# Astro- modelling a white dwarf via polytrope

laam
have solved the lane - emden eqn numerically for scaled radius, and the derivative of scaled pressure with respect of scaled radius, are given the eqn of state, n, and mass, how would i go about working out the central density and the radius?
thanks

## Answers and Replies

pattiecake
Huh? Sorry, but can you restate that a little more clearly? Maybe include the equations you worked with too?

Widdekind
have solved the lane - emden eqn numerically for scaled radius, and the derivative of scaled pressure with respect of scaled radius, are given the eqn of state, n, and mass, how would i go about working out the central density and the radius?
thanks

The Lane-Emden Equation only generates finite "stars" for low Polytropic Indices (0 to 4). For those indices, the maximum Scaled Radius is some constant (eg., Pi or sqrt(6)). Thus, the maximum "actual radius" is just that constant multiple of the Scale Length:
$$S_{n} = \sqrt{ \frac{(n+1) k_{B}}{4 \pi G m} \frac{T_{c}}{\rho_{c}} }$$​
The central density & temperature are Free Parameters*.
* For derivation, see: https://www.physicsforums.com/showthread.php?t=278009 [post #8]