EVOLUTION
The Stellar Evolution Demonstration Codes
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"Stellar Interiors," 2nd ed., by Hansen, Kawaler, & Trimble
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There are three executable codes for Windows based PCs in this
directory. They were written and copyrighted by Andy Odell (Department of
Mathematics and Physics, University of Tasmania, Hobart, Tasmania, Australia)
and Dean Pesnell (Nomad Research Inc., Arnold, MD, USA), whom we thank for
letting us include the code on our CD-ROM. The codes are based on the
"Paczynski code." The description of the codes and their use is given
below (written by Odell & Pesnell). The codes give plenty of very informative
graphical output!
If you have questions regarding the codes you might try contacting
one of the code's authors at EVOLUTION@NOMADRESEARCH.COM . There is also
a website at WWW.NOMADRESEARCH.COM
that has other material, such as a
sequence of plots of velocity fields for non-radial pulsations.
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The User Friendly Paczynski Code
Put the CD-ROM in the drive of a PC and open its directory. Double-
click on the MAINSEQ.BAT to run the Main Sequence model builder.
The model composition is set by the opacity tables to X=0.70, Z=0.03
and alfa (mixing length to pressure scale height) is 1.0; the mass in
the static envelope is 10% the mass of the star.
The program will ask for the mass of the star you would like to generate;
you can choose either 1.0 or 10.0 Msun.
You must guess log L/Lsun, log Teff (K), log Tc (K), and log rhoc
(central density in g/cc). If your guess is really far from a usable value, it
will remind you of the units to use and ask again. If you are close but not
close enough, it will just ask for a better guess.
The program draws a graph of the first attempt to fit (i.e. using the
guessed boundary conditions), plotting R/Rsun (in red), L/Lmax (in blue),
T/Tc (magenta), and rho/rhoc (density, in yellow), as a function of M/M*.
Note that the curves have discontinuities at M/M* = 0.5 - this is because
your first guesses to boundary conditions are not exactly right. Push
and the program updates your guesses with better ones (hopefully)
and tries again. Each time you push , the discontinuities should
get smaller, or at least tend that way.
When the model converges, the program draws a final graph which is a
theoretical H-R diagram of your model, with two well-determined stars
marked in white, with error bars. Spica is a binary with primary being
11 Msun and somewhat evolved from the main sequence, and the sun is a
1 Msun star close to the main sequence.
Sometimes your initial guesses create a situation that doesn't
converge, but rather jumps between two bad fits, one on either side of
the correct one. If this happens, just try again, with somewhat
different initial guesses.
When you finish, close the windows.
To run the evolution code, double-click on EVOLVE.BAT. This program
allows you to choose 1 or 10 Msun, and draws a graph of model 0 (on the
ZAMS, the same as for the ZAMS) with the addition of a line for X (hydrogen
mass fraction; dark blue) and Y (helium mass fraction; green). Note
that the composition is constant throughout the star. Also of interest
is the line representing L/Lsun (light blue), because it tells where
the energy is generated in the star.
If you have chosen a 10 Msun star, there is a gray shaded region over the
central third of the mass indicating the extent of the convective core.
You will also notice that the energy generation is confined to the inner
few percent of the stellar mass; remember that the slope of this line is
epsilon, the energy generation rate. If you are computing a 1 Msun model,
there is no convective core, and the energy generation extends much
further out from the core.
Push (twice) to get model 1, the first evolved model. Note the time
given at the top of the screen, and also note the run of X and Y (chemical
composition) through the star. Push several more times, watching
these same features as the star evolves.
For the case of 10 Msun the shrinking convective core leaves a linear
decrease in hydrogen inward in mass, with a constant hydrogen abundance
in the still-convective region, whereas the 1 Msun star exhibits a
gradually decreasing hydrogen abundance inward toward the core. This is
a primary difference between massive and low-mass stars near the main
sequence which is reflected in the H-R diagram by considerably different
shaped tracks.
If you are doing the 1 Msun model, you will get to the correct age for
the sun at model 14; you will notice that the model is somewhat fainter
and cooler than the real sun. This is because we haven't chosen the
composition to be exactly solar. By the time you get to model 35, X
(hydrogen) is pretty much depleted in the core. By looking at the tables
presented in between the graphs, you can follow what your star is doing
in terms of observable characteristics - in particular, notice that from
one model to the next, the star is getting brighter and cooler at this
point, so it never looks exactly like the sun. Continue pushing
until you reach model 50, (age over 10 billion years) where the program
will quit.
If you are doing the 10 Msun model, you will notice a considerably
different hydrogen profile and luminosity distribution from the 1 Msun
case. By model 5, the X and Y are about equal in the core, and by
model 30, X has decreased to about zero in the core. Note that there
is still a convective region so that the place where X is depleted is
nowhere near hot enough to have helium formed. Thus the core of the
star must contract to heat this region; this is reflected in the
luminosity (light blue) curve, which takes on a double-humped shape.
Energy is still being produced by residual hydrogen being burnt in
the core, but contraction of the star outside of the convective region
contributes more and more to the luminosity. By model 45, the inner part
of the star is contracting quickly to produce the energy for the star to
shine, while the outer layers are expanding slightly, causing the
luminosity to drop in the region outside M/M* > 0.2. Note that this
star depletes hydrogen in the core in less than 16 million years - less
than 1% the age of the 1 Msun model.
When the evolution finishes, close the windows.
To see a summary of the evolution, double-click SUMMARY.BAT; this program
will give a graphical summary of important model stellar characteristics as
a function of time, and end with a theoretical H-R diagram with the model
track on it. It asks for the mass you would like to see and then plots
luminosity (L/Lsun) as a function of time. Note that the luminosity goes
up gradually, then very quickly; also note the time involved. will
change the graph to radius (R) and then effective temperature (Teff).
More 's will produce a graph of central temperature and central
density (log Tc and log rhoc; note these are logarithms!) and the central
hydrogen content (Xc). Finally a theoretical H-R diagram is made, showing
luminosity vs effective temperature.
A final program computes a gray stellar atmosphere (opacity not
wavelength dependent).
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