PLAN DE MANEJO DE RESIDUOS

Here I introduce the basic concepts of evolutionary population synthesis mod- els. They represent the fundamental tool for the interpretation of galaxy spectra in terms of the physical parameters of their underlying stellar popu- lations.

Distant galaxies cannot be resolved in their stellar populations, rather what we can observe is their integrated light, which is the result of the superposi- tion of different stellar populations of various age and metallicity. In the 70’s attempts were made to interpret the integrated spectra of galaxies by repro- ducing the spectrum with a linear combination of individual spectra of stars of different types. This idea was soon abandoned because it involved too many free parameters, and replaced in the 80’s by evolutionary population syn- thesis technique (Tinsley 1978; Arimoto & Yoshii 1987; Guiderdoni & Rocca- Volmerange 1987; Bruzual A. & Charlot 1993; Fioc & Rocca-Volmerange 1997; Maraston 1998; Vazdekis 1999; Bruzual & Charlot 2003). The only free pa- rameters involved here are the star formation rate, the initial mass function and, in some cases, the chemical enrichment rate. The technique is based on the idea that a stellar population with any star formation history can be decomposed into a series of instantaneous starbursts, or ‘Simple Stellar Pop- ulations’ (SSP, i.e. a coeval population of stars formed instantaneously). The goal of population synthesis models is to describe the time-dependent distri- bution of stars in the colour-magnitude diagram and derive the integrated spectral evolution of the stellar population.

The spectral energy distribution of a stellar population characterized by star formation rate ψ(t) and metallicity Z(t) can be written as:

Fλ(t) = Z t

0

ψ(t−t0)Sλ(t0, Z(t−t0))dt (1.22)

whereSλ(t0, Z(t−t0)) is the spectral energy distribution of the isochrone8 of an SSP of age t and metallicity Z(t−t0). Stars are distributed along the

8_{An isochrone describes an SSP of given age and metallicity, by specifying the stellar param-} eters bolometric luminosity, effective temperature and surface gravity of the individual stellar masses.

1 Introduction

isochrone according to the IMF.

The two main ingredients necessary for the calculation ofSλ are the stellar evolution prescription, which gives the theoretical stellar evolutionary tracks of single stars of mass m, and the stellar spectral libraries. Both theoretical stellar atmosphere libraries and observed stellar spectra can be used. Obser- vational stellar libraries are limited to spectra of stars in the Milky Way and in the Magellanic Clouds (and thus they have scaled-solar elements abundance ratios). The libraries of individual stellar spectra are necessary to assign spec- tra to stars in the various evolutionary stages of the isochrone. Finally, the spectral energy distribution of the SSP is obtained by summing the spectra of individual stars along the isochrone.

Figure 1.6 illustrates the spectral evolution of an SSP of solar metallicity from 106 _{yr to 13 Gyr. When the population is young, the spectrum is dom-}

inated by short-lived, massive stars that produce a strong emission in the ultraviolet (UV), below 2000˚A. As time goes by the most massive stars leave the main sequence and evolve into red giant stars, causing a decrease in the UV light and an increase in the near-infrared (IR) light. After a few Gyrs, red giant stars account for most of the near-IR emission. The UV emission starts again to rise until 13 Gyr because of the accumulation of low-mass, post Asymptotic Giant Branch stars. From 4 to 13 Gyr the shape of the spectrum from the optical to the near-IR is almost unevolving, because low-mass stars cover a narrow temperature range during their entire evolution. The spectral evolution can be appreciated also in the strength of stellar absorption lines. In particular, between 0.1 and 1 Gyr there is a marked strengthening of all the Balmer lines (from Hα at 6563˚A to the continuum limit at 3646˚A). The strength of the Balmer lines represent a powerful diagnostic tool of recent burst of star formation. Another important spectral feature is the so-called 4000˚A-break which arises from the prominence in cool stars of many metallic lines blueward of 4000˚A. This feature is widely used as age indicator, but it shows also a dependence on metallicity at old ages. All these spectral lines, plus other metallic lines associated to Ca, Mg, Fe, continue to evolve even between 4 and 13 Gyr when the shape of the continuum is almost constant.

The interpretation of observed galaxy spectra in terms of physical parame- ters relies often on the comparison of their broad-band colours with the pre- dictions from population synthesis models9. The main problem in this respect is the similar effect that age and metallicity have on the integrated light of a stellar population. The ages and metallicities derived from integrated galaxy

9

The stellar ages and metallicities derived from galaxy spectra have to be interpreted as the light-weighted mean ages and metallicities of all the stellar population in a galaxy.

1.3 The stellar populations in galaxies

Figure 1.6: Spectral evolution from the ultraviolet to the infrared of a Simple Stellar Population of solar metallicity, obtained from the Bruzual & Charlot (2003) population synthesis code. At young ages (indicated on each spectrum in units of Gyr) the light is dominated by the UV emission of young, short- lived, massive stars. These stars soon leave the main sequence and evolve into Red Giants, causing a drop of the UV emission and a rise in the infrared. Between 1 and 13 Gyr the shape of the continuum does not change signif- icantly, because it is dominated by long-lived, low-mass stars, which cover a small temperature range. Over this time interval, it can be appreciated the strengthening of several absorption lines and the characteristic break at 4000˚A. These are important diagnostics of the ages and metallicities of stars in galaxies.

spectra are therefore highly degenerate. This problem is further complicated in galaxies with a significant content of dust, which produces a reddening of the optical spectrum similar to that caused by increasing age or metallicity.

A well-established method to try and solve this degeneracy is to use spectral diagnostics which involve single spectral absorption features that have differ- ent sensitivities to age and metallicity. The most successful combinations of absorption features are those involving a hydrogen Balmer line, as a diag- nostic of age, and ‘metallic’ features sensitive to the abundance of elements

1 Introduction

such as Fe or Mg. Moreover, these spectral absorption features are defined on narrower wavelength ranges than colours, and so they are believed to be almost insensitive to the reddening of the continuum due to dust absorption. In order to allow a universal analysis of galaxy spectra Burstein et al. (1984) and Faber et al. (1985) introduced a set of absorption line indices in the op- tical, known as the Lick system, which has become the most widely used set of absorption indices. It includes 25 features over the wavelength range from 4000 to 6400˚A. In the Lick system, an index is defined by a central ‘feature bandpass’, bracketed by two ‘pseudo-continuum bandpasses’ (Worthey 1994; Worthey & Ottaviani 1997). Atomic indices are conventionally expressed in ˚

A of equivalent width, while molecular indices in magnitudes. The strength of these features were originally parametrized as a function of stellar parameters, such as effective temperature Tef f and surface gravity g, using a sample of 460 Galactic stars. Thesefitting functionsare purely empirical and were used to measure index strengths of theoretical SSPs. There are several problems, however, related to the use of the fitting functions. The stellar library used to define the Lick system is sparse at supra-solar metallicities. Therefore, the fitting functions are well defined only around solar metallicity and are mostly extrapolated at higher metallicities. Moreover, the Lick stellar library lacks of hot stars, necessary for the interpretation of young populations, so this kind of studies were usually limited to old stellar populations. Moreover, the Lick spectra were not flux-calibrated and had low resolution (∆λ∼ 8˚A, al- most three times lower than the resolution of modern spectroscopic surveys). The calibration of the index strengths onto the Lick system requires therefore to degrade observed galaxy spectra to the lower resolution of the Lick spec- trograph. Since the Lick standards are not flux-calibrated, the shape of the continuum has to be corrected, introducing another source of uncertainty.

All these limits associated with the use of the fitting functions and the calibration onto the Lick system have now been overcome with population synthesis models based on higher-resolution stellar spectra that cover the en- tire temperature range (Bruzual & Charlot 2003). The 3˚A resolution matches the resolution of the spectra gathered by modern spectroscopic surveys, and allows to measure the indices on the model spectra using directly the band- pass definitions, in the same way as in observed spectra. There is no need to degrade the observed spectra to lower resolution. Moreover, the full tem- perature coverage allows to extend the use of the Lick indices to star-forming galaxies with younger stellar populations. As explained in Chapter 2 I will use these models in this work.