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Dust dynamics and planet formation
Although dust is thought to account for about 1% of the mass of PPDs, like in the ISM, it provides most of the disk opacity and constitutes the building blocks of terrestrial planets and the core of giant planets.
The dust dynamics involves di erent processes such as the growth of the dust grains via coag-ulation, dust mid-plane settling and the radial drift (see Fig. 1.8). The first stage of the planet formation starts with the smaller than a micron-sized dust well coupled to the motion of gas (Wolf et al., 2012). By colliding and sticking together, the size of the dust aggregates is increas-ing, and the particles start feeling friction while moving with respect to the gas and decouple from the gas motion. By su ering strong drag force, particles settle down to the mid-plane (also known as vertical settling) (Weidenschilling, 1980), increasing the dust density and forming pebbles and kilometre size bodies in the mid-plane of protoplanetary disks (Testi et al., 2014).
However, grain coagulation has to overcome several barriers in order to form future planets. With growth the surface-to-mass ratio declines and thus the sticking is less e cient which is referred in literature as a ”bouncing barrier”. However if the growth continues, another bar-rier emerges which is called a ”fragmentation barrier” when two large dust aggregates collide at high velocities and shatter instead of sticking together. Furthermore, if the dust aggregate reaches about one meter in size, it will start rapidly drift inwards toward the star and will be destroyed by the high temperature (Dullemond, 2013). The last two problems are commonly called a ”meter barrier”. To overcome a ”meter-size barrier”, a new theory involving turbu-lence was introduced by Cuzzi et al. (2001) when the particles cluster in turbulent flows. The turbulence can concentrate particles to severe over-densities and lead to the formation of very large gravitationally bound clusters of the dwarf planets size. This gravoturbulent method makes possible planetesimal formation.
After the planetesimals are about one kilometer in size, gravity becomes the dominant force. The next stage is the growth from planetesimals to protoplanets (with radii of order a thousand kilometers) which is rather challenging to study due to the unknown initial conditions of the formation mechanism and the distribution of the planetesimals.
The growth of planetary embryos and giant planet cores from a disk of planetesimals proceeds in two regimes: runaway and oligarchic growth which di er in the growth rates (see Fig. 1.10). The growth rates depend on the random velocity of the small bodies relative to the local circular motion (Wolf et al., 2012). In the case of ranaway growth, the most massive bodies grow the fastest, so that these runaway bodies detach from the remaining population of small planetesi-mals. However, with increasing mass, these big bodies start to stir-up the velocity of the smaller bodies, so that the growth becomes slower, and the mode changes to the so-called oligarchic mode. In this regime only the massive bodies keep growing, forming a population of oligarchs that dominate the dynamical evolution in the disk (Morbidelli et al., 2015).
Many oligarchs should merge in order to form solid cores of future terrestrial planets consisting of ice and rocks. This is a complex N-body interactions and the whole theory of planet formation is still under development. However, in spite of the complexity and uncertainties, the model converge on growing grains of sub-micron sizes to very large several thousands of kms planets.
Based on this model, there are several reasons for looking for the terrestrial planets within first 10 au in the PPDs. The first one is suggested by the basic structure of the Solar system where the low-mass terrestrial planets present in its innermost part and giant planets in the outer part. This arrangement is the result of the formation of multiple embryos with the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the PPDs (Morbidelli et al., 2015). The second reason is the most recent knowledge gathered by detecting exoplanets. Indeed, the majority of the discovered exoplanets including super-Earths lies within first 10 au from the hosting star (e.g., Mordasini, 2018).
PPDs: a silicate-rich composition in solids
The formation of telluric planets happens in the innermost regions of the PPDs. In those regions the dust, emitting mostly in the infrared domain, not only determines the thermal and geometri-cal structures of the disks but also serves as building blocks for the telluric planets.
Ubiquitously detected in PPDs (e.g., Bouwman et al., 2001; Juhasz´ et al., 2010) and in the inter-stellar medium (ISM; Draine, 2003), silicate minerals have been one main focus of solid phase studies because of their strong infrared (IR) signatures around 10 and 20 m.
Infrared (3 to 180 m) spectroscopic observations with the Infrared Space Observatory (ISO) or the Spitzer Space Telescope provided a large database of spatially unresolved IR spectra of pro-toplanetary disks. Coupled with theoretical models, such observations indicated that amorphous pyroxenes and olivines, crystalline forsterite (Mg2SiO4) and enstatite (MgSiO3), and amorphous silica (SiO2) are ubiquitous in the surface layer of disks (Mathis et al., 1977; Gail, 1998; van Boekel et al., 2005; Juhasz´ et al., 2010). Thus, it is generally assumed that the majority of the dust in disksis composed of these chemical species. As an illustration, Figure 1.11 shows the N-band spectra with a large variation in the strength and shape of this feature, for Her-big stars (HAe), T Tauri stars (TTS), brown dwarfs (BDs) and the spectra obtained in the labs (Lab.Sil.). In some cases, the shape of the feature is strongly peaked at about 10 m which probably indicates small (<< 1 m) grains. In other objects, the feature is very weak with re-spect to the continuum, and much less peaked. In other cases, many narrow features, typical of crystalline silicates, are clearly visible, superimposed on the smoother and broader amorphous silicate emission (Natta et al., 2007). van Boekel et al. (2005) first noted the correlation between the shape and the strength of the silicate bands which is consistent with the growth of silicate grains from submicrometer to micrometer sizes.
Radial variations of the disks mineralogy could be first addressed through the modelling of the 10 m and 20-30 m silicates features, assuming that the 10 m one is representative of the inner warmer disk regions while the 20-30 m one characterizes the outer cooler disk (Kessler-Silacci et al., 2006; Bouwman et al., 2008; Meeus et al., 2009). Infrared observations of T-Tauri disk’s upper layers suggested radial variations of the forsterite and enstatite distribution, with more enstatite in the warm inner regions than in the cooler outer regions where the contribution of forsterite would be stronger (Kessler-Silacci et al., 2006; Bouwman et al., 2001; Meeus et al., 2009). In parallel, MIR interferometric observations of three Herbig Ae stars by van Boekel et al. (2004) resolved the 1-2 au inner disk region. van Boekel et al. (2004) derived a dominant fractional abundance of crystalline forsterite, which is needed to best fit the 10 m region of the observed spectra. This finding of a forsterite-rich dust in the innermost hotter disk zone is compatible with the high temperature condensation of forsterite (Gail, 2004). From those results, it appears that silicates have been the main focus of solid phase studies in PPDs. However, recent MIR spectroscopic observations with the Infrared Space Observatory (ISO) or the Spitzer Space Telescope presented a large variety of spatially unresolved IR spectra of PPDs around YSOs with distinctive IR features (e.g., Seok and Li, 2017; Acke and van den Ancker, 2006) that were attributed to C-based dust species (as an example see Fig. 1.12). Such IR features were commonly ( 70%) detected around Herbig Ae stars (e.g., Acke et al., 2010) and more sparsely ( 10%) around T Tauri stars (Geers et al., 2007). It thus appears that carbon in solid form must be taken into account in the solid composition of disks following what was discovered in the ISM. This is the subject of the next section.
Carbon-based species
Dust models
In the early sixties Hoyle and Wickramasinghe suggested that the interstellar grains may be graphite. They proposed that small graphite flakes could explain the visible to near-IR extinc-tion. Soon after, with the measurement of the UV extinction and the UV bump around 0.12 m and 0.22 m (Stecher, 1965), it was shown that silicate and graphite grains fit best the observed extinction. The addition of data in the UV and IR wavelength regions enabled the new study of the size distribution and composition of dust: the new model of the power-law size distributions of separate populations of bare spherical silicate and graphite grains was proposed by Mathis et al. (1977) [MRN model]. In this model, the law distribution of sizes follows n(a) / a 3:5 and the graphite grains and the silicate grain range in size from 0.005 to 1 m and 0.025 to 0.25 m respectively.
However with the access to more data in mid-and far-IR, it became clear that the emission from very small grains is necessary to account for emission features in the IR.
Carbonaceous nano-grains were first discovered in the interstellar medium as ’unidentified’ IR features by Gillett et al. (1973) and later associated with PAHs (Leger and Puget, 1984) and hydrogenated amorphous carbons (Wickramasinghe and Allen, 1980). Leger and Puget (1984) introduced so-called PAH model – ”a mixture of free PAH molecules which is a major and ubiquitous component of the interstellar matter”.
In parallel with MRN-like studies, Zubko et al. (1996) suggest regularization where once a grain model is assumed then a unique size distribution is derived. ”His method results in size distri-bution with more structure than a simple power law”(Clayton et al., 2003).
Later on Draine and Li (2001) included PAHs to account for emission features and excess con-tinuum emission from single-photon heating. Some later dust models followed this same basic approach but abandoned astronomical graphite in favour of physically more-realistic amorphous carbons (e.g. Zubko et al., 2004).
However, such simple approach does not correspond to the realities in the ISM where dust can vary through environmentally-driven changes. Thus, Jones et al. (2013) and Kohler¨ et al. (2014) suggested a new dust modelling framework THEMIS (the standard The Heterogeneous dust In the second raw amorphous silicate grains in green are shown with a 5 nm thick coagulated/accreted a-C mantle. Credit: Jones et al.
Evolution Model for Interstellar Solids, hereafter THEMIS 4 model), which provides a core-mantle model for dust in the di use ISM and the evolution of the dust properties in response to their local environment. Silicate and carbonaceous dust populations are hardly ever com-pletely segregated due to the mixing. Thus, in the THEMIS model, the amorphous silicate and carbonaceous dust populations are mixed together: silicate core with a carbonaceous mantle (Jones et al., 2017). Figure 1.13 shows a schematics of the THEMIS model, with its typical sizes in the order of nm. The colors are attributed to the di erent grain types. In the upper part, a-C:H/a-C grains in black represent aromatic-rich material, white – aliphatic-rich material, and green amorphous silicate grains with a thick accreated a-C mantle are shown below.
Figure 1.14 shows computed temperature distributions for the THEMIS nano-grains of di erent size: 0.4, 0.7, 1.5 and 10 nm at di erent distances from the star. It shows that the smaller the grain is, the bigger the temperature excursion of the grain is, note that the biggest grain of 10 nm is in the thermal equilibrium which can be computed according to Eq. 1.15. This behaviour of the grains is explained in Section 1.2.2, showing that small grains do not reach steady state temperature. Their energy is time-variable and the probability (demonstrated in Fig. 1.15) describes these fluctuations. These particles with temperature excursions should be taken into account whenever the time interval between the absorption of photons with energy h (h is the Planck’s constant, and is the frequency of a photon) is comparable to the energy needed to heat up the particle to high temperatures.
Origin of the carbonaceous material
Most of the primary cosmic carbonaceous material likely is formed as nano- and sub-nm-sized particles via gas-phase condensation in envelopes of carbon-rich asymptotic giant branch (AGB) stars, as well as interstellar PAHs (Latter, 1991). AGB stars are important contributors to the chemical evolution of the ISM. Their inner processes driven by convection in the outer layers transport elemental C and O from their C-O cores to their surfaces which are then condensed in the gas form (Henning and Salama, 1998). In general, the formation of PAH occurs when three conditions are met: carbon-rich environment, high density and high temperature (Cherchne , 2011). Such conditions can be found not only in the AGB envelopes, but also in the ejecta of Type II supernovae, in the winds of R CrB stars and it can be due to the colliding winds of carbon-rich Wolf-Rayet (WR) stellar binaries (Cherchne , 2011).
Followed by the study by Buss et al. (1991) where they suggest that the formation of carbona-ceous grains could proceed through the formation of PAHs in C giant shells, the IR emission fea-tures have been detected in the ISO/SWS spectra of the carbon-rich AGB star TU Tau (Boersma et al., 2006). Later Sloan et al. (2007) found emission features from C-class PAHs in the spectra of the carbon-rich star HD 100764.
However, the formation process of carbon nano-particles is still not su ciently understood (Jager¨ et al., 2009).
Solid carbonaceous species and their spectral features
Figure 1.15 represents some C-based species such as amorphous carbon, hydrogenated amor-phous carbon, PAHs, graphite, fullerenes, and nano-diamonds. PAHs and other carbonaceous nano-grains (e.g., hydrogenated nanodiamonds, hydrogenated amorphous carbons) present C-H and C-C bonds (see Fig. 1.16) which can be used to trace the solid carbon reservoirs. There are di erent bonds which are characterized by the C–H stretching vibrational and bending modes, as well as C-C bending mode between atoms. For example, PAHs represent a ring of six C-atoms connected by alternating single (C-C) and double (C=C) bonds and hydrogen atoms attached to each of the C-atom (Fig. 1.16, red circle). Amorphous hydrogenated carbon materials, con-sisting of H-poor and H-rich amorphous carbon, are a broad family of compounds of polyaro-matic rings that are linked by olefinic and aliphatic bridges (Bouteraon´ et al., 2019). Aliphatic (Fig. 1.16, green circle) is a group of organic compounds of C and H in which the carbon atoms have linear chains. Olefinic (Fig. 1.16, yellow circle) is a group of hydrocarbon compounds that have one or more double or triple bonds between carbon atoms in the linear chain. Aromatic bands are at specific wavelengths: 3.3, 6.2 ,7.7, 8.6, 11.2 m and aliphatic are at 3.4, 6.9, 7.3 m
The absorption of a UV photon by a hydrogenated C-species induces a transition to an upper electronic state. Then it de-excites by making a rapid transition to the ground state leaving most of the initial excitation energy in the form of vibrational energy. Subsequently, this highly vibra-tionaly excited molecule cools down by IR emission in the C-C and C-H vibrational modes (see Fig. 1.17, a doctoral dissertation by E.Peeters, 2002). In other words, these species exhibit nar-row emission bands in L- and N-band from IR fluorescence following stochastic heating events by UV photons (e.g., Draine and Li, 2001; Leger and Puget, 1984). As an illustration, Fig. 1.12 shows the richness of IR features associated with the various types of carbonaceous nanograins present in the environment of YSOs. In the following section, I describe the state of the art of the observation of solid carbon in PPDs and the importance of detecting and characterizing such compounds, especially in the inner disk regions.
C-based species can be a part of carbon reservoirs in the inner 10 au region of disks and they can be incorporated into planetesimals and ultimately planets. However, this is still not yet well understood. Up to now, the spatial distribution of carbon species has mainly been performed at large scales (> 10 au) using mid-infrared spectro-imaging instruments such as VLT/NaCo, VLT/VISIR or GTC/CanariCam (Habart et al., 2004, 2006; Geers et al., 2007; Maaskant et al., 2013; Taha et al., 2018; Lagage et al., 2006). Figure 1.18 shows the detected features around four YSOs with VLT/NaCo. Bouteraon´ et al. (2019) decomposed this spectra obtaining the template of nano-sized dust species with characteristic features at the wavelengths depicted with arrows (see Fig. 1.19). Further this template is used in Chapter 5 and in paper Kokoulina et al. (2021).
In that context, accurate constraints are missing on the spatial distribution and properties of carbonaceous dust particles down to the astronomical unit in the inner disk regions. That is yet essential to determine whether or not the inner regions of PPDs are inherently depleted in solid carbon and to understand the physics, radiative properties and chemistry of these grains.
The other questions such as what other forms of C-based species are in the disks, is there enough carbonaceous material in the inner most regions and what is its spatial distribution are relevant to understanding the apparent carbon deficit in the primitive inner proto-solar nebula (e.g., Lee et al., 2010).
Why studying Carbon in PPDs?
Planet compositions are tightly linked to the structure and evolution of the PPDs in which they form (e.g., Piso et al., 2015). The chemistry of the planets is in part driven by the volatile compounds in which they are found in the disks. CO2, and CO, which are the main carriers of oxygen and carbon and have di erent condensation temperatures, can form di erent snowlines.
Figure 1.18: NACO spectra averaged (in black) for di erent distances from the four YSOs (HD 100546, HD 100453, HD 169142, HD 179218) in 0.1” step. Gaussian decomposition (in red) for each spectrum. Spectra are normalised to the continuum at 3.2 m. Credit: Bouteraon´ et al. (2019)
Figure 1.19: Gaussian decomposition of the spectra (in red) of HD 100546. Spectra is nor-malised to the continuum at 3.2 m. Arrows depict di erent bonds with di erent colors.
Such a study was reinforced by Eistrup et al. (2018), who showed how carbon ratio of several gas species in exoplanets atmospheres can link it to the formation site in the PPDs and provide information on the chemical evolution in it, independent on whether an atmosphere is built primarily from gas accretion or from planetesimal impacts. Eistrup et al. (2018) also showed that carbonaceous ices are essential for forming complex molecules like hydrocarbons. In the innermost regions, nano-carbons may play a pivotal role in the evolution of the most abundant molecule H2 and formation of organic fragments.
Carbon is the fourth most abundant component in the Universe. Carbon is detected in the form of carbonaceous ices, e.g. CO in the outer disk regions (Pontoppidan et al., 2014) and in ISM -60% of the cosmic carbon is locked in some form of graphite or amorphous carbon grains (Savage and Sembach, 1996). However, little is known about the carbon species in the inner part of the PPDs. Thus, the key questions are: is there a significant reservoir of C-based solid species in the inner 10 au region of disks? In what form? How can solid carbon be incorporated into planetessimals and ultimately planets?
Table of contents :
1 Introduction
1.1 Young stellar Objects
1.1.1 Star formation in a nutshell
1.1.2 Young stellar objects classification
1.2 Disk properties
1.2.1 Material distribution
1.2.2 Temperature distribution
1.2.3 Disk opacity
1.3 Dust dynamics and planet formation
1.4 PPDs: a silicate-rich composition in solids
1.5 Carbon-based species
1.5.1 Dust models
1.5.2 Origin of the carbonaceous material
1.5.3 Solid carbonaceous species and their spectral features
1.6 Why studying Carbon in PPDs?
2 Mid-infrared Interferometry with MATISSE
2.1 History of mid-infrared interferometry
2.2 Theoretical principles of interferometry
2.2.1 Main functions of an interferometer
2.3 MATISSE
2.3.1 Presentation
2.3.2 Instrumental design and optical train
2.3.3 Signal encoding
2.3.4 Dealing with the thermal background
2.3.5 Observing sequence
2.3.6 Data reduction
2.3.7 What does a MATISSE observer do?
2.3.8 MATISSE performances
3 Telluric lines
3.1 Atmospheric transmission
3.2 Efect of telluric lines on raw MATISSE data
3.3 Efect of water vapour on the calibrated MATISSE data
3.4 Molecfit – a telluric absorption correction tool
4 Interferometric models and minimization methods
4.1 Geometric approach
4.2 Temperature-gradient modeling
4.2.1 Theoretical aspects of temperature-gradient models
4.2.2 Vertical temperature-gradient
4.2.3 Temperature-gradient model parameters and observables
4.2.4 Feature emitting component
4.2.5 Asymmetry modeling
4.3 Model fitting with MCMC
5 Case of HD 179218: results and discussion
5.1 HD 179218
5.2 Observations of HD 179218
5.2.1 MATISSE data
5.2.2 MIDI data
5.2.3 PIONIER data
5.3 Qualitative analysis
5.3.1 Interferometric observables
5.3.2 Photometric observations
5.4 Modeling and results
5.4.1 Geometric modeling and results complementary to the article Kokoulina et al. (2021)
5.4.2 Temperature-gradient modeling and results
5.5 Parameter sensitivity analysis
5.6 Brand new MATISSE observations
6 Conclusion and perspectives
7 Appendix
7.1 Observation log of the January run: 2021.01.16–01.28
7.2 Data reduction and observables
7.3 Calculation of the radial optical depth
