Equation of State Constraints from Neutron Stars
James Lattimer [email protected]
Department of Physics & Astronomy Stony Brook University
J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.1/?? Credit: Dany Page, UNAMJ.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.2/?? ?? . 3 − 6 – p.3/ g cm 2 ) /M ⊙ (M 16 10 × 4 . 1 ρ< . ⊙ M (hyperons, Bose condensates, quarks). 5 . 1 > max M J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 Limits softening from ‘exotica’ Limits highest possible density in stars: New evidence for Observable Quantities (1) • • • Mass • ?? 6 – p.4/ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200
Observed Masses ?? 6 – p.5/ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 ⊙ ⇒ ⇒ M 68 . 1 M > 95% confidence Black hole? , 95% confidence
Observed Masses ⊙ M 6 . 1 Firm lower mass limit? M > ?? 6 – p.6/ 2 GM/c 3 ≥ R J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200
Maximum Possible Density in Stars Causality limit for compactness: (Lattimer, Masak, Prakash & Yahil 1990; Glendenning 1992) ?? for c ρ 6 – p.6/ 3 3 − − g cm g cm 2 ) 2 /M ⊙ ⊙ M M (M 15 15 10 (Lattimer & Prakash 2005) 10 ) ] × × . No realistic EOS has greater 2 4 ) 6 . . 6 = 0 13 r/R = 5 ( ≤ 2 2 − 1 M [1 3 c surface c,Inc ρ ρ GM/c ρ 3 2 5 2 = G c 3 ≥ ρ = R π 3 4 c,V II ρ ≤ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 3 M πR 3 4 = c,UD ρ Maximum Possible Density in Stars Tolman VII : than Tolman VII solution ( M But UD solution violates causality and Causality limit for compactness: (Lattimer, Masak, Prakash & Yahil 1990; Glendenning 1992) Uniform Density: given ?? for c ρ 6 – p.6/ 3 3 − − g cm g cm 2 ) 2 /M ⊙ ⊙ M M (M 15 15 10 (Lattimer & Prakash 2005) 10 ) ] × × . No realistic EOS has greater 2 4 ) 6 . . 6 = 0 13 r/R = 5 ( ≤ 2 2 − 1 M [1 3 c surface c,Inc ρ ρ GM/c ρ 3 2 5 2 = G c 3 3 ≥ ρ = − R π 3 4 c,V II ρ ≤ g cm J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 3 15 M πR 3 10 ⇒ 4 ⊙ × = 8 . 2 2 M c,UD . ρ Maximum Possible Density in Stars 2 Tolman VII : than Tolman VII solution ( < M max Maximum possible density: ρ But UD solution violates causality and Causality limit for compactness: (Lattimer, Masak, Prakash & Yahil 1990; Glendenning 1992) Uniform Density: given ?? 6 – p.7/ ⊙ 5 M . 1 − 4 1 R ∝ Pb could constrain ] 208 /dn ) n ( sym dE [ ∝ 6 ) (Lattimer & Prakash 2001) . ∼ measurements of n ( ) ⊙ max p P M M R (hyperons, Bose condensates, quarks). 5 . − 1 0: n > R ≃ ( , x max 2 M < J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 0 ) 0 < n/n currently uncertain to factor 1 n
causality: R > 2.94GM/c2
— normal NS — SQS
— R∞ contour
J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.9/?? ?? 6 – p.10/ ↓ 0 ⇓ ⇑ ρ 1 ) n ∼ − 1 (3 / ) − n 7 J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 − ρ 2) 2 (1 / 0 < ln 1 < 3 M ∗ − M ) 0 − ρ 1 ) n /n 4 0 P/d − ∗ − / ρ /ρ 1 ( ρ ∗ ∗ (3 2 ln 1+1 P P / n/ 1 Neutron Star Matter Pressure d (Lattimer & Prakash 2001) ∗ MeV fm < ρ ∝ Kρ P K = < (1 R 1 ≃ ∝ ∝ 2 − . R P 1 GR phenomenological result Wide variation: R n ?? 6 – p.11/ Masses Pulsars Spin Rates r-Process Glitches - Crust Magnetic Fields Moments of Inertia Binary Mergers of Neutron-Star Matter Decompression/Ejection dR/dM Mass/Radius Heavy Ion Flows Rare Isotope Beams Multi-Fragmentation Gravity Waves Nuclei Far from Stability Properties Observational Neutron Stars Composition: , z Kaon/Pion Condensates Maximum Mass, Radius ∞ R Hyperons, Deconfined Quarks Symmetry Energy X-ray Bursters Many-Body Theory (Magnitude and Density Dependence) Opacities ν Emissivities SN r-Process Metastability ν J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 , z ∞ R Proto-Neutron Stars Isospin Dependence of Strong Interactions Fission Direct Urca Temperature NS Cooling Superfluid Gaps Nuclear Masses e Neutron Skin Thickness ν Isovector Giant Dipole Resonances
The Role of the Symmetry Energy Mass Radius QPO's Supernovae Binding Energy Early Rise of L Weak Interactions Bounce Dynamics ?? ⊙ 6 – p.12/ 5 M . 1 − 4 1 ms R 2 ms / yield ∝ 1 Pb could constrain 2 ] / suggests 1 208 ⊙ /dn M M ) ⊙ n M ( M 2 / 3 sym 2 / 3 dE [ R ∝ 6 . 10 km ) R (Lattimer & Prakash 2001) . ∼ measurements in n ( ) 10 km ⊙ max p P 03 (Shapiro & Teukolsky) M . M (Lattimer & Prakash 2004) R (hyperons, Bose condensates, quarks). 0 0 5 . . − 1 ± 0: n = 1 > 96 R ≃ . ( , x max = 0 2 Roche min M refer to non-rotating values (EOS-independent relation). < P 0 min R J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 ) P 0 and < n/n M currently uncertain to factor 1 n J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.13/?? ?? 6 – p.14/ stances, low B X T 2 2 X X d R fR GM/Rc 2 πf 1 + 2 ), interstellar H absorption (hard UV − d p 1 = 4 ∝ = q ∞ opt 2 X R/ T R R 2 = + : ∞ 2 2 opt R d opt / R R X q T π = ∼ R = 4 J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 opt opt T F Nearby isolated neutron stars (parallaxQuiescent measurable) X-ray binaries in globularH-atmosperes) clusters (reliable di • • and X-rays), atmospheric composition Combination of flux and temperature measurements yield Uncertainties include distance ( Best chances are from Observable Quantities (2) • • • Radiation Radius • Optical flux on Rayleigh-Jeans tailX-ray 5-7 BB times and extrapolated RX J1856-3754: Walter & Lattimer 2002 Braje & Romani 2002 Truemper 2005 D=120 pc J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.15/?? X7 in 47 Tucanae: Rybicki, Heinke, Narayan & Grindlay 2005 ω Cen: Gendre, Barret & Webb 2003a M13: Gendre, Barret & Webb 2003b J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.16/?? ?? 6 – p.17/ , 4U1820-30 38 G . pling between 2 0 / ] stances, low B 2 z < − ) 2 z − 2 M 4 (1 + R t − P [1 1 ∝ GM/Rc (Cottam, Paerels & Mendez 2002) 2 − ) ), interstellar H absorption (hard UV − z 35 014 d . . 1 0 1 0 ∝ q − ≃ > (1 + ∞ 2 2 z (Link, Epstein & Lattimer 1999) R/ / c R 1 ∞ = star − ) /M R /I 2 2 ∞ = R R crust I core-crust interface pressure 3 GM/Rc ,M 1 2 − − , EXO 0748-676 − ) J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 z 30 . 0 MeV fn = (1 superfluid and star. (1 + z 65 n . ∞ 0 R Cottam, Paerels & Mendez 2002 Vela: ∆I/I > 0.014 Link, Epstein & Lattimer 1999 J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.18/?? ?? 6 – p.19/ us of accretion disk (Lamb & Miller 2000) > R A R and J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 2 GM/c 6 > A Possible association of observed frequency withR inner radi Observable Quantities (3) • QPOs • J.M. Lattimer, Isolated Neutron Stars, London, 27 April 2006 – p.20/?? ?? (1) 6 – p.21/ us of accretion disk 1 − 1) c ρ v H− ln dS d + R R ∆ )+ ( c u 2 H ( v R S R ∆ (Lamb & Miller 2000) − 4) + 1 2 > R − c ≃ A 03 u . R 2 1 (3 c Rc ≃ GM u and B K J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 18 2 /m ) 0 7+ (Watts & Strohmayer) n /κ GM/c µ 1 2 6 . − ≃− 0 15 n . > 0 µ 3 Md 0 ≃ n / A 2( µ 2 ∝ e ≃ Possible association of observed frequency withR inner radi Observable Quantities (3) − ≃ 2 = R/R • edd n c Rc GM H µ u QPOs Burst sources limited byF Eddington luminosity Neutron star oscillations ∆ • • • ?? 6 – p.22/ ian effects us of accretion disk e 2 MR ∝ (Lamb & Miller 2000) I : R > R A R and J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 2 (Watts & Strohmayer) /κ GM/c 1 2 6 . 0 > Md ≃ A ∝ Possible association of observed frequency withR inner radi Spin-orbit coupling of same magnitude(Barker as & post-post-Newton O’Connell 1975, Damour &Precession Schaeffer alters 1988) inclination angle and periastronMore advanc EOS sensitive than Double pulsar PSR J0737-3037 is candidate Observable Quantities (3) R/R • • • • • edd QPOs Burst sources limited byF Eddington luminosity Neutron star oscillations ∆ Moment of Inertia • • • • ?? 6 – p.23/ A ~ S × ~ L ) B 2 M c 3 a +3 A A M M 2 (4 G = ˙ ~ L − = A ˙ ~ S J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 Moments of Inertia and Precession Spin-orbit coupling: • ?? 6 – p.23/ 9 years . 74 A ~ ≃ S ) × 2 e ~ L ) − B 2 (1 M c 3 P a ) +3 A A B 2 M M M ac 2 ) (4 G B + 3 M A = ˙ + ~ L M A − (4 B M = 2( A ˙ ~ GM S J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 = p P Moments of Inertia and Precession Spin-orbit coupling: Precession Period: • • ?? 5 − 6 – p.23/ 10 × θ 2) sin . 9 years 7 . − 74 A 6 . ~ ≃ S (3 ) × 2 e ≃ ~ L ) θ − B 2 (1 sin M c 3 P A a ) +3 P P A A B 2 ) M M M ac 2 B ) (4 B M G B + 3 M + M A = A A ˙ + ~ L M M 2 M A − (4 ( a B M A = I 2( A ˙ ~ GM ≃ S θ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 = p sin P | | A ~ ~ L | S | = i δ Moments of Inertia and Precession Spin-orbit coupling: Precession Period: Precession Amplitude: • • • ?? 5 − 6 – p.23/ 10 × θ s θ µ 2) sin . 9 years 7 . − 0 sin 74 . A 6 4 . ~ ≃ S − (3 ) × 2 4 . e ≃ ~ L 0 ) θ − ≈ B 2 (1 i sin M c 3 P A a ) +3 P cos P A A i B 2 ) δ M M M c ac 2 a B ) (4 B M G B + 3 M B + M A = A M A ˙ + ~ L M M B 2 M + A − (4 ( M a A B M A = I M 2( A ˙ ~ GM ≃ S θ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 = = t p sin ∆ P | | A ~ ~ L | S | = i δ Moments of Inertia and Precession Spin-orbit coupling: Precession Period: Precession Amplitude: Delay in Time-of-Arrival: • • • • ?? θ cos 4 5 − − 6 – p.23/ 10 10 × × 3) θ . s 4 − θ µ 2 . 2) sin . 9 years (2 7 . − 0 sin ≃ 74 . A 6 4 θ . ~ ≃ S − (3 ) × cos 2 4 . e ≃ ~ L 0 B ) θ − M ≈ B 2 (1 i sin M c + Ga 3 P A a A ) +3 P cos = P A A i B 2 M ) δ M M M c ac 2 a B PN r ) (4 B M G B ! + 3 /A M B + M B P A = A A M A ˙ M + ~ L M M B : A 2 M + A − ~ (4 L ( M A a · M A B M A = I A /M M 2( A ~ S + 2 ˙ B ~ GM ≃ S 2 B ∝ θ M J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 = = M t p sin ∆ P | + 3 | 2 + 3 A ~ ~ L 2 A | S | M 3 = i δ Moments of Inertia and Precession A A πI P 2 Spin-orbit coupling: Precession Period: Precession Amplitude: Delay in Time-of-Arrival: Periastron Advance • • • • • ?? θ cos 4 5 − − 6 – p.23/ 10 10 # × × 4 3) θ . s 4 ⊙ − km M θ µ 2 . 2) sin . R M 9 years (2 7 . − 0 sin ≃ 74 . A 6 4 θ . ~ ≃ S + 90 − (3 ) × cos 2 4 ⊙ . e ≃ ~ L 0 B km ) M θ − M ≈ B R M 2 (1 i sin M c + 2 Ga . 3 P A a A ) +3 P cos = P A A i B 2 M ) δ M M 1 + 4 M c ac 2 a B PN r " ) (4 B 2 M G B ! + 3 /A M B + M B P A = A MR A M A ˙ M + ~ L M M B : A 2 M + A − ~ (4 L ( M A a · 008) M A B . M A = I 0 A /M M 2( A ~ S + 2 ˙ ± B ~ GM ≃ S 2 B ∝ θ M J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 = = M 237 t . p sin ∆ P (0 | + 3 | 2 + 3 A ~ ~ L ≃ 2 A | S | I M 3 = i δ Moments of Inertia and Precession A A πI P 2 Spin-orbit coupling: Precession Period: Precession Amplitude: Delay in Time-of-Arrival: Periastron Advance Moment of Inertia – Mass – Radius • • • • • • ?? 6 – p.24/ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 Moments of Inertia ?? 6 – p.24/ J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 Moments of Inertia ?? 6 – p.24/ Lattimer & Schutz (2005) J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 Moments of Inertia ?? , 6 – p.25/ ) cooling: are major direct Urca (Slane et al. 2004) (Kaplan et al. 2004) i.e., , supernova remnants 3C58 J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 (Pavlov et al. 2001) Growing database of cooling neutron stars. Atmosphere composition, magnetic field strength,uncertainties. distance Hints that some neutron stars may exhibit ’rapid’ ( G084.2-0.8, G093.3+6.9, G127.1+0.5 & G315.4-2.3 Probes superfluid properties of neutron star interior Vela Observable Quantities (4) • • • • Temperature and Age • ?? 6 – p.26/ Page, Lattimer, Prakash & Steiner (2004) J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 Neutron Star Cooling ?? 6 – p.27/ measurements ∞ R , limits EOS at high density. the density derivative of the ⊙ M i.e., 7 . 1 > J.M. Lattimer, Isolated Neutron Stars, London, 27 April 200 might be Conclusions measurement gives direct information about the max Masses may have a wide range. M Radii remain elusive, but some R EOS near the saturation densityasymmetric for matter, extremely Other observables (redshifts, QPOs, Eddington-limited fluxes from accreting sources, momentscould of yield inertia) mass/radius measurements in nearNeutron future. star cooling is richinterior source composition, of hints information that about rapidin cooling a necessary few cases. symmetry energy. imply relatively large values. • • • • • •