Numerically simulating stellar pulsation using a "one zone" model

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patrykh18
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Homework Statement
Write a code that will simulate stellar pulsation using a "one zone" model, and plot various graphs
Relevant Equations
The relevant equations are given in the image attached
The question is taken from An Introduction to Modern Astrophysics by Carroll and Ostlie. I did manage to do the entire question and plot the relevant graphs but I just want to to investigate a bit more. For example I want to look at how the graph would like in the case of the Sun. I don't know what the right value for pressure I would need to input in order to get the right graph, with the right amplitude and period. The value for P in part d of the question seems arbitrary to me.

Printed textbook problem 13 on nonlinear radial pulsation of a one-zone stellar model, showing Newton's second law equation (20), velocity definition (21), adiabatic relation (22), derived relation (23), and difference-form equations (24) and (25).


Textbook page with homework part (d) and (e): equations (24) v_f = v_i + (4πR_i^2 P_i/m - GM/R_i^2)Δt, (25) R_f = R_i + v_f Δt, and equation (14) Π = 2π / sqrt((4/3)πGρ0(3γ - 4)), with given values for a Cepheid model star.
 
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Discussion

Any help would be appreciated. Question: Consider a gaseous sphere in hydrostatic equilibrium. Assume that the gas is ideal, with no magnetic field and that the equation of state is given by P = Kρ^γ, where γ is a constant.(a) Derive an expression for the density as a function of radius.(b) Assume that the density at the center of the sphere is ρ_c and that the sound speed is given by c_s = (γP/ρ)^1/2. Obtain an expression for the frequency of radial pulsations of the sphere.(c) Show that for small amplitudes, the frequency is independent of the amplitude.(d) Assuming that P = P_0 cos (ωt), plot the behavior of the density as a function of r for two different values of ω.