The calculation of Afρ and mass loss rate for comets

Fink, Uwe; Rubin, Martin (2012). The calculation of Afρ and mass loss rate for comets. Icarus, 221(2), pp. 721-734. Elsevier 10.1016/j.icarus.2012.09.001

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Ab initio calculations of Afρ are presented using Mie scattering theory and a Direct Simulation Monte Carlo (DSMC) dust outflow model in support of the Rosetta mission and its target 67P/Churyumov-Gerasimenko (CG). These calculations are performed for particle sizes ranging from 0.010 μm to 1.0 cm. The present status of our knowledge of various differential particle size distributions is reviewed and a variety of particle size distributions is used to explore their effect on Afρ , and the dust mass production View the MathML sourcem˙. A new simple two parameter particle size distribution that curtails the effect of particles below 1 μm is developed. The contributions of all particle sizes are summed to get a resulting overall Afρ. The resultant Afρ could not easily be predicted a priori and turned out to be considerably more constraining regarding the mass loss rate than expected. It is found that a proper calculation of Afρ combined with a good Afρ measurement can constrain the dust/gas ratio in the coma of comets as well as other methods presently available. Phase curves of Afρ versus scattering angle are calculated and produce good agreement with observational data.

The major conclusions of our calculations are:

– The original definition of A in Afρ is problematical and Afρ should be: qsca(n,λ)×p(g)×f×ρqsca(n,λ)×p(g)×f×ρ.
Nevertheless, we keep the present nomenclature of Afρ as a measured quantity for an ensemble of coma particles.–
The ratio between Afρ and the dust mass loss rate View the MathML sourcem˙ is dominated by the particle size distribution.
– For most particle size distributions presently in use, small particles in the range from 0.10 to 1.0 μm contribute a large fraction to Afρ.
– Simplifying the calculation of Afρ by considering only large particles and approximating qsca does not represent a realistic model. Mie scattering theory or if necessary, more complex scattering calculations must be used.
– For the commonly used particle size distribution, dn/da ∼ a−3.5 to a−4, there is a natural cut off in Afρ contribution for both small and large particles.
– The scattering phase function must be taken into account for each particle size; otherwise the contribution of large particles can be over-estimated by a factor of 10.
– Using an imaginary index of refraction of i = 0.10 does not produce sufficient backscattering to match observational data.
– A mixture of dark particles with i ⩾ 0.10 and brighter silicate particles with i ⩽ 0.04 matches the observed phase curves quite well.
– Using current observational constraints, we find the dust/gas mass-production ratio of CG at 1.3 AU is confined to a range of 0.03–0.5 with a reasonably likely value around 0.1.

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