Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

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Stony Brook UniversityThe Graduate SchoolYeunhwan LimWe, the dissertation committee for the above candidate for the Doctor of Philosophy degree,hereby recommend acceptance of this dissertation.James M. Lattimer – Dissertation AdvisorProfessor, Department of Physics and AstronomyMichael Zingale – Chairperson of DefenseAssociate Professor, Department of Physics and AstronomyAlan C. CalderAssistant Professor, Department of Physics and AstronomyDominik SchnebleAssociate Professor, Department of Physics and AstronomyDaniel M. DavisProfessor, Department of GeosciencesDepartment of Geosciences, SUNY Stony BrookThis dissertation is accepted by the Graduate School.Lawrence Martinii
Abstract of the DissertationTheory of nuclear matter of neutron stars and corecollapsing supernovaebyYeunhwan LimDoctor of PhilosophyinPhysicsStony Brook University2012Nuclear astrophysics is essential to microphysics for the complex hydrodynamicssimulation of numerical supernovae explosions and neutron star merger calculations.Because many aspects of equation of state (hereafter, EOS) includingsymmetry and thermal properties are uncertain and not well constrained by experiments,it is important to develop EOS with easily adjustable parameters.The purpose of this thesis is to develop the nuclear matter theory and an EOScode for hot dense matter. This thesis has two major parts. In the first part, wedevelop a Finite-Range Thomas Fermi (hereafter, FRTF) model for supernovaeand neutron star matter based on the nuclear model of Seyler and Blanchard,and Myers and Swiatecki. The nuclear model is extended to finite temperatureand a Wigner-Seitz geometry to model dense matter. We also extend the modelto include additional density dependent interactions to better fit known nuclearincompressibilities, pure neutron matter, and the nuclear optical potential.Using our model, we evaluate nuclear surface properties using a semi-infiniteinterface. The coexistence curve of nuclear matter for two-phase equilibriumis calculated. Furthermore we calculate energy, radii, and surface thickness ofclosed shell nuclei inwhich thespin-orbit interactions canbeneglected. To getanoptimized parameter set for FRTF, we explore the allowed ranges of symmetryiii
Page 1: Theory of nuclear matter of neutron
Page 5 and 6: To Jaenyeong, Jonghyun, and Jongbum
Page 7 and 8: 3.3 Optimized Parameter Set . . . .
Page 9 and 10: List of Figures1.1 Mass and radius
Page 11 and 12: SymbolsNuclear Physics SymbolE ener
Page 13 and 14: ω δt 90−10QtT cTaylor expansion
Page 15 and 16: List of Tables1.1 Range of Tables .
Page 17 and 18: Chapter 1IntroductionStars give us
Page 19 and 20: Since the mass of neutron star is d
Page 21 and 22: shown in Fig. 1.2, LS220 is the onl
Page 23 and 24: density:p = ρ2ρ o[ K9µ n = −B
Page 25 and 26: nuclear energy density functional i
Page 27 and 28: 2.3.2 Thermodynamic QuantitiesThe t
Page 29 and 30: point r and with momentum p isU n (
Page 31 and 32: Thus, in the case of zero temperatu
Page 33 and 34: For standard nuclear matter, u = 1
Page 35 and 36: a α L α U β L β U σ0.5882 1.11
Page 37 and 38: Figure 2.2: Bulk equilibrium of T =
Page 39 and 40: Figure 2.4: Coexistence curves for
Page 41 and 42: proton fraction x are irrelevant fo
Page 43 and 44: potential model analogue for the Ha
Page 45 and 46: with the convention that z II is th
Page 47 and 48: Figure 2.10: The surface tension of
Page 49 and 50: Figure 2.12: Contour plots of surfa
Page 51 and 52: 2.6.2 Dense Matter and the Wigner-S
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Figure 2.15: Proton number per unit
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Chapter 3Modified model† The trun
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We choose the value ǫ = 1/3. One m
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where∆V t = T oρ o[( ρρ o) ǫ[
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Q 1 to a small number also results
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where p = (S v ,L) and M ij = 1 ∂
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3.4 Nuclear Surface TensionCompared
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1.41.2FRTF II ω 0 , T=0 MeVFRTF II
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For the finite-range term, we use a
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Landau’s quasi-particle formula g
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The symmetry energy in nuclear matt
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Figure 4.2: The left figure shows t
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Figure 4.4: This figure shows the b
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Figure 4.5: In a neutron star, heav
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The energy exchange from the gradie
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Figure 4.8: The left panel shows th
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4.5 Astrophysical application4.5.1
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0.550.5GaussianFRTF IIFRTF I0.450.4
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neutron matter respectively. Those
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Table 5.3: Nuclear properties of si
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which aref Rc = a 0 +a 1 x+a 2 x 2
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parametrized[ht]504540EDF, Z nucFit
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Chapter 6Nuclear Equation of State
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Coulomb, and, symmetry part [24], i
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We can eliminate N s , leading to t
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pressure from pure neutron matter,
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2.52GSRsSGISIVSkaSkI1SkI2SkI3SkI5St
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HNsn, p, α,eFigure 6.7: In the Wig
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Table 6.1: Surface tension analytic
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free energy density for the alpha p
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Here s ′ = ∂s(u)/∂u.The minim
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6.5.2 Determination of Coulomb surf
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gives analytic derivatives of therm
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200180160Atomic number, Y p =0.45,
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for Fermi integral. This fitting fu
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A.1 Taylor expansion integrationThe
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thenwhere0u − i+1 = fu− i +J
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We separate the two integrals as in
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Each w i can be obtained[ae −∆/
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By expanding e r 0/a −e −r 0/a
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M 3 2a 0.433 1p 0 (e 2 /a) √ π/3
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of find exact polynomial expression
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Appendix CPhase coexistenceBulk equ
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To summarize, we need to solve 5 eq
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D.1 Non-uniform electron density ap
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Appendix ENuclear Quantities in Non
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Table E.1: Non-relativistic Skyrme
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[20] C.J. Pethick and D.G. Ravenhal
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