Class eos_tov_polytrope (o2scl)¶
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class
o2scl
::
eos_tov_polytrope
: public o2scl::eos_tov¶ Standard polytropic EOS \( P = K \varepsilon^{1+1/n} \).
The quantity \( K \) must be in units of \( \left(M_{\odot}/km^3\right)^{-1/n} \) .
For a polytrope \( P = K \varepsilon^{1+1/n} \) beginning at a pressure of \( P_1 \), an energy density of \( \varepsilon_1 \) and a baryon density of \( n_{B,1} \), the baryon density along the polytrope is
\[ n_B = n_{B,1} \left(\frac{\varepsilon}{\varepsilon_1}\right)^{1+n} \left(\frac{\varepsilon_1+P_1}{\varepsilon+P}\right)^{n} \, . \]Similarly, the chemical potential is\[ \mu_B = \mu_{B,1} \left(1 + \frac{P_1}{\varepsilon_1}\right)^{1+n} \left(1 + \frac{P}{\varepsilon}\right)^{-(1+n)} \, . \]The expression for the baryon density can be inverted to determine \( \varepsilon(n_B) \)\[ \varepsilon(n_B) = \left[ \left(\frac{n_{B,1}} {n_B \varepsilon_1} \right)^{1/n} \left(1+\frac{P_1}{\varepsilon_1}\right)-K\right]^{-n} \, . \]Sometimes the baryon susceptibility is also useful\[ \frac{d \mu_B}{d n_B} = \left(1+1/n\right) \left( \frac{P}{\varepsilon}\right) \left( \frac{\mu_B}{n_B}\right) \, . \]- Idea for Future:
The simple formulation fo the expressions here more than likely break down when their arguments are sufficiently extreme.
Public Functions
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eos_tov_polytrope
()¶
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~eos_tov_polytrope
()¶
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void
set_coeff_index
(double coeff, double index)¶ Set the coefficient and polytropic index.
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void
set_baryon_density
(double nb, double ed)¶ Set the baryon density.
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double
ed_from_pr
(double pr)¶ From the pressure, return the energy density.
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double
pr_from_ed
(double ed)¶ From the energy density, return the pressure.
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double
nb_from_ed
(double ed)¶ From the energy density, return the baryon density.
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double
nb_from_pr
(double pr)¶ From the pressure, return the baryon density.
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double
ed_from_nb
(double nb)¶ From the baryon density, return the energy density.
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double
pr_from_nb
(double nb)¶ From the baryon density, return the pressure.
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void
ed_nb_from_pr
(double pr, double &ed, double &nb)¶ Given the pressure, produce the energy and number densities.