Our understanding of stellar systems depends on the adopted interpretation of the IMF, phi(m). Unfortunately, there is not a common interpretation of the IMF, which leads to different methodologies and diverging analysis of observational data.We stud
y the correlation between the most massive star that a cluster would host, mmax, and its total mass into stars, M, as an example where different views of the IMF lead to different results. We assume that the IMF is a probability distribution function and analyze the mmax-M correlation within this context. We also examine the meaning of the equation used to derive a theoretical M-char_mmax relationship, N x int[Char_mmax-mup] phi(m) dm = 1 with N the total number of stars in the system, according to different interpretations of the IMF. We find that only a probabilistic interpretation of the IMF, where stellar masses are identically independent distributed random variables, provides a self-consistent result. Neither M nor N, can be used as IMF scaling factors. In addition, Char_mmax is a characteristic maximum stellar mass in the cluster, but not the actual maximum stellar mass. A <M>-Char_mmax correlation is a natural result of a probabilistic interpretation of the IMF; however, the distribution of observational data in the N (or M)-cmmax plane includes a dependence on the distribution of the total number of stars, N (and M), in the system, Phi(N), which is not usually taken into consideration. We conclude that a random sampling IMF is not in contradiction to a possible mmax-M physical law. However, such a law cannot be obtained from IMF algebraic manipulation or included analytically in the IMF functional form. The possible physical information that would be obtained from the N (or M)-mmax correlation is closely linked with the Phi(M) and Phi(N) distributions; hence it depends on the star formation process and the assumed.
We present the underlying relations between colour-magnitude diagrams (CMDs) and synthesis models through the use of stellar luminosity distribution func- tions. CMDs studies make a direct use of the stellar luminosity distribution function while, in
general, synthesis models only use its mean value, even though high-order moments can also be obtained. We show that the mean, high-order moments and in- tegrated luminosity distribution functions of stellar ensembles are related to the stellar luminosity distribution function, within the formalism of probabilistic synthesis mod- els. More details have been yet presented in Cervin ~ o & Luridiana (2006) and references therein. As a direct application of this formalism, we discuss two key issues. First, in- ferences on the upper mass limit of the initial mass function as a function of the total mass of clusters. Second, we apply extreme value theory to show that that the cluster mass obtained from normalising the IMF between mmax and mup does not provide the cluster mass in the case where only one star in this mass range is present, as assumed in the IGIMF theory. It provides instead the cluster mass with a 60% probability to have a star with mass larger than mmax, and we argue that in light of this result the basic formulation ofthe IGIMF theory must be revised.
This work aims to provide a theoretical formulation of Surface Brightness Fluctuations (SBF) in the framework of probabilistic synthesis models, and to distinguish between the different distributions involved in the SBF definition. RESULTS: We propos
e three definitions of SBF: (i) stellar population SBF, which can be computed from synthesis models and provide an intrinsic metric of fit for stellar population studies; (ii) theoretical SBF, which include the stellar population SBF plus an additional term that takes into account the distribution of the number of stars per resolution element psi(N); theoretical SBF coincide with Tonry & Schneider (1998) definition in the very particular case that psi(N) is assumed to be a Poisson distribution. However, the Poisson contribution to theoretical SBF is around 0.1% of the contribution due to the stellar population SBF, so there is no justification to include any reference to Poisson statistics in the SBF definition; (iii) observational SBF, which are those obtained in observations that are distributed around the theoretical SBF. Finally, we show alternative ways to compute SBF and extend the application of stellar population SBF to defining a metric of fitting for standard stellar population studies. CONCLUSIONS: We demostrate that SBF are observational evidence of a probabilistic paradigm in population synthesis, where integrated luminosities have an intrinsic distributed nature, and they rule out the commonly assumed deterministic paradigm of stellar population modeling.
The fundamental properties of stellar clusters, such as the age or the total initial mass in stars, are often inferred from population synthesis models. The predicted properties are then used to constrain the physical mechanisms involved in the forma
tion of such clusters in a variety of environments. Population synthesis models cannot, however, be applied blindy to such systems. We show that synthesis models cannot be used in the usual straightforward way to small-mass clusters (say, M < few times 10**4 Mo). The reason is that the basic hypothesis underlying population synthesis (a fixed proportionality between the number of stars in the different evolutionary phases) is not fulfilled in these clusters due to their small number of stars. This incomplete sampling of the stellar mass function results in a non-gaussian distribution of the mass-luminosity ratio for clusters that share the same evolutionary conditions (age, metallicity and initial stellar mass distribution function). We review some tests that can be carried out a priori to check whether a given cluster can be analysed with the fully-sampled standard population synthesis models, or, on the contrary, a probabilistic framework must be used. This leads to a re-assessment in the estimation of the low-mass tail in the distribution function of initial masses of stellar clusters.
In general, synthesis models provide the mean value of the distribution of possible integrated luminosities, this distribution (and not only its mean value) being the actual description of the integrated luminosity. Therefore, to obtain the closest m
odel to an observation only provides confi- dence about the precision of such a fit, but not information about the accuracy of the result. In this contribution we show how to overcome this drawback and we propose the use of the theoretical mean-averaged dispersion that can be produced by synthesis models as a metric of fitting to infer accurate physical parameters of observed systems.
In this poster we present the analysis of the CMD of M67 (proposed in the Stellar Population Challenge) performed with VO applications. We found that, although the VO environment is still not ready to perform a complete analysis, its use provides hig
hly useful additional information for the analysis. Thanks to the current VO framework, we are able to identify stars in the provided CMD that are not suitable for isochrone fitting. Additionally, we can complete our knowledge of this cluster extending the analysis to IR colors, which were not provided in the original data but that are available thanks to the VO. On the negative side, we find it difficult to access theoretical data from VO applications, so, currently, it is not possible to perform completely the analysis of the cluster inside the VO framework. However it is expected that the situation will improve in a near future.
The theory interest group in the International Virtual Observatory Alliance (IVOA) has the goal of ensuring that theoretical data and services are taken into account in the IVOA standards process. In this poster we present some of the efforts carried
out by this group to include evolutionary synthesis models in the VO framework. In particular we present the VO tool PGos3, developed by the INAOE (Mexico) and the Spanish Virtual Observatory which includes most of public SSP models in the VO framework (e.g. VOSpec). We also describe the problems related with the inclusion of synthesis models in the VO framework and we try to encourage people to define the way in which synthesis models should be described. This issue has implications not only for the inclusion of synthesis models in the the VO framework but also for a proper usage of synthesis models.
