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1.4.1

Basics

The purpose of each stellar population model is the understanding of the formation and evolution of galaxies. As we will use such models to derive globular cluster ages, metallicities, and abundance ratios, some words are indicated to describe their basic architecture. Ideally, one would like to know the properties (such as the presence of certain stellar types, stellar ages, chemical composition, spatial distribution, and stellar kinematics) of each stellar population which contributes to the integrated light of a stellar system. As we have seen above, a galaxy can be assembled in many different ways opening a wide parameter space of ages and chemical compositions for the contributing stellar populations. Clearly, the integrated light of a galaxy will be the sum ofistellar populations which formed throughout its lifetime. These stellar populations can be fractionised into j units of simple stellar populations (Renzini & Buzzoni 1986). While stellar populations are associated with a specific star formation mechanism and/or epoch, a simple stellar population defines a sample of star with the same age andchemical composition. Hence, in a simplified form we can write for the integrated flux F as a function of total mass M, chemical abundancesXn and time

F(M, Xn, t)Galaxy= X i kiF(M, Xn, t)Population,i (1.1) F(M, Xn, t)Population= X j ljF( IMF, Xn, t)SSP,j (1.2)

way the integrated flux can be broken down in F(M, Xn, t)Galaxy=

X

x

mxF( IMF, Xn, t)SSP,x. (1.3)

The interpretation of the integrated light is based on the understanding of the systematics of stellar populations in the local neighbourhood, that is in the Milky Way. By means of spectral diagnostics, observed integrated spectra of distant stellar systems can be compared with synthesized spectra for simple stellar populations of known age and chemical composition or with reference spectra of well-studied objects.

In general, such observed spectra can be analysed in three different ways: (1) A library of stellar template spectra for a wide range of surface gravities logg, effec- tive temperaturesTeff, and chemical composition, is initially observed. This library is then used in combination with theoretical isochrones to obtain the best-fitting integrated spectrum (population synthesis technique). However, the lack of enough stellar spectra with high resolution to cover a wide range in age and chemical com- position, and the lack of local stars with extremely high abundances, which are found in extragalactic systems, hampers this approach. (2) Theoretical isochrones are the starting point of theevolutionary synthesis technique. Assuming an initial mass function (typically a Salpeter-type power law, Salpeter 1955), and an empiri- cal library of stellar fluxes to convert from logg,Teff, and chemical composition to observational parameters (e.g. Lejeune et al. 1997, 1998; Westera et al. 2002), one can compute the integrated spectrum of a stellar population of a given age and metal content. For predictions of line indices so-called fitting functions can be cal- culated using an empirical stellar library. These functions define the behaviour of an index I as a function ofTeff, logg, and [Fe/H] (Gorgas et al. 1993; Worthey 1994; Worthey & Ottaviani 1997). Another ingredient is the set of response functions which give the fractional change of an indexIas the result of an abundance change of a given element under the constraint of constant total metallicity. The only work published so far focused on theα-elements O, N, Mg, Ca, Na, Si, Ti and iron-peak elements Cr and Fe (Tripicco & Bell 1995). These empirical functions are used to predict line strengths for stellar populations which then need to be calibrated on local stellar populations, e.g. Galactic globular clusters, with well-known parame- ters (e.g. Thomas et al. 2003a). The advantage of this lengthy computation is the ability to extrapolate predictions for SSPs with chemical abundance patterns which are not found in the local neighbourhood. (3) Another widely used method is the comparison of observed spectra with the integrated spectra of well-studied reference objects. This can lead to a deeper understanding of the stellar populations in the ob- served object by examination of differences between reference and object spectrum (differential approach) if the differences in abundance pattern are under control. In a more liberal form (without a reference object), this technique can be used to study differences between similar objects with various properties, such as environmental density, morphology, mass, etc. (e.g. Bower et al. 1990; de Carvalho & Djorgovski 1992; Kuntschner et al. 2002a).

1.4.2

Diagnostics

There are two complementary observational techniques to study integrated spectra. (1) Low-resolution spectroscopy (R <_∼ 1000) aims at covering a long wavelength

baseline, ideally from the mid-UV (∼ 2500 ˚A) to the near-IR (∼ 2.6 µm). The goal is to completely sample the spectral energy distribution (SED) of a stellar sys- tem, including the contributions of all types of stars, from the hottest turn-off stars (i.e. hot blue horizontal branch stars) to the coolest stars at the tip of the post- asymptotic giant branch. A major problem of this approach is the uniqueness of the spectrum. It is well known that the integrated spectra are highly degenerate in age and metallicity (e.g. Faber 1972; O’Connell 1976; Worthey 1994). (2) Rather than aiming for the full wavelength coverage, higher-resolution spectra (R >_∼1000) can provide more detailed information on individual spectral features. Some absorption features with their different dependencies on stellar atmosphere parameters (logg, Teff, and chemical composition) can better constrain the contribution of specific stellar evolutionary phases to the integrated light. With this information, one then can attempt to solve the non-uniqueness problem of integrated low-resolution spec- tra. However, this latter approach works only for stellar systems with low velocity dispersion, such as globular clusters, where single spectral features can be resolved. Throughout this thesis, we follow the path of low-resolution spectroscopy using line indices as diagnostics for age and basic chemical composition. A major dif- ference between the two canonical galaxy-formation scenarios described above are the different predicted star-formation histories of early-type galaxies which stand in marked contrast to each other and allow a differentiation between the models. While in the hierarchical merging picture galaxies are thought to experience longer assembly timescales, the monolithic collapse scenario predicts early and short pe- riods of star formation. We will use two different techniques, direct and chemical clocking, to constrain the ages and formation timescales of extragalactic globular clusters and infer the formation histories of their host galaxies. Both techniques are presented below.

Direct Clocking

As a stellar population grows older, the main sequence temperature decreases, and, to the first order, the integrated light is consistent with a cooler stellar population. There are also higher-order effects which can influence this general trend, such as the horizontal branch morphology, which becomes significant at old ages and low metallicities. Such biases will be discussed in detail in the course of this thesis. In general, observables which trace the mean photospheric temperature can be used as diagnostics to determine the age of a stellar population. The Balmer line series is such a spectroscopic tracer. The strength of the Balmer line series shows a maximum at T ≈104 K and decreases towards higher and lower temperatures. Strongest Balmer lines are found in A-type stars with typical main sequence lifetimes of∼1 Gyr (Binney & Merrifield 1998). For older stellar populations weaker Balmer lines indicate higher ages. The strength of specific Balmer lines which fall in the optical spectral range of our data will be used to determine the ages of individual extragalactic globular clusters.

Chemical Clocking

Abundance ratios in stellar populations primarily depend on the specific stellar evo- lutionary phases which contributed to the chemical enrichment of the parent molec- ular cloud. Stars of different mass contribute with their specific mix of elements in their ejecta to the chemistry of the cloud on different timescales. These abundance patterns are imprinted in the stellar progeny of the cloud. Hence, abundance ratios can be used as clocks for star-formation timescales. The most prominent example is the ratio betweenα-elements (i.e. O, Mg, Si, S, Ca, Ti) and iron-peak elements (i.e. Cr, Mn, Fe, Co, Ni, Cu, Zn).

low−resolution spectrum

Digitized Sky Survey

M87, a giant elliptical galaxy

Figure 1.2: The figure illustrates the way to obtain a line-index measurement of the integrated light of an extragalactic globular cluster. Representatively, we show the rich globular cluster system in the giant elliptical galaxy M87, and in the enlarge- ment the Galactic globular cluster, NGC 6284, with the spectrograph slit projected ontop. A low resolution spectrum is obtained from the integrated light falling through the slit. At the very bottom of the plot, the graphical definition of a line index is shown. The feature passband with boundariesλmin andλmaxis flanked by two neighbouring continuum passbands. The mean flux in both continuum passband is used to linearly interpolate apseudo-continuum throughout the feature passband. The ratio between the observed flux Fl and the flux of thepseudo-continuum Fc per unit wavelength is used to calculate the line index.