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

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

Why haven't loose globular clusters collapsed yet?

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or VLT data. All the high-concentration clusters in the sample have a steep GMF, most likely reflecting their initial mass function. Conversely, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, more concentrated clusters should have lost proportionately more stars and have a shallower GMF than low concentration clusters, contrary to what is observed. It is possible that severely depleted GCs have also undergone core collapse and have already recovered a normal radial density profile. It is, however, more likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. In either case, we may have so far seriously underestimated the number of post core-collapse clusters and many may be lurking in the Milky Way.Comment: Four pages, one figure, accepted for publication in ApJ Letter

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

Apollo asteroids (1566) Icarus and 2007 MK6: Icarus family members?

Although it is more complicated to search for near-Earth object (NEO) families than main belt asteroid (MBA) families, since differential orbital evolution within a NEO family can cause current orbital elements to drastically differ from each other, we have found that Apollo asteroids (1566) Icarus and the newly discovered 2007 MK6 are almost certainly related. Specifically, their orbital evolutions show a similar profile, time shifted by only ~1000 yr, based on our time-lag theory. The dynamical relationship between Icarus and 2007 MK6 along with a possible dust band, the Taurid-Perseid meteor swarm, implies the first detection of an asteroidal NEO family, namely the "Icarus asteroid family".Comment: 11 pages, 1 figure, to appear on Astrophysical Journal Letters (journal info added

Contribution of White Dwarfs to Cluster Masses

I present a literature search through 31 July 1997 of white dwarfs (WDs) in open and globular clusters. There are 36 single WDs and 5 WDs in binaries known among 13 open clusters, and 340 single WDs and 11 WDs in binaries known among 11 globular clusters. From these data I have calculated WD mass fractions for four open clusters (the Pleiades, NGC 2168, NGC 3532, and the Hyades) and one globular cluster (NGC 6121). I develop a simple model of cluster evolution that incorporates stellar evolution but not dynamical evolution to interpret the WD mass fractions. I augment the results of my simple model with N-body simulations incorporating stellar evolution (Terlevich 1987; de la Feunte Marcos 1996; Vesperini & Heggie 1997). I find that even though these clusters undergo moderate to strong kinematical evolution the WD mass fraction is relatively insensitive to kinematical evolution. By comparing the cluster mass functions to that of the Galactic disk, and incorporating plausibility arguments for the mass function of the Galactic halo, I estimate the WD mass fraction in these two populations. I assume the Galactic disk is ~10 Gyrs old (Winget et al. 1987; Liebert, Dahn, & Monet 1988; Oswalt et al. 1996) and that the Galactic halo is ~12 Gyrs old (Reid 1997b; Gratton et al. 1997; Chaboyer et al. 1998), although the WD mass fraction is insensitive to age in this range. I find that the Galactic halo should contain 8 to 9% (alpha = -2.35) or perhaps as much as 15 to 17% (alpha = -2.0) of its stellar mass in the form of WDs. The Galactic disk WD mass fraction should be 6 to 7% (alpha = -2.35), consistent with the empirical estimates of 3 to 7% (Liebert, Dahn, & Monet 1988; Oswalt et al. 1996). (abridged)Comment: 20 pages, uuencoded gunzip'ed latex + 3 postscrip figures, to be published in AJ, April, 199

Starcounts in the Hubble Deep Field: Constraining Galactic Structure Models

Stellar sources are identified in the Hubble Deep Field, and accurate colours and magnitudes are presented. The predictions of a Galactic starcounts model are compared with the faint stellar counts in this field. The model reproduces the observations very well in the magnitude range 21.0 < V < 26.4, while it overpredicts the counts by a factor of four in the range 26.4 < V < 30.0. The luminosity function for halo objects must be a factor of two smaller than that predicted by an extrapolation of the solar-neighborhood luminosity function for disc stars (with 95% confidence level). This result, seen before in deep Hubble Space Telescope images of globular clusters, is therefore confirmed for the halo field population. The possible nature of a group of faint-blue objects is also investigated, concluding that they are most likely non-stellar. The possibility that they are QSOs is ruled out. If we insist upon their stellar nature, they would be halo white dwarfs, with either a very steep halo white dwarf luminosity function for Mv > +11.0, or a stellar density 0.4 times that of the disc white dwarfs in the solar-neighborhood.Comment: Tex type, 7 pages, 3 postscript figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society. A few typos corrected. Updated references. Note Added in Proof (including one table), containing a detailed photometric comparison (for point-like sources) between our results and those from other investigations of the HDF

The Evolution of Globular Clusters in the Galaxy

We investigate the evolution of globular clusters using N-body calculations and anisotropic Fokker-Planck (FP) calculations. The models include a mass spectrum, mass loss due to stellar evolution, and the tidal field of the parent galaxy. Recent N-body calculations have revealed a serious discrepancy between the results of N-body calculations and isotropic FP calculations. The main reason for the discrepancy is an oversimplified treatment of the tidal field employed in the isotropic FP models. In this paper we perform a series of calculations with anisotropic FP models with a better treatment of the tidal boundary and compare these with N-body calculations. The new tidal boundary condition in our FP model includes one free parameter. We find that a single value of this parameter gives satisfactory agreement between the N-body and FP models over a wide range of initial conditions. Using the improved FP model, we carry out an extensive survey of the evolution of globular clusters over a wide range of initial conditions varying the slope of the mass function, the central concentration, and the relaxation time. The evolution of clusters is followed up to the moment of core collapse or the disruption of the clusters in the tidal field of the parent galaxy. In general, our model clusters, calculated with the anisotropic FP model with the improved treatment for the tidal boundary, live longer than isotropic models. The difference in the lifetime between the isotropic and anisotropic models is particularly large when the effect of mass loss via stellar evolution is rather significant. On the other hand the difference is small for relaxation- dominated clusters which initially have steep mass functions and high central concentrations.Comment: 36 pages, 11 figures, LaTeX; added figures and tables; accepted by Ap

WIYN Open Cluster Study 1: Deep Photometry of NGC 188

We have employed precise V and I photometry of NGC 188 at WIYN to explore the cluster luminosity function (LF) and study the cluster white dwarfs (WDs). Our photometry is offset by V = 0.052 (fainter) from Sandage (1962) and Eggen & Sandage (1969). All published photometry for the past three decades have been based on these two calibrations, which are in error by 0.05 +- 0.01. We employ the Pinsonneault etal (1998) fiducial main sequence to derive a cluster distance modulus of 11.43 +- 0.08. We report observations that are >= 50% complete to V = 24.6 and find that the cluster central-field LF peaks at M_I ~ 3 to 4. This is unlike the solar neighborhood LF and unlike the LFs of dynamically unevolved portions of open and globular clusters, which rise continuously until M_I ~ 9.5. Although we find that >= 50% of the unresolved cluster objects are multiple systems, their presence cannot account for the shape of the NGC 188 LF. For theoretical reasons (Terlevich 1987; Vesperini & Heggie 1997) having to do with the survivability of NGC 188 we believe the cluster is highly dynamically evolved and that the missing low luminosity stars are either in the cluster outskirts or have left the cluster altogether. We identify nine candidate WDs, of which we expect three to six are bona fide cluster WDs. The luminosities of the faintest likely WD indicates an age (Bergeron, Wesemael, & Beauchamp 1995) of 1.14 +- 0.09 Gyrs. This is a lower limit to the cluster age and observations probing to V = 27 or 28 will be necessary to find the faintest cluster WDs and independently determine the cluster age. While our age limit is not surprising for this ~6 Gyr old cluster, our result demonstrates the value of the WD age technique with its very low internal errors. (abridged)Comment: 26 pages, uuencoded gunzip'ed latex + 16 postscrip figures, to be published in A

Idrocarburi e aree ad alta diversit\ue0 culturale e biologica: un\u2019analisi geografica in Amazzonia

Le operazioni di esplorazione ed estrazione di idrocarburi in diversi contesti geografici sono ampiamente documentate tra le attivit\ue0 antropiche di maggiore impatto sui sistemi socio-ecologici e sul cambiamento climatico, cosi come \ue8 riconosciuta la necessit\ue0 di politiche pi\uf9 efficaci e l'uso di tecnologie pi\uf9 pulite. Lo studio presentato in questo contributo mira a: 1) analizzare e mappare le interazioni tra le attivit\ue0 legate agli idrocarburi e le aree che presentano un'elevata diversit\ue0 e sensibilit\ue0 culturale e biologica; 2) Discutere proposte di criteri geografici per individuare aree unburnable, ovvero dove lasciare gli idrocarburi sottoterra. La metodologia si basa sulla costruzione di un geodatabase open source dell'area di studio, che corrisponde all'Amazzonia dell'Ecuador e alla Region amazzonica di Loreto in Per\uf9, area riconosciuta per la sua elevata diversit\ue0 ecologica e culturale. \uc8 stata condotta un\u2019analisi in ambiente QGIS delle sovrapposizioni tra gli aspetti socio-ecologici (aree protette, territori indigeni) e le attivit\ue0 di esplorazione e produzione di idrocarburi (riserve, blocchi, pozzi, oleodotti), oltre alla revisione di documenti scientifici e non su questi aspetti. Alcuni risultati dell'analisi GIS mostrano che quasi l'intera area di studio fa parte della provincia geologica del Putumayo-Oriente-Mara\uf1on, con una stima di 7290 milioni barili di petrolio equivalente sottoterra, dove le concessioni di idrocarburi coprono il 33% della superficie e si trovano circa 1780 pozzi. Le aree protette ricadenti nelle concessioni risultano essere il 18% e importanti sono anche le sovrapposizioni con i territori indigeni, evidenziando cos\uec l'urgenza di politiche pi\uf9 efficaci per garantire la sostenibilit\ue0 ambientale e sociale e la definizione di criteri geografici per individuare aree unburnable