Equation of state for compact stars Lecture 1 - LUTh
Equation of state for compact stars Lecture 1 - LUTh
Equation of state for compact stars Lecture 1 - LUTh
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Electrons<br />
Relativity parameter (<strong>of</strong>ten used instead <strong>of</strong> ne)<br />
xr ≡ pF<br />
<br />
ρ6〈Z〉<br />
≈ 1.00884<br />
mec A ′<br />
1/3 , (1)<br />
where<br />
pF = kF = (3π 2 ne) 1/3 , (2)<br />
is the electron Fermi momentum and ρ6 ≡ ρ/106 g cm−3 . The Fermi energy<br />
ɛF = c 2<br />
<br />
(mec) 2 + p2 F<br />
Notice: electron rest energy mec 2 is included. The electron Fermi temperature is<br />
where<br />
(3)<br />
TF = Tr (γr − 1) , (4)<br />
Tr = mec 2 /kB ≈ 5.930 × 10 9 K (5)<br />
is the relativistic temperature unit, γr = √ 1 + xr 2 , and kB is the Boltzmann<br />
constant. The electron gas is non-relativistic at T ≪ Tr and xr ≪ 1, and it is<br />
ultrarelativistic at xr ≫ 1 or T ≫ Tr. It is nondegenerate at T ≫ TF and strongly<br />
degenerate at T ≪ TF.<br />
Pawe̷l Haensel (CAMK) EOS <strong>for</strong> <strong>compact</strong> <strong>stars</strong> <strong>Lecture</strong> 1, IHP Paris, France 8 / 54
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