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Nuclear Equation of State and Neutron Stars

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Nuclear Equation of State and Neutron Stars Nuclear Equation of State and Neutron Stars Yeunhwan Lim Department of Science Education Ewha Womans University JUL 14, 2021 APCTP Focus Program in Nuclear Physics 2021 Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 1 / 32 Neutron Stars Formed after core collapsing supernovae. Suggested by Walter Baade and Fritz Zwicky (1934) - Only a year after the discovery of the neutron by James Chadwick Jocelyn Bell Burnell and Antony Hewish observed pulsar in 1965. Neutron star is cold after 30s 60s of its birth - inner core, outer core, inner∼ crust, outer crust, envelope - R : 10km ∼ +0:1 +0:07 - M : 1:2 2:x M (2:14 0:09(2:08 0:07) M PSR J0704+6620; 2:01 0∼:04 M PSR J0348+0432− − ; 1:97 0:04 M PSR J614-2230 ) - 2 10±11 earth g General relativity ± - B× field : 108 10!12G. ∼ - Central density : 3 10ρ0 Nuclear physics!! ∼ ! Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 2 / 32 Inner structure of neutron stars Envelope 8 3 ρ ρs(= 10 g/cm ) Outer crust Z, e ∼ ρ 1010g/cm3 BCC lattice ∼ ρ ρ (= 4 1011g/cm3) Inner crust ∼ d × n, Z, e 1 n S0 superfluidity ρ 0.5ρ (= 2 1014g/cm3) Outer core ∼ 0 × n, p, e, µ Uniform nuclear matter 8 3 1 ∼ n P2, p S0 superfluidity 15km ρ 2ρ0 Inner core ∼ Hyperons? Bose (K−, π−) condensation 1 Quarks? Hyperon S0 superfluidity Color superconductivity Neutron Stars: - Dense nuclear matter physics Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 3 / 32 TOV equations for macroscopic structure dp G(M(r) + 4πr 3p=c2)( + p) = ; dr − r(r 2GM(r)=c2)c2 − (1) dM = 4π r 2; dr c2 Nuclear physics provide the information for and p. Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 4 / 32 Nuclear matter properties Nuclear equation of state at T = 0 MeV 40 30 20 PNM (MeV) 10 E/A S 32 MeV 0 v ' SNM 10 − 20 − 0.00 0.08 0.16 0.24 0.32 3 ρ(fm− ) Figure: Energy per baryon for symmetric nuclear matter and pure neutron matter Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 5 / 32 Figure: Many body diagrams for nuclear matter calculation (C. Drischler, Phd thesis) Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 6 / 32 Most neutron matter results can be fitted using the quadratic expansion. 60 Chiral EFT Fit 40 (MeV) 20 PNM E/A 0 SNM 20 − 0.00 0.05 0.10 0.15 0.20 0.25 0.30 3 n (fm− ) 1 1 2 2 (n; x) = τn + τp + (1 2x) fn(n) + 1 (1 2x) fs (n) ; (2) E 2m 2m − − − 3 3 X (2+i=3) X (2+i=3) fs (n) = ai n ; fn(n) = bi n (3) i=0 i=0 Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 7 / 32 Neutron Star EOS constraints Exp. Theory EDF (n, x) E Obs. Experiments - SNM properties, Neutron skin thickness, binding energies Theory - Neutron matter calculations (QMC, MBPT, ..) Observation Gravitation wave : tidal deformabilities, Moment of inertia, Nicer (mass-radius), maximum mass(Mmax > 2:0M ) Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 8 / 32 EOS constraints Nuclear EOS constraints - Microscopic calculation(Pure neutron matter) - Nuclear structure: Neutron skin, binding energies of nuclei - Maximum mass of neutron stars(Mmax > 2:0M ) - Gravitational wave: tidal deformabilities(Λ1:4) - (Moment of inertia) - NICER(Neutron Star Interior Composition Explorer): mass and radius Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 9 / 32 EOSs and MR Statistical uncertainties from EOSs (Theory + Experiment) 1e-03 1e-02 1e-01 1 1.0 500 1 60 0.9 Prior 2.0 400 40 0.8 20 0.7 1e-01 1.5 ) 300 0 0.6 M ( (MeV) 20 − 0.5 200 0.00 0.05 0.10 0.15 0.20 0.25 0.30 M 1.0 E/A 1e-02 0.4 100 0.5 0.3 0.2 Posterior 0 1e-03 0.0 0.1 0.0 0.2 0.4 0.6 0.8 1.0 9 10 11 12 13 14 15 3 n(fm− ) R (km) Y. Lim & J.W. Holt, PRL 2018. Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 10 / 32 Tidal deformability from EOSs +169 +380 Λ1:4 = 350 114(EOSs) vs Λ1:4 = 190 120 (LIGO). − − 1000 800 600 Λ 400 200 0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 M(M ) Y. Lim & J.W. Holt, PRL 2018. Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 11 / 32 Probability distribution of central density I 1.2 1.2 1.0 1.0 M = 1.1M M = 1.2M 3 3 3 3 0.8 0.362 fm− nc σ 0.514 fm− 0.8 0.388 fm− nc σ 0.55 fm− ) ) c ≤ ± ≤ c ≤ ± ≤ n 3 3 n 3 3 ( 0.303 fm− nc 2σ 0.698 fm− ( 0.327 fm− nc 2σ 0.761 fm− ± ± P ≤ ≤ P ≤ ≤ 0.6 3 0.6 3 n˜c = 0.416 fm− n˜c = 0.443 fm− PDF, 0.4 PDF, 0.4 0.2 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.2 0.4 0.6 0.8 1.0 1.2 1.4 3 3 nc (fm− ) nc (fm− ) 1.2 1.2 1.0 1.0 M = 1.3M M = 1.4M 3 3 3 3 0.8 0.415 fm− nc σ 0.589 fm− 0.8 0.444 fm− nc σ 0.632 fm− ) ) c ≤ ± ≤ c ≤ ± ≤ n 3 3 n 3 3 ( 0.353 fm− nc 2σ 0.832 fm− ( 0.381 fm− nc 2σ 0.91 fm− ± ± P ≤ ≤ P ≤ ≤ 0.6 3 0.6 3 n˜c = 0.47 fm− n˜c = 0.497 fm− PDF, 0.4 PDF, 0.4 0.2 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.2 0.4 0.6 0.8 1.0 1.2 1.4 3 3 nc (fm− ) nc (fm− ) Figure: Lim & Holt, Eur. Phys. J. A 55, 209 (2019) Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 12 / 32 Probability distribution of central density II 1.2 1.2 1.0 1.0 M = 1.5M M = 1.6M 3 3 3 3 0.8 0.475 fm− nc σ 0.682 fm− 0.8 0.503 fm− nc σ 0.749 fm− ) ) c ≤ ± ≤ c ≤ ± ≤ n 3 3 n 3 3 ( 0.41 fm− nc 2σ 1.004 fm− ( 0.424 fm− nc 2σ 1.144 fm− ± ± P ≤ ≤ P ≤ ≤ 0.6 3 0.6 3 n˜c = 0.53 fm− n˜c = 0.569 fm− PDF, 0.4 PDF, 0.4 0.2 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.2 0.4 0.6 0.8 1.0 1.2 1.4 3 3 nc (fm− ) nc (fm− ) 1.2 1.2 1.0 1.0 M = 1.7M M = 1.8M 3 3 3 3 0.8 0.541 fm− nc σ 0.819 fm− 0.8 0.585 fm− nc σ 0.894 fm− ) ) c ≤ ± ≤ c ≤ ± ≤ n 3 3 n 3 3 ( 0.459 fm− nc 2σ 1.266 fm− ( 0.498 fm− nc 2σ 1.387 fm− ± ± P ≤ ≤ P ≤ ≤ 0.6 3 0.6 3 n˜c = 0.608 fm− n˜c = 0.653 fm− PDF, 0.4 PDF, 0.4 0.2 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.2 0.4 0.6 0.8 1.0 1.2 1.4 3 3 nc (fm− ) nc (fm− ) Figure: Lim & Holt, Eur. Phys. J. A 55, 209 (2019) Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 13 / 32 3 2 1 3 2 1 0 3 2 1 3 2 1 0 10− 10− 10− 10− 10− 10− 10 10− 10− 10− 10− 10− 10− 10 1.6 600 PNM32 PNM25 PNM32 PNM25 ) 2 1.4 400 g cm 4 . 45 1 1.2 Λ (10 338 . 1 1.0 200 I 0.8 0 5 10 15 20 25 30 35 10 15 20 25 30 35 5 10 15 20 25 30 35 10 15 20 25 30 35 3 3 3 3 p2n0 (MeV fm− ) p2n0 (MeV fm− ) p2n0 (MeV fm− ) p2n0 (MeV fm− ) 2 1 2 1 0 10− 10− 10− 10− 10 100 0.11 800 3.5 Λ = 37.109 + 181.540 (I45) 0.6 − R = 0.999986 0.10 xy 600 ) 3 − ) 0.5 3 0.09 − 1 Λ 10− 400 (fm t 0.08 (MeV fm n 0.4 t p 200 0.07 M = 1.338M 0.3 0.06 0 10 2 30 40 50 60 70 80 30 40 50 60 70 80 1.0 1.2 1.4 1.6 − 3 3 45 2 L (MeV fm− ) L (MeV fm− ) I (10 g cm ) Figure: Lim & Holt, EPJA 2019 Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 14 / 32 2 1 0 1 0 10− 10− 10 10− 10 3.0 Smooth high-density prior Modified high-density prior Miller 2.5 Riley ) 2.0 M ( 1.5 M 1.0 0.5 0.0 Posterior : Mmax > 2.59M Posterior : Mmax < 2.59M 3.0 2.5 ) 2.0 M ( 1.5 M 1.0 0.5 0.0 9 10 11 12 13 14 15 9 10 11 12 13 14 15 R (km) R (km) Figure: Mass radius confidence intervals, NICER, PNM, SNM, GW170817, GW190425, arXiv:2007.06526 Yeunhwan Lim (EWHA) Nuclear Equation of State and Neutron Stars JUL 14, 2021 15 / 32 Mass radius of neutron stars using various constraints (Y.Lim and A.
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