Spectral ratioing of Afρ to constrain the particle size distributions of comets

Introduction: Afρ is a measure for the brightness of a cometary coma [1]. In the past, Afρ has been commonly used as a proxy for the activity of comets [2]. In later studies it was found that the brightness of a coma (Afρ) is dominated by the particle size distribution [3] and that Afρ on its own is a poor predictor for the activity of a comet [4]. In this work we use a numerical model of cometary dust environments to get a better understanding of the relationship of Afρ and the particle size distribution and show how spectral ratioing of Afρ could provide constraints for the particle size distributions of comets. Methods: A numerical dust model is used to calculate the expected Afρ at two different wavelengths for a wide range of different parameters. Specifically, we calculate the ratio Afρ (425 nm) / Afρ (900 nm) in dependence to the power-law index of the particle size distribution. It is implicitly assumed that the particle size distribution follows a simple power-law. We use particles sizes in the range of 0.01 µm to 10 cm and choose  logarithmic particle size bins that are small enough to have a converging result. The scattering properties of each particle size are calculated for three different dust compositions. We use water ice to model bright particles, enstatite to model silicate particles and amorphous carbon to model dark particles. The scattering properties are calculated based on Mie-theory. Further, we studied day-night asymmetries, parameters related to the outflow velocity of the dust and phase angle effects. Results: We show that the spectral ratio of Afρ modelled at 425 nm and 900 nm correlate with the power-law index of the particle size distribution. Large particle dominated comas can be distinguished from small particle dominated comas. For small particle dominated coma the specral ratio of Afρ can be used to further constrain the power-law index. Acknowledgments: This work has been carried out within the framework of the National Centre of Competence in Research PlanetS supported by the Swiss National Science Foundation under grants 51NF40_182901 and 51NF40_205606. Additional financial support from the European Space Agency is also acknowledged. References: [1] A’Hearn, M. F. et. al. (1984), AJ, 89, 579 [2] Weiler, M. et. Al. (2003), A&A, 403, 313 [3] Fink, U. and Rubin, M. (2012), Icarus, 221, 721 [4] Marschall, R. et. al. (2022), A&A, 666, A151