Spectral ratioing of Afρ to constrain the dust particle size distribution of comets

A numerical model of cometary dust environments is used to gain a deeper understanding of the relationship between the brightness ($Af\rho$) and the dust particle size distribution in the coma. Specifically, the spectral ratio of $Af\rho$(425 nm)$/$ $Af\rho$(900 nm) is modelled for a wide range of parameters and tied to the power-law index. The studied parameters are dust composition, terminal outflow velocity and the dust production rate day–night asymmetry. We find that the spectral ratio of $Af\rho$ modelled at 425 nm and 900 nm correlates with the power-law index of the particle size distribution. This method could be used to place constraints on the dust size distributions of comets and as a result improve the use of $Af\rho$ as a proxy for cometary activity. Optically red dust indicates that the scattering is dominated by large particles.