Testing variograms for positive-definiteness

A method based on Bochner's theorem is described for demonstrating the positive-definiteness of variogram models and for generating classes of valid variogram functions.Work performed while on leave at the Centre de Géostatistique et de Morphologie Mathématique.     

Magnetic cleansing of weathered/tarry oiled feathers--the role of pre-conditioners

Iron powder has previously been demonstrated to be effective in the removal, via magnetic harvesting, of a wide variety of oil contaminants from feathers and plumage. This study investigates the efficacy of magnetic cleansing for the removal from feathers of tarry contamination that has been allowed to weather. Clusters of feathers from Mallard duck (Anas platyrhnchos) and Little Penguin (Eudyptula minor) were completely immersed in a tarry contaminant and allowed to weather from one to fourteen days. The contaminant was removed using a magnetic cleansing protocol and the removal efficacy assessed gravimetrically. For one, seven and fourteen days of weathering, a final removal (after fourteen treatments) of more than 99% and 97% was achieved for duck feathers and penguin feathers, respectively. Repeating the experiments (for a seven-day weathering period) for both duck and penguin feathers, with the judicious application of a pre-conditioner (olive oil), further improved removal efficacy. A convenient method to screen for improved pre-conditioning agents is suggested.     

Observable consequences of planet formation models in systems with close-in terrestrial planets

To date, two planetary systems have been discovered with close-in, terrestrial-mass planets     . Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form 'hot Earths' and their observable predictions. Models include: (1) in situ accretion; (2) formation at larger orbital distance followed by inward 'type 1' migration; (3) formation from material being 'shepherded' inward by a migrating gas giant planet; (4) formation from material being shepherded by moving secular resonances during dispersal of the protoplanetary disc; (5) tidal circularization of eccentric terrestrial planets with close-in perihelion distances and (6) photoevaporative mass-loss of a close-in giant planet. Models 1–4 have been validated in previous work. We show that tidal circularization can form hot Earths, but only for relatively massive planets     with very close-in perihelion distances (≲0.025 au), and even then the net inward movement in orbital distance is at most only 0.1–0.15 au. For planets of less than     , photoevaporation can remove the planet's envelope and leave behind the solid core on a Gyr time-scale, but only for planets inside 0.025–0.05 au. Using two quantities that are observable by current and upcoming missions, we show that these models each produce unique signatures, and can be observationally distinguished. These observables are the planetary system architecture (detectable with radial velocities, transits and transit timing) and the bulk composition of transiting close-in terrestrial planets (measured by transits via the planet's radius).     

Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields

We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. On 07/07/2007, the NLFFF team was saddened by the news that Tom Metcalf had died as the result of an accident. We remain grateful for having had the opportunity to benefit from his unwavering dedication to the problems encountered in attempting to understand the Sun’s magnetic field; Tom had completed this paper several months before his death, leading the team through the many steps described above.     

Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Theoretical Examination

We demonstrate that the azimuthal ambiguity that is present in solar vector magnetogram data can be resolved with line-of-sight and horizontal heliographic derivative information by using the divergence-free property of magnetic fields without additional assumptions. We discuss the specific derivative information that is sufficient to resolve the ambiguity away from disk centre, with particular emphasis on the line-of-sight derivative of the various components of the magnetic field. Conversely, we also show cases where ambiguity resolution fails because sufficient line-of-sight derivative information is not available. For example, knowledge of only the line-of-sight derivative of the line-of-sight component of the field is not sufficient to resolve the ambiguity away from disk centre.     

Spectroscopy, morphometry, and photoclinometry of Titan's dunefields from Cassini/VIMS

Fine-resolution (500 m/pixel) Cassini Visual and Infrared Mapping Spectrometer (VIMS) T20 observations of Titan resolve that moon's sand dunes. The spectral variability in some dune regions shows that there are sand-free interdune areas, wherein VIMS spectra reveal the exposed dune substrate. The interdunes from T20 are, variously, materials that correspond to the equatorial bright, 5-μm-bright, and dark blue spectral units. Our observations show that an enigmatic “dark red” spectral unit seen in T5 in fact represents a macroscopic mixture with 5-μm-bright material and dunes as its spectral endmembers. Looking more broadly, similar mixtures of varying amounts of dune and interdune units of varying composition can explain the spectral and albedo variability within the dark brown dune global spectral unit that is associated with dunes. The presence of interdunes indicates that Titan's dunefields are both mature and recently active. The spectrum of the dune endmember reveals the sand to be composed of less water ice than the rest of Titan; various organics are consistent with the dunes' measured reflectivity. We measure a mean dune spacing of 2.1 km, and find that the dunes are oriented on the average in an east-west direction, but angling up to 10° from parallel to the equator in specific cases. Where no interdunes are present, we determine the height of one set of dunes photoclinometrically to be between 30 and 70 m. These results pave the way for future exploration and interpretation of Titan's sand dunes.