Equation of state for compact stars Lecture 1 - LUTh

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$J. Phys. A: Math. Gen. 32 (1999) - LUTH - Observatoire de Paris$

Formation of the crust in newly born neutron stars NS is born as a very hot object - T ∼ 10 11 K. Cools rapidly due to neutrino emission, and within hours the bulk of outer 1% of mass has T < 10 10 K, and within a year it gets cooled to ∼ 10 9 K. Mass fractions of different constituents of the outer envelope of a newly born neutron star versus matter density in beta equilibrium at different temperatures T9 = T/(10 9 K) (after Haensel et al. 1996). Calculations are performed for the Lattimer & Swesty (1991) model of nuclear matter with a specific choice (K0 = 220 MeV) of the incompressibility of cold symmetric nuclear matter at the saturation density. After one year the thermal effects for ρ > 10 6 g cm −3 are negligible T = 0 approximation for the EOS is fine. Simplifying assumptions: single A, Z-nucleus; crust in the ground state. Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 28 / 54
Ground state crust - T = 0 Notation: enthalpy per nucleon = h; energy per nucleon=E; energy density - E. Neglect envelope of NS with ρ < 10 8 g cm −3 (it has mass < 10 −8 M⊙) - it could have been accreted, and the T -effects there might be significant. Consider crust at T = 0 and P = 0, i.e., h = E = E/nb. In this case the minimum energy per nucleon (ground state) is reached for a body-centered-cubic (bcc) lattice of 56 Fe, and is E( 56 Fe) = 930.4 MeV. It corresponds to ρ = 7.86 g cm −3 and nb = 4.73 × 10 24 cm −3 = 4.73 × 10 −15 fm −3 . Remark It is worth to mention that 56 Fe is not the most tightly bound free atomic nucleus. Binding energy per nucleon b ≡ [(A − Z)mnc 2 + Zmpc 2 − M(A, Z)c 2 ]/A in a nucleus with the ground-state mass M(A, Z) reaches maximum for 62 Ni, b( 62 Ni) = 8.7945 MeV, to be compared with b( 56 Fe) = 8.7902 MeV. Let us notice that b( 58 Fe) = 8.7921 MeV is also higher than b( 56 Fe). Ground state of matter at a given P or nb is called cold catalyzed matter. Cold - because T = 0. Catalyzed - because all reaction have been completed so that the ground state has been reached. Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 29 / 54
Page 1 and 2: Equation of state for compact stars
Page 3 and 4: Anticipation and prediction of neut
Page 5 and 6: EOS - an overview EOS of neutron st
Page 7 and 8: Plasma parameters Outer envelope: o
Page 9 and 10: Electrons - continued The density o
Page 11 and 12: ni = nN Ions The strength of the Co
Page 13 and 14: Ions - continued The scale-length t
Page 15 and 16: ρ − T diagram for the outer enve
Page 17 and 18: Pressure - electrons - main term (i
Page 19 and 20: Coulomb gas of ions (id)i Ideal cla
Page 21 and 22: N = N N = Ni = n N V Strongly coupl
Page 23 and 24: Melting - phase transition The soli
Page 25 and 26: Quantum zero-point vibrations and m
Page 27: Other corrections relevant to elect
Page 31 and 32: Ground state crust - T = 0 The latt
Page 33 and 34: Ground state crust - T = 0 - nuclei
Page 35 and 36: Matter should be in equilibrium wit
Page 37 and 38: Effective nucleon-nucleon interacti
Page 39 and 40: Nucleon density distribution in the
Page 41 and 42: Semi-classical - Thomas-Fermi metho
Page 43 and 44: Thomas-Fermi method - continued Neu
Page 45 and 46: Spherical unit cell radius rc, the
Page 47 and 48: Funny nuclei - ”nuclear pasta”
Page 49 and 50: Overall inner crust EOSs - SLy and
Page 51 and 52: Melting temperature Melting tempera
Page 53 and 54: Shear modulus of the crust Effectiv

Equation of state for compact stars Lecture 1 - LUTh

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