Symmetry Energy Constraints From Neutron Stars and Experiment

Transcription

1 Symmetry Energy Constraints From Neutron Stars and Experiment Department of Physics & Astronomy Stony Brook University 17 January 2012 Collaborators: E. Brown (MSU), K. Hebeler (OSU), C.J. Pethick (NORDITA), M. Prakash (Ohio U.), A. Schwenk (TU Darmstadt), A. Steiner (INT), Y. Lim (SBU) Hirschegg 2012 Facets of Strong-Interaction Physics

2 Outline Nuclear Symmetry Energy Neutron Star Structure Mass Measurements and Constraints Neutron Star Radii and Relation to Symmetry Energy Measuring Neutron Star Radii The Universal Mass-Radius Relation and the Neutron Star EOS Nuclear Experimental Constraints Masses Neutron Skin Thickness Isospin Diffusion in Heavy Ion Collisions Giant Dipole Resonances Dipole Polarizabilities Pygmy Dipole Resonances Neutron Matter Calculations

3 Nuclear Symmetry Energy Two definitions: 1. Difference between energies of pure neutron matter and symmetric nuclear matter S(ρ) = E(ρ, x = 0) E(ρ, x = 1/2) 2. Expansion around saturation density and symmetric matter E(ρ, x) = E(ρ, x = 1/2) + (1 2x) 2 E sym (ρ) [ E sym (ρ) = S v + L ρ ρ s + K ( ) ] 2 sym ρ ρs ρ s 18 ρ s S v = 1 2 E 8 x 2 L = ρs,1/2, 3 3 E 8 ρ x 2 K sym = ρs,1/2, 9 4 E 8 ρ 2 x 2 Thus, E sym (ρ) S(ρ), but S(ρ s ) = E N (ρ s ) + B S v p N (ρ s ) Lρ s /3 ρx,1/2

4 The Uncertain E sym (n) C. Fuchs, H.H. Wolter, EPJA 30(2006) 5

5 Neutron Star Structure Tolman-Oppenheimer-Volkov equations p(ε) dp dr dm dr = G (mc 2 + 4πpr 3 )(ε + p) c 4 r(r 2Gm/c 2 ) = 4π ε c 2 r 2 maximum mass R L1/4 M(R) Equation of State Observations

6 Mass-Radius Diagram and Theoretical Constraints GR: R > 2GM/c 2 P < : R > (9/4)GM/c 2 M < M max 1122 Hz 716 Hz causality: R > 2.9GM/c 2 normal NS SQS R = R 1 2GM/Rc 2 contours

7 Neutron Star Matter Pressure and the Radius p Kn γ γ = d ln p/d ln n 2 R K 1/(3γ 4) M (γ 2)/(3γ 4) R p 1/2 f n 1 f M 0 (1 < n f /n s < 2) Wide variation: 1.2 < p(ns ) MeV fm 3 < 7 GR phenomenological result (Lattimer & Prakash 2001) R p 1/4 f n 1/2 f p f n 2 ds/dn n s

8 Black hole? Firm lower mass limit? M > 1.68 M { 95% confidence Freire et al { Although simple average mass of w.d. companions is 0.27 M larger, weighted average is 0.08 M smaller } w.d. companion? statistics? Demorest et al Champion et al. 2008

9 Measuring Neutron Star Radii The measurement of flux and temperature yields an apparent angular size (pseudo-bb): R D = R D 1 1 2GM/Rc 2 Observational uncertainties include distance, interstellar absorption (UV and X-rays), atmospheric composition Best chances for accurate radius measurement: Nearby isolated neutron stars with parallax Quiescent X-ray binaries in globular clusters (reliable distances, low B H-atmosperes) Bursting sources with peak fluxes close to Eddington (where gravity balances radiation pressure) F Edd = cgm κd 2

10 Inferred M-R Probability Distributions Thermal Sources Steiner, Lattimer & Brown 2010

11 M R Probability Estimates from PRE Bursts EXO α = 0.14 ± 0.01 R ph = R 4U α = 0.18 ± 0.02 EXO α = 0.14 ± 0.01 R ph > R 4U α = 0.18 ± U α = 0.26 ± 0.10 Özel et al. 2009, 2010, 2011 α = 0.21 ± U Steiner, Lattimer & Brown 2010, 2011 α = 0.26 ± 0.10 α = 0.21 ± 0.06

12 Bayesian TOV Inversion ε < 0.5ε 0 : Known crustal EOS 0.5ε 0 < ε < ε 1 : EOS parametrized by K, K, S v, γ Polytropic EOS: ε 1 < ε < ε 2 : n 1 ; ε > ε 2 : n 2 inferred p(ε) EOS parameters K, K, S v, γ, ε 1, n 1, ε 2, n 2 uniformly distributed M max 1.97 M, causality enforced All stars equally weighted Steiner, Lattimer & Brown 2010 inferred M(R)

13 Nuclear Binding Energy E sym (N, Z) = I 2 (S v A S s A 2/3 ) χ 2 = i (E ex,i E sym,i ) 2 /N χ vv = 2 N i I i 4 A 2 i χ ss = 2 N i I i 4 A 4/3 i χ vs = 2 N i I i 4 A 5/3 i σ Sv = 2χss χ vv χ ss χ 2 sv σ Ss = 2χvv χ vv χ ss χ 2 sv α = 1 2 tan 1 r vs = χvs χvv χ ss 2χvs χ vv χ ss S s 0.95S v L S E sym (N, Z) = v AI 2 1+(S s/s v )A 1/3

14 Nuclear Binding Energy

15 Neutron Skin Thickness R n R p 3/5t np t np = 2ro 3 S si S v +S sa 1/3

16 Heavy Ion Collisions

17 Giant Dipole Resonances E 1 S v (1 + 5Ss 3S v A 1/3 ) 1 Correlation between E 1 and E sym maximized when E sym,208 /AI 2 = S v 1+(S s/s v )A 1/3 S(ρ = 0.1)

18 Dipole Polarizability α D and R n R p in 208 Pb are 98% correlated Reinhard & Nazawericz (2010)

19 Pygmy Dipole Resonances

20 Astronomical Observations

21 Neutron Matter

22 Combined Constraints

23 Astrophysical Consistency with Neutron Matter and Heavy-Ion Collisions