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Shamrock 2025.10.0
Astrophysical Code
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Shamrock 2025.10.0
Astrophysical Code
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Piecewise polytropic EOS from Machida et al. (2006) More...
#include <shamphys/include/shamphys/eos.hpp>
Static Public Member Functions | |
| static constexpr T | soundspeed (T P, T rho, T rho_c1, T rho_c2, T rho_c3) |
| static constexpr T | temperature (T P, T rho, T mu, T mh, T kb) |
| static constexpr T | pressure (T cs, T rho, T rho_c1, T rho_c2, T rho_c3) |
Piecewise polytropic EOS from Machida et al. (2006)
Uses different gamma values across density thresholds for gravitational collapse modeling.
Sound speed: \( c_s = \sqrt{\frac{\gamma P}{\rho}} \) where \( \gamma \) depends on density:
\[ \gamma = \begin{cases} 1.0 & \rho < \rho_{c1} \\ 7/5 & \rho_{c1} \leq \rho < \rho_{c2} \\ 1.1 & \rho_{c2} \leq \rho < \rho_{c3} \\ 5/3 & \rho \geq \rho_{c3} \end{cases} \]
Pressure (piecewise):
\[ P = \begin{cases} c_s^2 \rho & \rho < \rho_{c1} \\ c_s^2 \rho_{c1} \left(\frac{\rho}{\rho_{c1}}\right)^{7/5} & \rho_{c1} \leq \rho < \rho_{c2} \\ c_s^2 \rho_{c1} \left(\frac{\rho_{c2}}{\rho_{c1}}\right)^{7/5} \left(\frac{\rho}{\rho_{c2}}\right)^{1.1} & \rho_{c2} \leq \rho < \rho_{c3} \\ c_s^2 \rho_{c1} \left(\frac{\rho_{c2}}{\rho_{c1}}\right)^{7/5} \left(\frac{\rho_{c3}}{\rho_{c2}}\right)^{1.1} \left(\frac{\rho}{\rho_{c3}}\right)^{5/3} & \rho \geq \rho_{c3} \end{cases} \]
Temperature: \( T = \frac{\mu m_H P}{\rho k_B} \)
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1.9.8