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Abstract:
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The dissertation presents a program for modeling binary systems, Infinity, which
combines the traditional principles of modeling (Roche geometry, von Zeipel’s law of
temperature distribution and so forth) with a novel geometrical representation of the
system.
The study of binary stars has a long tradition in Serbia, mostly due to the research done
by dr Gojko Đurašević. The program presented in the dissertation is based on his
program for modeling of active close binary systems with an accretion disk (Đurašević,
1991) and brings several significant improvements that can be classified in two
categories:
The first group of improvements has to do with generalizing the model. First and
foremost, the new program is applicable to systems with eccentric orbits, and is capable
of computing and solving the inverse problem for radial velocities. It also features a
new algorithm for determining which elements of the stellar surface are visible during
the eclipse. The new algorithm allows for computing the light curves with greater
precision using a method of ‘adaptive subdivision’ in the region of eclipse. The
geometrical aspects of modeling the accretion disk are also improved and now include
the possibility to create both conical and toroidal disks.
The second group of improvements is related to the modeling of physical processes on
the binary system components. The most significant change is in the way the emergent
flux is calculated. Namely, the Đurašević program assumes that the elements of stellar
surface produce blackbody radiation, while the new program assigns a one-dimensional
Kurucz stellar atmosphere model calculated under the LTE assumption. Improvements
are also made in the treatment of the influence of photometric filters on the calculated
light curve, and the list of supported filters is extended.
A binary system is described by the Roche model, which assumes that the motion and
shape of the components are determined by the superposition of gravitational and
centrifugal forces, while all the other interactions are neglected. The stars are treated as
point masses (under the assumption of total central condensation), so their internal
structure is not considered. If the system contains an accretion disk, it is assumed that its
mass can be neglected, and that its presence doesn’t influence the dynamics of the
system and the shape of the stars.
The surface of the components is represented with a polygonal mesh. The stars are
approximated with a geodesic, and the accretion disk with an axially-symmetric mesh.
The new algorithm for solving the problem of visibility detection, proposed in the
dissertation, is based on the so called inverse painter’s algorithm that originates from the
field of computer graphics. The most important property of this algorithm is that, other
than the polygonal meshes representing the components, it doesn’t require any other
information about the geometry of the system. This makes the modeling program easily
extendable to more exotic geometric configurations such as systems with eccentric or
circumbinary disks, planetary and multiple systems, and so forth.
It is assumed that within a single element of stellar surface all the physical quantities –
local effective temperature, gravitational acceleration, emergent flux and radial velocity
– are constant. Its radiation is affected by gravity darkening, limb darkening and the
reflection effect. Gravity darkening is described using von Zeipel’s law, and the limb
darkening can be calculated using one of the five available approximations (linear,
logarithmic, square-root, quadratic and nonlinear fourth-order approximation). The
reflection effect, as well as the temperature distribution along the accretion disk, are
calculated using the approach from the Đurašević program (Đurašević, 1991). The local
amount of radiation can additionally be affected by active regions that are represented
with dark or bright circular spots.
The emergent flux is computed as the sum of fluxes from all the surface elements
visible in the given moment, and the radial velocity is calculated from the superposition
from three kinds of motion: the proper motion of the system center of mass, the motion
of the center of the star around the center of mass due to orbital revolution, and the
motion of elementary surface around the center of the star due to rotation.
Synthetic light and radial velocity curves obtained in this way can be directly compared
to observations. The new program solves the inverse problem – estimating the optimal
model parameters to fit the given observations – using the Nelder-Mead simplex
algorithm to minimize the sum of squares of deviations between the observed and
calculated light and radial velocity curves. The validity of the program and the proposed
improvements is done by analyzing several binary systems and comparing the results
with published solutions obtained with the Đurašević program. |