The heterogeneous coma of 67P/C-G seen by ROSINA 

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From naked-eye observation to in situ measurements

In this first chapter, we present an overview of the general knowledge about comets. We start with the observations and descriptions of comets through History. Then, we describe a scenario of formation of our Solar System to explain the origin of comets, their location and why studying comets is important for the comprehension of the Solar System and Earth’s history. We detail the comet’s types and classification defined by the International Astronomical Union (IAU), and the structure of a comet (nucleus, coma and tails). We then present the previous space missions targeting comets and their main results.

Observations through the ages

For ages, a spectacular phenomenon has been observed with fascination and anxiety. Once in a while, unpredictable bright stars with tails appeared in the night sky, some-times shined for days or months and finally faded away. The imagination of observers associated those apparitions to various interpretations, which supported thoughts and be-liefs, augured bad omens or important changes. We summarise the comet’s observations through history which were detailed in Brandt and Chapman (2004).
These mysterious objects were named comets. This English name came from the Latin cometa, which came from the greek kometes, and literally means long-hair star. Before the use of telescopes, one observer on Earth could only detect a comet close to the Sun, when it developed a huge bright cometary tail, visible with the naked-eye. At the time, astronomers reported precisely their observations, but they only had assumptions concerning the nature, the size, the orbit or the origin of those bodies.
Until the Renaissance period, following a suggestion of the greek scientist and philoso-pher Aristotle (384 BC – 322 BC), comets were generally considered to be closer than the Moon, suggesting they were atmospheric events. In 1577, Tycho Brahe (1546 – 1601), a Danish astronomer, observed precisely the trajectory of comet C/1577 V1 (i.e. The Great Comet of 1577), relative to the Moon and stars by triangulation. His calculations lead to the conclusion that this comet was located much further than the distance to the Moon. He suggested that comets orbited around the Sun in circular trajectories, in a helio-geocentric system, where the Moon and the Sun orbit the Earth and the other planets orbit the Sun (Brahe, 1602).
Finally, the periodicity of these small objects was proved by Edmond Halley (1656 – 1742) in A synopsis of the astronomy of comets, published in 1705. Born in 1656, this English scientist studied tables of orbital parameters of comets and realized the similarity between the values obtained for three observations, in 1531, 1607, and 1682. Halley used Newton’s theory (later published in 1687 in Philosophiae naturalis principia of mathematica) to calculate the orbital parameters of historical comets and discovered that three reported observations described the same object with a periodicity of about 76 years. He predicted the return of the comet, which appeared in the Christmas night of 1758 and became the most famous comet in history. This brought an additional proof of Newton’s gravitational theory and the comet was named Halley. This discovery changed completely the study of comets and allowed scientists to tentatively connect the old observations with the more recent ones.
Comets were well described and represented in the literature and arts. Their appari-tions were often linked to mythological, religious or historical scenes. Figure 1.1 shows a part of the Bayeux embroideries (a tapestry of 70 m long dating back to the 11th century), which represents men observing a passage of Halley’s comet during the Hastings battle in 1066, six centuries before the birth of Halley.
In the 19th century, study of comets benefited from the developments of astrophysics, in particular polarimetry (Arago, 1843) and spectroscopy (Donati, 1858; Huggins, 1868). The modern era in cometary science began in the 1950s, when Fred Whipple predicted the existence of the cometary nucleus and first described it with the model of icy conglomerate, which will be further detailed in Section 2.2.1.

ORIGIN OF COMETS AND THEIR IMPORTANCE 

Origin of comets and their importance

To investigate the origin of comets, we summarise the classical theory of formation of the Solar System (see Armitage (2010) and De Pater and Lissauer (2015) for a detailed introduction). The starting point of the Solar System formation happened about 4.6 bil-lion years ago. An interstellar molecular cloud called the protosolar nebula (PSN) was disturbed by an important perturbation, probably the explosion of a supernova (Cameron and Truran, 1977). The explosion’s resulting shock wave initiated irreversible perturba-tions of the nebula, starting with the collapse of the cloud and the associated acceleration of the rotation speed which induced a flattening of the cloud by conservation of momen-tum. Inside, the temperature and the density increased considerably, in particular in the center of the disk, where the condensation of the matter lead to the birth of a proto-star. The interaction between gas and dust implies that the dust settled in a very thin plane (smaller than the disk) and started the hierarchical accretion, i.e. small interstellar par-ticle of about 10-100 nm accreted into cm-size and larger aggregates (Rietmeijer, 1998, 2002).
The largest bodies are called planetesimals. They gravitationally draw the surrounding materials and continued to grow. When their diameter reached hundreds of kilometers, planetesimals became proto-planets which have evolved in one of the eight planets of our Solar System, Mercury, Venus, Mars or the Earth, the four terrestrials planets, or Jupiter, Saturn, Uranus or Neptune, the four Giant gaseous planets. The planets were formed rapidly, in about 10 million years (Yin et al., 2002). In the center of the disk, the proto-star started the nuclear fusion of hydrogen and became the Sun. At this time, the disk remained full of debris, and the planets were the targets of intense bombardments which cleaned the Solar System of a fraction of the small bodies. The remaining bodies became the comets, asteroids, moons and dwarf planets located in various reservoirs in the Solar System. As the temperature decreases with the distance to the Sun, small bodies formed at a distance where the temperature will aggregate dust and solid ice became the icy small bodies of the Solar System.
The Grand Tack is an hypothesis proposed by Walsh et al. (2011), based on hydro-dynamical simulations of a protoplanetary disk, simulating the migration of planets. They suggested that Jupiter was formed around 3 – 4 AU1 from the Sun and migrated inward, followed by Saturn. Around 1.5 AU, Jupiter was captured in resonance with the orbit of Saturn, whose period corresponds exactly to 3/2 that of Jupiter. The mean motion resonance reversed their directions of migration and the two giant planets migrated out-ward, beyond 5.5 AU. As a consequence, the main asteroid belt was depleted of bodies and Neptune and Uranus moved outward. After the Grand Tack, the four giant planets were in a compact configuration, in resonant nearly circular orbits. A scenario of the evolution of this configuration is given by the Nice Model, described in a series of papers (Morbidelli et al., 2005; Tsiganis et al., 2005; Gomes et al., 2005; Morbidelli et al., 2007). They suggested the presence of a massive disk of icy planetesimals, located further than the giant planets. After about 600 million years, the cumulative gravitational interactions between the planets and the disk perturbed the resonant configuration and destabilised the entire planetary system. In particular, a close encounter between Jupiter and Saturn provoked a shift of Uranus and Neptune, which moved much further than their previous orbits, to their current orbits. The two giant planets were propelled far from their initial position, inside the planetesimal disk. They induced a scattering of the small icy bodies, which were ejected in the outer Solar System or injected in the inner Solar System. Those small bodies impacted intensely the terrestrial planets during this period which is called the Late Heavy Bombardment (LHB). This probably explains the apparent simultaneous formation of impact basins on the Moon, Mars and Mercury (Morbidelli et al., 2001). The dynamical history of the Solar System described above is illustrated in Figure 1.2 from DeMeo and Carry (2014).
Figure 1.2: Representation of the planetary migration and their effect on the small bodies of the Solar System, as described by the Grand Tack and the Nice model (DeMeo and Carry, 2014).
Small bodies of the Solar System are located in different regions of the Solar System, as seen in Figure 1.3:
• The Main Belt or Asteroid Belt is situated between the orbit of Mars and Jupiter, with a semi-major axis ranging from 1.7 – 4.5 AU. The space mission Dawn explored the asteroids (1) Ceres (the largest object of the Main Belt, with a diameter of 946 km) and (4) Vesta (530 m of diameter).
• The Kuiper Belt, or Edgeworth-Kuiper belt, is located beyond Neptune’s orbit, be-tween 30 to 50 AU, and contains small bodies and dwarf planets (including Pluto). It was predicted by Edgeworth (1943) and named after Gerard Kuiper, who sug-gested the existence of small bodies beyond Pluto but actually rejected the presence of the Kuiper belt at its actual position, due to the presence of Pluto (Hynek, 1952). Except Pluto and Charon, respectively detected in 1930 and 1978, the first two ob-jects of the Kuiper belt were discovered in 1992 by Jewitt et al. (1992) and Luu et al. (1993). Two distinct populations of Kuiper belt objects have been described by Tegler and Romanishin (1998), based on the surface color of the objects, the reddest object and the object slightly redder than the Sun. The populations are recognized today as dynamically hot and dynamically cold, and we expect the hot population to have been emplaced by the Late Heavy Bombardment event. In ad-dition to the difference of surface color, the objects of the two populations have different physical properties, such as albedo, inclination and eccentricity.
• The Oort Cloud is an hypothetical reservoir of icy bodies inferred from the distri-bution of semi-major axis of long period comets (Oort et al., 1950). They described it as a large shell-shaped structure extending up to the limit of our Solar System (from 50 000 to 150 000 AU, i.e. 0.8 to 2.4-light years).
• Minor other groups of small bodies circulate in the Solar System. The Jupiter Trojans are on the orbit of Jupiter, at the Lagrangian points, the Hilda asteroids are situated between the asteroid belt and Jupiter, on a 3:2 orbital resonance with Jupiter (Armitage, 2010).
• The Scattered Disk contains icy objects with large range of eccentricities and incli-nations (Duncan and Levison, 1997). It extends from beyond the Kuiper belt up to hundreds of AU.
The Kuiper Belt and the Oort Cloud are the two largest reservoirs of icy bodies. Some of them were injected into the inner Solar System, probably because of a gravitational perturbation, and became detectable from Earth due to their activity and became comets.
Figure 1.3: Schematic of the Solar System, showing the Main Asteroid Belt (between the orbits of Mars and Jupiter), the Kuiper belt (from 30 to 50 AU from the Sun) and the Oort cloud (up to 50 000-100 000 AU). Modified from an illustration from Schwamb (2014).

Interest of the cometary science

The study of comets is motivated by several reasons. One of them is the possibility to look back in the past of our Solar System. Comets are formed from the most pristine material of the protosolar disk (since they did not become larger bodies), and they spent most of their lifetime far from the Sun, too far to be affected by solar temperature. The comets’ current composition should be very close to their original composition. Thus, comets are among the most pristine objects of the Solar System and their study may reveal important missing clues on the conditions of planets’ formation and on the composition of our planetary system. The study of the initial composition of the nucleus is the ultimate goal to investigate those issues. The in situ data and remote sensing observations recorded by instruments can only access the coma composition. The composition and relative abundance of the coma can however be very different from those inside the nucleus, due to molecular dissociation, dust fragmentation, chemical processes, etc., as described later in Section 2.1.2. The presence of specific molecules, abundances and isotopic ratios can give clues to the origin and formation process of the nucleus.

Table of contents :

I Comets: small icy bodies of the Solar System 
1 From naked-eye observation to in situ
1.1 Observations through the ages
1.2 Origin of comets and their importance
1.3 Interest of the cometary science
1.4 Comet types and classification
1.5 Structure
1.5.1 Nucleus
1.5.2 Coma
1.5.3 Tails
1.6 Observations before Rosetta
2 Our vision of the coma and the nucleus 
2.1 Coma
2.1.1 Chemical composition of the coma
2.1.2 Photo-reactions and chemical reactions
2.1.3 Models of gas expansion in the coma
2.2 Cometary nucleus
2.2.1 Model of the internal structure
2.2.2 Heat diffusion and physical processes
3 The Rosetta mission (2014-2016) 
3.1 Introduction
3.2 Comet 67P/Churyumov-Gerasimenko
3.3 On-board instruments
3.4 Trajectory
3.5 Overview of the main scientific results
II Description of the experiment and data analysis 
4 The ROSINA experiment 
4.1 General presentation
4.2 Science objectives and performance
4.3 Mass spectrometry
4.3.1 Time-of-flight mass spectrometry
4.4 Description of the ROSINA instruments
4.4.1 The Double Focusing Mass Spectrometer
4.4.2 The COmet Pressure Sensor
4.5 The Reflectron-type Time-Of-Flight mass spectrometer
4.5.1 Instrument description
4.5.2 Principle
4.5.3 Operating modes
4.5.4 In flight performance limitations
5 Data analysis of RTOF spectra 
5.1 RTOF raw spectra
5.1.1 Acquisition
5.1.2 ADC Correction
5.1.3 Baseline
5.1.4 Electronic noise and other non desirable peaks
5.2 RTOF L3 spectra
5.2.1 Mass calibration
5.2.2 Abundance of volatiles
5.3 Conversion to volatiles density
5.3.1 Fragmentation
5.3.2 Sensitivity
5.3.3 COPS calibration
III The heterogeneous coma of 67P/C-G seen by ROSINA 
6 Description of the datasets 
6.1 Orbitography parameters
6.1.1 Sub-spacecraft point coordinates
6.1.2 67P/C-G’s orbit
6.1.3 Spacecraft to comet distance
6.1.4 Nadir off-pointing
6.2 RTOF dataset
7 Global dynamics of the main volatiles 
7.1 Dependence on the comet-spacecraft distance
7.2 Diurnal variation
7.3 Evolution of the activity with the heliocentric distance
7.3.1 Global pattern
7.3.2 Deriving the outgassing rate
7.4 Seasonal variations
7.4.1 Approach
7.4.2 Pre-equinox 1
7.4.3 Pre-equinox 2
7.4.4 Post-equinox 2
7.4.5 End of mission
7.5 Evolution of density ratios
8 Spatial variation of the main volatiles 
8.1 The geographical coordinate system
8.2 Illumination model
8.3 Density maps through the mission
8.3.1 Description of the maps
8.3.2 Analysis of the density maps
8.3.3 Interpretation of the observations
8.3.4 Difference between the two lobes
8.4 Detection of molecular oxygen
8.4.1 Method
8.4.2 Analysis
9 Comparison with DFMS 
9.1 Cross correlation RTOF vs DFMS
9.2 DFMS density maps
10 Comparison with a numerical model of the coma
10.1 DSMC model
10.2 Comparison with RTOF density
10.3 Global comparison between ROSINA and the DSMC model
IV Simulating the nucleus to constrain properties 
11 The thermo-physical model 
11.1 Description of the model
11.1.1 Description of the algorithm
11.2 Previous studies
11.3 Application of the model
11.3.1 Orbital parameters
11.3.2 Physical parameters
11.3.3 Computed locations and description of the cases
12 Analysis of the nucleus model results
12.1 Evolution of the surface and interior’s temperature
12.2 Evolution of the stratification
12.3 Evolution of the fluxes
12.4 Effect of the dust layer and of the trapping conditions
12.4.1 Impact of the initial dust mantle thickness
12.4.2 Effect of the trapped CO on the averaged fluxes
12.5 Analysis of the production rate
13 Comparison with fluxes derived from RTOF
13.1 Global comparison with RTOF
13.1.1 Deriving surface production rates from RTOF
13.1.2 Comparison with RTOF global production rates
13.2 Comparison of the flux geographical maps
13.2.1 Visualisation and Interpolation
13.2.2 Analysis of the model maps
13.2.3 Comparison with the RTOF spatial variation
13.3 Discussion and perspectives
Conclusion and perspectives (English version)
Conclusion et perspectives (french version)

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