by the density dependence of the EoS at 1-2 n0 (large Λw soft EoS @1-2 n0 small R)

Implications for atomic nuclei

Horowitz et al ’12 Tarbert et al (MAMI) ’14 Roca-Maza et al ’15

The differences between FSU2R and the experimental energies and radii are at the level of 1% or smaller

208Pb neutron skin thickness

Excellent agreement with recent empirical and theoretical constraints

Energies and charge radii Symmetry energy and slope

Fairly compatible within errors

Esym = E/A(n0, xp = 0) − E/A(n0, xp = 0.5) L = 3n0 ✓∂Esym(n) ∂n ◆

n0

Hyperons soften EoS: Mmax gets reduced by ~15% (Mmax< 2 M for FSU2R) while R insensitive We tense FSU2 to make EoS stiffer: FSU2H (ζ= 0.008; Λw= 0.05), compatible with atomic nuclei and HiCs for neutron matter FSU2R FSU2H npeµ

Mmax 2.05M 2.38M R1.5M 12.8 Km 13.2 Km npeµY Mmax 1.77M 2.03M R1.5M 12.8 Km 13.2 Km

10 11 12 13 14 R [km] 0.5 1 1.5 2 2.5 M/M sun 10 11 12 13 14 15 R [km] 0.5 1 1.5 2 2.5 M/Msun nuc, B=0 hyp, B=0

FSU2R FSU2H

Hyperons..

U

(N) Λ

(n0) = −28 MeV U

(N) Σ (n0) = +30 MeV

U

(N) Ξ

(n0) = −18 MeV U

(Λ) Λ (n0/5) = +0.67 MeV

Hypernuclear observables

Hashimoto and Tamura ‘06; Gal et al. ’16

Chakrabarty et al ‘97

• magnetic fields produce larger Mmax

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

Bc~2x1018 G, Bs~1015 G

..and Magnetic Fields

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 Esym=30.2 MeV & L=44.3 MeV and producing Δrnp=0.133fm

• hyperons soften EoS and FSU2R produces M< 2Mwhile R is insensitive:

a slight modified parametrization, FSU2H, still compatible with the properties

• f 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

• f strongly magnetised NSs