Equation of state for compact stars Lecture 1 - LUTh

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

Latent heat at freezing The latent heat released at freezing equals Qlatent = Um,liq − Um,solid ≈ ∆Ui, (28) where and Um,liq and Um,solid are the corresponding values of the internal energy at T = Tm. Qlatent is only ≈ 0.5% of the ion contribution Ui, which is only a tiny fraction of the total internal energy U (mainly determined by degenerate electrons at the conditions mentioned above). Nevertheless, the absolute value of Qlatent (≈ 0.76k BT per ion) is a substantial fraction of thermal thermal energy of the ions. It is sufficient, for instance, to delay the cooling of old white dwarfs with crystallizing cores (Chabrier 1999, Hansen 2004). =⇒ important for the white dwarf chronology. Note: dense matter may form a supercooled liquid and freeze at T < Tm. Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 24 / 54
Quantum zero-point vibrations and melting At high densities the amplitude of zero-point quantum vibrations of ions may become comparable to the lattice constant and make lattice ordering difficult: Tm(ρ) becomes then significantly lower than the classical melting temperature and at some critical density ρm zero-point vibrations destroy the lattice even at T = 0 (i.e., Tm(ρm) = 0). Hence at ρ > ρm the liquid does not solidify at all, and one obtains the quantum liquid domain at T Tpi and ρ ρm. In that domain spin statistics of ions (fermion or boson) is important. In practice the appearance of quantum liquid is actually important only for hydrogen and helium in the outer neutron star envelope, where zero-point motion drastically suppresses the crystallization of these ions. Pawe̷l Haensel (CAMK) EOS for compact stars Lecture 1, IHP Paris, France 25 / 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: Melting - phase transition The soli
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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