Abstract. We present the results of a double analysis of the ionizing cluster in NGC 588, a giant H region (GHR) in the outskirts of the nearby galaxy M 33. For this purpose, we obtained ground based long-slit spectroscopy and combined it with archival ground based and space borne imaging and spectroscopy, in the wavelength range 1100−9800 Å. A first modeling of the cluster was performed using integrated properties, such as the spectral energy distribution (SED), broad band colors, nebular emission Hβ equivalent width, the main ultraviolet resonance lines, and the presence of Wolf-Rayet star features. By applying standard assumptions about the initial mass function (IMF), we were unable to fit satisfactorily these observational data. This contradictory result led us to carry out a second modeling, based on a resolved photometric analysis of individual stars in Hubble Space Telescope (HST) images, by means of finding the best fit isochrone in color−magnitude diagrams (CMD), and assigning a theoretical SED to each individual star. The overall SED of the cluster, obtained by integrating the individual stellar SEDs, is found to fit better the observed SED than the best solution found through the integrated first analysis, but at a significantly later stage of evolution of the cluster of 4.2 Myr, as obtained from the best fit to the CMD. A comparative analysis of both methods traces the different results to the effects of statistical fluctuations in the upper end of the IMF, which are significant in NGC 588, with a computed cluster mass of 5600 M , as predicted by Cerviño et al. (2002, A&A, 381, 51). We discuss the results in terms of the strong influence of the few most massive stars, six in the case of NGC 588, that dominate the overall SED and, in particular, the ionizing far ultraviolet range beyond the Lyman limit.

The planetary nebula TS 01 (also called PN G 135.9+55.9 or SBS 1150+599A) with its record-holding low oxygen abundance and its double degenerate close binary core (period 3.9 h) is an exceptional object located in the Galactic halo. We have secured observational data in a complete wavelength range to pin down the abundances of half a dozen elements in the nebula. The abundances are obtained via detailed photoionization modelling which takes into account all the observational constraints (including geometry and aperture effects) using the pseudo-3D photoionization code Cloudy_3D. The spectral energy distribution of the ionizing radiation is taken from appropriate model atmospheres. Incidentally we find from the new observational constraints that both stellar components contribute to the ionization: the "cool" one provides the bulk of hydrogen ionization, while the "hot" one is responsible for the presence of the most highly charged ions, which explains why previous attempts to model the nebula experienced difficulties. The nebular abundances of C, N, O, and Ne are found to be 1/3.5, 1/4.2, 1/70, and 1/11 of the solar value respectively, with uncertainties of a factor 2. Thus the extreme O deficiency of this object is confirmed. The abundances of S and Ar are less than 1/30 of solar. The abundance of He relative to H is 0.089 ± 0.009. Standard models of stellar evolution and nucleosynthesis cannot explain the abundance pattern observed in the nebula. To obtain an extreme oxygen deficiency in a star whose progenitor has an initial mass of about 1 M requires an additional mixing process, which can be induced by stellar rotation and/or by the presence of the close companion. We have computed a stellar model with an initial mass of 1 M , appropriate metallicity, and initial rotation of 100 km s −1 , and find that rotation greatly improves the agreement between the predicted and observed abundances.

We present the results of an exhaustive study of the ionized gas in NGC 588, a giant Hii region in the nearby spiral galaxy M 33. This analysis uses a high number of diagnostics in the optical and infrared ranges. Four temperature diagnostics obtained with optical lines agree with a gas temperature of 11 000 K, while the [Oiii] λ5007/λ88 µm ratio yields a much lower temperature of ≈8000 K. This discrepancy suggests the presence of large temperature inhomogeneities in the nebula. We investigated the cause of this discrepancy by constructing photoionization models of increasing complexity. In particular, we used the constraints from the Hα and Hβ surface brightness distributions and state-of-theart models of the stellar ionizing spectrum. None of the successive attempts was able to reproduce the discrepancy between the temperature diagnostics, so the thermal balance of NGC 588 remains unexplained. We give an estimate of the effect of this failure on the O/H and Ne/O estimates and show that O/H is known to within ±0.2 dex.

Aims. This work aims to provide a theoretical formulation of surface brightness fluctuations (SBF) in the framework of probabilistic population synthesis models that have no deterministic relations between the different stellar components of a population but only relations on average, and to distinguish between the different distributions involved in the definition of SBF. Methods. By applying the probabilistic theory of stellar population synthesis models, we estimate the shape (mean, variance, skewness, and kurtosis) of the distribution of fluctuations across resolution elements, and examine the implications for SBF determination, definition and application. Results. We distinguish between three definitions of SBF: (i) stellar population SBF, which can be computed from synthesis models and provide an intrinsic metric for fit for stellar population studies; (ii) theoretical SBF, which include the stellar population SBF plus a term accounts for the distribution of the number of stars per resolution element ψ(N); theoretical SBF that coincides with the Tonry & Schneider (1998) definition in the special case when ψ(N) has a Poisson distribution. We find that the Poisson contribution to theoretical SBF is around 0.1stellar population SBF and is negligible; (iii) observational SBF. We present alternative ways to compute the SBF and extend the application of stellar population SBF to defining a metric for fitting for standard stellar population studies. Conclusions. We demonstrate 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.