Numerical Integration of Chandrasekhar's Equation

[vmr101]

Homework Statement

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.

Homework Equations

We are given equations for C₁, C₂, K, eta, alpha, Radius, Mass and density.
rho = C₂*x³=C₂*z_c³(phi²-1/(z_c²))^3/2

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.

 

[Charles Link]

Homework Statement

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.

Homework Equations

We are given equations for C₁, C₂, K, eta, alpha, Radius, Mass and density.
rho = C₂*x³=C₂*z_c³(phi²-1/(z_c²))^3/2

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.
ce1 = functools.partial(le.ce,zc=zc) #this uses the initial conditions and sets an array for the ce
a = functools.partial(le.rk4,h=h) #this sets the integrator as rk4
x, y = le.integrate(ce1,x,y,a,t,zc) #this integrates the CE

rho = c2*zc**3*(y[:,0]**2 -1/zc**2)**(3/2)
alpha = ((2*c1)/(pi*G))**(1/2) * 1/(c2*zc)
pr = K*rho**gamma
temp = (pr*mewe)(rho/Rgas) ##error here
r = alpha*x
M = ((4*pi)/c2**2)*(((2*c1)/(pi*G))**(3/2))*((-x**2)*y[:,0])
Mmax = 4*pi*(2.01824)*(K/pi*G)**(3/2)
#Plot r vs rho, r vs temp etc..

Any suggestions would be much appreciated.

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

 

[vmr101]

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

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 isn't plotting anything.

 

[vmr101]

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