Physical limits to the validity of synthesis models

Abstract

Abstract. In this paper we establish a necessary condition for the application of stellar population synthesis models to observed star clusters. Such a condition is expressed by the requirement that the total luminosity of the cluster modeled be larger than the contribution of the most luminous star included in the assumed isochrones, which is referred to as the Lowest Luminosity Limit (LLL). This limit is independent of the assumptions on the IMF and almost independent of the star formation history. We have obtained the Lowest Luminosity Limit for a wide range of ages (5 Myr to 20 Gyr) and metallicities (Z = 0 to Z = 0.019) from the Girardi et al. (2002) isochrones. Using the results of evolutionary synthesis models, we have also obtained the minimal cluster mass associated with the LLL, M min , which is the mass value below which the observed colors are severely biased with respect to the predictions of synthesis models. We explore the relationship between M min and the statistical properties of clusters, showing that the magnitudes of clusters with mass equal to M min have a relative dispersion of 32% at least (i.e., 0.35 mag) in all the photometric bands considered; analogously, the magnitudes of clusters with mass larger than 10 × M min have a relative dispersion of 10% at least. The dispersion is comparatively larger in the near infrared bands: in particular, M min takes values between 10 4 and 10 5 M for the K band, implying that severe sampling effects may affect the infrared emission of many observed stellar clusters. As an example of an application to observations, we show that in surveys that reach the Lowest Luminosity Limit the color distributions will be skewed toward the color with the smallest number of effective sources, which is usually the red, and that the skewness is a signature of the cluster mass distribution in the survey. We also apply our results to a sample of Globular Clusters, showing that they seem to be affected by sampling effects, a circumstance that could explain, at least partially, the bias of the observed colors with respect to the predictions of synthesis models. Finally, we extensively discuss the advantages and the drawbacks of our method: it is, on the one hand, a very simple criterion for the detection of severe sampling problems that bypasses the need for sophisticated statistical tools; on the other hand, it is not very sensitive, and it does not identify all the objects in which sampling effects are important and a statistical analysis is required. As such, it defines a condition necessary but not sufficient for the application of synthesis models to observed clusters.

Modeling the ionizing spectra of H II regions: individual stars versus stellar ensembles

“…cluster masses around 10 3 M ) to produce Q(H 0 ) similar to an individual 100 M star. This allows us to establish a mass limit for the use of synthesis models in stellar clusters: clusters with masses lower than 10 3 M are less luminous than the individual stars that the cluster model contains when described as the average obtained by synthesis models (the lowest luminosity limit established by Cerviño & Luridiana 2004;. As we have shown (cf.…”

“…We rebin neither the stellar masses nor the cluster masses, so our results correctly map the underlying distribution of physical properties (see Cerviño & Luridiana 2004, for different ways of implementing the Monte Carlo simulation).…”

“…We can, however, determine information about particular stars in the cluster (the most luminous ones). This is the case for clusters below the lowest luminosity limit (Cerviño & Luridiana 2004) 2 , where extreme sampling effects occur, information about only these particular stars is accessible, not for the cluster as a whole.…”

Accounting for stochastic fluctuations when analysing the integrated light of star clusters

“…Some of these can be quantified using selected information provided by continuous population synthesis models (e.g. Lançon & Mouhcine 2000;Cerviño et al 2002;Cerviño & Luridiana 2004, 2006, but others require using discrete population synthesis models (Barbaro & Bertelli 1977;Girardi & Bica 1993;Bruzual 2002;Deveikis et al 2008;Piskunov et al 2009;Popescu & Hanson 2010). The predicted luminosity and colour distributions depend strongly on the total mass (or star number) in the cluster, and can be far from Gaussian even when the total mass exceeds 10 5 M .…”

Stellar Populations in Luminous and Ultraluminous Infrared Galaxies

“…The former uses the GRANADA stellar library (Martins et al 2005) that contains high (0.3Å sampling) spectral resolution synthetic stellar models covering a wide range of effective temperature (3000-55000 K) and gravity (-0.5 log g 5). The library was implemented in the code SED@ (Cerviño & Luridiana 2006) …”