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.     

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).     

Optical properties of solid and liquid sulfur at visible and infrared wavelengths

Knowledge of the optical constants of elemental sulfur has potential applications to Venus, Jupiter, Io, Amalthea, and the Earth. The real part, n, of the index of refraction of liquid sulfur (at 133°C) and of solid orthorhombic sulfur (at 25°C) for the wavelength range 0.4–2.0 μm were measured ellipsometrically. The imaginary part, k, of the refractive index of liquid sulfur was obtained by transmittance measurements at the same temperature and wavelength range. The reflectance of semi-infinite slabs of solid and liquid sulfur is calculated using the measured n and k values. We confirm that sulfur melts on Io would be classified as “black” by the Voyager imaging system.