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Trans-Neptunian Objects (TNOs) and Centaurs show remarkable colour variations in the visual and near-infrared spectral regions. Surface alteration processes such as space weathering (e.g., bombardment with ions) and impact resurfacing may play an important role in the colour diversity of such bodies. Ion irradiation of hydrocarbon ices and their mixtures with water ice transforms neutral (grey) surface colours of ices to red and further to grey. Along with the ices, TNOs and Centaurs probably contain complex carbonaceous compounds, in particular, complex hydrocarbons. Unlike ices, such refractory organic materials have originally low visual albedos and red colours in the visible and near-infrared ranges. Here we present the first results of ion irradiation experiments on asphaltite. Asphaltite is a natural complex hydrocarbon material. The reflectance spectra of asphaltite in the 0.4–0.8 μm range have been recorded before irradiation and after each irradiation step. We demonstrate that irradiation of this red dark material with 30 keV H+ and 15 keV N+ ions gradually transforms its colour from red to grey as a result of carbonization. A moderate increase in the visual albedo has been observed. These results may imply that the surfaces of primitive red objects optically dominated by complex refractory organics may show a similar space weathering trend. Our laboratory results were compared with published colours of TNOs and Centaurs. A broad variety of spectral colours observed for TNOs and Centaurs may be reproduced by various spectra of irradiated organics corresponding to different ion fluences. However, such objects probably also contain ices and silicate components which show different space weathering trends. This fact, together with a lack of information about albedos, may explain difficulties to reveal correlations between surface colours within TNO and Centaur populations and their other properties, such as absolute magnitudes and orbital parameters.