STELLAR MODELS

A SET OF GRIDS COMPUTED IN GRANADA

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

binaries

Granada, 2000

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/models91/additional/table.n
==> additional stellar models for Z=0.01, 0.02, 0.03

evolmodels/models91/additional/adi91.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.

evolmodels/models95_98/oversh/z0004/ReadMe

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.

evolmodels/model95_98/oversh/z001/ReadMe

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

I

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.

evolmodels/model95_98/oversh/z002/ReadMe

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

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.

evolmodels/model95_98/oversh/z003/ReadMe

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

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.

IRRADIATION_ALGOL

This subdirectory contains one paper on irradiation of stellar atmospheres.

/irradiation_algol/irradia_algol.ps ==> paper postscript

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

(see ReadMe).

/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,

quadratic and root square limb-darkening
coefficients (see ReadMe).

/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

linear, quadratic and root square
limb-darkening coefficients (see ReadMe).

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.

FOR FURTHER INFORMATIONS/REQUESTS/SUGGESTIONS AND OTHER

MATERIAL NOT PRESENTED HERE, PLEASE CONTACT WITH

A. CLARET

INSTITUTO DE ASTROFISICA DE ANDALUCIA

CALLE SANCHO PANZA, SN

APARTADO 3004

18080 - GRANADA - SPAIN

E-MAIL: CLARET@IAA.ES

If you are interested in the complete CD ROM, please send me an e-mail.