Learning Basics of Stellar Modelling

[jon]

I'm trying to teach myself some of the early basics of stellar modelling and hope to write some code to calculate conditions within the star

Assuming a constant and homogenous composition and simplified calculations of pressure equation of state and opacity. Simplified assumption of adiabatic convection.

From what I've been able to figure out:

1. Use the ideal gas law and radiation pressure equation to solve for local density.

2. Use local density to determine opacity and energy generation rate of that layer.

3. Now use the differential equations for pressure, internal mass, temperature and luminosity to solve for those quanitities. Convert them to "difference equations" and solve for an outer layer and an inner layer that is very close to the outer.

4. Now use those quantities to solve for a new local density as in step one

5. Repeat process, going deeper into the star.

Is this a simplified way of doing this, or at least a decent starting point?

I'd appreciate any input, keeping in mind I am just learning the basics

 

[enigma]

I'm no expert on this, so take it with a grain of salt:

You will probably need to use van der Waals (or other) equations of state. At the high temperatures in the star, it can't be modeled as an ideal gas.

You're probably going to need to have the program iterate several times to get it to converge.

 

[Kurdt]

Enigma,

The high temperature of stars makes them the perfect candidates for the ideal gas law as the inter-atomic forces are negligible with respect to the thermal energy present and the ideal gas law is the equation of state for stars.

Kurdt

 

[Kurdt]

Jon,

Your approach seems reasonable. May i suggest doing some research on the topic of fluid mechanics. Most modelling of stars and stellar material are done on the basis of this theory which also takes into account important magnetic effects.

 

[Nereid]

Just one or two quick inputs:
- be careful that you don't enter into white dwarf (degenerate electron gas), neutron star, ... territory (test your densities at each stage)
- 'opacity' isn't all that straight-forward: the composition and temperature of the gas is of considerable importance (at least until everything's fully ionised)
- decide, for each layer, whether energy transport is radiation, convection, or both; this will make your code both easier and more difficult to write
- you forgot (?) to say your star isn't rotating; fast rotation makes things more 'interesting'

 

[chroot]

Pick up a book on astrophysics like Carrol and Ostlie's "Intro to Modern Astrophysics." You'll find lots of codes (programs) in books like that for calculating models of stars, along with their derivations.

- Warren

 

[jon]

Thanks to everyone who answered my query! A couple of things:

-No I'm only going to be looking at main sequence adult stars. Really since it's my first attempt I am using textbook values for temp/press/density within the sun as the standard for success of my model

-I'm using equations for bound-free, free-free, and electron scattering with simplified assumptions for most of the constants and assuming constant composition throughout

-Yes, I've managed to included the delimiter between convection and radiation and it seems to kick into gear approximately where it is expected to at about 0.28 solar radius depth, indicating a change to mainly radiative transport. For now I am assuming one type of transport will be dominant enough over the other to limit it to only one kind at a time.

-No I'm not including rotation, magnetic effects, etc...trying to keep things very simple while I learn the basic structure.

So far I've had pretty good success with modelling the sun, down to 0.5 solar radius depth. My temperatures are bang on --though my density/pressure values are a little off. I haven't yet included radiation term in the pressure equation of state though, so this might make a difference.

I have a question though...the luminosity is constant down to about 0.25 solar radius then once there is energy generation the interior luminosity decreases as I go deeper...would it be a reasonable method to have this luminosity differential equation kick in once temperature reaches some critical value that will ignite the proton-proton reaction? Is there a specific temperature that will "generally" start nuclear reactions? Also within stars that are not too different from the sun is the proton-proton reaction much more dominant over CNO cycle, regarding its contribution to the energy generation rate? ...ie...could I assume proton-proton only and still get reasonable results?


Thanks in advance for anyone that can help out!

 

[Kurdt]

In stars like the sun and of much lower mass the proton-proton reaction is the most dominant. Once we start climbing to the higher mass stars the CNO cycle starts to kick in and become dominant. The luminosity is proportional to the amount of energy generating mass beneath a spherical shell of the sun so it should be fairly easy to set up a radially dependant integral for luminosity at different shells of specific radius.

 

[travwg33]

Hey I would love to learn the basics of this too, where did you learn this? A website a book?