Class eos_tov_polytrope (o2scl)

O2scl_eos : Class List

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

eos_tov_polytrope()
inline virtual ~eos_tov_polytrope()
void set_coeff_index(double coeff, double index)

Set the coefficient and polytropic index.

void set_baryon_density(double nb, double ed)

Set the baryon density.

virtual double ed_from_pr(double pr)

From the pressure, return the energy density.

virtual double pr_from_ed(double ed)

From the energy density, return the pressure.

virtual double nb_from_ed(double ed)

From the energy density, return the baryon density.

virtual double nb_from_pr(double pr)

From the pressure, return the baryon density.

virtual double ed_from_nb(double nb)

From the baryon density, return the energy density.

virtual double pr_from_nb(double nb)

From the baryon density, return the pressure.

virtual void ed_nb_from_pr(double pr, double &ed, double &nb)

Given the pressure, produce the energy and number densities.

Protected Attributes

double nb1

The baryon density at ed1.

double ed1

The energy density for which the baryon density is known.

double pr1

The pressure at ed1.

double K

Coefficient (default 1.0)

double n

Index (default 3.0)