Surface ages of mid-size Saturnian satellites

The observations of the surfaces of the mid sized Saturnian satellites made by Cassini Huygens mission have shown a variety of features that allows study of the processes that took place and are taking place on those worlds. Research of the Saturnian satellite surfaces has clear implications for Saturn history and surroundings. In a recent paper, the production of craters on the mid sized Saturnian satellites by Centaur objects was calculated considering the current Solar System. We have compared our results with crater counts from Cassini images and we have noted that the number of observed small craters is less than our calculated number. In this paper we estimate the age of the surface for each observed terrain on each mid sized satellite of Saturn. We have noticed that since there are less observed small craters than calculated (except on Iapetus), this results in younger ages. This could be the result of efficient endogenous or exogenous process(es) for erasing small craters and or crater saturation at those sizes. The size limit from which the observed number of smaller craters is less than the calculated is different for each satellite, possibly indicating processes that are unique to each, but other potential common explanations would be crater saturation and or deposition of E ring particles. These processes are also suggested by the findings that the smaller craters are being preferentially removed, and the erasure process is gradual. On Enceladus, only mid and high latitude plains have remnants of old terrains; the other regions could be young; the regions near the South Polar Terrain could be as young as 50 Myr old. On the contrary for Iapetus, all the surface is old and it notably registers a primordial source of craters. As the crater size is decreased, it would be perceived to approach saturation until D less than 2 km craters, where saturation is complete.Comment: Accepted for publication in Icarus, 40 pages, 11 figure

Dynamical evolution of escaped plutinos, another source of Centaurs

It was shown in previous works the existence of weakly chaotic orbits in the plutino population that diffuse very slowly. These orbits correspond to long-term plutino escapers and then represent the plutinos that are escaping from the resonance at present. In this paper we perform numerical simulations in order to explore the dynamical evolution of plutinos recently escaped from the resonance. The numerical simulations were divided in two parts. In the first one we evolved 20,000 test particles in the resonance in order to detect and select the long-term escapers. In the second one, we numerically integrate the selected escaped plutinos in order to study their dynamical post escaped behavior. Our main results include the characterization of the routes of escape of plutinos and their evolution in the Centaur zone. We obtained a present rate of escape of plutinos between 1 and 10 every 10 years. The escaped plutinos have a mean lifetime in the Centaur zone of 108 Myr and their contribution to the Centaur population would be a fraction of less than 6 % of the total Centaur population. In this way, escaped plutinos would be a secondary source of Centaurs.Comment: Accepted for publication in A&

Gli effetti della violenza assistita e dei maltrattamenti sui minori.

La violenza assistita e i maltrattamenti sui minori sono due fenomeni complessi e delicati da analizzare. La famiglia è da un lato, una potente risorsa per lo sviluppo e la crescita degli individui, ma dall’altro può diventare proprio in virtù di tale evidenza, un luogo di sofferenze e disagi che possono emergere quando sono messi in atto comportamenti di violenza diretta o indiretta. Lo scopo dell’elaborato è di mettere in luce molti aspetti che in una prima analisi non emergono e che possono sembrare ovvi. Questi ultimi risultano fondamentali per una panoramica oggettiva delle dinamiche interne vissute dalle famiglie e per un approccio realistico verso gli interventi di prevenzione. Le implicazioni riportate dai minori di tipo psicologico, cognitivo, comportamentale e fisiologico possono essere davvero devastanti se non affrontate in maniera adeguata. Gli studi, le ricerche, le teorie servono a mettere in luce una corretta definizione degli indicatori e delle cause che la violenza assistita provoca rispetto ai maltrattamenti fisici. Le conseguenze derivanti dai due fenomeni analizzati, rimangono impresse inevitabilmente sui minori e si ripercuotono poi nella vita adulta, soprattutto nella relazionalità con gli altri. L’entità di tali effetti e strettamente legata all’importanza che svolge il legame filiale nella vita di ogni essere umano poiché la relazione d’attaccamento definisce quella dimensione specifica dell’affettività che si esplica tramite la regolazione della prossimità, della sicurezza e della fiducia. Spesso i genitori sono i primi a misconoscere gli sviluppi che si costruiscono, ritenendo che i loro figli, non essendo colpiti direttamente dalle violenze, non vengono danneggiati da ciò che accade. Le motivazioni che spingono gli adulti ad avallare determinati stili educativi basati sulla violenza sono molte, ma mai giustificabili. I luoghi comuni, la cultura, gli stereotipi possono essere alcuni dei fattori culturali che portano alla giustificazione e all’invisibilità di un’educazione aggressiva. I servizi si trovano davanti numerose difficoltà in tutti i casi di violenza assistita e di maltrattamenti fisici, poiché i rischi, le implicazioni emotive, la conoscenza su tali dinamiche non è mai esaustiva, ma tali fenomeni risultano essere molte volte incontrollabili e in continuo mutamento. Gli aspetti principali messi in evidenza dall’elaborato vertono proprio su quegli elementi che devono essere di aiuto per la promozione di una cultura fondata sul rispetto del minore e del suo diritto a ricevere cure, affetto, sostegno e educazione

A problem with the escort distribution representation of nonextensive statistical mechanics

It is pointed out that the Tsallis entropy functional represented in terms of the escort distribution is not concave of the entropic index $q$ is less than unity. It is emphasized that the escort distribution is a secondary object calculated from the basic original distribution.Comment: 8 pages, 1 figur

Axioms and uniqueness theorem for Tsallis entropy

The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the Tsallis entropy is presented.Comment: 14 pages. To appear in Physics Letters

The production of craters on the mid-sized saturnian satelites by Centaur objects

Context. The Saturnian satellite system has been observed in detail by the Cassini-Huygens mission. These satellites present different surface features, including impact craters caused by small objects probably coming from the trans-Neptunian region. Aims. In this paper we calculate the production of craters on the mid-sized Saturnian satellites produced by Centaurs from the scattered disk (SD) and plutinos in order to determine this contribution, and we compare our estimations with the Cassini observations. Methods. We used a method developed in a previous paper that uses a numerical investigation of the dynamical evolution of Centaur objects to calculate the production of craters. We used a size-frequency distribution (SFD) of scattered disk objects (SDOs) as a power law with a break at diameters d = 60 km considering two cases for the differential power-law index: s2 = 2.5 and s2 = 3.5 for d < 60 km. Results. We calculated the number of craters, the greatest crater produced by Centaurs from the SD and plutinos, and the present cratering rate on each of the mid-sized satellites, for both cases of the SFD of SDOs considered. The contribution of plutinos is negligible compared to SDOs. From our calculations and the comparison with observations we note that the calculated number of craters for s2 = 3.5 is in general nearer the observed number. However, in general for smaller craters, the observed number is less than the calculated one. This trend can be explained by at least two mechanisms. On the one hand, this could be caused by an erasing process that gradually buries the craters, which does not affect large craters. On the other hand, the comparison of the calculated and observed crater size-frequency distribution for different size ranges implies that for d < 60 km, the SFD of SDOs is consistent with the assumed index s2 = 3.5, for d ≳ 0.2−1.4 km and for d ≲ 0.2−1.4 km, it is consistent with s2 = 2.5. Then in the range d ~ 0.2−1.4 km, the SFD of SDOs could have a new break. This change of slope could explain the reduction of small craters, at least for some cases. Conclusions. We found a good agreement when comparing our results with observations. However, independent determination of surface ages and geological processes are needed to determine if there is a new break on the SFD of SDOs, if there is a planetocentric source of craters in the Saturnian system, and which craters are primordial.Fil: Di Sisto, Romina Paula. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Astrofísica de la Plata; ArgentinaFil: Zanardi, M.. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

The production of craters on the mid-sized Saturnian satellites by Centaur objects

Context. The Saturnian satellite system has been observed in detail by the Cassini-Huygens mission. These satellites present different surface features, including impact craters caused by small objects probably coming from the trans-Neptunian region. Aims. In this paper we calculate the production of craters on the mid-sized Saturnian satellites produced by Centaurs from the scattered disk (SD) and plutinos in order to determine this contribution, and we compare our estimations with the Cassini observations. Methods. We used a method developed in a previous paper that uses a numerical investigation of the dynamical evolution of Centaur objects to calculate the production of craters. We used a size-frequency distribution (SFD) of scattered disk objects (SDOs) as a power law with a break at diameters d = 60 km considering two cases for the differential power-law index: s2 = 2.5 and s2 = 3.5 for d < 60 km. Results. We calculated the number of craters, the greatest crater produced by Centaurs from the SD and plutinos, and the present cratering rate on each of the mid-sized satellites, for both cases of the SFD of SDOs considered. The contribution of plutinos is negligible compared to SDOs. From our calculations and the comparison with observations we note that the calculated number of craters for s2 = 3.5 is in general nearer the observed number. However, in general for smaller craters, the observed number is less than the calculated one. This trend can be explained by at least two mechanisms. On the one hand, this could be caused by an erasing process that gradually buries the craters, which does not affect large craters. On the other hand, the comparison of the calculated and observed crater size-frequency distribution for different size ranges implies that for d < 60 km, the SFD of SDOs is consistent with the assumed index s2 = 3.5, for d ≥ 0.2-1.4 kmand for d ≤ 0.2-1.4 km, it is consistent with s2 = 2.5. Then in the range d ~ 0.2-1.4 km, the SFD of SDOs could have a new break. This change of slope could explain the reduction of small craters, at least for some cases. Conclusions. We found a good agreement when comparing our results with observations. However, independent determination of surface ages and geological processes are needed to determine if there is a new break on the SFD of SDOs, if there is a planetocentric source of craters in the Saturnian system, and which craters are primordial.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Origin of craters on Phoebe: comparison with Cassini's data

Phoebe is one of the irregular satellites of Saturn; the images taken by Cassini-Huygens spacecraft allowed us to analyze its surface and the craters on it. We study the craters on Phoebe produced by Centaur objects from the Scattered Disk (SD) and plutinos escaped from the 3:2 mean motion resonance with Neptune and compare our results with the observations by Cassini. We use previous simulations on trans-Neptunian Objects and a method that allows us to obtain the number of craters and the cratering rate on Phoebe. We obtain the number of craters and the greatest crater on Phoebe produced by Centaurs in the present configuration of the Solar System. Moreover, we obtain a present normalized rate of encounters of Centaurs with Saturn of $\dot F = 7.1 \times 10^{-11}$ per year, from which we can infer the current cratering rate on Phoebe for each crater diameter. Our study and the comparison with the observations suggest that the main crater features on Phoebe are unlikely to have been produced in the present configuration of the Solar System and that they must have been acquired when the SD were depleted in the early Solar System. If this is what happened and the craters were produced when Phoebe was a satellite of Saturn, then it had to be captured, very early in the evolution of the Solar System.Comment: Accepted for publication in Astronomy & Astrophysic

Origin of craters on Phoebe: Comparison with Cassini's data

Context. Phoebe is one of the irregular satellites of Saturn. The images taken by the Cassini-Huygens spacecraft have allowed us to analyze its surface and the craters on it. Aims. We study the craters on Phoebe produced by both Centaur objects from the scattered disk (SD) and plutinos that have escaped from the 3:2 mean motion resonance with Neptune and compare our results with the observations by Cassini. Methods. We use previously developed simulations of trans-Neptunian objects and a method that allows us to derive the number of craters and the cratering rate on Phoebe. Results. We determine the number of craters and the largest crater on Phoebe produced by Centaurs in the present configuration of the solar system. We obtain a present normalized rate of encounters of Centaurs with Saturn of F = 7.1 × 10-11 per year, from which we can infer the current cratering rate on Phoebe for each crater diameter. Conclusions. Our study and comparison with observations suggest that the main crater features on Phoebe are unlikely to have been produced in the present configuration of the solar system but that they must have been created instead when the SD were depleted in the early solar system. If this is indeed what happened and the craters were produced when Phoebe was a satellite of Saturn, then it must have been captured, very early on in the evolution of the solar system.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat