Equation of state for compact stars Lecture 1 - LUTh

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

Instructive figure Comparison of the fit (25) with the Debye-Hückel (see, e.g., Landau & Lifshitz Stat. Phys. 1, Abe (1959), and Cohen-Murphy (1969) approximate expressions valid at small Γ ≪ 1 and with very precise extensive Monte Carlo and HNC calculations. It is clear that Coulomb contribution to the EOS of strongly-coupled OCP with Γ > 1 is difficult to calculate. One has to be very careful, and not use approximate low-Γ expressions if Γ > 1! Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 20 / 54
N = N N = Ni = n N V Strongly coupled Coulomb liquid In the gaseous regime the Coulomb energy is small, |Uii| ≪ NkBT , so that the Coulomb binding is lower than the thermal energy of ions, and the ions are nearly free. In the strongly coupled liquid (Γ 1) one has |Uii| NkBT and the Coulomb energy exceeds the thermal one. In this regime the ions are bound in Coulomb potential wells (whose depth is ∼ Z 2 e 2 /ai) and slightly oscillate there due to thermal motion. In a Coulomb liquid there is no exact order and the wells slowly migrate within the liquid. In the limit of Γ ≫ 1 from Eq. (25) one obtains the linear Γ dependence, Uii/NkBT ≈ A1 Γ. In this limit Uii ≈ NA1Z 2 e 2 /ai and Pii ≈ A1 n N Z 2 e 2 /(3ai) are nearly independent of temperature. Numerical factor A1 is very close to the value A IS 1 = −0.9 predicted by the ion-sphere model. In that model ne = const., Coulomb energy of one ion sphere is equal to −0.9Z 2 e 2 /ai: it is a sum of (repulsive) electron-electron contribution 0.6Z 2 e 2 /ai, and the attractive electron-ion term −1.5Z 2 e 2 /ai (see, e.g., Shapiro & Teukolsky 1983). Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 21 / 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: Coulomb gas of ions (id)i Ideal cla
Page 23 and 24: Melting - phase transition The soli
Page 25 and 26: Quantum zero-point vibrations and m
Page 27 and 28: Other corrections relevant to elect
Page 29 and 30: Ground state crust - T = 0 Notation
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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