Beside the problems related with the track interpolation and the impact of different atmosphere models, there are other unconsiderered problems related with the use of synthesis models.

Maybe, the most trivial Limit for the usage of a synthesis model is the following one:

The total luminosity of the cluster modeled must be larger than the individual contribution of any of the stars included in the model

This obvious statement defines a natural theoretical limit for the use of such models that has not always been considered when they are applied to real observations. Whereas the original formulation performed by B. Tinsley did not need to take into account this limit due to the observational limitations at that epoch, the increasing sensitivity of current observatories has reached a level where this limitation plays a fundamental role for a correct interpretation of current data.

Based on this limitation, we can establish a Lowest Luminosity Limit (hereinafter LLL, Cerviño & Luridiana 2003 submitted) for the application of synthesis models that corresponds to the situation where the total luminosity of a cluster equals the luminosity of the most luminous individual star included in the synthesis model. Under this definition, the LLL is only defined by the used isochrone and the band under consideration, however its exact value at a given age is also partially dependent on the star formation history.


Then, for each luminosity band and age, we can obtain a minimal initial cluster mass, ^min(t), for which the total luminosity of the cluster simulated by a SSP model (with normalized magnitude m^ssp) equals the luminosity of the most luminous star in the band, M_*^min(t):

Note that ^min depends on the age and the band, but also on the IMF and the star formation history since integrated quantities depend on such distributions. The results computed for In our case, we have used the models from Girardi et al. 2002, A&A 391, 195 that compute the integrated magnitudes of SSP models assuming a Kroupa 2001, MNRAS 322, 231 IMF in its corrected version (his Eq. 6) and a total SSP initial mass equal to 1 Mo in the mass range 0.01 -- 120 Mo. The results for different ages and metallicities and bands are shown in the Figure:

This kind of exercise can be also done for the ionizing continuum, for example, and establish when the ionization is due to a cluster of ionizing stars (an hence a representation of the ionizing continuum can be modelized with a synthesis model) or when the ionization is due to a single star in the model (and then the ionizng continuum may be better represented by a single star). A paper on this subject is under preparation.

So, when standard synthesis models fails, it is needed to consider a different aproach: Sinthesis models that include stadistical effects due to the IMF sampling, that is our next subject.