Published in New Astronomy Reviews, Volume 57, Issue 5, p. 123-139, 2013.
http://arxiv.org/abs/1312.0015

For a PDF version of the article, click here.

THE STOCHASTIC NATURE OF STELLAR POPULATION MODELLING

Miguel Cerviño a, b, c


a Instituto de Astrofísica de Andlucía (IAA-CSIC), Placeta de la Astronomía s/n, 18028, Granada, Spain
b Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain
c Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Spain


Abstract: Since the early 1970s, stellar population modelling has been one of the basic tools for understanding the physics of unresolved systems from observation of their integrated light. Models allow us to relate the integrated spectra (or colours) of a system with the evolutionary status of the stars of which it is composed and hence to infer how the system has evolved from its formation to its present stage. On average, observational data follow model predictions, but with some scatter, so that systems with the same physical parameters (age, metallicity, total mass) produce a variety of integrated spectra. The fewer the stars in a system, the larger is the scatter. Such scatter is sometimes much larger than the observational errors, reflecting its physical nature. This situation has led to the development in recent years (especially since 2010) of Monte Carlo models of stellar populations. Some authors have proposed that such models are more realistic than state-of-the-art standard synthesis codes that produce the mean of the distribution of Monte Carlo models.

In this review, I show that these two modelling strategies are actually equivalent, and that they are not in opposition to each other. They are just different ways of describing the probability distributions intrinsic in the very modelling of stellar populations. I show the advantages and limitations of each strategy and how they complement each other. I also show the implications of the probabilistic description of stellar populations in the application of models to observational data obtained with high-resolution observational facilities. Finally, I outline some possible developments that could be realized in stellar population modelling in the near future.


Keywords : stars: evolution, galaxies: stellar content, Hertzprung-Russell (HR) and C-M diagrams, methods: data analysis


Table of Contents

INTRODUCTION
Motivation
A short historical review

THE ORIGIN OF STOCHASTICITY IN STELLAR POPULATION MODELLING
From the stellar birth rate to the stellar luminosity function
From resolved CMD to integrated luminosities and the dependence on N

STELLAR POPULATION MODELLING: THE PARAMETRIC APPROACH AND ITS LIMITATIONS
The mean and variance obtained using standard models

STELLAR POPULATIONS USING MONTE CARLO MODELLING
Understanding Monte Carlo simulations: the revenge of the stellar luminosity function
What we can learn from Monte Carlo simulations?

IMPLICATIONS OF PROBABILISTIC MODELLING
Metrics of fitting
The population and the sample definition
Some rules of thumb

THE (STILL) POORLY EXPLORED ARENA

CONCLUSIONS

REFERENCES

You only get a measure of order and control
when you embrace randomness.
(N.N. Taleb, Antifragile)

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