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The stellar populations of bulges provide a fossil record of their formation and evolutionary history, including insights into the duration and efficiency of the primary epochs of star formation. In previous chapters, we have learnt that there are three main types of bulges: the classical, the disky, and the boxy/peanut. All of them show different structural and kinematical properties and different formation scenarios are proposed to explain them. In these scenarios, the star formation history is predicted to be different, e.g., the proposed mechanisms to form classical bulges imply rapid and efficient star formation while disky bulges are believed to form slowly and at lower redshifts from the inflow of mainly gaseous material to the center of the galaxy (see Wyse et al. 1997, Kormendy & Kennicutt 2004 for reviews).

Boxy/peanut bulges are believed to be parts of bars seen edge-on and have their origin in vertical instabilities of the disk. Therefore they are expected to have a similar stellar population compared to the inner disk. In principle then we should be able to distinguish between different formation scenarios simply by studying the different ages, metallicities and abundances ratios of the bulges. The situation, however, it is not that straightforward; as discussed in other chapters (see e.g. Chapter 2.3) internal processes related with disk instabilities can also occur at high redshift and in short timescales. Furthermore, bulges with properties resembling pseudobulges can form, not only by internal processes related with the presence of non-axisymmetric components, but also by accretion of gas and galaxies (Guedes et al. 2013, Querejeta et al. 2015, Eliche-Moral et al. 2011, Obreja et al. 2013). However, getting information on the ages, metallicities and abundances ratios in the different types of bulges constitute, undoubtedly, a strong constrain for scenarios of bulge formation and, therefore, several authors have studied the problem. With the exception of the MW and M31, in which we can resolve individual stars, studies of bulges have to deal with integrated properties, through their mean color or absorption lines. Such unresolved stellar populations studies have been far less common for bulges than for elliptical galaxies. The reason is that disk galaxies have more dust and ionized gas. The first affects the colors and the second fills the Balmer lines, the most important age diagnostics in the optical. In addition, bulges have, in general, lower surface brightness than ellipticals and the presence of several morphological components, such as disks, bars, rings, etc., complicates the interpretation of the results. Lastly, the light coming from the disk may contaminate the bulge spectrum in a way that is difficult to quantify. This problem is especially acute for studies of stellar population gradients.

Furthermore, over many years, unresolved stellar populations studies have been done comparing the integrated colors or absorption lines with the theoretical predictions for single stellar populations (SSP); that is, an essentially coeval population of stars formed with a given initial mass function with the same chemical abundance pattern. While this scenario may not be a bad approximation for massive elliptical galaxies, bulges, especially those formed secularly, are believed to have a more extended star formation history. This means that the young populations, which have low mass-to-light ratios, bias the analyses of composite populations, if present (e.g. Trager et al. 2000).

The relatively low number of studies, the small – and biased – samples, and the difficulties pointed out above have led to a lack of consensus about important results concerning the stellar populations of bulges, as I will show in this review. However, in the last decade, stellar population models which predict not only individual spectral features, but the entire synthetic spectra for a population of a given age and metallicity (Vazdekis 1999, Bruzual & Charlot 2003, Vazdekis et al. 2010, Coelho et al. 2007, Walcher et al. 2009, Conroy et al. 2014) have been released. The availability of these models is stimulating the development of numerical algorithms to invert the observed galaxy spectrum onto a basis of independent components (combination of single stellar populations, age-metallicity relation, and dust extinction). Also, new specialized software allow the separation of the light coming from the stars and ionized gas in a reliable way (e.g. Sarzi et al. 2006). In addition to this, new data from integral field spectrographs (e.g. Bacon et al. 2001, Cappellari & et al. 2011, Blanc et al. 2013) are changing the way we see galaxies (Sánchez & et al. 2012, Rosales-Ortega et al. 2010). The analysis of these datasets allows one to associate stellar population properties with morphological and kinematical characteristics of the galaxies, making the interpretation of stellar populations more secure. Therefore, the development of the field is very promising and we foresee important advances in the decades to come.

In this chapter, I will try to review the state of the art in the area, trying to highlight the necessary steps to get a better understanding of the star formation histories of these complex systems. Section 2 summarizes the general results obtained with single apertures. Section 3 compile the works on the possible influence of bars in the stellar populations of bulges and on the stellar populations of bars themselves. Section 4 outline the results obtained with full spectral fitting techniques and Sect. 5 reports on the studies of stellar population gradients in bulges. In Sect. 6, I show the results about the possible connection between the stellar populations of bulges and disks while in Sect. 7 the main results are summarized. In Sect. 8, I give some thoughts of what I think the next steps for the study of stellar populations in bulges should be.

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