The Stellar Interior Construction Site

The form will below can be used to generate a "Zero Age Main Sequence" (ZAMS) stellar model. Such a model is a reasonably appropriate snapshot of the interior state of a star shortly after its formation, i.e., before it has had a chance to substantially alter its composition (and therefore structure) through nucleosynthesis.

The model represents the solution to the equations of stellar structure - the ballance between the force of gas pressure pushing down and the gas pressure pushing back (see the equation for hydrostatic equilibrium). Indeed, it has always amazed me that there are only really four equations involved in this, plus one "approximation:"

1. Conservation/continuity of mass
2. Hydrostatic equilibrium
3. Energy generation through nucleosynthesis
4. Energy transport (either via radiation, or convection - convection needing a semi-empirical treatment)

This form will execute a series of programs collectively known as "Starcode", written by Steve Ratcliff, which will solve the above equations and print out a table of temperature, pressure, etc., from your inout parameters.

The basic procedure consists of two steps:
1) Generating an opacity table for a specific composition.
2) Compute a ZAMS model which satisfies the equations of stellar structure.

The calculation of the opacity table is straight forward and will take place once your initial choice of composition has been made (you need only specify X and Z). It uses the Alexander et al opacities (which include molecules and grains) for log10 T < 4.0, and the Los Alamos tables + Hubbard-Lampe/Canuto tables for opacities for log10 T >= 4.0.

Output:
There will be a bit of stuff output once you've run the program. The first table of numbers is an initial guess as to the structure of the star. This guess is then itterated until a consistent state is obtained. The bits you are probably most interested in are found in the last tablse of numbers - the final state of the converged model.

At the top will be a summary of the input parameters. Something like:

MASS= 1.000 X= 0.730000 Y= 0.240000 Z= 0.030000

This will be followed by some other information about the overall properties of the initial model, including the first guess as to its luminosity relative to the Sun, effective temperature, radius rrelative to the Sun, central core temperature and density, bolometric magnitude, and the masses of the convective core and envelope.

What you want to look for is further down - at the final (hopefully converged) equilibrium model for the star. This will be after the line:

After X SCH iterations:

where X is some number. This will be followed by the basic properties of the final model:

Log L = -0.3170 Log Tsurf = 3.6530 Log Tc = 7.1430 Log RHOc = 1.9949

Again, L is the luminosity (with repsect to the Sun), Tsurf is the surface temperature, Tc is the core temperature, and RHOc is the core density (in gm/cm^3).

What comes next is a listing of the changes in the models as the itterations were made, and then yet another statment of the model's basic properties:

MASS= 1.000 X= 0.730000 Y= 0.240000 Z= 0.030000
LOG L=-0.3073 LOG TEF= 3.7273 RADIUS= 0.8249 LOG TC= 7.1366 LOG RHOC= 1.9917
M BOL= 5.508 MCC= 0.001 MCE= 0.950

Everything should be familiar to you in this line, except maybe MCC and MCE, which is the mass in the convective core and convective envelope (respectively).

This is followed by the age of the model (naturally zero) and a timestep for further evolution (should you want to start following the changes with time - see the evol page):

TIME= 0.00000000E+00YEARS, DT= 1.64387E+09 YEARS

Next will be a formatting statement which can be ignored:

MAIN POINTS 2 -1 -1 -1 -1 -1 -1 -1 -1 72

Then finally, the model itself. The columns are:

K - depth point number.
MR - mass interior to the depth point.
R - radius at the depth point.
LR - luminosity at the depth point.
LOG T - log of the temperature at the depth point.
LOG RHO - log of the density at the depth point.
X - composition (H) at the depth point.
Y - composition (He) at the depth point.
He3 - composition (He3) at the depth point.
lg grR/grA - a measure of convective stability (positive = convection).

The required inputs are composition (X and Z), M (the total stellar mass in solar units), FM (the envelope mass in solar units), and Alpha (the mixing length ratio):