The efficiency of the spiral-in of a black hole to the Galactic Centre

We study the efficiency at which a black hole or dense star cluster spirals in to the Galactic Centre. This process takes place on a dynamical friction time-scale, which depends on the value of the Coulomb logarithm (ln Λ). We determine the accurate value of this parameter using the direct N -body method, a tree algorithm and a particle-mesh technique with up to two million plus one particles. The three different techniques are in excellent agreement. Our measurement for the Coulomb logarithm appears to be independent of the number of particles. We conclude that  ln Λ= 6.6 ± 0.6  for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, such as a dense star cluster, ln Λ is smaller, with a value of the logarithm argument Λ inversely proportional to the object size.     

“Comet‐tail” ejecta streaks: A predicted cratering landform unique to Titan

Abstract— A model for an impact ejecta landform peculiar to Saturn's moon Titan is presented. Expansion of the ejecta plume from moderate‐sized craters is constrained by Titan's thick atmosphere. Much of the plume is collimated along the incoming bolide's trajectory, as was observed for plumes from impacts on Jupiter of P/Shoemaker‐Levy‐9, but is retained as a linear, diagonal ejecta cloud, unlike on Venus where the plume “blows out.” On Titan, the blowout is suppressed because the vertically‐extended atmosphere requires a long wake to reach the vacuum of space, and the modest impact velocities mean plume expansion along the wake is slow enough to allow the wake to close off. Beyond the immediate ejecta blanket around the crater, distal ejecta is released into the atmosphere from an oblique line source: this material is winnowed by the zonal wind field to form streaks, with coarse radar‐bright particles transported less far than fine radar‐dark material. Thus, the ejecta form two distinct streaks faintly reminiscent of dual comet tails, a sharply W‐E radar‐dark one, and a less swept and sometimes comma‐shaped radar‐bright one.     

Non-Newtonian topographic relaxation on Europa

Models of topographic support on Europa by lateral shell thickness variations have previously assumed a Newtonian ice viscosity. Here I show that using a more realistic stress-dependent viscosity gives relaxation times which can be significantly different. Topography of wavelength 100 km cannot be supported by lateral shell thickness variations for ∼50 Myr, unless the shell thickness is <10 km or the ice grain size >10 mm. Shorter wavelength topography would require even thinner shells, but may be supported elastically. Global-scale variations in shell thickness, however, can be supported for geological timescales if the shell thickness is O(10 km).     

Tribute to Justus Perthes

Conclusion The above account is just a selection of Perthes' multifarious activities. As such it is fragmentary and incomplete. Many other publications and collaborators could have been mentioned. Even in its incompleteness the report may justify the statement that the success of Justus Perthes Geographische Verlagsanstalt, was apart from the managing qualities of its governors, undoubtedly due to the long series of scholarly competent collaborators whom they succeeded in engaging. As illustrated above most of theme were among the avant garde of the profession. Apparently they were at ease with Justus Perthes where they were granted enough freedom of action to realise their ambitious projects under the vigilant eye of the management. In fact the history of the firm is a continuous story of their achievements. Their combined effort initiated modern scientific atlas-making, laid down the foundation of methodic school cartography and accelerated the growth of thematic cartography. The Justus Perthes maps and atlasses stand for intellectual honestly and have an authoritative appearance of truth and exactness. For a long time to come the name of the firm will be considered as a classical example of the promotion of geography and cartography by private enterprise.