On emission-line spectra obtained from evolutionary synthesis models I. Dispersion in the ionising flux and Lowest Luminosity Limits

(abriged) 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 due to the smaller absolute number of massive stars. The dispersion in the number of massive stars also produces a dispersion in the properties of the corresponding ionising spectra. In this paper, we lay the bases for the future analysis of this effect by evaluating the dispersion in the ionising fluxes of synthetic spectra. As an important consequence, 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. Additionally, we find convincing suggestions that the He II lines are strongly affected by sampling, 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, ranging from 10^3 to more than 10^6 Mo. As a consequence, synthesis models should not be used to try to account for the properties of clusters with smaller masses.Comment: Replaced with accepted versio

On surface brightness fluctuations: probabilistic and statistical bases I: Stellar population and theoretical SBF

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 propose 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.Comment: A&A accepte

Confidence limits of evolutionary synthesis models III. On time-integrated quantities

Evolutionary synthesis models are a fundamental tool to interpret the properties of observed stellar systems. In order to achieve a meaningful comparison between models and real data, it is necessary to calibrate the models themselves, i.e. to evaluate the dispersion due to the discreteness of star formation as well as the possible model errors. In this paper we show that linear interpolations in the log M - log t_k plane, that are customary in the evaluation of isochrones in evolutionary synthesis codes, produce unphysical results. We also show that some of the methods used in the calculation of time-integrated quantities (kinetic energy, and total ejected masses of different elements) may produce unrealistic results. We propose alternative solutions to solve both problems. Moreover, we have quantified the expected dispersion of these quantities due to stochastic effects in stellar populations. As a particular result, we show that the dispersion in the 14N/12C ratio increases with time.Comment: 11 pages, 8 figures, accepted by A&

Confidence levels of evolutionary synthesis models III: On sampling and Poissonian fluctuations

In terms of statistical fluctuations, stellar population synthesis models are only asymptotically correct in the limit of a large number of stars, where sampling errors become asymptotically small. When dealing with stellar clusters, starbursts, dwarf galaxies or stellar populations within pixels, sampling errors introduce a large dispersion in the predicted integrated properties of these populations. We present here an approximate but generic statistical formalism which allows a very good estimation of the uncertainties and confidence levels in any integrated property, bypassing extensive Monte Carlo simulations, and including the effects of partial correlations between different observables. Tests of the formalism are presented and compared with proper estimates. We derive the minimum mass of stellar populations which is required to reach a given confidence limit for a given integrated property. As an example of this general formalism, which can be included in any synthesis code, we apply it to the case of young (t < 20 Myr) starburst populations. We show that, in general, the UV continuum is more reliable than other continuum bands for the comparison of models with observed data. We also show that clusters where more than 10^5 Mo have been transformed into stars have a relative dispersion of about 10% in Q(He+) for ages smaller than 3 Myr. During the WR phase the dispersion increases to about 25% for such massive clusters. We further find that the most reliable observable for the determination of the WR population is the ratio of the luminosity of the WR bump over the Hbeta luminosity. A fraction of the observed scatter in the integrated properties of clusters and starbursts can be accounted for by sampling fluctuations.Comment: accepted by A&A. 13 figures, a&a style packages see also http://www.laeff.esa.es/users/mcs for tables (by end October) and for high resolution figure

The connection between missing AGB stars and extended horizontal branches

Recent surveys confirm early results about a deficiency or even absence of CN-strong stars on the asymptotic giant branch (AGB) of globular clusters (GCs), although with quite large cluster-to-cluster variations. In general, this is at odds with the distribution of CN band strengths among first ascent red giant branch (RGB) stars. Norris et al. proposed that the lack of CN-strong stars in some clusters is a consequence of a smaller mass of these stars that cannot evolve through the full AGB phase. In this short paper we found that the relative frequency of AGB stars can change by a factor of two between different clusters. We also find a very good correlation between the minimum mass of stars along the horizontal branch (Gratton et al. 2010) and the relative frequency of AGB stars, with a further dependence on metallicity. We conclude that indeed the stars with the smallest mass on the HB cannot evolve through the full AGB phase, being AGB-manque'. These stars likely had large He and N content, and large O-depletion. We then argue that there should not be AGB stars with extreme O depletion, and few of them with a moderate one.Comment: 5 Pages, 2 figures, A&A Accepte

M75, a Globular Cluster with a Trimodal Horizontal Branch. I. Color-Magnitude Diagram

Deep UBVI photometry for a large field covering the distant globular cluster M75 (NGC 6864) is presented. We confirm a previous suggestion (Catelan et al. 1998a) that M75 possesses a bimodal horizontal branch (HB) bearing striking resemblance to the well-known case of NGC 1851. In addition, we detect a third, smaller grouping of stars on the M75 blue tail, separated from the bulk of the blue HB stars by a gap spanning about 0.5 mag in V. Such a group of stars may correspond to the upper part of a very extended, though thinly populated, blue tail. Thus M75 appears to have a trimodal HB. The presence of the "Grundahl jump" is verified using the broadband U filter. We explore the color-magnitude diagram of M75 with the purpose of deriving the cluster's fundamental parameters, and find a metallicity of [Fe/H] = -1.03 +/- 0.17 dex and -1.24 +/- 0.21 dex in the Carretta & Gratton (1997) and Zinn & West (1984) scales, respectively. We discuss earlier suggestions that the cluster has an anomalously low ratio of bright red giants to HB stars. A differential age analysis with respect to NGC 1851 suggests that the two clusters are essentially coeval.Comment: 19 pages, 15 figures, emulateapj5/apjfonts style. Astronomical Journal, in press. This version contains some very low-resolution figures, due to the size constraints of astro-ph. We strongly encourage the interested reader to download instead the preprint with full-resolution figures, which can be found at http://www.astro.puc.cl/~mcatelan

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RR Lyrae variables in Galactic globular clusters: IV. Synthetic HB and RR Lyrae predictions

We present theoretical predictions concerning horizontal branch stars in globular clusters, including RR Lyrae variables, as derived from synthetic procedures collating evolutionary and pulsational constraints. On this basis, we explore the predicted behavior of the pulsators as a function of the horizontal branch morphology and over the metallicity range Z=0.0001 to 0.006, revealing an encouraging concordance with the observed distribution of fundamentalised periods with metallicity. Theoretical relations connecting periods to K magnitudes and BV or VI Wesenheit functions are presented, both appearing quite independent of the horizontal branch morphology only with Z greater or equal than 0.001. Predictions concerning the parameter R are also discussed and compared under various assumptions about the horizontal branch reference luminosity level.Comment: 11 pages, 10 figures. Accepted for publication in "Astronomy and Astrophysics

Confidence limits of evolutionary synthesis models. IV Moving forward to a probabilistic formulation

Synthesis models predict the integrated properties of stellar populations. Several problems exist in this field, mostly related to the fact that integrated properties are distributed. To date, this aspect has been either ignored (as in standard synthesis models, which are inherently deterministic) or interpreted phenomenologically (as in Monte Carlo simulations, which describe distributed properties rather than explain them). We approach population synthesis as a problem in probability theory, in which stellar luminosities are random variables extracted from the stellar luminosity distribution function (sLDF). We derive the population LDF (pLDF) for clusters of any size from the sLDF, obtaining the scale relations that link the sLDF to the pLDF. We recover the predictions of standard synthesis models, which are shown to compute the mean of the sLDF. We provide diagnostic diagrams and a simplified recipe for testing the statistical richness of observed clusters, thereby assessing whether standard synthesis models can be safely used or a statistical treatment is mandatory. We also recover the predictions of Monte Carlo simulations, with the additional bonus of being able to interpret them in mathematical and physical terms. We give examples of problems that can be addressed through our probabilistic formalism. Though still under development, ours is a powerful approach to population synthesis. In an era of resolved observations and pipelined analyses of large surveys, this paper is offered as a signpost in the field of stellar populations.Comment: Accepted by A&A. Substantially modified with respect to the 1st draft. 26 pages, 14 fig