Short Description of the code HMS11 (B. Paczynski, Princeton, 1997)
                      *********************


      The program integrates stellar structure equations from the surface
inwards to the fitting point located at the mass fraction = 0.3 * M, and
from the center outwards to the fitting point.  The total mass of the star
M, the mass at the fitting point Mf, and the chemical composition X, Z, are
fixed.  The values of boundary parameters, two at the surface: effective
temperature Te and luminosity L, and two at the center: central temperature
Tc and central density rhc, are adjusted so as to make four physical
variables: temperature, density, radius and luminosity, continuous at the
fitting point.  The process is iterative, and it is continued until the
results of integrations carried from the surface (envelope) and from the
center (core) to the fitting point agree to within one part in 10,000.
 
      The fitting process is carried out by the subroutine sch, which uses
subroutines envel and core to integrate stellar structure equations, calculate
values of all physical quantities at the fitting point as a function of four
boundary parameters, and also the derivatives of the differences at the
fitting point with respect to the boundary parameters.  Subroutine sch uses
subroutine solve to solve a 4x4 matrix, and later calculates the corrections 
to the boundary parameters.
 
      All the information about "input physics" is provided with the 
subroutines state, opact and nburn that calculate the equation of state, the
opacities and the energy release in nuclear burning.  All these subroutines
give rather crude description of the real physics.  The equation of state is
assumed to be that of fully ionized gas with radiation, but pressure due to
partially degenerate and partially relativistic electron gas is calculated
rather well.  Nuclear burning rate is approximated with just one effective
reaction for the p-p cycle, and one for C-N-O cycle.  The opacities include
a very crude analytic description of molecules, negative hydrogen ion, the
Kramers opacity (i.e. free-free, bound-free, and bound-bound), electron
scattering with the corrections due to high temperature and high density,
and electron conductivity.  The main virtue of these subroutines is their
simplicity, and they may be changed to be more precise (and complicated)
without changing the structure of the program, provided the input and output
to and from the subroutines is kept in the same format.   At present no
allowance is made for the "mixing length theory", and the temperature
gradient is calculated as the smaller of the two: radiative and adiabatic.
 
      Eddington approximation is used for the model atmosphere.  The
integrations are started at a very small density:  10**(-12) grams per cubic
centimeters, and the optical depth is assumed to be zero there.
 
      A second order Runge-Kutta method is used for numerical integrations,
and the simplest Newton-Raphson technique is used to find the corrections
to the boundary parameters.

(DDS, 11/24/97).