Modelling the nebular emission from star-forming galaxies

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Chemical composition of galaxies

To constrain the past history of star formation, gas accretion and out ow of a galaxy, it is necessary to accurately measure the relative abundances of di erent chemical elements, and thus exploit the fact that elements are produced by di erent types of stars and supernovae arising on di erent timescales. The thermonuclear reactions taking place in stellar interiors produce metals, which for massive stars lead to the classical \onion-like » structure shown in Fig. 1.2. The pollution of the ISM when a supernova explodes is linked to this stellar nucleosynthesis. The enrichment is di erent according to the type of supernova, as brie y mentioned in Section 1.1.2 above. Type II supernovae, which are the nal evolutionary stages of massive stars (M 8 M ), explode on a short timescale ( 10 Myr) after the onset of star formation and enrich primarily the ISM in elements (e.g., O, Ne, Mg, Si, S, Ca, Ti), which are those composing the di erent layers of the massive star in Fig. 1.2. On the other hand, Type Ia supernovae, which are the nal evolutionary stages of accreting white dwarfs, explode on a longer timescale (between a few 108 yr and 1 Gyr) and produce massively iron-peak elements (e.g., Mn, Fe, Ni).
Figure 1.2: Stellar nucleosynthesis: chemical elements composing massive stars, in an \onion-like » structure.
Hence, the explosions of Type II and Type Ia supernovae occur on di erent timescales, and the chemical composition of their ejecta is di erent, which will produce di erent ratios of elements over iron-peak elements in galaxies with di erent star formation histories. For example, if some primeval galaxies form a large fraction of stars in a rapid episode (lasting around 10 Myr) of intense star formation at high redshift, before their ISM can be enriched in iron-peak elements by Type Ia supernovae, they may evolve today in galaxies exhibiting enhanced [ /Fe]1 ratios: this is the reason why the chemical composition of the rst stars to have formed in galaxies are typically expected to be \ -enhanced ». We can thereby expect primeval galaxies to exhibit speci c signatures in diagnostics line-ratio diagrams (see Sections 1.3.2, 3.3 and 3.4). This is not the case for more evolved galaxies, which are typically expected to have \scaled-solar » chemical compositions. The enrichment in heavy elements is thus a crucial tracer of the history of star formation of a galaxy, and that is why we must be able to accurately measure the relative abundances of di erent chemical elements (see Section 1.3.1).
To interpret the emission-line signatures of gas ionized by young stars in terms of the chemical composition of a galaxy, one may appeal to a photoionization code (see Section 2.2). However, current studies of this kind generally rely on the assumption that the interstellar gas has scaled-solar abundances of heavy-elements. That is, the relative ratios of heavy elements are taken to be the same as in the Sun, at any metallicity (solar or not). This assumption cannot be made to interpret the emission-line properties of high-redshift galaxies, in which the abundance ratios of heavy elements are expected to be non-solar, as described above. A main feature of my work is to overcome this limitation by developing models allowing one to properly explore the emission-line signatures of non-solar metal abundance ratios, and hence, the properties of chemically young galaxies out to the reionization epoch.

Nebular emission from ionized gas

In my thesis, I focus primarily on the emission-line spectrum produced by star-forming galax-ies (except in Chapter 4). I provide here a basic introduction to the properties of H ii regions ionized by young stars in a galaxy and to nebular emission in general.

Basic properties of HII region

H ii regions are extensive, di use nebulae { i.e., regions of interstellar gas { associated with regions of recent massive-star formation. They are concentrated in the spiral arms of galaxies, and have often irregular morphology and variable size, depending on the structure of their parent molecular cloud (see some examples of such H ii regions in Fig. 1.3). In 1939, Bengt Stromgren rst described the general properties of H ii regions (Stromgren, 1939). He estab-lished the link between the rate of ionizing photons, the hydrogen density and the size of an H ii region. Each H ii region typically contains one or more hot, massive young O-B stars, with e ective temperature ranging typically between T=30,000 and 50,000 K. These stars are the main sources of ionizing radiation in the region: the ionizing photons they emit transfer energy to the nebula through photoionization (see Section 1.2.2 next). In an H ii region, the ultraviolet radiation eld is so intense that the surrounding hydrogen gas is nearly fully ionized (i.e., in the form of H+), hence the name H ii region. The \Stromgren sphere » is the ionized region formed around the central source, which is separated from the outer neutral gas cloud by a thin transition beyond which no further ionizing photon arrives because they have been all absorbed by hydrogen atoms inside the Stromgren sphere. The typical mass of an H ii region is 102 to 104 M ; the typical hydrogen density is around 103 104 cm3 in compact H ii regions, and more modest in giant extragalactic H ii regions 10 to 102 atoms cm3 (e.g., Hunt & Hirashita, 2009); a di use H ii region is therefore large, from around 1 to hundreds of parsecs. An H ii region can also contain dust, and it typically exhibits a complex spectrum including lines and continuum, which I describe below (see Section 1.2.3).

Photoionization and recombination processes

I now describe the main general physical processes operating in these ionized regions of the ISM in galaxies, most importantly photoionization and recombination, as well as the di erent components of the spectra emerging from H ii regions and their physical origin: emission lines (recombination lines, collisionally excited lines) and continuum (free-free continuum, free-bound continuum, two-photon process, dust).
In an H ii region, the energy of the ultraviolet photons emitted by the ionizing source is transferred to the surrounding gas by photoionization. More precisely, the central star (or the cluster of young massive stars in the center of the cloud) is hot enough (T 30; 000 K) to emit ionizing photons. These are photons with energy above the ionization threshold, i.e., in the case or hydrogen, greater than the H-ionization potential of 13.6 eV (corresponding to wavelengths 912 A). These photons are called \Lyman-continuum photons » and are on the extreme ultraviolet side of the electromagnetic spectrum. If there is enough matter, the gas extends beyond the Stromgren radius and the nebula is called ionization bounded, as all the ionizing photons have been absorbed by ionized species. Otherwise, the nebula is truncated inside the Stromgren radius and is referred to as a density bounded nebula. A photoionization leads to the release of a photoelectron. This thermal electron tends to be recaptured by an ion, i.e., in the case of hydrogen, a proton H+ oating in the cloud: this is the recombination process, which produces a new neutral hydrogen atom. Fig. 1.4 illustrates the photoionization and recombination processes that determine the properties of H ii regions.
During recapture, the electron can land on any excited level of the newly formed H atom and then decay to lower and lower levels through radiative transitions. During each de-energizing of the radiative cascade, a photon is emitted with a particular wavelength, which will contribute to the intensity of the corresponding emission line in the spectrum of the H ii region: this is referred to as an “Hi recombination line” (see Section 1.2.3; Fig. 1.6).
An equilibrium stage is established if, for each species, the rate of ionization equals that of recombination. For an ionization-bounded H ii region composed of hydrogen, we can write the balance of the total number of ionizing photons emitted per unit time (by stars and during recombination to the ground level) with the total number of recombinations:
Q(H0) + n(H+)ne α1 (H, Te)dV = n(H+)ne αtot (H, Te )dV, (1.1)
where Q(H0) is the total number of ionizing photons produced per second, n(H+) the number density of protons, ne the electronic density, the volume filling factor of the nebular gas, α1 (H, Te ) the H-recombination coefficient of a transition to the ground level and αtot (H, Te ) the total H-recombination coe cient. For an H ii region with constant density and lling factor, we will see in Chapter 3 that we can thus derive the Stromgren radius by means of equation (3.6).
Ionized-gas regions are traditionally divided into two types: the optically thin one, corre-sponding to case A recombination (all Lyman-line photons produced though recombination escape from the nebula before they are reabsorbed by another atom); and the optically thick one, corresponding to case B recombination (all Lyman line photons are re-absorbed by other atoms until they nally cascade down to the n = 2 level and produce either a Lyman photon or a two-photon decay; Section 1.2.3). The latter is the most common case in the Universe, and the one I will consider in my work. It is worth noting that, in Case B recombination, every ionization must eventually produce a decay to the n = 2 state, accompanied by the emission of an optical \Balmer-line » photon. Hence the number of Balmer-line photons is directly related to the number of ionizing photons from the central source.
Likewise, if an atom of helium in the nebula is photoionized and creates an He+ ion, the photoelectron will be recaptured and contribute to the He i recombination spectrum (the energy of rst ionization for helium is 24.6 eV, so the central stars must be hot enough to produce such energetic photons); in the most highly ionized regions, we can even nd He2+ ions, which recombine and emit an He ii recombination spectrum (the energy of second ionization is 54.4 eV, the incident photons must thus be really energetic). Much weaker recombination lines can also be emitted by elements other than H and He (i.e. metals, for instance C, N, O) such as C iii and C iv emission lines.
To summarize, therefore, throughout an H ii region, H is fully ionized, He can be singly or even doubly ionized, and other elements, such as carbon, oxygen, nitrogen, magnesium, silicon, sulfur, etc., can be multiply ionized. The details depend primarily on the nature of the ionizing source, i.e. the cluster of massive stars.

Spectra: lines and continuum

An H ii region is characterized by a speci c emission spectrum. This spectrum presents an important emission-line component, including strong recombination lines of hydrogen and helium, but also collisionally excited lines of ions of common elements; these lines are super-imposed on a continuous spectrum, as I now describe.
We can start by showing in Fig. 1.5 the spectrum of the Sun observed by Joseph von Fraunhofer in 1814. He discovered the continuum and superimposed absorption lines (in black), of which he classi ed more than 500, and which represent today a ubiquitous means of investigation in spectroscopic astrophysics. He deepened his work for a few years and observed spectra of the moon, Venus, Mars and stars other than the Sun.
Figure 1.5: The spectrum of the Sun observed by Joseph von Fraun-hofer in 1814. We can see the Sun’s continuum spectrum, on which are superimposed the dark lines corresponding to the di erent known chemical elements. The curve above shows overall brightness.
Recombination lines As we have just seen, recombinations following the ionization of neu-tral gas by the energetic photons from hot stars produce prominent H i recombination lines in the spectrum of an H ii region. The line nomenclature depends on the energy level down to which the electron cascades: \Lyman » lines are emitted when the electron reaches the energy level n = 1, \Balmer » lines when it reaches the level n = 2, \Paschen » lines the level n = 3, and so on (see Fig. 1.6).
The strongest H-recombination line (aside from the ultraviolet Lyman line at 1216 A) is the Balmer H line, with a wavelength of 6563 A. It occurs when a hydrogen electron falls from the third to second lowest energy level. We also have the H line at 4861 A in the blue range (n = 4 to n = 2 transition), H at 4340 A in the violet range (n = 5 to n = 2), and so on. As I mentioned previously, because of the ionization of He gas, we can also nd He recombination lines, such as He i 5876 A (which is weaker than H-recombination lines), and even He ii 4686 A in higher-ionization nebulae.
Figure 1.6: Electronic transitions of the hydrogen atom: depending on the energy level the electron cascades down to, we refer to “Lyman” lines when the electron reaches the energy level n = 1, “Balmer” lines when it reaches the level n = 2, “Paschen” lines the level n = 3, and so on.
Collisionally excited lines The emission spectrum of an H ii region is also characterized by the presence of collisionally excited lines. Metals present in the H ii region (i.e., chemical elements heavier than H and He), in either atomic or ionized state, can be excited through collisions with thermal electrons. In the atom or ion, an electron passes from a lower to an upper energy level and can end up on an excited metastable energy level with a long lifetime. Usually, in such cases, in “normal” gas density conditions, the spontaneous de-energizing from that level has no time to happen, as the atom or ion can be collisionally deexcited on a short timescale (without the emission of a photon). In an H ii region, however, the density is so low that even over the lifetime of the metastable energy level, collisions between the atom or ion and an electron are quite unlikely. This is why the electron has time to spontaneously de-energize from its metastable state to a lower level: the emitted radiation gives rise to a “forbidden line” in the spectrum. Such lines are designed in square bracket. In an H ii region, we find forbidden lines of common species, such as the strong doublets of [O ii] at 3726 A and 3729 A, [O iii] at 4959 A and 5007 A, [N ii] at 6548 A and 6583 A and [S ii] at 6717 A and 6731 A. We note that, depending on the spontaneous transition probabilities, we also find semi-forbidden lines, designed by a single bracket, for some elements such as carbon, oxygen and silicon (e.g., C iii], O iii] and Si iii]).
To summarize, therefore, the gas in an H ii region is ionized and heated by an energetic central source. This gas emits radiation both via recombination (mostly hydrogen and helium recombination lines) and through the radiative decay of collisionally excited metals (which can lead to permitted, semi-forbidden or forbidden lines). To summarize and illustrate this, I present an example of emission-line spectrum of an H ii region in Fig. 1.7: this is the optical spectrum of an H ii region observed in the galaxy NGC 2541. We can see in particular strong recombination lines of hydrogen (in the Balmer series, i.e., from energy levels n ≥ 3 to n = 2), and strong forbidden lines of a few heavier elements (oxygen, neon). These are among the emission-line features I compute in my work to model the nebular emission from star-forming galaxies.
Figure 1.7: Example of a typical H ii region spectrum observed in the spiral galaxy NGC 2541. We can see the strong emission lines of hydro-gen, oxygen and neon that dominate the spectrum (Zaritsky, Kennicutt & Huchra, 1994).
An H ii region also emits continuum radiation across the entire electromagnetic spectrum. This arises from free-free radiation, free-bound transitions and a component due to the pres-ence of dust in the ionized region.
Free-free continumm Free-free emission is produced when free electrons pass close to ions without being caught: the electrons are slowed down, scattered off by the ions, and we know that any decelerating charge in space radiates electromagnetic energy: this is the Brehmsstrahlung radiation, as illustrated by Fig. 1.8.
This emission involves a transition of the electron from one free kinetic energy state to another. The result for an H ii region is a continuum extending across the entire electromag-netic spectrum. It is the main component of the radio continuum of an H ii region. This type of emission is one of the different contributions to the continuum in the spectrum of an H ii region.
Free-bound continuum Another component of the continuum is the free-bound radiation, or recombination continuum. This is produced during the recapture of a free electron to a bound state of an atom (see Section 1.2.2). Fig. 1.9 shows the free-free and free-bound emission of hydrogen gas at a temperature of 7 ×103 K. The free electrons that are recaptured by ions initially have a range of energies (usually drawn from the thermal distribution), and according to the energy level on which they land, we can see different discontinuities in the spectrum: the “Balmer discontinuity” (recombination on the level n = 2), the “Paschen discontinuity” (recombination on the level n = 3), and so on. These discontinuities appear in the spectrum as an edge followed by a continuum of emission to higher and higher energies in Fig. 1.9.
Two-photons process This is a spontaneous transition into a virtual level between the rst two excited states of an atom, which leads to the emission of two photons rather than a single one; the total energy of the two photons is then equal to the energy of the transition. The probability for such a double emission to occur is weak, but it cannot be ignored for the de-energizing from a metastable level when there are few collisions in the region. This continuum emission arises from any metastable excited state, particularly in the case of neutral hydrogen, when the electron ends up, by direct recombination or by cascades following recombinations to higher levels, into a metastable 2s 2 S excited state: the only downward radiative transition from this state is a two-photon decay in the 1s ground state. A similar process also happens in neutral helium.
This continuum emission becomes important at ultraviolet wavelengths, where it is stronger than the free-free and free-bound continuum.
Dust H ii regions contain dust, which can scatter and absorb the light emitted by the ionizing hot stars. The energy absorbed by dust is reradiated in the mid and far infrared. This gives rise to a thermal continuum, which is an additional component of the continuum spectrum of an H ii region. I provide further details on this in Section 3.2.4.

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Emission-line diagnostics

The detection of emission lines produced by ionized gas in star-forming galaxies provides insight into the physical properties of stars and the interstellar medium, such as the gas electronic temperature and chemical composition, of particular interest to me, but also the properties of the ionizing stars and the gas kinematics (Rubin et al., 1985). In this section, I give an overview of abundance determination in H ii regions, which is one of the most important applications we can perform based on emission-line measurements. I also introduce emission line-ratio diagnostic diagrams, which I will widely use in the following chapters.

Abundance determination in HII regions

Nebular emission lines have been used to derive abundances in extragalactic H ii regions since the 1940s (Aller, 1942). Indeed, as collisional emission lines are strongly sensitive to the local thermodynamic state of the gas (see Figs 1.10 and 1.11), temperature and density determinations using emission lines allow measurements of ionic abundance ratios, and hence, elemental abundances relative to hydrogen.
Two main types of approach exist: the so-called “direct method” and statistical ap-proaches.
Figure 1.10: Dependence of some line ratios on the electronic tempera-ture (Osterbrock & Ferland, 2006).
Figure 1.11: Dependence of some optical line ratios of forbidden lines on the electronic density (Osterbrock & Ferland, 2006).

Direct method

The best methods to measure chemical abundances from optical nebular emission lines are generally considered to be those involving an estimate of the thermodynamic state of the ionized gas – in terms of temperature and density. This can be achieved by using the in-tensity ratio of two lines of the same ion with different excitation levels to derive the elec-tronic temperature Te (we note that, while intensity ratios of recombination lines do not strongly depend on Te, those involving collisionally excited, optical and ultraviolet line do if the line excitation levels are different). Some widely used line ratios for Te estimates are [O iii]λ4363/λ5007, [N ii]λ5755/λ6584 and [S iii]λ6312/λ9532. Estimates of the electronic density ne can be achieved using the intensity ratio of two lines of the same ion arising from levels with the same excitation energy but different radiative transition probabilities or collisional deexcitation rates, such as for instance [S ii]λ6717/λ6731, [O ii]λ3729/λ3726 and C iii]λ1909/λ1907.
The lines required to reliably measure the electronic temperature, such as [O iii] 4363, are typically weak and cannot always be observed in external galaxies. For this reason, other statistical approaches have been developed to measure metal abundances based on ratios of prominent emission lines, generally termed \strong-line methods », as rst proposed by Pagel et al. (1979). In these methods, the abundance of an element is usually inferred from theoretical calibrations of strong-line ratios using photoionization models. For example, it is customary to estimate the oxygen abundance O/H by computing the ratio of combined O+ and O2+ lines to H , i.e., R23 = ([O ii] 3727 + [O iii] 4959; 5007)=H . It is worth noting that in this method, the solution is not unique because the ratio R23 behaves di erently depending on the metallicity regime, as shown by Fig. 1.12. At low metallicity, R23 increases with metallicity (as the oxygen abundance rises), while at higher metallicity, it starts to drop with increasing metallicity (as cooling through the infrared lines becomes more e cient; see Section 3.3.3). Other lines must then be investigated to settle the metallicity regime. I will develop on this approach using the cloudy photoionization code to compute abundances of heavy elements (Section 2.2).
It is worth noting that, even in the direct method, photoionization models are traditionally invoked to compute the abundances of other heavy elements, based on that of the first ion measured. In the example of the O2+ ion given above (equation 1.2), photoionization models are required to estimate the electron temperatures and ionization corrections for other ions, based on those corresponding to the O2+ ionization zone (e.g., Izotov et al., 2006). Absolute abundances computed in this way are therefore tied to the assumptions inherent in standard photoionization models about abundance ratios, which are generally taken to be scaled-solar, and may also be prone to biaises arising from the specific electronic density and ionization structure of these models. There is an inconsistency, therefore, in using any of these standard approaches (direct and strong-line methods) to constrain the presumably non-solar abundance ratios of high-redshift galaxies. One of the goal of my thesis is to address this issue (see Section 3.5).

Emission line-ratio diagrams

The sensitivity of individual emission-line intensities to the nature of the ionizing radiation (stars of different mass and composition, AGN, shocks; see Chapter 3) and the physical pa-rameters of interstellar gas (density, excitation, chemical composition, etc.) has led to the development of emission line-ratio diagnostic diagrams. In practice, the method consists in plotting a ratio of two emission lines – produced in partially ionized zones – as a function of an-other such ratio. This approach was first advertised by Baldwin, Phillips & Terlevich (1981), who used line ratios based on several strong optical lines, such as [O ii]λ3727, [O iii]λ5007, H β, [N ii]λ6584 and Hα, to distinguish between different types of ionizing sources, as ex-emplified in Fig. 1.13. We note that the [O iii]λ5007/H β and [N ii]λ6584/Hα ratios shown in this figure both involve lines with very close wavelengths, in order to limit sensitivity to reddening and spectrophotometric calibration.

Table of contents :

1 Introduction
1.1 The early Universe
1.1.1 First steps
1.1.2 Stars and galaxies
1.1.3 Chemical composition of galaxies
1.2 Nebular emission from ionized gas
1.2.1 Basic properties of HII regions
1.2.2 Photoionization and recombination processes
1.2.3 Spectra: lines and continuum
1.3 Emission-line diagnostics
1.3.1 Abundance determination in HII regions
1.3.2 Emission line-ratio diagrams
1.3.3 Other use of emission lines
1.4 Outline
2 Tools 
2.1 Stellar population synthesis codes
2.1.1 Generalities
2.1.2 Stellar evolutionary tracks
2.1.3 Stellar Initial Mass Function
2.1.4 Library of stellar spectra
2.1.5 In this work (galaxev)
2.2 Photoionization codes
2.2.1 Generalities
2.2.2 In this work (cloudy)
2.3 Conclusion
3 Modelling the nebular emission from star-forming galaxies
3.1 Introduction
3.2 Modelling
3.2.1 Stellar emission
3.2.2 Transmission function of the ISM
3.2.3 Interstellar abundances and depletion factors
3.2.4 Dust in ISM
3.3 Optical emission-line properties
3.3.1 Grid of photoionization models
3.3.2 Comparison with observations
3.3.3 Inuence of model parameters on optical emission-line properties
3.4 Ultraviolet emission-line properties
3.5 Limitations of standard methods of abundance measurements
3.5.1 The `direct-Te’ method
3.5.2 A case study: the C/O ratio
3.6 Conclusions
4 Comparison between star-forming galaxies and AGN 
4.1 Introduction
4.2 Photoionization models from AGN
4.2.1 Narrow-line regions of AGN
4.2.2 Dierences between AGN and SF models
4.3 Optical emission lines and standard AGN/star-formation diagnostics
4.3.1 SDSS observational sample
4.3.2 [Oiii]5007 H versus [Nii]6584 H diagram
4.3.3 Other AGN/star-formation diagnostic diagrams
4.4 Ultraviolet emission lines and new AGN/star-formation diagnostics
4.4.1 Ultraviolet observational samples
4.4.2 Diagnostics based on the Civ1550, Heii1640 and Ciii]1908 emission lines
4.4.3 Nv1240-based diagnostics
4.4.4 Heii1640-based diagnostics
4.4.5 O-based diagnostics in the far and near ultraviolet
4.4.6 Ne-based diagnostics in the near ultraviolet
4.4.7 Distinguishing active from inactive galaxies in emission line-ratio diagrams
4.5 Ultraviolet line-ratio diagnostic diagrams of active and inactive galaxies
4.6 Conclusions
5 Linking my nebular emission modelling with observations
5.1 Ultraviolet emission lines in young low-mass galaxies at z ‘ 2
5.1.1 Introduction
5.1.2 Observational sample
5.1.3 Photoionization modelling
5.1.4 Conclusion
5.2 Spectroscopic detections of CIII]1909 at z ‘ 6 􀀀 7
5.2.1 Introduction
5.2.2 Observational sample
5.2.3 Modelling the continuum and emission lines of A383-5.2
5.2.4 Conclusion
5.3 Spectroscopic detection of CIV1548 in a galaxy at z = 7:045
5.3.1 Introduction
5.3.2 Observational sample
5.3.3 A hard ionizing spectrum at z = 7
5.3.4 Conclusion
5.4 Ly and CIII] emission in z = 7 􀀀 9 galaxies
5.4.1 Introduction
5.4.2 Observational sample
5.4.3 Photoionization modelling
5.4.4 Conclusion
5.5 Conclusion

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