On the structure of cometary dust tails

Abstract

The structure of cometary dust tails is studied in the frame of mechanical theory with special regard to the three dimensional aspect of the problem. The orbital mechanics of cometary particles is first re-examined. Use is made of Hamilton's integral b to derive the equation of orbit in a vectorial form valid for any value of the force parameter μ. A criterion to check the applicability of the FP (Finson and Probstein) -method is then derived. It is also shown that a structure, to be called “neck-line structure” (NLS), should appear in the dust tail of a comet after its perihelion passage. It is shown that the emergence and development of the NLS can provide an adequate explanation for the behaviour of the anomalous tail of C/Arend-Roland, 1957 III. The NLS-interpretation seems to be also compatible with statistical data of sunward tails since 1801. A new method of numerical analysis of tail brightness is developed by combining the exact treatment of the motion of a large number of sample particles with a counting technique. This method is essentially exact for given source functions (the emission rate, the size distribution and the velocity distribution). This method is applied to C/Arend-Roland, assuming the emission rate to vary as the inverse square of the heliocentric distance and the velocity distribution to be isotropic with a single speed. A comparison with observed profiles suggests that these assumptions are reasonable and the derived size distribution (assumed time-independent) shows a broad peak around 1− μ = 0.10 ∼ 0.12, and possibly a secondary peak around 0.015. It is to be noted that both the main and the anomalous tails are treated in a unified manner.