CD ROM:
STELLAR MODELS

A SET OF GRIDS COMPUTED IN GRANADA

Research on stellar structure and evolution with special attention to modeling close
binaries

This extract of the CD ROM contains some results of the research carried out on stellar
structure and evolution in Granada during the last years. It is divided in sub-directories
with names indicating the specific area of investigation. For example, EVOLMODELS
contains all stellar evolutionary models computed since 1989. Such stellar models were
used to investigate different astrophysical problems, like apsidal motion or tidal evolution
in binary stars. Our research is devoted mainly to the evolution and structure of stars in
detached binary systems but may have some impact in other areas of stellar physics,
like the grid of models themselves, the computation of limb-darkening coefficients for
standard and irradiated models (from 2.000 K up to 50.000 K), the irradiation of secondaries
of Algol-type binaries, lithium burning or delta Scuti stars. In addition to the data we
provide the corresponding paper (in postscript) and a ReadMe file to guide the reader.

SCHEME OF THE SUB-DIRECTORY EVOLMODELS:

grids of stellar models and isochrones (for some of them)

evolmodels/models89: stellar models with LAOL OPACITIES, without overshoting

evolmodels/models89/inercia/tableii.n ==> Contains stellar models and the moment
of inertia for several models (X=0.70, Z=0.02)
evolmodels/models89/inercia/moniner89.ps ==> paper postscript

evolmodels/models89/standard==> stellar models for Z=0.01, 0.02, 0.03

Metal     Hydrogen
evolmodels/models89/standard/z001x71                Z=0.01         0.71
evolmodels/models89/standard/z002x66                Z=0.02         0.66
evolmodels/models89/standard/z002x70                Z=0.02         0.70
evolmodels/models89/standard/z002x74                Z=0.02         0.74
evolmodels/models89/standard/z003x69                Z=0.03         0.69

evolmodels/models89/standard/model1989a.ps, model1989b.ps, model1989c.ps,
model1989d.ps ==> paper postscript

stellar models with LAOL opacities

evolmodels/models91/z002x70/table.n ==> stellar models for Z=0.02, X=0.70 (with core overshooting)
evolmodels/models91/z002x70/model91.ps ==> paper postscript

evolmodels/models92: stellar models OPAL OPACITIES, with core overshoting and mass loss

Metal    Hydrogen
evolmodels/models92/z001x723/paper92.25_48                    Z=0.01    0.723
evolmodels/models92/z002x70/paper92.1-24                        Z=0.02    0.70
evolmodels/models92/z003x649/paper92.49_72                    Z=0.03    0.649
evolmodels/models92/model92.ps ==> paper postscript

evolmodels/models95_98/oversh/z0004: Stellar models OPAL OPACITIES (LS coupling),
with core overshoting, mass loss and new nuclear network.

Metal         Hydrogen
evolmodels/models95_98/oversh/z0004/modelIV.CDS                     Z=0.004    0.65
evolmodels/models95_98/oversh/z0004/modelIV.CDS                     Z=0.004    0.744
evolmodels/models95_98/oversh/z0004/modelIV.CDS                     Z=0.004    0.80
evolmodels/models95_98/oversh/z0004/modelIV.ps.gz ==> postscript paper

evolmodels/models95_98/oversh/z001: Stellar models OPAL OPACITIES (LS coupling),
with core overshoting, mass loss and new nuclear network.

Metal     Hydrogen
evolmodels/model95_98/oversh/z001/modelII.CDS                Z=0.01    0.63
evolmodels/model95_98/oversh/z001/modelII.CDS                Z=0.01    0.73
evolmodels/model95_98/oversh/z001/modelII.CDS                Z=0.01    0.80
evolmodels/model95_98/oversh/z001/modelII.ps.gz ==> postscript paper

ISOCHRONES

evolmodels/model95_98/oversh/z001/iso Isochones for Z=0.01 (X=0.63, 0.73, 0.80 (step 0.20 in log age)

evolmodels/model95_98/oversh/z001/iso/z001x63/z001x63.B Z=0.01 0.63
evolmodels/model95_98/oversh/z001/iso/z001x73/z001x73.B Z=0.01 0.73
evolmodels/model95_98/oversh/z001/iso/z001x80/z001x80.B Z=0.01 0.80
Note: the files containing the isochrones are z001xA.B where A is the Hydrogen content and B is log (age).

evolmodels/models95_98/oversh/z002: Stellar models OPAL OPACITIES (LS coupling),
with core overshoting, mass loss and new nuclear network.

Metal     Hydrogen
evolmodels/model95_98/oversh/z002/modelI.CDS              Z=0.02    0.60
evolmodels/model95_98/oversh/z002/modelI.CDS              Z=0.02    0.70
evolmodels/model95_98/oversh/z002/modelI.CDS              Z=0.02    0.80
evolmodels/model95_98/oversh/z002/modelI.ps.gz ==> postscript paper

ISOCHRONES

evolmodels/model95_98/oversh/z002/iso Isochones for Z=0.02 (X=0.60, 0.70, 0.80 (step 0.20 in log age)

evolmodels/model95_98/oversh/z002/iso/z002x60/z002x60.B Z=0.02 0.60
evolmodels/model95_98/oversh/z002/iso/z002x70/z002x70.B Z=0.02 0.70
evolmodels/model95_98/oversh/z002/iso/z002x80/z002x80.B Z=0.02 0.80
Note: the files containing the isochrones are z001xA.B where A is the Hydrogen content and B is log (age).

evolmodels/models95_98/oversh/z003: Stellar models OPAL OPACITIES (LS coupling),
with core overshoting, mass loss and new nuclear network.

Metal    Hydrogen
evolmodels/model95_98/oversh/z003/modelIII.CDS                   Z=0.03    0.55
evolmodels/model95_98/oversh/z003/modelIII.CDS                   Z=0.03    0.65
evolmodels/model95_98/oversh/z003/modelIII.CDS                   Z=0.03    0.75
evolmodels/model95_98/oversh/z003/modelIII.ps.gz ==> postscript paper

ISOCHRONES

evolmodels/model95_98/oversh/z003/iso Isochones for Z=0.03 (X=0.55, 0.65, 0.75 (step 0.20 in log age)

evolmodels/model95_98/oversh/z003/iso/z003x55/z003x55.B Z=0.03 0.55
evolmodels/model95_98/oversh/z003/iso/z003x65/z003x65.B Z=0.03 0.65
evolmodels/model95_98/oversh/z003/iso/z003x75/z003x75.B Z=0.03 0.75
Note: the files containing the isochrones are z001xA.B where A is the Hydrogen content and B is log (age).

Stellar models OPAL OPACITIES (LS coupling), WITHOUT core overshoting and
new nuclear networok.

NOTE:THESE STANDARD MODELS (WITHOUT CORE OVERSHOOTING)
ARE AVAILABLE ONLY ON REQUEST

evolmodels/models95_98/gravity_darkening
This sub-directory contains the paper "Comprehensive tables for the interpretation and
modeling of the light curves of eclipsing binaries". In such a work we developed a method
to compute the gravity-darkening using interior models. The gravity-darkening exponents
are presented as a function of age and mass. The old values of beta (0.32 , 1.0) for convective
and radiative envelopes are superseded and a smooth transition is achieved between both
energy transport mechanisms. In addition to the parameters needed for the study of the
dynamical behavior and tidal evolution of binary systems, we supply linear and non-linear
limb-darkening coefficients in 12 photometric bands for each point along the evoluionary tracks.

evolmodels/gravity_darkening/table.n ==> contains evolutionary models and the respective
gravity-darkening exponents, gravity-darkening exponents and synthetic colors (see ReadMe) evolmodels/gravity_darkening/tablesbig/*mz02x70.beta ==> the same as before but with
more points.
evolmodels/gravity_darkening/gravity_dar.ps paper
We present parameters used in the investigation of the light curves of eclipsing binaries
together with other data needed for the interpretation of their stellar and dynamical evolution.
Parameters include limb-darkening coefficients and gravity darkening exponents, while data
includes the apsidal motion constants, the moment of inertia, and the potential energy. The adopted
stellar models are those computed by Claret (1995) for a representative chemical composition
of X=0.70 and Z=0.02. In addition to the parameters needed for the study of the dynamical behavior
and tidal evolution of binary systems, we supply the linear limb-darkening coefficients computed in
12 different photometric bands, as well as the gravity darkening exponent for each point along the
evolutionary track. We have developed a method, based on the triangles strategy by Kippenhahn et al. 1967
to compute the gravity-darkening exponent using interior models. For the first time, the gravity-darkening
exponents are presented as a function of mass and age. The old values of $\beta_1$ - 0.32 and 1.0 -
for convective and radiative envelopes are thus superseded by the present calculations and a smooth
transition is achieved between both energy transport mechanisms. The tables presented here assist
modeling of the light curves of close binaries using limb-darkening and gravity darkening coefficients
which are consistent with the observed masses, radii and effective temperatures. In order to facilitate
the use of the grid of models presented here in a variety of different research fields other than binary stars,
synthetic colors (U-B, B-V, u-b, b-y) and M_v are also given.
evolmodels/gravity_darkening/rotfot.ps paper
We have computed the photometric magnitudes of rotating atmospheres based on the simple model of
Collins for a grid suitable for main-sequence and slightly evolved stars of spectral type A0 to F5.
A gravity-darkening law valid for radiative and convective envelopes has been considered. The
general results are given as magnitudes differences between rotating and non-rotating copartners
to allow for the use of any photometric calibration. A simple interpolation on these results gives the
photometric parameters for interior rotating models but we also indicate how they can be used to
correct for the effect of rotation when an investigation with non-rotating models is carried out. We
illustrate the procedure with the interesting case of the Praesepe Cluster.

APDIDAL_MOTION:
This subdirectory contains some papers on apsidal motion in binary stars.
apsidal_motion/k2_93.ps ==> paper postscript
An extensive comparison between stellar models and the best available data of apsidal motion for
double-lined eclipsing binaries. After introduction of new opacities, core overshooting and rotation
we have found that the systematic deviation between observational and theoretical values of log k_2
are not significantly detected.
apsidal_motion/rotk2.ps ==> paper postscript
The quasi-spherical approximation, with some modifications, was implemented in our stellar
evolution code to take into account the effect of rotation on the internal structure of the stars
and, in particular, on the apsidal motion constant. Three models with masses 2, 7 and 15 M$_{\odot}$
were used since they are representative of the mass range where apsidal motion is detected in binary
stars. We adopted two limiting cases of angular momentum redistribution: local conservation and
rigid body rotation. It was found that the influence of rotation on internal structure depends strongly
on the distortion of the configuration characterized by the parameter $\lambda$ = 2v$^2$/(3gR) at
the surface of the model. Such results make the work of introducing the correction for rotation in the
apsidal motion analysis an easier task since it is sufficient to decrease the theoretical log k$_2$ by
0.87 $\lambda_s$.
apsidal_motion/ekcephei.ps ==> paper postscript
We have carried out a comparison between the observed parameters of EK Cep with theoretical
values. We have found that both stars are on the same isochrone and the secondary has been confirm
as pre main-sequence star. The observed apsidal motion is in a perfect agreement with the predicted
value as well as the lithium depletiumof the secondary.
apsidal_motion/HV2274I.ps ==> paper postscript
Theoretical apsidal motion rates based on evolutionary stellar models are used to evaluate masses
and radii of an extragalactic eclipsing binary (HV 2274) in the Large Magellanic Cloud. Since radial
velocity curves are not available, from the results of the analysis of the light curve and the detected
apsidal motion it was possible to constrain the values of the masses and radii for both components.
Assuming a mass ratio of 1 (which is supported by evidence from the light curves), the masses of
HV 2274 were inferred to be between 10 and 12 M_solar.
apsidal_motion/HV2274II.ps ==> paper postscript
About three years ago we did predict, only on the base of theoretical evolutionary models and of the
measured apsidal motion rate, the radii and masses for the components of the extragalactic eclipsing
binary HV 2274 in the Large Magellanic Cloud. At that time the radial velocity curves were not
available and the need of more complete observations to compare with the evolution theory was
emphasized. Recently, through ground-based photometry, spectroscopy and spectrophotometry on
board the Hubble Space Telescope the absolute dimensions of that system were obtained. In this
research note we perform a more complete comparison between observations and theoretical
predictions since the light and radial velocity curves are now available. The theoretical radii and
apsidal motion rate inferred from models computed for the precise observed masses were found
to be in good agreement with observational data. The importance of the case of HV2274 lies mainly
in the fact that this system is the first extragalactic binary system where it has been possible to i
nvestigate its surface astrophysical parameters as well as the tidal interactions using the techniques
of apsidal motion.
apsidal_motion/relati.ps ==> paper postscript
We have compared observational data of apsidal motion rates for relativistic eclipsing binaries with
theoretical predictions based on stellar theoretical models. Ten double-lined eclipsing binaries with
high quality light curves and radial velocities were selected. The analysis of the data available indicate
that the predictions by the General Relativity and the new stellar models are able to explain the
shift in the periastron position.
apsidal_motion/diher.ps ==> paper postscript
DI Her is a double-lined eclipsing binary presenting a very slow apsidal motion for which the relativistic
contribution is of the order of the newtonian one. The observed apsidal motion is around 4 times that
predicted by stellar evolutionary models and by General Relativity. This trend is known for non-relativistic
systems although in a minor scale. The magnitude of such a disagreement led some authors to propose
several mechanisms to explain it, including a revision of the gravitation theory. In this paper some aspects
of these processes are analyzed using modern stellar models, recent absolute dimensions and apsidal
motion rate. New alternative explanations for the problem as for example, the intrinsic observational
difficulties to obtain very slow apsidal motion rates with confidence, are also introduced.
NOTE: SEE erratumdiher.ps apsidal_motion/erratumdiher.ps.gz

DELTASCUTI:
This subdirectory contains some papers on delta scuti stars.
/deltascuti/BNBUCnc.ps ==> paper postscript
The results reported in this paper concern two delta Scuti in the Praesepe cluster. Five or six peaks were
recorded and rotation effects in the frequencies are considered up to second order. More severe constraint
were imposed since two stars belong to the same cluster.
/deltascuti/abcas.ps ==> paper postscript This paper presents uvby light curves for the Algol-type binary
system AB Cas, in wich the primary is a delta scuti-type pulsating star. The pulsation analysis suggests the
hotter component as monoperiodic with a period P=0.05828741 days oscillating in the fundamental radial
mode. It is also shown that binarity, in this case, has no special effect on the pulsation.
/deltascuti/delsct90.ps ==> paper postscript
Recent uvbybeta observations of high amplitude delta scuti stars obtained at Sierra Nevada (Spain) and
La Silla (Chile) observatories are compared with standard evolution models.

This subdirectory contains one paper on irradiation of stellar atmospheres.
We present a study of the most relevant effects of irradiation in the secondary components of Algol-type
binaries. A comparison between the spectral energy distribution of model atmospheres with and without i
rradiation, for the T_ef and log g, denotes clear differences mainly in the depth of the absortion lines.
Furthermore, we have found that the computed irradiated spectra are very similar, in some spectral regions,
to the equivalent model atmosphere without irradiation but a lower metalicity. On the other hand, irradiation
produces an increase in T_ef due to the heating of the upper layers. We argue that this shift could be responsible,
at least partly, for the observed overluminosity of the secondaries of classical Algols.

LIMB-DARKENING
This subdirectory contains papers on the limb-darkening coefficients between 2.000 K and 50.000 K in
uvby, UBV, RIJHK pass-bands.

/limb_darkening/infra/limbRI.ps ==> paper postscript
We have computed limb-darkening coefficients for five commonly used near infrared photometric bands,
namely R, I, J, H, and K, using the stellar atmosphere models by Kurucz (1991). Since the behaviour of the
specific intensities is very dependent on the range of effective temperatures considered, we have adopted
three analytical approximations to the limb darkening: linear, quadratic and square root. The least-squares
method has been adopted for the fit of the limb-darkening coefficients to the model atmospheres.
Table1 , table2 and table3 contain the linear, quadratic and root square limb-darkening coefficients
/limb_darkening/low_mass/limblow.ps ==> paper postscript
Linear and non-linear limb-darkening coefficients for the photometric bands u v b y U B V R I J H K
are computed for very low effective temperatures stars. The atmosphere models used (PHOENIX-NextGen)
do not include the effects of dust formation and dust opacities. These calculations are presented for the first time.
The calculations extend the range of effective temperatures (2000 K - 50000 K) covered by our previous
papers. These data are important in order to deal with stars in the lower part of Main-Sequence like M or
brown dwarfs. The non-linear behavior of the limb-darkening laws, particularly in this effective temperature
range, is emphasized and we urge users to take it into account. Table1 , Table2 and Table3 contain the linear,
/limb_darkening/visible/1990/limb90.ps ==> paper postscript
Linear and quadratic limb-darkening coefficients have been calculated by means of a least squares fitting
to a sample of stellar model atmospheres corresponding to late-type stars. A detailed discussion of the effect
of irradiation of stellar atmospheres by a hotter companion star on the predicted limb-darkening coefficients is
presented for the first time adopting realistic binary star parameters. An important difference, in the sense that
brightness distribution becomes more uniform, is found for systems representative of classical Algol-types
binaries. Tables 1.1 and 1.2 contain the linear and quadratic limb-darkening coefficients.
/limb_darkening/visible/1995/limbvis.ps ==> paper postscript Linear, quadratic and square root limb-darkening
coefficients have been computed by means of lrast squares fits to model atmospheres by Kurucz with the main
purpose of facilitating the analysis of light curves of eclipsing binaries. Table1, table2 and table3 contain the

TIDAL_EVOLUTION
/tidal_evolution/TZfor.ps ==> paper postscript
In this paper we intend to explain the behavior of the evolved double-lined eclipsing binary TZ Fornacis on
the basis of tidal evolution theory and the use of modern internal structure stellar models. Results show that
the integration of the differential equations provides a satisfactory explanation for the tidal and evolutionary
status of TZ For.
/tidal_evolution/circulariI.ps ==> paper postscript
In the present investigation we pay special attention to stars with radiative envelopes though some stars
with outer layers in convective equilibrium have been included to show different aspects of tidal evolution.
In the present paper, we have adopted for the comparison with observational parameters, the tidal theory
by Tasssoul (1987, 1988) The comparison of observed rotational velocities with expected values for each
binary system configuration has shown that nearly all systems in our sample are actually pseudo-synchronized
with their orbital periods (i.e. with the fastest orbital velocity in eccentric systems) in good agreement with
theoretical predictions. These results, however, should be taken with some caution since the rotation of the
stellar interior may be decoupled from that of the surface layers. The comparison of observed rotational
velocities with expected values for each binary system configuration has shown that nearly all systems i
n our sample are actually pseudo-synchronized with their orbital periods (i.e. with the fastest orbital velocity
in eccentric systems) in good agreement with theoretical predictions. With respect to circularization, a cutoff
value around log t = log \tcri/ (or log \gobs/ = log \gcri/) shows a satisfactory agreement for observational values
of the eccentricity. Furthermore, we concluded that the circularization process is still active during the main
sequence stage for early-type binaries.
/tidal_evolution/circulariII.ps ==> paper postscript
Double-lined eclipsing binaries with accurate absolute dimensions are the best stellar data to test tidal
evolution theories due to the high dependency of the time scales on masses, relative radii and periods.
In a preceding paper we have probed the hydrodynamical mechanism against the observed levels of
synchronization and circularization for about 40 close binary systems with accurate absolute dimensions.
In the present work we extend our investigations, using the same systems as a control, to the turbulent
dissipation and radiative damping mechanisms which have been studied by Zahn. The time scales for
these processes are characterized by the parameters $\lambda_2$ and E$_2$ respectively. These
parameters were computed for a wide grid of stellar models and they are presented, for the first time,
as functions of the mass and time. The differential equations which govern the orbital parameters were
integrated using our recent grids of stellar models (Claret 1995,1996 ; Claret \& Gim\'enez 1995). The
derived critical times and radii were compared with observations of synchronization and circularization
levels. Within uncertainties, the formalisms by Zahn seem to be able to explain the eccentricity distribution
around the zero point of the diagram log (age/t$_{cri}$) $\times$ eccentricity although they can not explain
some systems with circular orbits which present ages smaller than their respective critical times. We have
also introduced a diagram based on the integration of the differential equations which proved to be useful
to test theoretical predictions for the relationship age $\times$ Period (cut-off) for clusters. Using this
diagram we have shown that the turbulent friction mechanism is not dissipative enough to explain such an
observational relationship.

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