The Abel transformation deconvolves comets: Gas structure of comet C/2013 R1 (Lovejoy)

Abstract

Abstract The Abel transformation is introduced and applied to the surface brightness of gas emission from C/2013 R1 (Lovejoy) to reproduce the local volume luminosity density and the shell luminosity, which represents the luminosity density over the spherical surface. This transformation may be more extensively and objectively applied than the Haser model (1957, Bull. Acad. Roy. de Belgique, Classe de Sci., 43, 740), which is limited to the gas emission produced by a two-step process. The scale lengths of the emission from C/2013 R1 are measured for CN and C3; compared with the scale length at the time of solar maxima in the literature, the CN emission had a longer lifetime, whereas a typical scale length is observed for the parent molecule. The emission of C3 is much more compact than recorded in the literature. More importantly, apart from these two-step processes, the “core” region of CN is reported in the shell luminosity with a scale length shorter than 8.4 × 103 km (observed at 0.85 au). The Abel transformation is thus powerful in time-domain analysis for radially expanding multiple zones of gas emission from comets.