Workshop on Spectroscopy, Photometry, and Polarimetry of Airless Solar System Objects, Tuusula, Helsinki (Finland), 2017 September 15-16,
The compositional structures of the asteroid main belt and the Kuiper belt result from the dynamical mixing they suffered in the early stages of planetary formation, in particular during planetary migrations. Revealing these structures, in link with the orbital distribution of these belts, is key in decoding the history of the Solar System .
Decades of targeted photometric and spectroscopic surveys of minor bodies have been the foundation of spectral classification and mineralogical analysis, leading to the first inventories of minerals in the main belt and ices in the Kuiper belt, links with meteorites, and description of their compositional structures [2,3]. However, with only a few thousands objects observed in the visible, and a few hundreds in the near-infrared, these targeted surveys have only glimpsed the tip of the iceberg .
A revolution was brought by large multi-filter imaging surveys, such as the Sloan Digital Sky Survey (SDSS), providing visible colors for hundreds of thousands of minor bodies . Large imaging surveys are indeed goldmines to crudely characterize the surface properties of huge samples, inheriting the interpretation from the targeted surveys with higher spectral resolving power. For instance, the SDSS opened a new era in the study of asteroid families , space weathering , distribution of material in the inner solar system , and origin of the near-Earth asteroids . In a few years, the current ESA Gaia mission will deliver low resolution visible spectra for 300,000 asteroids with an apparent magnitude V<20, increasing by two orders of magnitude the sample of minor bodies with visible spectra . Starting its operations in 2021, the Large Synoptic Sky Survey (LSST) will provide colors in the visible for millions of minor bodies  in less than a decade. These will however remain limited to visible wavelengths.
The ESA Euclid mission, scheduled for a launch in 2021 and operating during six years from the Sun-Earth Lagrange L2 point, will carry out an imaging and spectroscopic survey of the extra-galactic sky of 15,000 deg2 . Euclid imaging detection limits are required at mAB = 24.5 in the visible and mAB = 24 in the near-infrared (Y, J, H filters). The access to the near-infrared sky, about 7 magnitudes fainter than 2MASS and 2-3 magnitudes fainter than current ESO VISTA VHS makes Euclid appealing for the surface characterization of minor bodies.
After presenting the main characteristics of the ESA Euclid mission, I will describe how the multi-filter images and spectra collected by Euclid in the visible and near-infrared will complement the ESA Gaia and LSST data sets to study the surface properties of minor bodies.
 DeMeo & Carry, 2014;  McCord et al., 1970;  Gradie & Tedesco, 1982;  http://smass.mit.edu/;  Iveviz et al., 2001;  Carruba et al., 2013;  Nesvorny, 2005;  DeMeo & Carry, 2013;  Carry et al., 2016;  Delbo et al., 2012;  LSST Collaboration, 2011;  Laureijs et al., 2011
B. Carry & F. E. DeMeo
The asteroid main belt between Mars and Jupiter holds evidences from the early Solar System history. The original chemical stratification of the accretion disk has been scrambled by planetary migrations, resulting in a radial mixing of compositions. Since the 1970s, spectral surveys have characterized the surface compositions of the largest members first, then of smaller bodies, slowly tapering into the size-frequency distribution. These surveys led to major discoveries, including the succession of dominating taxonomic classes along heliocentric distances, stained by the presence of interlopers in this over-arching structure. In the 2000s, these results have sustained the emergence of the current paradigm of Solar System formation: the Nice model, in which planets migrated from their formation locations to their current orbits.Since then, all-sky surveys in the visible and mid-infrared, the Sloan Digital Sky Survey and NASA WISE mission, have observed tens of thousands of asteroids, allowing characterization of their surface composition and estimation of their diameter. Simultaneously, our knowledge on asteroid density greatly improved: the sample of density determinations presented a tenfold increase. Such a rich dataset opened the possibility to scrutinize asteroid compositions to smaller sizes and to study the distribution of material in the main belt by mass, rather than by numbers. The picture resulting from these data go back over the previous view, and the few interlopers seem to be rule. The large scale structure seen on the largest bodies holds, but mixing increases at smaller sizes. This detailed picture supports the main results from recent dynamical models of planetary migration and radial mixing of smaller bodies, albeit several observed structures remain yet to be explained: numerous primitive D-type in the inner belt, apparently missing mantle counterpart (A-types) to the crustal and iron core-like (V- and M-types) material.Observational evidences from past decade will be reviewed, current picture of the compositional distribution of material in the main belt presented; open questions, inherited from past spectral surveys, summarized; and prospectives drawn.
M. Delbo, P. Tanga, F. Mignard, B. Carry, A. Dell'Oro, D. Hestroffer, M. Granvik, K. Muinonen, T. Pauwels, J.-M. Petit, & W. Thuillot
The astrometric mission Gaia of the European Space Agency (ESA) was launched in December 2013 and started the scientific phase of its 5-years-long, whole-sky survey in July 2014. Gaia characterise all astrophysical sources with V<=20, by measuring their position, motion and spectral properties. The high-precision astrometry (~25 micro-arcsec at V=15) is the unbeatable science driver of Gaia, promising a revolution in astrophysics, with the first data release in 2016.Solar system objects are serendipitously observed in the visible light by Gaia wide-field telescopes, with these observations providing astrometry and colour photometry for ~250,000 asteroids.Here, we report on the analysis of Gaia observations performed by the Data Processing and Analysis Consortium (DPAC). Regarding astrometry, the most important products are epoch positions of minor bodies and the stellar catalogue that will be used to improve the orbits of virtually all observed solar system bodies.We will detail how, from measurements of the orbital gravitational perturbations on small asteroids that have close encounters with more massive ones, Gaia data will allow the determination of the masses of about 150 of the largets asteroids, with important repercussion on dynamical and physical models of our solar system.Furthermore, Gaia is observing several near-Earth asteroids. For those with the longest arc, Gaia observations could help the detection of the drift in orbital semi-major axis due to the Yarkovsky effect. Beyond the Gaia observations themselves, one of the most important improvements for solar system science will be the Gaia stellar catalogue. This will allow recalibrating all astrometric (and photometric) measurements of solar system minor bodies obtained so far, with important improvements in the measurements of drift of the orbital semi-major axes of asteroids, in the modelling of the spreading of asteroid families, and in the ephemeris of the planets.
B. Carry & M. Viikinkoski
Spin and 3-D shape are basic geometrical properties of an asteroid, yet required in understanding some of its most fundamental features, from its density to its sensitiveness to YORP and Yarkovsky non-gravitational effects. Technological advancements have made it possible to obtain highly detailed images of asteroids, yet 3-D shape modeling remains a challenge. Shape inversion is an ill-posed inverse problem as systematic errors, shading effects due to non-convex features, and the limitations of the imaging systems render the direct inversion impossible. Moreover, the image coverage of one observation session is often insufficient for 3-D reconstruction, necessitating the combination of different imaging methods.
We will discuss parametric shape representation methods, applicable to all asteroid surfaces, including strongly non-convex and geometrically non-starlike shapes. Additionally, we will demonstrate the usefulness of Fourier transform in shape reconstruction, showing that the frequency domain is a natural setting for shape inversion of image data obtained from generalized projection operators, which include virtually all disk-resolved astronomical observation methods. Finally, we present several examples and applications of our method to range-Doppler radar, adaptive optics, and thermal infrared interferometry.
B. Carry & F. E. DeMeo
ASSG2013 : Asteroid Spectroscopy in Support of Gaia, Nice (France), 2014 June 6-7,
The distribution of asteroids across the Main Belt has been studied for decades to understand the current compositional distribution and what that tells us about the formation and evolution of our solar system. In this work, we reexamine the architecture of the asteroid belt by determining the bias-corrected distribution of 99.99% of its mass based on compositional information provided by ground-based and space-based measurements, mainly the Sloan Digital Sky Survey and the WISE mid-infrared satellite. The main belt's most massive classes are C, B, P, V and S in decreasing order. Excluding the four most massive asteroids, (1) Ceres, (2) Pallas, (4) Vesta and (10) Hygiea that heavily skew the values, primitive material (C-, P-types) account for more than half main-belt and Trojan asteroids by mass, most of the remaining mass being in the S-types. All the other classes are minor contributors to the material between Mars and Jupiter. Additionally, we present the taxonomic distribution of asteroids as a function of size. The relative mass contribution of each class changes as a function of size in each region of the Main Belt. We report an updated view of the distribution of asteroid compositions according to distance and size.
GREAT Workshop on Solar System Science before and after Gaia, Pisa (Italy), 2011 May 4-6,
During its mission, Gaia will observe many close encounters between asteroids. The study of the orbital deflections will lead to the determinaton of several tens of mass estimates, with a relative accuracy better than about 50%. I will present how multi-data 3-D shape reconstruction will provide accurate volume for these targets, allowing for the first time the determination of a statistical set of asteroid densityes spanning all the taxonomic classes.
Workshop on Earth-based Support to Gaia Solar-System Science, Beaulieu-sur-Mer (France), 2008 Octobre 27-28,
The Gaia mission of the ESA is expected to produce a huge step in asteroid science,and more precisely, in our knowledge of their dynamics and physical properties. During the Gaia mission, the physical properties (spin and shape) of about 10,000 asteroids will be determined, as well as sizes of about 1,000 of the largest ones. Among them, direct measurement of masses will be obtained for approx. 100 asteroids, either from satellite observation (for multiple systems), or from the analysis of their gravitational perturbation on smaller bodies. We intend to acquire imaging observations for 57 of them at high angular-resolution with NACO/VLT. The resolution power of the 8m telescope will enable us to calibrate the size and shape determination done with Gaia, mandatory to derive accurate density estimates. This will also allow us to calibrate the model and computation of the offset between the observed photocentre and the computed center of mass, necessary to derive accurate astrometry of the largest bodies. In addition, we will be able to derive refined shape models and the bulk density with unprecedented precision.