EVOLUTIONARY TRACKS & ISOCHRONES: CANONICAL MODELS (AGB - EXTENDED)

readme file

last modification: 6 Dec 2005

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This database contains the grid of evolutionary tracks described in Pietrinferni, Cassisi, Salaris & Castelli (2004, ApJ, 612, 168). Both stellar evolution models and isochrones, stored in this archive, have been extended along the Asymptotic Giant Branch (AGB) stage to cover the full thermal pulse phase, using the synthetic AGB technique (Iben & Truran 1978, ApJ, 220, 980) (see below).

The models do not include gravitational settling, radiative acceleration, convective overshooting, rotational mixing, but otherwise they are based on up-to-date physics, as detailed in the quoted paper.

We strongly encourage people interested in a specific set of evolutionary tracks (not yet available in this database) to contact us, either by e_mail or by compiling the request form (present in this web site). We'll try to perform these computations within a week upon receiving the request.

We have presently stored evolutionary models with the following chemical compositions:

The values Z=0.0198 (zsun) and Y=0.2734 (ysun) correspond to the abundances obtained from the calibration of the solar model (for more details we refer to Pietrinferni et al. 2004).

All models have been computed using a scaled solar distribution (Grevesse & Noels 1993) for the heavy elements, and include mass loss according to the Reimers (1975) law. The mass loss efficiency parameter eta has been fixed to eta=0.4 for the full set of models. To allow investigations about the effect of different mass loss efficiencies on the properties of individual stars and stellar populations, we have computed an additional set of low-mass models - for the same chemical compositions - using eta=0.2. We have verified that the evolution of more massive stars is not appreciably affected when changing eta= from 0.4 down to 0.2. This enables one to use consistently in population synthesis studies the low-mass models computed with eta=0.2 together with the more massive ones computed with eta=0.4, to mimick the effect of a global reduction of eta= from 0.4 to 0.2.

The mass range goes from 0.5Mo to 10.0Mo. Please note that the mass spacing is suitably small: we adopt a mass step equal to, respectively, 0.1Mo in the range (0.5 - 2.6) Mo, 0.2Mo between 2.6Mo and 3.0Mo, and 0.5Mo for more massive models. Please note that in this archive we have not stored those evolutionary tracks that in the (link) "normal tracks" archive have been computed until the central hydrogen exhaustion. In any case these models have been accounted for when computing isochrones.

Each file contains:

in the fifth line - 1) the number of evolutionary points, 2) the global metallicity [M/H], 3) the abundance by mass of metals (Z), 4) the initial He abundance (Y), 5) the inital mass (in solar unit); starting from the ninth line the following quantities are listed:

  1 column) the logarithm of the age in years;
  2 column) the actual mass in solar unit;
  3 column) the logarithm of the surface luminosity in solar unit;
  4 column) the logarithm of the effective temperature (K);
  5 column) the visual absolute magnitude;
  6 column) the (B-V) colour;
  7 column) the (U-B) colour;
  8 column) the (V-I) colour;
  9 column) the (V-R) colour;
 10 column) the (V-J) colour; 
 11 column) the (V-K) colour;
 12 column) the (V-L) colour; 
 13 column) the (H-K) colour; 

The synthetic AGB evolution

We have employed a simplified treatment of the AGB synthetic evolution that - as demonstrated by the few tests shown below - allows one to reproduce satisfactorily several integrated properties of stellar populations in the near-IR bands, which are greatly affected by the presence of AGB thermal pulsing stars. Given that the purpose of this library of stellar models and isochrones is to provide a reliable tool to be employed in stellar population synthesis studies, we feel confident that our simplified AGB treatment is adequate for our purposes.

For each stellar model of a given initial chemical composition and mass, we started the synthetic AGB evolution at the beginning of the Thermal Pulse (TP) phase, where the full evolutionary models were stopped. The first model of the synthetic TP-AGB evolution is characterized by the total mass M, Carbon-Oxygen (CO) core mass Mco, luminosity L, effective temperature T_eff and surface chemical composition (X,Y,Z) of the last fully evolutionary model.
The TP-AGB phase is then followed by increasing (after a given timestep dt) Mco and L according to Eqs. 5-7 in Wagenhuber & Groenewegen (1998, A&A, 340, 183 - WG98), which contain a term mimicking the effect of the Hot Bottom Burning, when appropriate. The hydrogen mass fraction in the envelope (an input of Eq. 6 of WG98) is approximated as 1-(Y+0.01)-Z all along the TP evolution. Mass loss from the envelope is included using Eqs. 17-18 in Girardi & Bertelli (1998, MNRAS, 300, 533). For any given value of M and Mco, the effective temperatures are computed using the relationships plotted in Fig.8 of WG98 (see Wagenhuber 1996, PhD thesis, TU Muenchen). To ensure continuity, the zero points of the equations describing the evolution of L, Mco and T_eff have been adjusted to reproduce the corresponding values of the last fully evolutionary model, at the beginning of the TP phase.
The synthetic evolution is stopped when the mass of the envelope has been reduced below 10E-4 Mo. At this stage the models have already started to evolve at constant luminosity towards their White Dwarf cooling sequence.

From the full evolution extended until the end of the TP phase we have computed theoretical isochrones in exactly the same way as for the non extended models. The only difference is that we added two additional key-point (key-point number 17 and 18 - see below ), corresponding respectively to the start of the first TP and to the end of the TP phase, when the models start to turn towards higher T_eff. A total of 10 points is distributed between key-points 16 and 17, and 240 points are distributed between key-points 17 and 18. The total number of points along each isochrone is 2250.

Broadband colours and magnitudes of both models and isochrones have been computed by supplementing the transformations used in Pietrinferni A. et al. (2004, ApJ, 612, 168) with the Westera et al.(2000, A&A, 381, 524) ones for RGB and AGB stars with T_eff < 3750K. To ensure continuity, the bolometric corrections and colours of Westera et al.(2000) have been shifted to match the other sets of transformations when T_eff = 3750K.
Along the TP-AGB phase, when the (J-K) colours reach (J-K)=1.2 mag, we used the (J-K)-T_eff and (H-K)-T_eff relationships by Bergeat, Knapik & Rutily (2001, A&A, 178, 209) that are appropriate in the Carbon star regime.

The coding of the file names is as follows:

 abcdZedfYghis_agb.nor_c04ext
      |
      | evolutionary track for a model with --> initial mass = ab.cd Mo 
                                            --> metallicity Z= e.d x 10^(-f)
                                            --> initial He abundance Y = 0.ghi
 

The suffix "s" denotes models computed by adopting a Standard evolutionary scenario (no atomic diffusion, no overshooting). The suffix "nor" indicates that the evolutionary sequence has been "reduced" to a suitable number of points. This has been accomplished by fixing some key stage along the evolutionary path, and distributing for each track the same number of points between two consecutive stages. This allows a straightforward interpolation for producing isochrones of a given age, and for determining tracks and isochrones for other metallicities within the range spanned by the computed grid of models.

  Example:

  0130z402y303s_agb.nor_c04ext ---> 1.30 Mo AGB-extended canonical model with Z=4.0E-2 and Y=0.303

The whole set of evolutionary tracks can be downloaded as a single compressed tar archive.

The full set of evolutionary models has been also transferred from the theoretical plane to the WFC3 (IR) - on board of HST - Vega-mag. Each set of models can be downloaded as a single compressed tar archive. Each file contains:

on the fifth line - 1) the number of evolutionary points, 2) the global metallicity [M/H], 3) the abundance by mass of metals (Z), 4) the initial He abundance (Y), 5) the inital mass (in solar unit); starting from the ninth line the following quantities are listed, from the Zero Age Main Sequence until the first few thermal pulses (for masses larger than 0.7Mo):

WFC3(IR) system

 
  1 column) the logarithm of the age in years;
  2 column) the actual mass in solar units;
  3 column) the logarithm of the surface luminosity in solar units;
  4 column) the logarithm of the effective temperature (K);
  5 column) F098M magnitude;
  6 column) F105W magnitude;
  7 column) F110W magnitude;
  8 column) F125W magnitude;
  9 column) F126N magnitude;
 10 column) F127M magnitude;
 11 column) F128N magnitude;
 12 column) F130N magnitude;
 13 column) F132N magnitude;
 14 column) F139M magnitude;
 15 column) F140W magnitude;
 16 column) F153M magnitude;
 17 column) F160W magnitude;
 18 column) F164N magnitude;
 19 column) F167N magnitude;

As for the choice of the key stages, we provide some information in the following.

In the present version of BASTI, we have accounted for 17 key stages along the evolutionary track, more in detail:

Low-mass stars denotes in this case all objects which do not develop a convective core during the whole central H-burning phase; the high-mass structures are all the others.

For those structures which do not present the Bump along the RGB, we have - arbitrarily - chosen as representative of the key points 6 and 7, two points whose brightness was intermediate between the luminosities corresponding to the key points 5 and 8.
For those structures which do not experience the TP-AGB phase (i.e. those models which ignite C-burning) we have - arbitrarily - chosen as representative of the key points 17 and 18 the evolutionary stages immediately subsequent that chosen as key point 16.

The correspondence between key stages and rows is the following:

For more details about the adopted key stages, please contact one of the authors.

Comparisons between theory and empirical evidence

In the following table we provide theoretical predictions about the bolometric magnitude ( Mbol=-2.5*log(L/Lo)+4.74 ) of the tip of the AGB for selected scaled-solar models (that include overshooting and with eta=0.2 for the evolution prior to the TP phase) and three metallicities.

In the following we show some comparisons between various empirical evidence and theoretical predictions based on current set of AGB-extended stellar models:

Figure 1: K-band Surface Brightness Fluctuation (SBF) magnitudes vs age derived by Gonzalez, Liu & Bruzual (2004 ApJ, 611, 270) for Magellanic Cloud superclusters (obtained by coadding clusters belonging to the same SWB class - Searle, Wilkinson & Bagnuolo 1980, ApJ, 239, 803). The colour-code denotes the typical metallicity of each supercluster. The Ks data (2MASS system) have been transformed onto the Johnson system combining the relationships by Carpenter et al. (2001, AJ, 121, 2851) and Bessell & Brett (1988, PASP, 100, 1134) Theoretical SBF magnitudes for the metallicity (denoted by the appropriate colour) and age range (obtained from Gonzalez et al. 2004) of the individual superclusters are also displayed. The theoretical SBF magnitudes are obtained from our isochrones including convective core overshooting, with a mass loss parameter eta=0.2. In case of Z=0.0006 models we also show (dashed line) the predictions for a larger mass loss, i.e. eta=0.4.

Figure 2: As in the case of the previous figure but for the J-band SBF magnitudes. The J-band magnitudes (2MASS system) have been transformed onto the Johnson system combining the appropriate relationships from Carpenter (2001) and Bessell & Brett (1988).

Figure 3: Integrated (H-K) colours of a sample of Magellanic Cloud clusters (Persson et al. 1983, ApJ, 266, 105) as a function of their age. The individual ages have been obtained using the age calibration given in Eq.2 of Ferraro et al. (1995, MNRAS, 272, 391); metallicities are assigned consistently with the SWB class-metallicity relationship used by Gonzalez et al. (2004). Appropriate theoretical integrated colour predictions (from isochrones including convective core overshooting) are also displayed.

Figure 4: Cumulative K-(J-K) Colour-Magnitude-Diagrams of AGB stars in a sample of LMC clusters (Frogel & Cohen 1982, ApJ, 253, 580). K and (J-K) magnitudes have been transformed from the CIT system to the Johnson one using the relationships in Bessell & Brett (1988). Reddenings are from Frogel & Cohen (1982) and we used a distance modulus (m-M)o=18.50. The individual CMDs are coadded according to the cluster SWB type. Theoretical isochrones for the appropriate age and metallicity range (taken from Gonzalez et al. 2004) of each cluster type are also displayed.

In case one is interested in the complete evolutionary track (i.e, a non normalized track) as well as to more information about the models (such as burnings, internal structure and so on) we will be pleased to provide them upon request. All comments/suggestions/requests are welcome. We hope that this database will be useful to your work!

Our best regards!!!