Temporal deconvolution of the hydrogen coma I. A hybrid model

This paper describes a semi-analytical model, tentatively called the time-resolved model (TRM), for calculating the proper temporally resolved column density and Lyman-alpha intensity profiles of the extended cometary hydrogen coma, with potentially arbitrary number of photodissociation sources with different initial velocity profiles. The non-analytical part consists of a true 3D particle simulator whose results are used to obtain the necessary corrective parameters for the analytical, spherically symmetric formulas for the column density and intensity profiles. The hybrid approach provides a physically accurate and computationally effective method to recreate the extended coma profiles and supports a new analysis method that can provide hydrogen lifetime estimates and a much enhanced temporal resolution for the water production curve, for which a method is described. The ability to recreate the water production profile by different analysis methods is studied with a combination of real and simulated data. This is the first part of a two part publication with the second part dedicated to real data analysis.