Equation of state for compact stars Lecture 1 - LUTh

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

The electron pressure P = P (e) id versus density for an ideal strongly degenerate electron gas (the solid line) together with non-relativistic and ultrarelativistic asymptotes (the dotted and dashed lines). The internal energy is given by V =volume of plasma U (e) id V 4 k = √ BT π λ3 I3/2(χ, tr) + tr I5/2(χ, tr) e . (22) Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 18 / 54
Coulomb gas of ions (id)i Ideal classical gas. The free energy of N = N N = n N V (n N = ni) - non-relativistic classical ions is F (i) id = N N kBT ln(n N λ 3 i /gi) − 1 , (23) where gi is the spin degeneracy (the rest-mass energy is not included here). The internal energy and pressure contributions from the ideal gas of ions are simply U (i) id = 3 2 N N kBT, P (i) id = n N kBT. (24) (ii)Ion correlations Additional terms from Coulomb interactions. In a classical OCP the quantity Fii/N N kBT is a function of a single argument Γ. This function determines all other ”excess” quantities which can also be expressed via some universal functions of Γ. Methods for calculation of the ”ii” term - Monte Carlo simulations and hypernetted chain (HNC) method. Very precise fitting formula to numerical results of DeWitt et al. (1996) is uii ≡ Uii kBT N N = Γ 3/2 where Ai and Bi are constants. A1 A3 √ + + A2 + Γ 1 + Γ B1 Γ2 B2 + Γ + B3 Γ 2 , (25) B4 + Γ2 Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 19 / 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: Pressure - electrons - main term (i
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 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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