Did the Hilda collisional family form during the late heavy bombardment?

We model the long-term evolution of the Hilda collisional family located in the 3/2 mean-motion resonance with Jupiter. Its eccentricity distribution evolves mostly due to the Yarkovsky/YORP effect and assuming that: (i) impact disruption was isotropic, and (ii) albedo distribution of small asteroids is the same as for large ones, we can estimate the age of the Hilda family to be $4_{-1}^{+0}\,{\rm Gyr}$. We also calculate collisional activity in the J3/2 region. Our results indicate that current collisional rates are very low for a 200\,km parent body such that the number of expected events over Gyrs is much smaller than one. The large age and the low probability of the collisional disruption lead us to the conclusion that the Hilda family might have been created during the Late Heavy Bombardment when the collisions were much more frequent. The Hilda family may thus serve as a test of orbital behavior of planets during the LHB. We tested the influence of the giant-planet migration on the distribution of the family members. The scenarios that are consistent with the observed Hilda family are those with fast migration time scales $\simeq 0.3\,{\rm Myr}$ to $3\,{\rm Myr}$, because longer time scales produce a family that is depleted and too much spread in eccentricity. Moreover, there is an indication that Jupiter and Saturn were no longer in a compact configuration (with period ratio $P_{\rm S}/P_{\rm J} > 2.09$) at the time when the Hilda family was created

Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations

Understanding the growth of the cores of giant planets is a difficult problem. Recently, Lambrechts and Johansen (2012; LJ12) proposed a new model in which the cores grow by the accretion of pebble-size objects, as the latter drift towards the star due to gas drag. Here, we investigate the dynamics of pebble-size objects in the vicinity of planetary embryos of 1 and 5 Earth masses and the resulting accretion rates. We use hydrodynamical simulations, in which the embryo influences the dynamics of the gas and the pebbles suffer gas drag according to the local gas density and velocities. The pebble dynamics in the vicinity of the planetary embryo is non-trivial, and it changes significantly with the pebble size. Nevertheless, the accretion rate of the embryo that we measure is within an order of magnitude of the rate estimated in LJ12 and tends to their value with increasing pebble-size. We conclude that the model by LJ12 has the potential to explain the rapid growth of giant planet cores. The actual accretion rates however, depend on the surface density of pebble size objects in the disk, which is unknown to date.Comment: In press in Astronomy and Astrophysic

Detectability of Terrestrial Planets in Multi-Planet Systems: Preliminary Report

We ask if Earth-like planets (terrestrial mass and habitable-zone orbit) can be detected in multi-planet systems, using astrometric and radial velocity observations. We report here the preliminary results of double-blind calculations designed to answer this question.Comment: 10 pages, 0 figure

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

Symplectic integrators with adaptive time steps

In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, \Delta=\Delta(t). In this case, backwards error analysis shows that while the algorithms remain symplectic, parametric instabilities arise because of resonance between oscillations of \Delta(t) and the orbital motion. In the second category the time step is a function of phase space variables \Delta=\Delta(q,p). In this case, the system of equations to be solved is analyzed by introducing a new time variable \tau with dt=\Delta(q,p) d\tau. The transformed equations are no longer in Hamiltonian form, and thus are not guaranteed to be stable even when integrated using a method which is symplectic for constant \Delta. We analyze two methods for integrating the transformed equations which do, however, preserve the structure of the original equations. The first is an extended phase space method, which has been successfully used in previous studies of adaptive time step symplectic integrators. The second, novel, method is based on a non-canonical mixed-variable generating function. Numerical trials for both of these methods show good results, without parametric instabilities or spurious growth or damping. It is then shown how to adapt the time step to an error estimate found by backward error analysis, in order to optimize the time-stepping scheme. Numerical results are obtained using this formulation and compared with other time-stepping schemes for the extended phase space symplectic method.Comment: 23 pages, 9 figures, submitted to Plasma Phys. Control. Fusio

Pathological prognostic factors in the second British Stomach Cancer Group trial of adjuvant therapy in resectable gastric cancer.

The second British Stomach Cancer Group trial was a prospective randomised controlled trial of adjuvant radiotherapy or cytotoxic chemotherapy after gastrectomy for adenocarcinoma. It recruited between 1981 and 1986. No survival advantage has been demonstrated for the patients receiving either type of adjuvant therapy compared with those undergoing surgery alone. We report on 436 patients randomised into the trial together with 203 patients, who did not fulfil the trial criteria, referred to the trial. A univariate (log-rank) analysis of pathological factors obtained from the local referring centres showed that tumour size, macroscopic type, number os sites involved, depth of invasion, involvement of resection lines and lymph nodes and histological grade were significant determinants of survival. Histological review by two experienced histopathologists found that the Lauren classification and histological grade, but not the Ming classification, were significant prognostic factors. The degree of lymphocytic and eosinophilic infiltration and presence of dysplasia assessed by one of the pathologists showed a significant correlation with survival. However, inter-observer correlation for these histological parameters and grade was poor. Multivariate analysis identified only depth of invasion, resection line and nodal involvement as significant independent pathological variables influencing survival. This study confirms the need for expert preparation of the resected specimen to obtain the important information on depth of invasion and nodal status and also reveals some variation in histological assessment, particularly grading, in gastric carcinoma

The formation of Uranus and Neptune among Jupiter and Saturn

The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the Solar System where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies ($\sim$ 15 and 17 times as massive as the Earth, respectively) very difficult. Previously, we proposed a model which addresses this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and -Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogues to our Solar System for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.Comment: Submitted to AJ; 38 pages, 16 figure