The global shape, density and rotation of Comet 67P/Churyumov-Gerasimenko from preperihelion Rosetta/OSIRIS observations
Introduction
Comets constitute a large population of objects formed at the early stage of the formation of the Solar System and partially preserved in the Kuiper belt and in the Oort cloud. The present physico-chemical properties of these bodies result from a long and complex history of dynamical, collisional, and chemical evolution. In particular, the sublimation of ices trapped in the nuclei is expected to significantly alter their surface properties as they periodically come close to the Sun. The detailed study of individual comets is therefore expected to give new insights into these processes and to shed light on the processes which led to their formation in the solar nebula.
Rosetta is an ESA-led mission, one of the cornerstone missions of ESA’s “Horizon 2000” scientific program, whose ultimate aim is the in-depth physico-chemical characterization of the surface and interior of a comet nucleus in order to understand the processes which led to the formation of the planetesimals in the early Solar System. In complement, the Rosetta mission has also been designed to shed light on the physical processes at the origin of cometary activity and on those which drive the evolution of comet nuclei.
The Rosetta spacecraft was launched in March 2004 to perform a rendezvous with the Jupiter-family Comet 67P/Churyumov-Gerasimenko (hereafter “67P/C-G”) in 2014 and to escort it throughout its 2015 perihelion passage and beyond. After two encounters with Asteroids 2867 Steins and 21 Lutetia, the spacecraft was put in hibernation between June 2011 and January 2014, and successfully re-activated on January 21, 2014.
67P/C-G is a Jupiter-family comet discovered by K. I. Churyumov and S. I. Gerasimenko of the Kiev Shevchenko National University in 1969. The comet became the new target of the Rosetta mission in 2003 after the cancellation of its launch to Comet 46P/Wirtanen. The dynamical history of Comet 67P/C-G has been studied by Carusi et al. (1985), Belyaev et al. (1986), and more recently by Groussin et al. (2007) who estimated its dynamical lifetime to be about 105, 000 years, although they pointed out that the long-term orbital evolution is chaotic, a fact confirmed by very recent dynamical studies (Guzzo, Lega, 2015, Maquet, 2015). Dynamical lifetimes from ≈ 20, 000 to more than 450, 000 years are also possible depending on the initial orbital parameters, active fraction, and amplitude of the non-gravitational forces considered during the numerical integration of the orbit (Groussin et al., 2007). In the recent past, the comet experienced a relatively close encounter with Jupiter in 1923 and a very close one (at 0.05 a.u., or ∼100 Jupiter radii) in 1959 (Maquet, 2015). They significantly reduced the perihelion distance of Comet 67P/C-G, especially after the 1959 encounter.
Its nucleus has been observed extensively since 2003 in order to retrieve its physical and dynamical parameters in preparation for the Rosetta observations. Lamy et al. (2007) used the visible light curves inversion method to retrieve the rotational parameters, the size and rough shape of the nucleus. The spin axis was found to be oriented in the Equatorial direction (RA, Dec) = for the retrograde solution and (RA, Dec) = for the prograde one. The spin period deduced from the light curves was found to be between 12.4 and 12.7 h. Lowry et al. (2012) used the same data sets, enhanced with three visible light curves obtained at the European Southern Observatory, to construct a very low-resolution shape and to measure the rotational parameters of 67P/C-G’s nucleus. They found a very accurate period of 12.76137 ± 0.00006 h and the direction of the spin axis at (RA, Dec) = close to the prograde solution of Lamy et al. (2007). Observations of dust jets have been used by Vincent et al. (2013) to retrieve a direction of the spin axis in close agreement with the prograde solution of Lamy et al. (2007). Mottola et al. (2014) used a set of light curves obtained by the OSIRIS instrument (see below) during the far approach phase with a very high signal-to-noise ratio to re-determine the rotational parameters of the comet. These measurements were quite important as comet nuclei in general, and Comet 67P/C-G in particular (Gutiérrez et al., 2005), are known to experience detectable changes of their rotational parameters, including the apparition of non-principal axis rotation. The new light curves analyzed by Mottola et al. (2014) imply a reduction of the spin period from the 2009 perihelion passage from 12.76 h to 12.4043 ± 0.0007 h. Two complementary solutions for the spin axis were found at (RA, Dec) = and (RA, Dec) = – this ambiguity being due to the symmetry of the observational geometry (Kaasalainen and Lamberg, 2006).
The measurement of the density of cometary nuclei is a long-standing challenge in cometary science. Density has implications for internal structure as it in part depends upon the porosity of the aggregated cometary material (e.g., Weissman and Lowry, 2008). The main method used to determine the mass of cometary nuclei relies on the effect of the non-gravitational force (NGF) due to the outgassing of the comet as it passes through perihelion. The density is inferred from volume estimates obtained by space missions combined with masses deduced from the effect of the NGF on the orbit. Skorov and Rickman (1999), Sagdeev et al. (1988), Farnham and Cochran (2002) and Davidsson, Gutiérrez, 2004, Davidsson, Gutiérrez, 2005, Davidsson, Gutiérrez, 2006 estimated the density of four cometary nuclei also observed by several space probes. Their estimates lie in the range with error bars of factors 2–8 between the two extreme values for individual comets. Another method relies on the modeling of the effect of the tidal force, which can overcome the self-gravity of the nucleus to disrupt it during a close encounters with a planet. Asphaug and Benz (1996) estimated the density of the nucleus of Comet D/Schoemaker–Levy 9 to be from a smooth particle hydrodynamics (SPH) simulation of its tidal disruption after a close encounter with Jupiter in 1994. Solem (1995) found that the density of the original building blocks was by modeling the disruption of the original nucleus into a collection of fragments observed by the Hubble Space Telescope (HST). From an analysis of the ejecta plume created by the impactor during the Deep Impact experiment, Richardson et al. (2007) derived a nominal value of for the density of 9P/Tempel 1. However, due to non-gravitational perturbations of the trajectory of the particles, the authors could not rule out values in the range between 200 and . This value was later refined to a mean value of and a range of based on new images from the Stardust-Next mission in the calculation of the volume (Thomas et al., 2013a). Finally, A’Hearn et al. (2011) estimated the density of the nucleus of Comet 103P/Hartley 2 assuming that the waist observed between the two lobes is an equipotential surface. They found a mean value of but with acceptable values ranging between 140 and (Richardson and Bowling, 2014). All these estimates of the density of cometary nuclei are summarized in Table 1.
Two attempts have been made to estimate the density of the nucleus of Comet 67P/C-G before its encounter with Rosetta. A detailed modeling of the effect on non-gravitational forces on the trajectory of Comet 67P/C-G has been performed by Davidsson and Gutiérrez (2005) using the non-gravitational acceleration parameters calculated by Królikowska (2003). Their analysis led to an upper value of for the bulk density of Comet 67P/C-G, with nominal values in the range . Kamoun et al. (2014) inferred a value for the dielectric permittivity of the surface from the non-detection of the nucleus in 1982 by radar observations, when Comet 67P/C-G passed at a geocentric distance of only 0.4 a.u. From this constraint, combined with laboratory measurements and modeling, they could derive the porosity of the upper 2.5 m layer (55–65%), and a density between 600 and .
The first images of the nucleus of Comet 1P/Halley acquired by the Vega and Giotto space probes revealed an elongated irregular body (Merenyi, Foldy, Szego, et al., 1990, Stooke, Abergel, 1991). Merenyi et al. (1990) interactively deformed a simple polyhedron model rendered using the Minnaert reflectance law to adjust the CCD images acquired by the two Vega space probes. They also accounted for shadows visible on some of their images. Their reconstructed “avocado shape” exhibited a change of slope, which they attributed to a possible chain of hills, and a depression thought to be a possible cavity. Nevertheless, the low quality of the images obtained during fast flybys only allowed a partial reconstruction of the nucleus at a modest resolution of ∼0.5 km which made it difficult to unambiguously identify (and reconstruct) any surface feature. Stooke and Abergel (1991) used a similar method to reconstruct the shape of 1P/Halley’s nucleus from eleven images obtained by the cameras aboard the Vega’s and Giotto space probes. Starting from a triaxial ellipsoid, they modified the radii of the vertices describing the surface to match the limbs and terminators detected on the images. In spite of these two pioneering works, no clear picture of the 3D topography of the surface of Comet 1P/Halley, even at large scale, could be deduced from the shape models due to the very low resolution of the input images and to the complex rotation of its nucleus (Samarasinha and A’Hearn, 1991).
Subsequent NASA space missions to comet nuclei (Deep Space 1, Deep Impact, Epoxi, Stardust) secured higher resolution images of several cometary nuclei, thereby enabling the morphological analysis of their surface. In parallel, significant efforts have been made to retrieve the global shape of these nuclei. Oberst et al. (2004) used a state-of-the-art stereophotogrammetric technique to obtain a digital terrain model (hereafter DTM) of the sunlit hemisphere of Comet 19P/Borrelly using two stereo pairs obtained by the Deep Space 1 spacecraft. Although their DTM revealed a comet with a very elongated irregular shape, the limited resolution of the model (∼500 m) did not allow them to get a detailed topographic description of the comet surface in 3D. Kirk et al. (2004) also retrieved the topography of Comet 19P/Borrelly. Like Oberst et al. (2004), they applied stereophotogrammetry to a pair of Deep Space 1 images, but this time using a commercial software called “SOCET Set”. They measured the difference between their DTM and that of Oberst et al. (2004): they found a standard deviation of 120 m between the two models, with differences up to ∼500 m locally. Shape models of Comets 9P/Tempel 1 and 103P/Hartley 2 have been obtained by Thomas, et al., 2013, Thomas, et al., 2007, Thomas, et al., 2013 using a method developed at Cornell University (Simonelli et al., 1993). It combines limbs and terminators constraints, the location of several hundred stereo control points, and light curves obtained during the approach for the rotational parameters.
In this article, we first describe how the nucleus of Comet 67P/C-G has been reconstructed and modeled in 3D at low-resolution using ground-based and Rosetta light curves (Section 2). We then explain how high-resolution imaging data have been acquired by the OSIRIS instrument aboard Rosetta until perihelion to map the surface of the nucleus (Section 3). From these images, we use a stereophotoclinometry (SPC) method combined with several computer graphics algorithms to reconstruct the topography of the nucleus at high-resolution (Section 4). A discussion of the nucleus bulk properties and shape is given in Section 5, which leads us to our conclusions (Section 6). In the appendix, we also describe how the early shape models have been complemented by limb profiles provided by the MIRO instrument (Gulkis et al., 2015). A companion article by Preusker et al. (2015) describes the reconstruction of Comet 67P/C-G with the stereophotogrammetry (SPG) method developed and operated at the “Deutsche Zentrum für Luft- und Raumfahrt” (DLR, Berlin, Germany). These two models constitute by far the highest resolution 3D models of a cometary nucleus obtained so far.
A comparison of these two detailed models of 67P/C-G is of great interest to assess the strengths and the limitations of the two approaches. However, several difficulties appear when trying to perform an inter-comparison of two models: (i) the coordinates of the two sets of vertices need to be represented in a common frame with an accuracy much better than the expected differences between the models, (ii) the sampling and the coverage of the models are not the same, and (iii) to our knowledge, no existing standalone point cloud or mesh comparison software entirely satisfies our requirements for such a high-accuracy model comparison. A large amount of work is needed to overcome these difficulties, which leads us to exclude this topic from the present article.
Section snippets
Pre-Rosetta light curves
Following the cancellation of the January 2003 launch of the Rosetta spacecraft to Comet 46P/Wirtanen, Comet 67P/C-G emerged as the most suitable candidate on the basis of orbital considerations. Its nucleus, however, was essentially “terra incognita”. There was therefore an urgent need to pin down its basic physical properties, in particular its size, a critical parameter for the safe landing of the Philae surface module. The very first characterization of the nucleus was achieved by Lamy
The OSIRIS imaging system
The “OSIRIS” Optical Spectroscopic and Infrared Remote Imaging System (Keller et al., 2007) is composed of two distinct cameras. The narrow angle camera is a three-mirror anastigmat telescope with a field-of-view of 2.2°, a focal length of 717 mm and a focal ratio of 8. The wide angle camera (WAC) is a two-mirror off-axis telescope with a field-of-view of 12°, a focal length of 130 mm and a focal ratio of 5.6. Both telescopes have unobstructed apertures. The point-spread-function of the NAC and
Early reconstruction with MPCD
We used a new method called “Multi-resolution PhotoClinometry by Deformation” (hereafter MPCD) developed by Capanna et al. (2013) to reconstruct the global shape of the comet from images acquired during the “SHAP1” rotational movie (see Section 3.1 and Table 2). The method applies deformation to the vertices of a triangular mesh, initially a sphere of radius 1.9 km (Lamy et al., 2007), until synthetic images of the deformed shape model match the observed ones (Fig. 1). A total of 30 images has
Size and shape
The volume of the SPC shape model of Section 4.2 amounts to 18.8 ± 0.3 km3, and the surface to 46.9 ± 2.5 km2. As a point of comparison, the two solutions obtained by Lamy et al. (2007) had a volume of 21 km3 and an area of 40 km2, a difference naturally explained by the bilobed shape of the nucleus. The radius of the sphere having the same volume is in good agreement with the value initially derived by Lamy et al. (2007), but slightly smaller than values published afterwards (
Conclusions
We reached the following conclusions in the article.
- •
The light curve inversion technique has been applied to the reconstruction of the nucleus of Comet 67P/C-G. The subsequent reconstruction of its shape at higher resolution from OSIRIS images offered a unique opportunity to test the accuracy of the method from the very limited data sets available for 67P/C-G (and cometary nuclei in general). Whereas the gross dimensions of the nucleus of 67P/C-G have been successfully retrieved, its highly
Acknowledgments
OSIRIS was built by a consortium of the Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany, the Laboratoire d’Astrophysique de Marseille, France, the Centro Interdipartimentale Studi e Attivita’ Spaziali, University of Padova, Italy, the Instituto de Astrofísica de Andalucía, Granada, Spain, the Research and Scientific Support Department of the European Space Agency (ESA/ESTEC), Noordwijk, The Netherlands, the Instituto Nacional de Tecnica Aerospacial, Madrid, Spain, the Institut
References (82)
- et al.
Size, density, and structure of Comet Shoemaker–Levy 9 inferred from the physics of tidal breakup
Icarus
(1996) Density of asteroids
Planet. Space Sci.
(2012)The primordialnucleus of Comet 67P/Churyumov-Gerasimenko
Astron. Astrophys.
(2016)- et al.
Non-gravitational force modeling of Comet 81P/Wild 2. I. A nucleus bulk density estimate
Icarus
(2006) - et al.
Nucleus properties of Comet 9P/Tempel 1 estimated from non-gravitational force modeling
Icarus
(2007) - et al.
A mcdonald observatory study of Comet 19P/Borrelly: Placing the deep space 1 observations into a broader context
Icarus
(2002) Gaskell Eros Shape Model V1.0
(2008)- et al.
High Resolution Global Topography of Itokawa From Hayabusa Imaging and LIDAR Data
AGU Spring Meeting Abstracts
(2006) - et al.
Radar observations of 8P/Tuttle: A contact-binary comet
Icarus
(2010) - et al.
143P/Kowal-Mrkos and the shapes of cometary nuclei
Astron. J.
(2003)