On emission-line spectra obtained from evolutionary synthesis models: I. Dispersion in the ionising flux and lowest luminosity limits

Stellar clusters with the same general physical properties (e.g., total mass, age, and star-formation mode) may have very different stellar mass spectra due to the incomplete sampling of the underlying mass function; such differences are especially relevant in the high-mass tail of the mass function due to the smaller absolute number of massive stars. Since the ionising spectra of star-forming regions are mainly produced by massive stars and their by-products, the dispersion in the number of massive stars across individual clusters also produces a dispersion in the properties of the corresponding ionising spectra. This implies that regions with the same physical properties may produce very different emission line spectra, and occupy different positions in emission-line diagnostic diagrams. In this paper, we lay the basis for a future analysis of this effect by evaluating the dispersion in the ionising fluxes of synthetic spectra computed with evolutionary models. As an important consequence of the explicit consideration of sampling effects, we found that the intensities of synthetic fluxes at different ionisation edges are strongly correlated, a fact suggesting that no additional dispersion will result from the inclusion of sampling effects in the analysis of diagnostic diagrams; this is true for HII regions on all scales, those ionised by single massive stars through those ionised by super stellar clusters. This finding is especially relevant in consideration of the fact that real H II regions are found in a band sensibly narrower than predicted by standard methods. Additionally, we find convincing suggestions that the He II line intensities are strongly affected by sampling, especially during the WR phase, and so cannot be used to constrain the evolutionary status of stellar clusters. We also establish the range of applicability of synthesis models set by the Lowest Luminosity Limit for the ionising flux, that is the lowest limit in cluster mass for which synthesis models can be applied to predict ionising spectra. This limit marks the boundary between the situations in which the ionising flux is better modeled with a single star as opposed to a star cluster; this boundary depends on the metallicity and age of the stellar population, ranging from 103 to more than 106 M⊙ in the case of a single burst event. As a consequence, synthesis models should not be used to try to account for the properties of clusters with smaller masses.