Once a low-mass star leaves the main sequence and ascends the red giant branch, its luminosity is provided by hydrogen burning in a thin shell surrounding a degenerate helium core. As hydrogen is burned in the shell, the mass of the helium core grows and the star continues to ascend the giant branch. Both the luminosity and radius of red giants can be written as functions of their helium core mass (nearly independent of any other quantity). These expressions are represented (empirically) by:
where m c is the helium core mass, and L and R are the luminosity and radius of the (entire) red giant, respectively. Use these relations to compute the evolution of a star (L and R as functions of time) as it ascends the red giant branch. Take the initial core mass value to be m c,i = 0.25MSun and the final value (at the tip of the giant branch) to be m c,f = 0.45MSun . Note that,
where ∆M/∆t represents the rate that hydrogen is burned in the shell around the core, and is proportional to the rate of growth of the degenerate helium core. Plot the radius, luminosity, and effective temperature of the star as a function of time on the giant branch. Also, plot the track of the evolving giant on an H-R diagram (i.e., log L versus log Te ). Assume a standard composition of X = 0.70, Y = 0.28, Z = 0.02.
By purchasing this product, you will get the step by step solution of the above problem in pdf format and the corresponding images, Fortran code, and latex file where you can edit the solution. I am also available to help you with any possible question you may have.
If you have any question about this solution, please contact to email@example.com
I'm available to help students with their homework assignments and computer simulation projects.