Practical relations for assessments of the dusty-gas coma parameters

To ensure the safety of a spacecraft and efficiency of the instrument operations it is indispensable to have simple (i.e. with minimal number of parameters and which does not require long time simulations) models for the assessments of the dusty-gas coma parameters. The dusty-gas flow preserves typical general features regardless the particular coma model and the characteristics of the real cometary coma. Therefore, elementary models which account only for the main factors (due to the absence of reliable information on the surface and the interior) affecting the dusty-gas motion could be used for rough estimations of integral characteristics and asymptotic behavior of dusty-gas motion (e.g. terminal velocity, and distance and time when it is reached). At the same time, over-simplification of coma representation is undesirable also. For example, the assumption of spherical symmetry of the flow makes no difference between day and night sides of the coma.

We propose a simple approximation of the gas coma parameters based on the numerical solutions of axisymmetric coma with different activity of the night side (see for example Crifo et al. 2002). This model is given by heliocentric distance r_h, total production rate Q, radius of the nucleus R_n, surface temperature T_n, mechanism of gas production (surface sublimation or diffusion from interior) and level of activity of the night side a_n. This model is able to reproduce typical anisotropy of gas density distribution in real coma and it better conform the physics of real coma than the frequently used model of spherical expansion. In the polar frame with axis directed to the Sun and polar angle φ (solar zenith angle), the spatial distribution of gas density is approximated by third order polynomial of cos(φ):

where coefficients a_i are tabulated for a given mechanism of gas production (surface sublimation or diffusion from interior) and level of activity of the night side a_n. This approximation gives the relative deviation from numerical solution less than 10% in the most part of the coma.

For the dust environment it is assumed that dust grains are spherical homogeneous isothermal particles, non-rotating, with invariable mass (i.e. non-sublimating and noncondensing). The grains released from the surface are submitted to the nucleus gravity F_G, the gas drag F_A, and the solar radiation pressure F_S. We do not allow for solar tidal effects, nor for mutual dust collisions, even though these effects are not always negligible. The theoretical basis of such approach is given in Crifo et al. 2005.

In order to cover a broad range of physical conditions we use dimensionless description of dust dynamics proposed in Zakharov et al. 2018. In this case it is possible to limit the parameter space to three general dimensionless factors Iv, Fu, Ro. The factor Iv characterizes the efficiency of entrainment of the particle within the gas flow; Fu characterizes the efficiency of gravitational attraction; Ro characterizes the contribution of solar radiation pressure. In contrast to the gas environment, the structure of the dust environment can change drastically depending on the particular combination of Iv, Fu, Ro. Therefore, the spatial distribution of dust density can be approximated only for separate combinations of Iv, Fu, Ro within a certain range. The present study covers the range of 5·10^-6 < Iv < 0.1, 10^-7 < Fu < 3·10^-7, 1.5·10^-10 <Ro < 6·10^-6 (i.e. 10^-3 < Ro/Fu < 40.0). For the dust density along sunward direction we propose the approximation:

where coefficients b_i are tabulated for a given mechanism of gas production (surface sublimation or diffusion from interior) and level of activity of the night side a_n. This approximation gives the relative deviation from numerical solution less than 5% for n=4 and 17% for n=3.

Acknowledgements:

This research was also supported by the Italian Space Agency (ASI) within the ''Partecipazione italiana alla fase 0 della missione ESA Comet Interceptor'' (ASIINAF agreement n.Accordo Attuativo" numero 2020-4-HH.0 ).

References:

Crifo,J.F., Lukianov,G.A.,  Rodionov,A.V.,  Khanlarov,G.O., Zakharov, V.V., Comparison between Navier–Stokes and Direct Monte–Carlo Simulations of the Circumnuclear Coma. I. Homogeneous, Spherical Source, Icarus 156, 249–268, 2002.

Crifo, J.-F., Loukianov, G.A., Rodionov, A.V., Zakharov, V.V., Direct Monte Carlo and multifluid modeling of the circumnuclear dust coma Spherical grain dynamics revisited. Icarus 176, 192–219, 2005.

Zakharov, V.V., Ivanovski, S.L., Crifo, J.-F., Della Corte, V., Rotundi, A. , Fulle, M., Asymptotics for spherical particle motion in a spherically expanding flow, Icarus, Volume 312, p. 121-127, 2018.