Extrasolar planet taxonomy: a new statistical approach

In this paper we present the guidelines for an extrasolar planet taxonomy. The discovery of an increasing number of extrasolar planets showing a vast variety of planetary parameters, like Keplerian orbital elements and environmental parameters, like stellar masses, spectral types, metallicity etc., prompts the development of a planetary taxonomy. In this work via principal component analysis followed by hierarchical clustering analysis, we report the definition of five robust groups of planets. We also discuss the physical relevance of such analysis, which may provide a valid basis for disentangling the role of the several physical parameters involved in the processes of planet formation and subsequent evolution. For instance, we were able to divide the hot Jupiters into two main groups on the basis of their stellar masses and metallicities. Moreover, for some groups, we find strong correlations between metallicity, semi-major axis and eccentricity. The implications of these findings are discussed.Comment: accepted for publication on Ap

Footprints of a possible Ceres asteroid paleo-family

Ceres is the largest and most massive body in the asteroid main belt. Observational data from the Dawn spacecraft reveal the presence of at least two impact craters about 280~km in diameter on the Ceres surface, that could have expelled a significant number of fragments. Yet, standard techniques for identifying dynamical asteroid families have not detected any Ceres family. In this work, we argue that linear secular resonances with Ceres deplete the population of objects near Ceres. Also, because of the high escape velocity from Ceres, family members are expected to be very dispersed, with a considerable fraction of km-sized fragments that should be able to reach the pristine region of the main belt, the area between the 5J:-2A and 7J:-3A mean-motion resonances, where the observed number of asteroids is low. Rather than looking for possible Ceres family members near Ceres, here we propose to search in the pristine region. We identified 156 asteroids whose taxonomy, colors, albedo could be compatible with being fragments from Ceres. Remarkably, most of these objects have inclinations near that of Ceres itself.Comment: 12 pages, 6 figures, 1 table. Accepted for publication in MNRA

I. Collisional evolution and reddening of asteroid surfaces: The problem of conflicting timescales and the role of size-dependent effects

Space weathering is the generic term used for processes that modify the optical properties of surfaces of atmosphereless rocky bodies under exposure to the space environment. The general agreement about the relevance of the effects of space weathering on the spectral properties of S-complex asteroids fails when some basic quantitative estimates are attempted. In particular, there is severe disagreement regarding the typical timescales for significant spectral reddening to occur, ranging from 1 Myr to 1 Gyr. Generally speaking, the spectral reddening of an individual object can be considered as the sum of three terms, one (which is relevant for statistical analyses) depending on the exposure of the object to space weathering during its lifetime, a second one due to the original surface composition, and a third one (a "noise" term) due to the combination of poorly constrained effects (e.g., structure and texture of the surface). The surface of an asteroid is usually covered by regolith, and its presence and properties presumably play a critical role in the weathering processes. In this paper we discuss the role played by collisional evolution in affecting the spectral properties of asteroids and refreshing the surfaces due to the formation of ejecta, and the necessity of a simultaneous modeling of collisions and weathering processes. We introduce a new idea, based on the possibility of a sort of saturation of the refreshing process whenever a massive reaccumulation of the impact ejecta takes place. In this case, a dependence of the overall reddening on the asteroid size should naturally come out. We show that this conclusion is indeed supported by available main belt asteroid spectroscopic data.Comment: Accepted by MNRA

Image reconstruction from scattered Radon data by weighted positive definite kernel functions

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented

The global mass function of M15

Data obtained with the NICMOS instrument on board the Hubble Space Telescope (HST) have been used to determine the H-band luminosity function (LF) and mass function (MF) of three stellar fields in the globular cluster M15, located ~7' from the cluster centre. The data confirm that the cluster MF has a characteristic mass of ~0.3 Msolar, as obtained by Paresce & De Marchi (2000) for a stellar field at 4.6' from the centre. By combining the present data with those published by other authors for various radial distances (near the centre, at 20" and at 4.6'), we have studied the radial variation of the LF due to the effects of mass segregation and derived the global mass function (GMF) using the Michie-King approach. The model that simultaneously best fits the LF at various locations, the surface brightness profile and the velocity dispersion profile suggests that the GMF should resemble a segmented power-law with the following indices: x ~ 0.8 for stars more massive than 0.8 Msolar, x ~ 0.9 for 0.3 - 0.8 Msolar and x ~ -2.2 at smaller masses (Salpeter's IMF would have x=1.35). The best fitting model also suggests that the cluster mass is ~5.4 10^5 Msolar and that the mass-to-light ratio is on average M/L_V ~ 2.1, with M/L_V ~ 3.7 in the core. A large amount of mass (~ 44 %) is found in the cluster core in the form of stellar heavy remnants, which may be sufficient to explain the mass segregation in M15 without invoking the presence of an intermediate-mass black hole.Comment: 12 pages, 10 figures, accepted for publication in A&

The Cratering History of Asteroid (2867) Steins

The cratering history of main belt asteroid (2867) Steins has been investigated using OSIRIS imagery acquired during the Rosetta flyby that took place on the 5th of September 2008. For this purpose, we applied current models describing the formation and evolution of main belt asteroids, that provide the rate and velocity distributions of impactors. These models coupled with appropriate crater scaling laws, allow the cratering history to be estimated. Hence, we derive Steins' cratering retention age, namely the time lapsed since its formation or global surface reset. We also investigate the influence of various factors -like bulk structure and crater erasing- on the estimated age, which spans from a few hundred Myrs to more than 1Gyr, depending on the adopted scaling law and asteroid physical parameters. Moreover, a marked lack of craters smaller than about 0.6km has been found and interpreted as a result of a peculiar evolution of Steins cratering record, possibly related either to the formation of the 2.1km wide impact crater near the south pole or to YORP reshaping.Comment: Accepted by Planetary and Space Scienc

Late movement of basin-edge lobate scarps on Mercury

Basin-edge lobate scarps are a sub-type of tectonic shortening structure on the surface of Mercury that have formed at the edge of volcanic units that fill or partly fill impact basins. We have performed a global survey of these features and find that they are widespread in basins across the planet. We obtained model ages from crater size–frequency distribution analysis for a subset of our surveyed basins, for both the smooth plains infill and for the last resolvable tectonic activity on the associated basin-edge scarps. Our results indicate that some of these lobate scarps were still accumulating strain in the late Mansurian (approximately 1 Ga). From a photogeological assessment, we find that the orientations of these basin-edge lobate scarps are similar to those reported for the global population of lobate scarps in earlier studies, appearing to align ∼north–south at low latitudes and ∼east–west at higher latitudes. However, reassessing these landforms’ orientation with artificially illuminated topographic data does not allow us to rule out the effect of illumination bias. We propose that these landforms, the result of crustal shortening in response to global contraction, formed along the interface between the basin floor and the smooth plains unit, which acted as a mechanical discontinuity along which shortening strains were concentrated

Partition of unity interpolation using stable kernel-based techniques

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient

Greedy kernel methods for accelerating implicit integrators for parametric ODEs

We present a novel acceleration method for the solution of parametric ODEs by single-step implicit solvers by means of greedy kernel-based surrogate models. In an offline phase, a set of trajectories is precomputed with a high-accuracy ODE solver for a selected set of parameter samples, and used to train a kernel model which predicts the next point in the trajectory as a function of the last one. This model is cheap to evaluate, and it is used in an online phase for new parameter samples to provide a good initialization point for the nonlinear solver of the implicit integrator. The accuracy of the surrogate reflects into a reduction of the number of iterations until convergence of the solver, thus providing an overall speedup of the full simulation. Interestingly, in addition to providing an acceleration, the accuracy of the solution is maintained, since the ODE solver is still used to guarantee the required precision. Although the method can be applied to a large variety of solvers and different ODEs, we will present in details its use with the Implicit Euler method for the solution of the Burgers equation, which results to be a meaningful test case to demonstrate the method's features