# Equation of State¶

Consider a composite polytrope composed of $$\nreg$$ regions extending from the origin out to the stellar surface. In the $$i$$’th region ($$1 \leq i \leq \nreg$$), the pressure $$P$$ and density $$\rho$$ are related by the polytropic equation-of-state

(11)$\frac{P_{i}}{P_{i,0}} = \left( \frac{\rho_{i}}{\rho_{i,0}} \right)^{(n_{i} + 1)/n_{i}}$

where the normalizing pressure $$P_{i,0}$$ and density $$\rho_{i,0}$$, together with the polytropic index $$n_{i}$$, are constant across the region but may change from one region to the next. At the $$\nreg-1$$ boundaries between adjacent regions, the pressure and interior mass $$M_{r}$$ are required to be continuous, but the density may jump.