A photometric-dynamic model to simulate coma and jets from a comet

A&A 382, 342-358 (2002)
DOI: 10.1051/0004-6361:20011592

Application to comet Hale-Bopp (C/1995 O1)

R. Vasundhara

Indian Institute of Astrophysics, Bangalore 560034, India

(Received 29 December 1998 / Accepted 5 November 2001 )

Abstract
A model to compute the trajectories of dust grains ejected by comets to simulate intensity and polarization maps on the sky plane is presented. The model is used to constrain the silicate to organic mass ratio, porosity and size distribution of the grains in the shells and coma of comet Hale-Bopp to explain 1) the published polarizations at three continuum wavelengths at $0.6840~\mu {\rm m}$ , $0.4845~\mu {\rm m}$ and $0.3650~\mu {\rm m}$ at different phase angles, 2) higher polarization and bluer colour of the shells compared to the coma, 3) the intensity variation and rapid decline of polarization on the sunward side and 4) higher polarization on the anti-sunward direction. The present results obtained using Mie theory in the model indicate that although it is impossible to determine the nature of the silicate (pyroxenes/olivines or amorphous/crystalline) using the present technique, the porosity, organic fraction and size distribution of the grains can be constrained. The fit to the data set indicates an ensemble of grains in which $\approx$ $60 \%$ are silicate grains with a range in silicate to organic mass ratio $r_{\rm m}$ between 1 and 2 and of medium porosity < $50 \%$ . A higher silicate content of $r_{\rm m} >8$ on the shells can explain their bluer colour. A narrow size distribution between $0.08~\mu {\rm m} {-} 0.6~\mu {\rm m}$ is inferred for $70 \%$ of the grains in the coma and shell. These small grains may not be individual grains but part of loosely bound grains in which larger grains may also be present which may control the dynamics. The narrow size distribution may therefore represent statistically the size range of individual subunits of larger highly porous aggregates of fractal dimension close to two. The polarizations in JHK bands also support the aggregate structure. Despite the availability of an extensive and wide range of data set on this comet, the inclusion of a large parameter space, lack of knowledge on the nature of organic material found in comets and use of Mie theory, which does not adequately represent the polarization phase curves of natural grains, set limitations in getting a unique solution in the present work. The results presented here are open to improvements when more realistic light scattering theories are used in the model and our understanding on the nature of the organic content of the grains improves. However, visibility of up to 8-10 shells in well exposed images implies $\beta <1$ for these grains. As a result of this dynamical constraint which is independent of the assumptions on the scattering characteristics of the grains, the results for the dust grains in the shell may be more robust compared to that of the coma.

Key words: comets -- Hale-Bopp: scattering -- polarization -- colour