Constraining the physical properties of 3D-HST galaxies through the combination of photometric and spectroscopic data 

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History of star formation in a hierarchical universe

In recent years, sophisticated star formation and metal enrichment histories of galax- ies have been modeled by appealing to the combination of cosmological N-body sim- ulations (to trace the evolution of dark matter haloes) with semi-analytical recipes or gas-dynamics codes (to simulate the behavior of baryons in the dark-matter structures). In this Section, we first present a few simulations of the evolution of dark-matter particles. Then, we describe possible treatments for the baryonic com- ponent. For simplicity, we analyze these two components separately, although often single codes follow their evolution simultaneously. Cosmological N-body simulations rely on the standard cosmological scenario that structures grow from weak density fluctuations present in the otherwise homo- geneous and rapidly expanding early Universe. These fluctuations are amplified by gravity, turning into the structures we observe today.1 The evolution of these fluc- tuations is a highly non-linear process, which can be assessed most readily through numerical simulations. In this framework, cold dark matter is assumed to be made of elementary particles which interact only gravitationally. The representation of this fluid as an N-body system is a good approximation, which improves as the size of the simulation increases (in number of particles and size of the simulated box).
The first N-body simulation used 300 particles [Peebles, 1970]. Cosmological simulations have since improved in size and resolution. Cosmological simulations built to study the large-scale structure of the Universe tend to favor large size and low resolution. In contrast, simulations designed to study galaxy formation tend to favor resolution over size. One of the most widely used simulations today is the Millennium Simulation [Springel et al., 2005]. It is one of the largest existing simulations, with sufficient mass resolution to obtain good statistical samples of rare objects, such as massive cluster haloes. The possibility to sample large volumes is required to build mock catalogues for future galaxy surveys. Kim et al. [2009] hold so far the record of the largest simulation (the Horizon Run) with 69.9 billion particles and a box of 6.6 Gpc on a side, but with low mass resolution compared to the Millennium. Smaller volumes with higher mass resolution (much more compu- tationally demanding) can improve the understanding of galaxy formation tracing the evolution of low-mass galaxies. An example which fulfills this requirement is the Millennium II simulation [Boylan-Kolchin et al., 2009]. Among the other N-body cosmological simulations that have been run more recently, we can cite the Hori- zon simulation by Teyssier et al. [2009] and the most recent Bolshoi simulation by Klypin et al. [2011]. These simulations were all run in the framework of a CDM Universe, with slightly different parameter variants. Their main characteristics are given in Table 2.1.

Emission from stellar populations

In this Section, we describe the techniques used to model the emission from the primary component of galaxies: stellar populations. Stellar population synthesis models have been developed for over 40 years to interpret the light from galaxies in terms of physical parameters. The first attempts to model and interpret spectra of galaxies relied on trial and error analyses ([Spinrad and Taylor, 1971, Faber, 1972, O’connell, 1976, Turnrose, 1976, Pritchet, 1977]). In this technique, one reproduces the spectral energy distribution of an observed galaxy with a linear combination of individual stellar spectra of various spectral types and luminosity classes taken from a comprehensive library. The solution is found by minimizing numerically the difference between models and data and by invoking additional constraints such as positive star numbers, increasing number of stars with decreasing mass on the main sequence and consistent numbers of evolved red giant stars and main-sequence progenitors. This technique was abandoned in the early 80’s because the number of free parameters was too large to be constrained by typical galaxy spectra. More recent models are based on the evolutionary population synthesis technique (see Guiderdoni and Rocca-Volmerange 1987, Bruzual and Charlot 1993, Leitherer and Heckman 1995, Maraston 1998, and references therein). This technique is based on the property that stellar populations can be expanded in series of instantaneous starbursts, called simple stellar populations (SSPs). The main adjustable parameters are the stellar initial mass function, the star formation rate and the rate of chemical enrichment as a function of time.
We describe below the main ingredients required to perform this modeling: 1 – a prescription for the mass distribution of newly born stars; 2 – a theory for the evolution of stars of given initial mass and chemical composition; 3 – a library of stellar spectral energy distributions to describe the emission  from any single star.

Stellar initial mass function

Stars of different initial mass evolve differently, thus the observed properties of a simple stellar population at any time depend on the stellar initial mass function. Salpeter [1955] proposes a simple parametrization of the initial mass function from counts of main-sequence stars in the solar neighborhood. This representation is a single power law which has long been considered universal [(m) = dN/dm ∝ m−(1+x), with x ≈ 1.35]. Only later in the Seventies, a few studies started to reveal discrepancies from this simple form when observing different samples of stars (for example from globular clusters or the Magellanic Clouds) and improving the statistics for very low-mass stars. Scalo [2005] reviews different prescriptions for the initial mass function and suggests that the main problems in the computation of the initial mass function arise from the possible incompleteness of the data, the uncertainties in the evolution of massive stars and the corrections of star counts for extinction by dust.


Modeling the spectral energy distribution of stellar populations

The spectral energy distribution of a simple stellar population at any age is the superposition of the individual spectra of stars at all points along the isochrone, weighted by the initial mass function. Several codes have been developed to compute the spectral evolution of stellar populations as a function of the star formation and chemical enrichment histories, using the principles described in the previous sections: PÉGASE [Fioc and Rocca-Volmerange, 1997, Le Borgne et al., 2004], GALAXEV [Bruzual and Charlot, 2003], and the codes of Maraston [1998] (see also Maras- ton 2005, Maraston and Strömbäck 2011) and Vazdekis [1999] (see also Vazdekis et al. 2010) differ in the algorithms used to compute the evolution of stars in the Hertzsprung-Russell diagram and in the prescriptions adopted for stellar evolution and stellar spectra; the GALEV evolutionary synthesis model [Kotulla et al., 2009] has been designed specifically to follow the chemical enrichment of the gas associated with stellar populations; Starburst99 [Leitherer et al., 1999] is optimized to model the spectral evolution of young stellar populations; BPASS [binary population and spectral synthesis; Eldridge and Stanway, 2009] has been developed to explore the influence of massive binary stars on the evolution of stellar populations. We describe here in slightly more detail the GALAXEV code [Bruzual and Char-lot, 2003], which we will use in Chapter 3. In this code, the spectral energy distri- bution at time t of a composite stellar population can be written as Lλ,stars(t) = Z t 0 dt′ (t − t′) Sλ[t′,Z(t − t′)] .

General properties of interstellar dust

Dust grains are solid particles composed of elements heavier than hydrogen. As seen in Section 2.2.2, heavy elements are produced in thermonuclear reactions during the evolution of stars. Stellar winds and supernova explosions cause these metals to be spread into the interstellar medium, where they condense to form dust grains. The main observational evidence for the depletion of heavy elements onto dust grains is that the gas-phase abundances of metals are generally lower in interstellar clouds than in stellar atmospheres (where hydrogen and heavy elements are in the gas phase).
The elements contributing the most to the mass of interstellar grains are carbon, nitrogen, oxygen, magnesium, silicon and iron. Grains can be divided into graphitic grains, ices and silicates [Whittet, 2003]. Graphitic (carbon) grains are particularly small in size (< 2μm). They produce a strong absorption feature in the ultraviolet (the bump at 2175 Å, see Section 2.4.2 below). Ices refer to any volatile molecular solid composed of primarily the CHON group of elements. They require high den-
sities to condense and survive and produce strong emission features by vibrational transitions in the near-infrared (∼ 3μm). At longer wavelength (∼ 10 − 20μm), emission and absorption features are generally attributed to silicate grains, which have a wide range of possible chemical compositions based on SiO4 units.
Dust grains mix with the interstellar medium and experience chemical and iso- topic changes through interactions with the gas and radiation in interstellar space. For this reason, different types of dust grains form and survive in different regions of the interstellar medium. Ices tend to form in dense molecular clouds (see Sec- tion 2.3.1), where they contribute to the formation of H2.7 Graphitic grains and silicates instead can form in both low-density and high-density environment.

Table of contents :

List of Figures
List of Tables
1 Introduction 
1.1 The Universe
1.2 Galaxies
1.2.1 Galaxy morphologies
1.2.2 Galaxy spectral energy distributions
1.3 Outline
2 Modeling galaxy spectral energy distributions 
2.1 The star formation history of galaxies
2.1.1 The star formation history of the Universe
2.1.2 The star formation history of individual galaxies
2.2 Emission from stellar populations
2.2.1 Stellar initial mass function
2.2.2 Stellar evolutionary tracks
2.2.3 Library of stellar spectra
2.2.4 Modeling the spectral energy distribution of stellar populations
2.3 Nebular emission
2.3.1 The interstellar medium
2.3.2 Spectral features of the nebular emission
2.3.3 Nebular emission models
2.4 Attenuation by dust
2.4.1 General properties of interstellar dust
2.4.2 Modeling attenuation by dust in galaxies
2.5 Absorption by the Intergalactic Medium
2.6 Summary
3 Relative merits of different types of rest-frame optical observations to constrain galaxy physical parameters 
3.1 Introduction
3.2 Modeling approach
3.2.1 Library of star formation and chemical enrichment histories
3.2.2 Galaxy spectral modeling
3.2.3 Library of galaxy spectral energy distributions
3.2.4 Retrievability of galaxy physical parameters
3.3 Constraints on galaxy physical parameters from different types of observations
3.3.1 Constraints from multi-band photometry
3.3.2 Spectroscopic constraints
3.4 Application to a real sample
3.4.1 Physical parameters of SDSS galaxies
3.4.2 Influence of the prior distributions of physical parameters
3.5 Summary and conclusion
4 Constraining the physical properties of 3D-HST galaxies through the combination of photometric and spectroscopic data 
4.1 Introduction
4.2 The data
4.3 Fits of the spectral energy distribution
4.3.1 Photometric approach
4.3.2 Spectroscopic approach
4.4 Results from photometric versus spectroscopic fits
4.4.1 Redshift
4.4.2 Mass and specific star formation rate
4.5 Possible causes of discrepancy between photometric and spectroscopic estimates
4.6 Summary and next steps
5 ACS and NICMOS photometry in the Hubble Ultra Deep Field 
5.1 Introduction
5.2 The data
5.3 Modeling
5.3.1 Library of spectral energy distributions
5.3.2 The ultraviolet spectral slope
5.4 Fitting procedure
5.4.1 Estimates of the physical parameters
5.4.2 Preliminary pseudo-observed scene
5.5 Discussion
5.5.1 Comparison of redshift estimates
5.5.2 Correlation between ultraviolet spectral slope and optical depth of the dust
5.6 Summary and next steps
6 Conclusions 
A Intrinsic correlations between spectral pixels 
B Number of model galaxies in the library 
C UDF data 


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