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The star formation history of galaxies
The star formation history is the evolution of the rate of star formation as a func-tion of galaxy age. The light arising from a galaxy should reflect the past episodes of star formation it underwent, through the spectral signatures of different stellar generations and the implied enrichment of the interstellar medium. Dissecting the integrated light of an individual galaxy into components of different ages is a com-plicated process. If one considers the galaxy population as a whole, a more direct way to gain at least some clues on the global star formation history of the Universe is to explore the star formation rate density at different cosmic epochs. This can be achieved because measurements of the current rate of star formation at any cosmic epoch through the emission from bright young stars is less challenging than inter-preting the spectral signatures of old stars in the spectra of today’s galaxies. To interpret, instead, the evolution of individual galaxies, requires more complicated models of the history of star formation. In this Section, we first briefly recall the con-clusions that can be drawn from analyses of the global star formation rate density of the Universe at various cosmic epochs and the different sources of uncertainty affecting these analyses. Then, we describe in more detail the models that have been developed to follow the star formation and chemical enrichment histories of individual galaxies, in the framework of a hierarchical universe, and the successes and limitations of such models.
The star formation history of the Universe
The study of the star formation history of galaxies through the assessment of the star formation rate density at different epochs has been pioneered by Lilly et al. [1996] and Madau et al. [1996], combining observations from the local Universe to z ∼ 3−4. Hopkins [2004] and Hopkins and Beacom [2006] have improved the statistics out to z ∼ 6 and have analyzed the various sources of uncertainties that can contribute to the normalization of the star formation rate density. More recently, Cucciati et al. [2011] have investigated the star formation rate density from z ∼ 0.05 to z ∼ 4.5 using data from a single galaxy redshift survey (VIMOS-VLT Deep Survey, VVDS, Garilli et al. 2008, Le Fèvre et al. 2004, Le Fèvre et al. 2005), to avoid merging different datasets. In their work, they assess also the various sources of uncertainties, and in particular, the treatment of dust attenuation.
In Figures 2.1 and 2.2, respectively, we present the original and the most recent determinations of the evolution of the star formation rate density of the Universe as a function of redshift. Despite the inhomogeneity of the galaxy samples used in these studies and the differences in the adopted star-formation-rate indicators (far ultraviolet, far infrared, Hα emission line luminosity, radio observations), the Universe appears to have undergone a phase of most active star formation around z ∼ 1 − 2. Other uncertainties affect this measurement, leading to large error bars. For example, the correction for attenuation by dust at ultraviolet and optical wavelengths and the interpretation of dust emission at infrared wavelengths can alter estimates of the star formation rate. Moreover, the lack of statistics beyond redshift of 2–3 precludes the interpretation of the decline of star-formation at cosmic epochs earlier than z ∼ 1.
Although the evolution of the star formation rate density gives us important clues about the global history of star formation of the Universe, the interpretation of the results of Figures 2.1 and 2.2 is very limited. To gain more insight into the evolution of different types of galaxies, we thus need to investigate in more detail the star formation history of individual galaxies.
The star formation history of individual galaxies
Constraining the star formation history of individual galaxies requires models that can describe the spectral evolution implied by different scenarios of star formation and chemical enrichment. By comparing such models with observations, one can infer the most likely scenario for the evolution of individual galaxies. In practice, even idealized representations of the star formation history can reproduce reasonably well the colors of nearby galaxies. Here, we first briefly describe different idealized representations of the star formation history of individual galaxies. We then describe more sophisticated approaches based on detailed cosmological simulations.
The star formation history of galaxies
Figure 2.1: Fig. 9 from Madau et al. [1996], showing on the left the Universal metal ejection density, ρ˙Z , and on the right the total star formation rate density, ρ˙∗, as a function of redshift. Triangle: Gallego et al. [1995]. Filled dots: Lilly et al. [1996]. Filled squares: lower limits from Hubble Deep Field images.
Figure 2.2: Fig. 5 from Cucciati et al. [2011], showing the total dust-corrected UV-derived star formation rate density as a function of redshift from the VVDS sample (red filled circles). The black dashed line is the star formation rate density as a function of z implied from the stellar mass density in Ilbert et al. [2010]. Other data sets are overplotted and labeled on the figure. All data have been converted into a star formation rate density with the scaling relation from Madau et al. [1998].
Simple idealized models of star formation history
Galaxy star formation histories have been traditionally approximated by simple analytic functions: single bursts of star formation, constant star formation rate, ex-ponentially declining star formation rate or a combination of these three. Figure 2.3 shows 3 templates of star formation histories and the corresponding spectral en-ergy distributions, computed using the latest version of Bruzual and Charlot [2003] for fixed solar metallicity, with a Chabrier initial mass function [Chabrier, 2003]. Emission lines are computed consistently following the prescription by Charlot and Longhetti [2001]. Attenuation by dust is neglected in this example. A constant star formation history (panel a) gives a relatively blue spectral energy distribution (panel e). A single burst of star formation at early times (panel b) does not include the emission from any young stars, resulting in a fairly red spectral energy distribution (panel e). In panel (c), we show an exponentially declining star formation history, with e-folding time 2.5 Gyr, and the corresponding spectral energy distribution is shown in panel (f).
Previous studies (e.g. Kauffmann et al. 2003a, Brinchmann et al. 2004, da Cunha et al. 2008) have shown that these simplistic formulations of star formation histories are able to reproduce the colors of low-redshift galaxies. For example, Kauffmann et al. [2003a] show that exponentially declining star formation histories, with random superimposed bursts of star formation, reproduce reasonably well the colors of a representative sample of galaxies from the SDSS at redshift 0.03 and 0.11, once corrected for dust attenuation (see Figure 2.4). We note that these authors also correct the SDSS colors for the contamination by emission lines. We will return in Chapter 3 (Figure 3.7) on the non-negligible influence of nebular emission lines when interpreting the observed colors of star-forming galaxies.
Wuyts et al. [2009] specifically investigate the limitations arising from the in-terpretation of complex star formation histories of galaxies using idealized repre-sentations of the type shown in Figure 2.3. Their approach consists of 2 steps: 1– building ‘realistic’ galaxy spectral energy distributions based on star formation histories derived from a sophisticated simulation of galaxy formation (they adopt a simulation based on a smoothed-particle-hydrodynamic code, see Section 2.1.2.2); 2 – comparing the colors of these galaxies with colors of model galaxies computed using simplistic star formation histories. They consider the spectral evolution over a period of only 2 Gyr, as they focus on studies of high-redshift galaxies. Wuyts et al. [2009] show that the spectral energy distributions of galaxies derived from a cosmological simulation are better represented by exponentially declining star for-mation histories with e-folding time of 300 Myr than by single-burst and constant star formation histories. They also find that, in the case of starburst galaxies, age and mass are systematically underestimated when adopting simple exponentially declining star formation histories. They show that models allowing for secondary bursts of star formation on top of an exponentially declining star formation history allow for larger total stellar masses, providing a better match for blue objects than without secondary bursts (see also Papovich et al.
The star formation history of galaxies
Figure 2.3: Idealized star formation histories (panels a, b, c) and the relative spec-tral energy distributions (panels d, e, f). The model spectral energy distributions are computed using the latest version of Bruzual and Charlot [2003] at fixed so-lar metallicity, with a Chabrier initial mass function [Chabrier, 2003]. Emission lines are computed consistently following the prescription by Charlot and Longhetti [2001]. The attenuation by dust is neglected in these examples.
Figure 2.4: Fig. 10 from Kauffmann et al. [2003a]. Observed g − r versus r − i colors of a representative sample of SDSS galaxies (black points) for 2 particular redshifts (0.11 and 0.03). Blue points represent the model grid, computed applying Bruzual and Charlot [2003] models to exponentially declining star formation histories, with random superimposed burst of star formation. In the left panels, data are not corrected for dust attenuation, while in the right panels, data are corrected with an attenuation law of the form τλ ∝ λ−0.7. The red arrow shows the predicted reddening vector.
The star formation history of galaxies
et al. 2007). In any case, the results of Wuyts et al. [2009] suggest that sophisti-cated simulations of galaxy formation can help us better constrain the history of star formation in galaxies than simple idealized models.
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 sim-ulations, 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.
Klypin et al. [2011]. These simulations were all run in the framework of a ΛCDM Universe, with slightly different parameter variants. Their main characteristics are given in Table 2.1.
The formation and evolution of galaxies in the framework of dark-matter N-body simulations is dictated by the merger history of dark-matter haloes, which baryons follow. We show in Figure 2.5 an example of merger tree of a dark-matter halo computed with the Millennium Simulation (from Fig. 2 of De Lucia and Blaizot [2007]). In this example, the halo has a mass of about 9 × 1014 M⊙ at z = 0 and lies on top of the plot, with all the progenitors plotted downward as a function of lookback time. The green branch represents the main branch, which follows the evolution of the main progenitors of the final halo. In this framework, the evolution of the halo can be drawn as a series of accretion events. The other progenitors are shown in orange: circles indicate haloes which belong to the same friends-of-friends2 group, while triangles mark haloes which have not yet joined the friends-of-friends group. The trees on the right-hand side, which are not connected to the main branch, are substructures which have not merged into the main halo.
2 friends-of-friends is a simple algorithm [Davis et al., 1985], which links two particles in the same group if their distance is less than a certain linking length. This distance can be also expressed as a density and in general friends-of-friends algorithms pick up structures with density ≈ 200 times higher than the mean density of the system.
Within the hierarchy of haloes produced by dark-matter N-body simulations, the evolution of the baryons can be followed using different approaches: semi-analytic models (SAM), smoothed-particle-hydrodynamic techniques (SPH), adaptive mesh refinement methods (AMR) and the latest moving-mesh code AREPO. We briefly summarize below the main characteristics of these 4 approaches (in Chapter 3 in this thesis we focus on the first one).
Semi-analytic models (see for example Bower et al. 2006 and references therein) are a simple and powerful approach to describe the evolution of baryons in a cosmo-logical context, without computing the hydrodynamic evolution of the gas. These models can be performed through a post-treatment of dark-matter N-body simula-tions, thus they are computationally efficient. The design of semi-analytic models requires the specification of a few key parameters, defined using empirical relations (feedback from supernovae, AGN, stellar winds). It is worth pausing here to de-scribe in slightly more detail the characteristics of the Croton et al. [2006] model, which we will be using in Chapter 3.
Croton et al. [2006] (see also De Lucia and Blaizot 2007) propose an approach to study the formation and evolution of galaxies in the framework of the Millennium N-body Simulation [Springel et al., 2005, see Table 2.1]. The full dataset from the dark-matter simulation is stored in 60 time steps between z = 20 and z = 0 and four more steps at z = 30, 50, 80 and 127. The merger trees do not have to be re-run to explore the parameter space. At z ∼ 0 the time resolution is of approximately 300 Myr. The code produces a friends-of-friends group catalogue, saving only haloes with at least 20 particles (∼ 1.7 × 1010 M⊙). At z = 0 this procedure identifies 17.7 × 106 friends-of-friends groups, down from a maximum of 19.8 × 106 at z = 1.4, when groups are more abundant but of lower mass on average. Once the resulting merging history is stored, it is possible to perform the semi-analytic treatment. Croton et al. [2006] follow the standard paradigm by White and Frenk [1991], as adapted for implementation into high-resolution N-body simulations by Springel et al. [2001] and De Lucia et al. [2004]. This assumes that when a dark-matter halo collapses, the baryons in it collapse as well. Baryons are initially in the form of diffuse gas of primordial composition. They transform into stars and heavy elements during the evolution of the halo. When the gas collapses on to a central object (which is assumed to be a cold gas disk), episodes of star formation, either quiescent or in a burst, are ignited. The prescription for quiescent star formation is based on Kennicutt [1998], while starbursts arise in merger events, between the central galaxy of a halo and a satellite galaxy. When the mass of the satellite is small compared to the central galaxy, the event is called minor merger and the stars of the satellite are added to the bulge of the central galaxy, causing a minor starburst. When the two masses are comparable, the starburst is more significant, with the merger destroying the discs of both galaxies to form a spheroid in which all stars are placed. Croton et al. [2006] find that galaxies are better represented when accretion and cooling are inefficient. Active galactic nuclei and supernova feedback have an important role in suppressing cooling flows. In particular, supernova events inject gas, metals and energy into the surrounding medium, reheating cold-disc gas and possibly ejecting gas from the surrounding halo. This process prevents the gas from cooling down and also contributes to the metal enrichment of the gas.
In contrast to the semi-analytic model described above, the other approaches (smoothed particle hydrodynamics, adaptive mesh refinement and moving mesh) run in parallel to N-body dark-matter simulations. Smoothed particle hydrodynamics methods (see for example Katz et al. 1996, Springel et al. 2001) are called Lagrangian methods. They discretize mass, using a set of fluid particles to model the flow. They are particularly suited to follow the gravitational growth of structures and resolution is automatically increased in the central regions of galactic haloes, with no discontinuous jumps. The main disadvantage is that they appear to suppress fluid instabilities and thus they have to rely on artificial viscosity.
Adaptive-mesh-refinement codes follow an Eulerian approach (see for example Cen and Ostriker 1992, Teyssier 2002). In this approach, space is discretized and fluid variables are represented on a mesh. The building blocks of the mesh are rectangular patches of various sizes. The position and dimension of the patches depend on speed and memory constraints. AMR codes are faster than smoothed particle hydrodynamics codes and do not need artificial viscosity. Usually, individual galaxies are poorly resolved and only a very fine mesh can allow the code to reach the resolving power of an SPH code. Moreover, the results may change when a velocity field is applied to the system (no Galilean invariance).
The approach proposed by Springel [2010] combines the advantages of La-grangian and Eulerian methods by letting the mesh itself move. This is the basic principle of the new code AREPO. The mesh is defined as a set of discrete mesh-generating points, which move freely. AREPO allows the continuous adjustment of resolution and it is Galilean invariant when the mesh is moved along with the flow. It inherits the geometric flexibility of smoothed-particle-hydrodynamic codes and also the absence of artificial viscosity of adaptive-mesh-refinement codes.
Scannapieco et al. [2011] show that when SPH, AMR or AREPO codes are run on the same initial conditions, the differences in the codes themselves and the dif-ferent treatments for cooling, star formation and feedback cause large variations in the resulting stellar mass, size, morphology and gas content of the galaxies at the end of the evolution. For example, the stellar mass in AREPO and in adaptive mesh refinement codes is typically twice as high as that in smoothed particle hydro-dynamics simulations. All three codes tend to produce too many massive galaxies compared to theoretical expectations and also to observations. The peak of star formation is predicted to arise at redshifts around z ∼ 4 with basically insignificant star formation in recent times. This as well does not match with observations (see Section 2.1.1). The codes differ also in the gas fraction at z = 0: AREPO predicts a larger gas fraction compared to smoothed particle hydrodynamics methods, while adaptive-mesh-refinement codes tend to predict gas fractions intermediate between these two.
A general limitation of all the approaches mentioned above is that they tend to produce a too large fraction of quiescent galaxies, along with too small spirals (see for example Weinmann et al. 2006, Guo et al. 2010).
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.
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 [φ(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.
In all applications in this thesis, we always adopt the Chabrier [2003] initial mass function. We must also define lower and upper mass limits. The lower mass limit usually corresponds to the minimum mass required to ignite hydrogen burning in the stellar core, i.e. about 0.1M⊙ (we note that the stellar initial mass function can be extended down to lower masses to include brown dwarfs; e.g. Kroupa [2001]). The upper limit is less well defined, with a conventional value around 100 M⊙. Roughly, above this value, a star cannot radiate energy fast enough to remain stable.
Stellar evolutionary tracks
Stars of different initial masses burn their fuel at different rates, thus they evolve through different paths in the Hertzsprung-Russell (H-R) diagram. In this diagram, shown in Figure 2.7, luminosity is plotted as a function of effective temperature of a star. The position of a star in the H-R diagram depends on chemical composition, mass and age. A star is on the zero-age main sequence (black line) when thermonu-clear reactions have begun in the core and it has reached hydrostatic equilibrium.
Emission from stellar populations
Figure 2.7: The Hertzsprung-Russell diagram (H-R) shows the evolutionary stages of stars in terms of their luminosity and temperature. Different evolutionary paths for stars of different initial masses are plotted in different colors. The zero-age main sequence is shown as a black solid line. The labels indicate the main stages of the evolution.
A main-sequence star burns hydrogen in the core, converting it into helium. The higher the initial mass of the star, the higher the energy required to remain in hydrostatic equilibrium, balancing the gravitational force. The higher the energy produced, the brighter the star, which, in this way, burns all the hydrogen in the core faster than a low-initial-mass star. As a consequence, the lifetime of a star with high initial mass is shorter than that of a low-initial-mass star.3 We can summarize the different evolutionary paths of stars of different initial mass as follows (the numerical values below correspond to stars with solar metal composition).
Low-mass stars (0.3 M⊙ < m < 2.0 M⊙) leave the main sequence when hydro-gen in their core is completely exhausted. The helium core contracts, converting gravitational potential energy into thermal energy. Then, hydrogen starts burning in a shell around the core, causing the outer layers of the star to expand. The radius gets larger and the surface temperature lower. These stars are called red giants. The helium core increases in mass because of the infall of helium produced in the outer shell. At this point, electrons in the core become degenerate, the core contracts and the star starts burning helium. This increases the temperature in the core, enhancing the rate of helium-burning reactions (helium flash). The temperature in the core keeps increasing until the gas becomes non-degenerate and can cool down. The outer layers contract and the star steadily burns helium in the core and hydrogen in the outer shell. The star settles down in this regime until all the helium in the core has been converted into carbon and oxygen. At this stage, helium starts burning in an outer shell and the star expands evolving toward the asymptotic giant branch (AGB, green track on Figure 2.7). This phase can be broken into two parts: early AGB (E-AGB) and thermally pulsing AGB (TP-AGB) [Iben and Renzini, 1983]. In the early-AGB phase, the hydrogen-burning shell is extinct, and the helium-burning shell accounts for most of the emission by the star. The duration of this phase is roughly 10 Myr, although this depends on mass and composition of the star. When helium in the inner shell is nearly exhausted, hydrogen is reignited in a thin outer shell and the star begins to thermally pulse. Expansion is caused by the energy liberated by violent burning processes occurring in the helium shells. This happens because helium is highly sensitive to temperature changes. The star contracts when helium cools down. The duration of the thermally-pulsing AGB phase is essentially determined by the mass-loss rate and ranges between 0.2 and 2 Myr [Vassiliadis and Wood, 1993, Table 1]. Eventually, the strong stellar winds provide enough energy for the outer layers to be ejected, forming a planetary nebula. When helium in the shell is also exhausted, the envelope collapses and the electron gas in the core becomes degenerate. At this point, the star never reaches high enough temperatures to ignite carbon and thus becomes a white dwarf.
Intermediate-mass stars (2 M⊙ < m < 8 M⊙) evolve like low-mass stars but have sufficient mass for quiet helium ignition in their core. Helium burns at a higher rate compared to low-mass stars, and the evolution is faster. An intermediate-mass star evolves towards the asymptotic giant branch and passes the thermally-pulsing AGB phase, ejecting the outer envelop in the interstellar medium (planetary nebula). The lower and upper mass limits of this category of stars strongly depend on metallicity and other model details. This issue is discussed by Marigo [2001], who suggests that the maximum initial mass for a star to develop a degenerate helium-core (helium-flash phase) is comprised between 1.7 and 2.5 M⊙. The upper limit instead is defined as the critical stellar mass over which carbon ignition occurs and is comprised between 5 and 8 M⊙. It is interesting to note that, without mass loss, the mass of the carbon-oxygen core in these stars would easily reach ∼ 1.4 M⊙, the effective Chandrasekhar limit, at which point carbon ignition (carbon-flash phase) would lead to a supernova explosion. The rate of supernova explosions in our Galaxy is much smaller than the amount of intermediate-mass stars [Iben, 1991], thus it is evident that not all intermediate-mass stars evolve to a supernova stage. If the temperature in the core is too low to undergo a carbon flash, the star loses its outer envelop and cools down as a white dwarf.
Table of contents :
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
