Aqueous alteration on main belt primitive asteroids: results from visible spectroscopy

This work focuses on the study of the aqueous alteration process which acted in the main belt and produced hydrated minerals on the altered asteroids. The aqueous alteration is particularly important for unraveling the processes occurring during the earliest times of the Solar System history, as it can give information both on the asteroids thermal evolution and on the localization of water sources in the asteroid belt. We present new spectral observations in the visible region of 80 asteroids belonging to the primitive classes C, G, F, B and P. We combine the present observations with the visible spectra of asteroids available in the literature for a total of 600 primitive main belt asteroids. Our analysis shows that the aqueous alteration sequence starts from the P-type objects, practically unaltered, and increases through the F, B, C, and G asteroids. Around 50% of the observed C-type asteroids show absorption features in the vis. range due to hydrated silicates, implying that more than 70% of them will have a 3 $\mu$m absorption band and thus hydrated minerals on their surfaces. The process dominates in primitive asteroids located between 2.3 and 3.1 AU, that is at smaller heliocentric distances than previously suggested. The aqueous alteration process dominates in the 50--240 km sized primitive asteroids, while it is less effective for bodies smaller than 50 km. No correlation is found between the aqueous alteration process and the asteroids albedo or orbital elements. Comparing the $\sim$ 0.7 $\mu$m band parameters of hydrated silicates and CM2 carbonaceous chondrites, we see that the band center of meteorites is at longer wavelengths than that of asteroids. This difference on center positions may be attributed to different minerals abundances, and to the fact that CM2 available on Earth might not be representative of the whole aqueous altered asteroids population.Comment: Icarus, accepted for publication on 28 January 2014 Manuscript pages: 38; Figures: 13 ; Tables:

Colors and taxonomy of Centaurs and Trans-Neptunian Objects

The study of the surface properties of Centaurs and Trans-Neptunian Objects (TNOs) provides essential information about the early conditions and evolution of the outer Solar System. Due to the faintness of most of these distant and icy bodies, photometry currently constitutes the best technique to survey a statistically significant number of them. Our aim is to investigate color properties of a large sample of minor bodies of the outer Solar System, and set their taxonomic classification. We carried out visible and near-infrared photometry of Centaurs and TNOs, making use, respectively, of the FORS2 and ISAAC instruments at the Very Large Telescope (European Southern Observatory). Using G-mode analysis, we derived taxonomic classifications according to the Barucci et al. (2005a) system. We report photometric observations of 31 objects, 10 of them have their colors reported for the first time ever. 28 Centaurs and TNOs have been assigned to a taxon. We combined the entire sample of 38 objects taxonomically classified in the framework of our programme (28 objects from this work; 10 objects from DeMeo et al. 2009a) with previously classified TNOs and Centaurs, looking for correlations between taxonomy and dynamics. We compared our photometric results to literature data, finding hints of heterogeneity for the surfaces of 4 objects.Comment: 7 pages, 4 figures. To be published in Astronomy and Astrophysic

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Spectral variability on primitive asteroids of the Themis and Beagle families: space weathering effects or parent body heterogeneity?

Themis is an old and statistically robust asteroid family populating the outer main belt, and resulting from a catastrophic collision that took place 2.5$\pm$1.0 Gyr ago. Within the old Themis family a young sub-family, Beagle, formed less than 10 Myr ago, has been identified. We present the results of a spectroscopic survey in the visible and near infrared range of 22 Themis and 8 Beagle families members. The Themis members investigated exhibit a wide range of spectral behaviors, while the younger Beagle family members look spectrally bluer with a smaller spectral slope variability. The best meteorite spectral analogues found for both Themis and Beagle families members are carbonaceous chondrites having experienced different degrees of aqueous alteration, prevalently CM2 but also CV3 and CI, and some of them are chondrite samples being unusual or heated. We extended the spectral analysis including the data available in the literature on Themis and Beagle families members, and we looked for correlations between spectral behavior and physical parameters using the albedo and size values derived from the WISE data. The analysis of this larger sample confirm the spectral diversity within the Themis family and that Beagle members tend to be bluer and to have an higher albedo. The differences between the two family may be partially explained by space weathering processes, which act on these primitive surfaces in a similar way than on S-type asteroids, i.e. producing reddening and darkening. However we see several Themis members having albedos and spectral slopes similar to the young Beagle members. Alternative scenarios are proposed including heterogeneity in the parent body having a compositional gradient with depth, and/or the survival of projectile fragments having a different composition than the parent body.Comment: Manuscript pages: 40; Figures: 15 ; Tables: 4 Icarus (2016),in pres

The Rise of Complex Beliefs Dynamics

We prove that complex beliefs dynamics may emerge in linear stochastic models as the outcome of bounded rationality learning. If agents believe in a misspecified law of motion (which is correctly specified at the Rational Expectations Equilibria of the model) and update their beliefs observing the evolving economy, their beliefs can follow in the limit a beliefs cycle which is not a self-fulfilling solution of the model. The stochastic process induced by the learning rule is analyzed by means of an associated ordinary differential equation (ODE). The existence of a uniformly asymptotically stable attractor for the ODE implies the existence of a beliefs attractor, to which the learning process converges. We prove almost sure convergence by assuming that agents employ a projection facility and convergence with positive probability dropping this assumption. The rise of a limit cycle and of even more complex attractors is established in some monetary economics models assuming that agents update their beliefs with the Recursive Ordinary Least Squares and the Least Mean Squares algorithm

Philosophy and updating of the asteroid photometric catalogue

The Asteroid Photometric Catalogue now contains photometric lightcurves for 584 asteroids. We discuss some of the guiding principles behind it. This concerns both observers who offer input to it and users of the product

Visible spectroscopy of the new ESO Large Program on trans-Neptunian objects and Centaurs: final results

A second large programme (LP) for the physical studies of TNOs and Centaurs, started at ESO Cerro Paranal on October 2006 to obtain high-quality data, has recently been concluded. In this paper we present the spectra of these pristine bodies obtained in the visible range during the last two semesters of the LP. We investigate the spectral behaviour of the TNOs and Centaurs observed, and we analyse the spectral slopes distribution of the full data set coming from this LP and from the literature. We computed the spectral slope for each observed object, and searched for possible weak absorption features. A statistical analysis was performed on a total sample of 73 TNOs and Centaurs to look for possible correlations between dynamical classes, orbital parameters, and spectral gradient. We obtained new spectra for 28 bodies, 15 of which were observed for the first time. All the new presented spectra are featureless, including 2003 AZ84, for which a faint and broad absorption band possibly attributed to hydrated silicates on its surface has been reported. The data confirm a wide variety of spectral behaviours, with neutral--grey to very red gradients. An analysis of the spectral slopes available from this LP and in the literature for a total sample of 73 Centaurs and TNOs shows that there is a lack of very red objects in the classical population. We present the results of the statistical analysis of the spectral slope distribution versus orbital parameters. In particular, we confirm a strong anticorrelation between spectral slope and orbital inclination for the classical population. A strong correlation is also found between the spectral slope and orbital eccentricity for resonant TNOs, with objects having higher spectral slope values with increasing eccentricity.Comment: 11 pages, 9 figure

Physical Properties of OSIRIS-REx Target Asteroid (101955) 1999 RQ36 derived from Herschel, ESO-VISIR and Spitzer observations

In September 2011, the Herschel Space Observatory performed an observation campaign with the PACS photometer observing the asteroid (101955) 1999 RQ36 in the far infrared. The Herschel observations were analysed, together with ESO VLT-VISIR and Spitzer-IRS data, by means of a thermophysical model in order to derive the physical properties of 1999 RQ36. We find the asteroid has an effective diameter in the range 480 to 511 m, a slightly elongated shape with a semi-major axis ratio of a/b=1.04, a geometric albedo of 0.045 +0.015/-0.012, and a retrograde rotation with a spin vector between -70 and -90 deg ecliptic latitude. The thermal emission at wavelengths below 12 micron -originating in the hot sub-solar region- shows that there may be large variations in roughness on the surface along the equatorial zone of 1999 RQ36, but further measurements are required for final proof. We determine that the asteroid has a disk-averaged thermal inertia of Gamma = 650 Jm-2s-0.5K-1 with a 3-sigma confidence range of 350 to 950 Jm-2s-0.5K-1, equivalent to what is observed for 25143 Itokawa and suggestive that 1999 RQ36 has a similar surface texture and may also be a rubble-pile in nature. The low albedo indicates that 1999 RQ36 very likely contains primitive volatile-rich material, consistent with its spectral type, and that it is an ideal target for the OSIRIS-REx sample return mission.Comment: Accepted for publication in Astronomy & Astrophysics, 9 pages, 7 figure

First albedo determination of 2867 Steins, target of the Rosetta mission

We present the first albedo determination of 2867 Steins, the asteroid target o f the Rosetta space mission together with 21 Lutetia. The data were obtained in polarimetric mode at the ESO-VLT telescope with the FORS1 instrument in the V and R filters. Observations were carried out from Jun e to August 2005 covering the phase angle range from 10.3 deg. to 28.3 deg., allowing the determination of the asteroid albedo by the well known experimenta l relationship between the albedo and the slope of the polarimetric curve at th e inversion angle. The measured polarization values of Steins are small, confirming an E-type cla ssification for this asteroid, as already suggested from its spectral propertie s. The inversion angle of the polarization curve in the V and R filters is resp ectively of 17.3 +/-1.5deg. and 18.4+/-1.0 deg., and the corresponding sl ope parameter is of 0.037+/-0.003 %/deg and 0.032+/-0.003 %/deg. On the basis of its polarimetric slope value, we have derived an albedo of 0.45 +/-0.1, that gives an estimated diameter of 4.6 km, assuming an absolute V ma gnitude of 13.18 mag.Comment: 4 pages, 4 figures, letter accepted for pubblication on A&