Main model ingredients

The main model ingredients are:

Initial Mass Function

We adopt the IMF shapes described in Vazdekis et al. 1996 (often regarded as Unimodal and Bimodal), the two IMFs of Kroupa 2001 (MNRAS,322,231) and the one of Chabrier (2003):

Theoretical isochrones

We employ two sets of theoretical isochrones. The scaled-solar isochrones of Girardi et al. (2000) (hereafter Padova+00) and Pietrinferni et al. (2004) and the alpha -enhanced models of Pietrinferni et al. (2006). The latter two will be regarded hereafter as BaSTI. The Padova isochrones cover a wide range of ages, from 0.063 to 17.8 Gyr, and six metallicity bins (Z = 0.0004, 0.001, 0.004, 0.008, 0.019 and 0.03), where 0.019 represents the solar value. The isochrones also include the later stages of stellar evolution, using a simple synthetic prescription for incorporating the thermally pulsing AGB regime to the point of complete envelope ejection. The range of initial stellar masses extends from 0.15 to 7M⊙. The input physics of these models was updated with respect to Bertelli et al. (1994) with an improved version of the equation of state, the opacities of Alexander & Ferguson (1994) and a milder convective overshoot scheme. A helium fraction was adopted according to the relation: Y= 0.23 + 2.25Z.

We also use here the BaSTI theoretical isochrones ( The original sets of models have been supplemented by additional computations specifically performed for our project. The BaSTI metallicity grid adopted in present analysis was based on 12 grid points: Z = 0.0001, 0.0003, 0.0006, 0.001, 0.002, 0.004, 0.008, 0.0100, 0.0198, 0.0240, 0.0300 and 0.0400. For each metallicity, the isochrone age range covers the interval from 0:03 to 14 Gyr, with a fne age grid. See Vazdekis et al. (2015) for more details.

Stellar photometric libraries

Stellar photometric libraries are used to transform the theoretical parameters of the isochrones to magnitudes and colours. We use extensive empirical (not theoretical) stellar libraries to obtain each colour as a function of temperature, metallicity and gravity. We use the metallicity-dependent relations of Alonso, Arribas & Martinez-Roger (1996,1999) (A&A,117,227; A&AS,140,261) for dwarfs and giants respectively. This treatment for the giants is the most important difference with respect to the models of Vazdekis et al (1996), where we used the calibrations of Ridgway et al. 1980 (ApJ,235,126) and Johnson 1966 (ARA&A,4,193). The empirical (not the theoretical) compilation of Lejeune, Cuisinier & Buser (1997, 1998) (A&AS,125,229; A&AS,130,65) are used for the coolest and hottest dwarfs (Teff<4000K) and giants (Teff<3500K), respectively, for solar metallicity; a semi-empirical approach was applied to other metallicities on the basis of these relations and the model atmospheres of Bessell et al. (1989,1991) (A&AS,77,1; A&AS,89,335) and the library of Fluks et al. 1994 (A&AS,105,311). We use the metal-dependent bolometric corrections given by Alonso, Arribas & Martinez-Roger (1995,1999) (A&A,297,197; A&AS,140,261) for dwarfs and giants, respectively. For the Sun we adopt the bolometric correction -0.12, with a bolometric magnitude of 4.70.

Stellar spectral libraries

Extensive empirical stellar libraries are used to predict the spectral properties of the stellar populations. Two set of predictions are computed: