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This chapter expands and updates the paper: Renzini, A. (2005) The Initial Mass Function 50 Years later, ed. E. Corbelli et al. , Ap. Sp. Sci. Library, 327, 221.

Most Popular Initial Mass Functions

Chabrier, G. (2003) Publ. Astron. Soc. Pac., 115, 763.
Kroupa, P. (2002) Science, 295, 82.
Salpeter, E.E. (1955) Astrophys. J., 121, 161.
Scalo, J.M. (1986) Fund. Cosm. Phys., 11, 1.

Recent review

Bastian, N. et al. (2010) Annu. Rev. Astron. Astrophys., 48, 339.

The IMF at High Redshift

Davé, R. (2008) Mon. Not. R. Astron. Soc., 385, 147.
Tacconi, L.J. (2008) Astrophys. J., 680, 246.
van Dokkum, P. G. (2008) Astrophys. J., 674, 29.

Table of Contents of the whole book

1 Firm and Less Firm Outcomes of Stellar Evolution Theory
1.1 A Brief Journey through Stellar Evolution
1.1.1 A 9Modot Star
1.1.2 The Evolution of Stars with Solar Composition
1.1.3 Dependence on Initial Chemical Composition
1.1.4 The Asymptotic Giant Branch Phase
1.2 Strengths and Weaknesses of Stellar Evolutionary Models
1.2.1 Microphysics
1.2.2 Macrophysics
1.3 The Initial Mass-Final Mass Relation

2 The Fundamentals of Evolutionary Population Synthesis
2.1 The Stellar Evolution Clock
2.2 The Evolutionary Flux
2.3 The Fuel Consumption Theorem
2.4 Fuel Consumptions
2.5 Population Synthesis Using Isochrones
2.6 The Luminosity Evolution of Stellar Populations
2.7 The Specific Evolutionary Flux
2.8 The IMF Scale Factor
2.9 Total and Specific Rates of Mass Return
2.10 Mass and Mass-to-Light Ratio
2.11 IMF-Dependent and IMF-Independent Quantities
2.12 The Age-Metallicity Degeneracy

3 Resolving Stellar Populations
3.1 The Stellar Populations of Pixels and Frames
3.1.1 The Stellar 1 Population of a Frame
3.1.2 The Stellar Population of a Pixel
3.2 Simulated Observations and Their Reduction

4 Age Dating Resolved Stellar Populations
4.1 Globular Cluster Ages
4.1.1 Absolute and Relative Globular Cluster Ages
4.1.2 Globular Clusters with Multiple Populations
4.2 The Age of the Galactic Bulge
4.3 Globular Clusters in the Magellanic Clouds
4.4 Stellar Ages of the M31 Spheroid
4.4.1 The Bulge of M31
4.4.2 The M31 Halo and Giant Stream
4.5 The Star Formation Histories of Resolved Galaxies
4.5.1 The Mass-Specific Production
4.5.2 Decoding the CMD
4.5.3 The Specific Production Method
4.5.4 The Synthetic CMD Method
4.5.5 An Example: the Stellar Population in the Halo of the Centaurus A Galaxy

5 The Evolutionary Synthesis of Stellar Populations
5.1 Simple Stellar Populations
5.2 Spectral Libraries
5.2.1 Empirical Spectral Libraries
5.2.2 Model Atmosphere Libraries
5.3 Composite Stellar Populations
5.4 Evolving Spectra
5.4.1 The Spectral Evolution of a SSP
5.4.2 The Spectral Evolution of Composite Stellar Populations
5.4.3 There are Also Binaries

6 Stellar Population Diagnostics of Galaxies
6.1 Measuring Star Formation Rates
6.1.1 The SFR from the Ultraviolet Continuum
6.1.2 The SFR from the Far-Infrared Luminosity
6.1.3 The SFR from Optical Emission Lines
6.1.4 The SFR from the Soft X-ray Luminosity
6.1.5 The SFR from the Radio Luminosity
6.2 Measuring the Stellar Mass of Galaxies
6.3 Age and Metallicity Diagnostics
6.3.1 Star-Forming Galaxies
6.3.2 Quenched Galaxies
6.4 Star-Forming and Quenched Galaxies through Cosmic Times
6.4.1 The Main Sequence of Star-Forming Galaxies
6.4.2 The Mass and Environment of Quenched Galaxies
6.4.3 Mass Functions

7 Supernovae
7.1 Observed SN Rates
7.2 Core Collapse SNe
7.2.1 Theoretical Rates
7.2.2 Nucleosynthetic Yields
7.3 Thermonuclear Supernovae
7.3.1 Evolutionary Scenarios for SNIa Progenitors
7.3.2 The Distribution of Delay Times
7.3.3 The SD Channel
7.3.4 The DD Channel
7.3.5 Constraining the DTD and the SNIa Productivity
7.3.6 SNIa Yields

8 The IMF From low to High Redshift
8.1 How the IMF Affects Stellar Demography
8.2 The M / L Ratio of Elliptical Galaxies and the IMF Slope Below 1 Modot
8.3 The Redshift Evolution of the M / L Ratio of Cluster Ellipticals and the IMF Slope Between ~ 1 and ~ 1.4 Modot
8.4 The Metal Content of Galaxy Clusters and the IMF Slope Between ~ 1 and ~ 40 Modot, and Above

9 Evolutionary Links Across Cosmic Time: an Empirical History of Galaxies
9.1 The Growth and Overgrowth of Galaxies
9.2 A Phenomenological Model of Galaxy Evolution
9.2.1 How Mass Quenching Operates
9.2.2 How Environmental Quenching Operates
9.2.3 The Evolving Demography of Galaxies
9.2.4 Caveats
9.2.5 The Physics of Quenching

10 The Chemical Evolution of Galaxies, Clusters, and the Whole Universe
10.1 Clusters of Galaxies
10.1.1 Iron in the Intracluster Medium and the Iron Mass-to-Light Ratio
10.1.2 The Iron Share Between ICM and Cluster Galaxies
10.1.3 Elemental Ratios
10.1.4 Metal Production: the Parent 1 Stellar Populations
10.1.5 Iron from SNIa
10.1.6 Iron and Metals from Core Collapse SNe
10.2 Metals from Galaxies to the ICM: Ejection versus Extraction
10.3 Clusters versus Field and the Overall Metallicity of the Universe
10.4 Clusters versus the Chemical Evolution of the Milky Way

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