Radio observations and chemical modeling 

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Thermal balance in molecular clouds

The temperature reached by the gas at equilibrium is the result of competing radiative cooling (through line emission) and heating processes. The processes of thermal equilibrium were detailed by Goldsmith and Langer (1978). Radiative cooling mostly depends on the gas density and the molecular composition, two co-dependent parameters. For instance, the main cooling transitions for the neutral gas from ∼ 300 K down to ∼ 50 K (this corresponds to PDR) are the fine structure lines of the abundant C+ and O atoms. Below 50 K, at densities 102 − 104 cm−3, cooling from CO lines becomes dominant.
Due to its very high abundance, transitions of the main CO isotopologue 12CO usually get optically thick and cooling becomes less efficient. The contribution of rarer isotopologues like 13CO and C18O become more and more important with increasing density and can contribute up to 70% of the total CO cooling. This is because these transitions can remain optically thin, in other words photons emitted through these transitions can escape the cloud, taking away some energy. Molecular depletion can reduce the gas-phase cooling efficiency, but this effect is limited by the large contribution of optically thick lines to cooling (Goldsmith, 2001).
At 103 − 104 cm−3 densities, the time scale for radiative cooling (∼ 105 yr) is about one order of magnitude shorter than the free-fall time scale. In absence of UV photons, this implies the existence of other heating sources to reach equilibrium (Goldsmith and Langer, 1978). Heating is dominated in molecular clouds by CRs at lower (￿ 105 cm−3) densities, and by dust-gas collisions at higher densities (Tielens, 2005, Chapter 3).Other sources are gravitational contraction or ambipolar diffusion.

Formation of molecules

In molecular clouds, the relatively large density favors encounters, yet the temperature is very low and the gas-phase chemistry is governed by kinetics over thermodynamics. Neutral-neutral reactions are especially slow, and the gas-phase chemistry is dominated by ion-neutral reactions. Ion-neutral reactions are in general exothermal and have no energy activation barriers, therefore they play a crucial role in cold molecular clouds, despite the low ionisation fraction xe = n(e−)/nH (see e.g. Herbst, 2005). In those regions shielded from the interstellar UV radiation field, CRs are the only source of ionisation, as they can still penetrate deep inside the cloud, at AV > 10 mag. CRs will ionise H2 which will rapidly lead to H+3 and initiate the formation of many subsequent ions. They will also ionise He and form He+, which will destroy molecules in the gas. Chapter 3 is dedicated to the description of the CR induced chemistry in molecular clouds.
The nature of molecular clouds enables the accretion of molecules onto grains, where they can undergo further reactions. The freeze-out of CO can for instance reach 50% in cloud interiors, and even 80-90% in prestellar cores (see e.g. Caselli and Ceccarelli, 2012). The freeze-out time scale is tfreeze−out ∝ 109/nH yr (Jones and Williams, 1985), which is significantly shorter than the free-fall time scale (tff ∼ 4 × 107 √nH2 ) or estimated life time in > 104 cm−3 clouds. Therefore one would expect CO to be totally depleted. Yet, CO is still observed in high density regions, which means there is a desorption process other than thermal evaporation (the dust is cold) or photodesorption (the visual extinction is high), or that there is still some C+ atoms to form CO. Once again, CRs are believed to be the dominant source of desorption (Leger et al., 1985). They let CO be re-injected in the gas along with other molecules, which formed on the grain surface.
The dense ISM is where molecular complexity builds up. The chemistry is dominated by ion-neutral
reactions in the gas phase, enabled by the presence of CRs. It is possible that CRs also have a role in the formation of large (￿ 6 atoms) molecules on grain mantles (e.g. Garrod and Herbst, 2006). This rich chemistry will then be included from the initial steps all along stellar and planetary formation.

ISM-star cycle

Since the early photographs by E. Barnard, molecular clouds are known to exhibit filamentary structures.
The recent observations from the Herschel satellite show the ubiquity of filaments in molecular clouds (Andr´e et al., 2014). Stars are formed within the densest clumps in molecular clouds, called pre-stellar cores, where the density can reach 106 − 107 cm−3. Small-scale observations of the mass distribution indicate that filaments are not a consequence of star formation but rather precede it, and protostellar cores inherit this spatial distribution.
An ongoing debate addresses the question of the dynamics of star formation (Bergin and Tafalla, 2007). At first, molecular clouds were thought to be in quasistatic equilibrium in their evolution toward star formation, but this view was recently challenged by observations and numerical simulations which suggest a faster evolution of clouds and star formation. In this view, molecular clouds would result from turbulent flows, evolve and dissipate before reaching equilibrium.
The presence of heavy elements (heavier than H and He) in the gas phase, and the presence of dust tell us that the cloud material results from previous generations of stars, as these heavy elements can only be formed by stellar nucleosynthesis. This reveals a wide process of ISM-star cycle, where stars are born inside molecular clouds and give some of their material back to the ISM. This material can either be delivered by stellar winds during the late phases of star evolution, or it can be expelled during supernova explosions.
The next generation of stars will thus incorporate metal-enriched material compared to previous generations.
This ISM-star cycle will gradually enrich locally the ISM in heavier elements across the Galaxy, and lead to the existence Galactic gradients of the gas composition.

The solar cosmic-ray spectrum

Figure 2.1 shows the overall CR spectrum in the solar environment, i.e. CRs that actually reach Earth’s orbit or atmosphere. It is a collection of results from various experiments that are sensitive to complementary energy ranges. One can divide this overall spectrum into 3 parts that can be fitted by three different powerlaws, and which are limited by two characteristic features, the knee and the ankle (if you wish to identify this spectrum with a leg). These two “body parts” mark a modification in the origin and composition of CRs (Blandford et al., 2014). Low energy particles (￿ 30 × 109 eV) originate in the Sun, solar wind and planets.
At these low energies, the Heliosphere alters the flux and spectrum of CRs as it prevents Galactic CRs from entering the Solar System, with variations in efficiency that follow the Solar activity (in a process called modulation, see e.g. Blasi, 2013). It is generally assumed that supernovae can accelerate CRs up to the knee at ∼ 3 × 1015 eV (see section 4.1.3). At energies higher than the knee, the spectrum is dominated by heavy nuclei. The ankle (∼ 5×1018 eV) allegedly marks the change from a Galactic origin of CRs at lower energies to an extragalactic origin at higher energies. Spectral breaks up to the knee can be naturally explained by the superposition of energy cut-offs, i.e. limitations from the physical processes involved in the acceleration and propagation of CRs. These processes and the actual sources of CRs are yet not fully understood and are awaiting more observational evidence (e.g. Blasi, 2013).
The flux of CRs reaching Earth decreasese with energy (see Figure 2.1), down to 1 particle/km2/ century for the highest energies. Whereas at lower energies detectors onboard satellites can easily detect CRs, the low fluxes at highest energies beg for the construction of detectors with very large surfaces, if one is to detect these particles. This naturally led to two families of CR detectors: those which can fit in satellites or ballon experiments and directly detect the incoming particles that didn’t interact with the atmosphere, and detectors that look for secondary particles created when CRs enter the atmosphere.
Today, the most common technique for the detection of CRs is based on Cherenkov radiation. When a particle encounters a medium at a speed greater than the speed at which photons can travel through this medium, it will slow down and lose energy by emitting a characteristic blue light. Cherenkov radiation is actually broader than visible light and spread to UV. It is emitted within a cone whose angle gives a direct measure of the initial particle energy. Cherenkov was a Russian physicist who was awarded the Nobel Price in 1960 for his discovery.

Direct measurement

The electroscopes used by Hess which measured the amount of electrons in the atmosphere became obsolete, and several types of detectors have been since invented. In the early 1920’s, another technique was already available, when Anderson used cloud chambers to discover the positron. In these chambers, ionising particles leave tracks, each track being characteristic of the type of particle. Other types of chambers were later developed to observe the tracks of incoming particles. For instance, the 1 − 100 GeV energy range in Figure 2.1 was determined by the LEAP ballon experiment in the 1980’s. It aimed at direct particle detection and included a liquid Cherenkov detector (Seo, 1991). Capabilities of particle detectors are constantly improved and used in particle physics experiments, for instance at CERN, or the AMS experiment aboard the International Space Station.

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Indirect measurement

The second main family of detectors was designed for higher energy CRs. These detectors will look for the secondary particles at ground level generated by CRs in the atmosphere. When entering the atmosphere, particles of high energies will generate a shower of secondary particles, mostly electrons and positrons, and also muons in a smaller amount. The shower is beamed, depending on the initial particle energy, but since it is initiated at high altitude, it will spread over a large region. The shower is associated with fluorescence, Cherenkov radiation, and radio emission.
For instance, the Pierre Auger Observatory was specifically designed to detect the highest-energy CRs above 1018 eV, on the far-right side in Figure 2.1. The total detection area is of almost 3000 km2, spread over Argentina, in order to detect a significant amount of such particles. It was named after Pierre Auger, a French physicist who showed the association of air showers with CR events.

Beyond the Solar System

The CR spectrum observed from Earth is modified by the Solar modulation. The Heliosphere, where the influence of the solar magnetic field predominates, acts indeed like a deflective shield and prevents many particles from entering the Solar System.
The Voyager probes were launched in 1977 to visit the planets of the Solar System. They are now on the way out and Voyager 1 showed evidence that it left the inner part of the Heliosphere on 2012 August 25 and it gave the first glimpse at the extrasolar CR spectrum (Stone et al., 2013). As evidence of its entry into unknown territory, Voyager 1 measured a drop in the amount of low-energy ions (∼ 1 GeV) and an increase in Galactic CRs. The intensity of the CR flux indeed apparently became isotropic, confirming their Galactic origin, since CRs no longer originated in the Sun.

Gamma-ray observations

It is important to keep in mind that CRs are particles and not photons. Dedicated telescopes have been built aiming at the direct or indirect detection of these particles from Earth. Nevertheless, CRs can also induce gamma-ray emission. As an example, a molecular cloud under intense CR irradiation will be a bright source of GeV to TeV gamma rays: in that case, gamma rays are induced by the disintegration of neutral pions following collisions of protons with the dense material (see Chapter 4). Therefore, gamma-ray observatories can be used for indirect observations of Galactic CRs close to supernova remnants. Telescopes such as the space Fermi -LAT experiment (1−100 GeV) and the ground-based H.E.S.S. Cherenkov array (0.01−10 TeV) or MAGIC (0.05 − 30 TeV) are dedicated to the observation of gamma-ray sources and can trace indirect signature of Galactic CRs. Observations from these facilities will be valuable in the source selection process for this work (Section 5.3).
Gamma-ray observations are based on techniques similar to CR detection. Detectors aboard satellites use photon interaction processes, such as Compton scattering or pair production, whereas ground-based telescopes are Cerenkov detectors observing particle showers induced by gamma rays entering the atmosphere.
Because of differences in their structure and composition, air showers initiated by gamma rays or CRs can be distinguished.
Gamma-ray telescopes can therefore also directly detect CRs, aside their primary objectives. Their measurements of faint gamma-ray sources are actually disturbed by the intense CR flux on Earth. Therefore, both Fermi and H.E.S.S. have been designed to rule out CRs in the detection process of gamma rays. They are disregarding about 105 −106 CR signatures for each detected gamma ray when pointing to a gamma-ray source. Collecting these CR events allowed to derive the spectrum of CR electrons at GeV to TeV energies (Thompson et al., 2012; Aharonian and Collaboration, 2008b).

Influence of cosmic rays

CRs pervade the Galaxy and play a crucial role in the physical heating and the chemical ionisation of the ISM. They have a major impact on the chemistry of the cloud, as they initiate efficient chemical reactions and the formation of molecular ions. Chapter 3 is dedicated to the description of the CR induced chemistry.
CRs also create light elements (Li, Be, B) via spallation of heavier nuclei in the ISM. In the following, I focus on CR effects in dense clouds.
The interstellar UV radiation cannot penetrate dense regions with AV ￿ 2 mag where CRs become the dominant source of ionisation and control the ionisation degree. The ionisation degree in the molecular gas is a fundamental parameter throughout the star and planet forming process. The abundances of ions indeed regulate the coupling of the gas to the magnetic field in a process called ambipolar diffusion. Collisions of neutrals with ions which remain bound to magnetic field lines slow down the gravitational collapse and decrease the star formation rate. Typical measurements in prestellar cores give ionisation fractions between xe = 10−8 and 10−6 (Caselli et al., 1998). The time scale for ambipolar diffusion varies linearly with the ionisation fraction and can get 2 to 200 times larger than free-fall time scales (see Caselli and Ceccarelli, 2012, and references within). In addition, ions sustain turbulence within protoplanetary discs and introduce non-ideal magnetohydrodynamics effects, which influence the accretion rate onto the protostar (Balbus and
Hawley, 1998; Lesur et al., 2014).
In the absence of UV radiation, CRs may also be the dominant source of heating in low-density dark clouds, where they counteract the efficient radiative cooling by molecules. Each CR ionisation (mainly with H2, He or H in molecular clouds) produces electrons with enough energy to produce a secondary ionisation. Slow electrons will then deposit some of their kinetic energy in the gas. They will heat the gas through several effects such as ionisation, electronic or vibrational excitation (followed by collisional de-excitation), and dissociation (Dalgarno et al., 1999). In a recent paper, Glassgold et al. (2012) showed that the dominant contribution to heating in molecular clouds (outside protostellar cores) comes from chemical heating. Chemical heating corresponds to the energy released by chemical reactions following the formation of primary ions induced by CRs: H+2 , He+ and H+. The next contributors are H2 dissociation and rotational excitation, vibrational excitation is ineffective.
Finally, UV photo-desorption in well-shielded regions is inefficient. It is believed that CRs allow the desorption of molecular material from dust grains into the gas phase (Leger et al., 1985; Hasegawa and Herbst, 1993). This concerns species that were accreted onto the grains due to low temperatures in the dense gas, such as CO, or species that were formed by chemical reactions at the surface of the grains and are otherwise absent from the gas phase. CRs therefore counteract a possible complete freeze-out (Walmsley et al., 2004) of molecular species on the grains and contribute to the release of complex molecules in the gas phase.

Table of contents :

I Context: CR irradiated molecular clouds 
1 The interstellar medium (ISM)
1.1 Structure of the ISM
1.2 Classification of gas clouds
1.3 Dense molecular clouds
1.4 ISM-star cycle
2 Cosmic rays
2.1 Discovery
2.2 Observations
2.3 Influence of cosmic rays
3 Cosmic-ray induced chemistry
3.1 The cosmic-ray ionisation rate
3.2 Diffuse molecular clouds
3.3 Dense molecular clouds
3.4 Propagation of the cosmic-ray spectrum
4 Interaction of supernova remnants with molecular clouds
4.1 Supernova remnants
4.2 Physical processes associated with gamma-ray emission
4.3 Evidence of the SNR interaction with molecular clouds
5 Thesis work: targets and methods 43
5.1 Open questions addressed by the thesis
5.2 Methods
5.3 Selection of the studied regions
II Methods: Radio observations and chemical modeling 
6 Observations
6.1 Radio astronomy
6.2 Molecular spectroscopy
6.3 IRAM 30m observations
7 Derivation of the column densities
7.1 Methodology
7.2 Data reduction
7.3 Derivation of physical conditions
7.4 Derivation of column densities
8 Chemical modeling
8.1 Chemical models
8.2 The astrochem code
8.3 Steady-state abundances
8.4 Comparison to observations
III Results 
9 Enhanced ionisation in W28 and CR properties
9.1 Introduction
9.2 Summary of the article and main results
9.3 Further considerations
10 Probing the passage of the W51C supernova remnant shock through a molecular cloud
10.1 Introduction
10.2 IRAM 30m observations
10.3 Dumas et al. 2014
11 New tracers of the ionisation
11.1 Introduction
11.2 Model predictions
11.3 Observations and results
11.4 Discussion
12 The W44 SNR-cloud association
12.1 Introduction
12.2 W44: Source background and strategy of observations
12.3 Observations and results
12.4 Analysis
12.5 Chemical modeling
12.6 Conclusions
13 Summary of the results and limits of the method
13.1 Summary of the results
13.2 Limitations of the method
Summary and perspectives
Résumé et perspectives
Bibliography 
Slides of the PhD defense

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