# Numerical Integration of Chandrasekhar's Equation

1. Oct 15, 2016

### vmr101

1. The problem statement, all variables and given/known data
We need to write an integrator for the Chandrasekhars Equation (CE) for White Dwarfs (WD) using python3/NumPy/Matplotlib. We then need to compute the structure of a WD made of our varying elements. We also need to compute and plot the mass-radius relation for WD.

2. Relevant equations
We are given equations for C1, C2, K, eta, alpha, Radius, Mass and density.
rho = C2*x3=C2*zc3(phi2-1/(zc2))3/2

3. The attempt at a solution
I have never used python3 before so this is a bit of a challenge.
My script sets up all the constants and variables, sets up the arrays.
#then uses the initial conditions and sets an array for the ce
#then sets the integrator as rk4
#then integrates the CE
#calculates rho, alpha, p, temp, r
M = ((4*pi)/c2**2)*(((2*c1)/(pi*G))**(3/2))*((-x**2)*y[:,0])
#Plot r vs rho, r vs temp etc..

I need to figure out where to vary zc to find a certain WD mass
Any suggestions would be much appreciated.

Last edited: Oct 15, 2016
2. Oct 15, 2016

Your line where you have "this is where I get my error" needs a phi^2 in place of the $(1/zc)^2$.

3. Oct 15, 2016

### vmr101

I just noticed and updated this too! Thanks for confirming it for me.

Looks like it produces a density plot, but I need to vary zc to suit the WD mass.
Also my mass isnt plotting anything.

#### Attached Files:

• ###### rho.pdf
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14.1 KB
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Last edited: Oct 16, 2016
4. Oct 17, 2016

### vmr101

This was mostly python issues, and not issues with the physics itself.
I managed to work through it.