ARlogo Annu. Rev. Astron. Astrophys. 2013. 51:393-455
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1. INTRODUCTION

Many of the fundamental properties of unresolved stellar populations are encoded in their SEDs. These properties include the star formation history (SFH), stellar metallicity and abundance pattern, stellar initial mass function (IMF), total mass in stars, and the physical state and quantity of dust and gas. Some of these properties are easier to measure than others, and each provides important clues regarding the formation and evolution of galaxies. It is precisely these quantities, measured from the SEDs of galaxies, that have provided the foundation for our modern understanding of galaxy formation and evolution.

Over the past several decades considerable effort has been devoted to extracting information from the SEDs of galaxies, exploiting information from the FUV to the FIR. Early attempts at understanding the visible and NIR spectral windows approached the problem by combining mixtures of stars in ad hoc ways until a match was achieved with observations (e.g., Spinrad & Taylor 1971). More sophisticated versions of this technique were developed that incorporated physical constraints and automated fitting techniques (Faber 1972). At about the same time, synthesis models were being developed that relied on stellar evolution theory to constrain the range of possible stellar types at a given age and metallicity (e.g., Tinsley 1968, Searle, Sargent & Bagnuolo 1973, Tinsley & Gunn 1976, Bruzual 1983). The substantial progress made in stellar evolution theory in the 1980s and 1990s paved the way for the latter approach to become the de facto standard in modeling the SEDs of galaxies (e.g., Charlot & Bruzual 1991, Bruzual & Charlot 1993, Bressan, Chiosi & Fagotto 1994, Worthey 1994, Fioc & Rocca-Volmerange 1997, Leitherer et al. 1999, Vazdekis 1999). This modeling technique, which will be described in detail in the next section, is sometimes referred to as `evolutionary population synthesis' (e.g., Maraston 1998), although the term `stellar population synthesis' (SPS) has garnered wider use. The latter term will be used throughout this review.

The UV and IR spectral windows are rather more difficult to probe owing to the obscuring effects of the atmosphere. Nonetheless, numerous balloon and space-based observatories have opened up the ultraviolet and infrared to detailed investigations. In these spectral regions dust plays a major role; it absorbs and scatters much of the UV light emitted by stars and re-radiates that energy in the IR. In young stellar populations the UV is dominated by hot massive stars, while in old stellar populations the UV can be influenced by hot evolved stellar types such as post-AGB and extreme HB stars (see the review by O'Connell 1999 for details).

The development of models for the IR SEDs of galaxies (e.g., Draine & Lee 1984, Zubko, Dwek & Arendt 2004) has proceeded in parallel with the development of models for UV, optical, and NIR SEDs, and it is only recently that models have been developed to simultaneously and self-consistently predict the FUV through FIR SEDs (e.g., Devriendt, Guiderdoni & Sadat 1999, Silva et al. 1998, da Cunha, Charlot & Elbaz 2008, Groves et al. 2008, Noll et al. 2009a).

Several broad questions will serve to focus this review. They are:

The first question is relatively straightforward to address, while the second and third are necessarily more complicated. Attention will be given to cases where answers to these questions are presently unknown, but knowable (the `unknown unknowns', in Rumsfeld's sense, are of course the most interesting, but most difficult to discuss).

There are surprisingly few thorough reviews of stellar population synthesis and its application to modeling SEDs. The foundational review by Tinsley (1980) is highly recommended to anyone seeking a broad yet intuitive understanding of stellar populations and galaxy formation. The reviews by Faber (1977) and Frogel (1988) are more narrowly focused on old stellar populations but they are informative because many of the issues raised therein are still relevant today. Recently, Walcher et al. (2011) has presented an excellent review of many aspects related to the modeling of galaxy SEDs.

The topic of modeling galaxy SEDs is vast, and it would be impossible to provide a thorough review of the entire field. Hard decisions therefore had to be made. With regard to wavelength, energies higher than the FUV (roughly the Lyman limit), and lower than the submillimeter (roughly 1 mm) will not be discussed. Nebular emission lines will also be neglected, except in a few cases. The measurement of and uncertainty induced by photometric redshifts will not be discussed and active galactic nuclei (AGN) will be ignored. The technique of fitting models to data was reviewed recently by Walcher et al. (2011) and so will not be discussed here. A whole review could (and should) be written on the evaluation and comparison of existing SPS models. This will not be undertaken herein, except in cases where different models, when applied to data, produce starkly different results. The reader is referred to Conroy & Gunn (2010) for a recent comparison of several popular models. Finally, it is worth emphasizing what this review is not: it is not a summary of science results derived with SPS models. There is an extensive literature devoted to applying SPS models to data in order to derive insights into the formation and evolution of galaxies. Results of this nature, though fascinating in their own right, will not feature prominently in this review. Readers are referred to Renzini (2006) and Blanton & Moustakas (2009) for recent reviews along these lines.

This review is organized as follows. An overview of SPS model construction and application is provided in Section 2. We then turn to the topics of mass-to-light ratios and stellar masses (Section 3), star formation rates, histories, and stellar ages (Section 4), stellar metallicities and abundances patterns (Section 5), dust (Section 6), and the initial mass function (Section 7). Several concluding remarks are provided in Section 8.

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