Curves of growth for transiting exocomets: Application to Fe II lines in the β Pictoris system

Using transit spectroscopy, exocomets are routinely observed in the young planetary system of β Pic. However, despite more than 35 yr of observations, we still have very little information on the physical properties and almost no information on the abundances of the gaseous clouds surrounding the cometsa nuclei, the difficulty being the conversion of the observed absorption profiles into column density measurements. Here, we present a new method to interpret the exocomet absorptions observed in β Pic spectrum and link them to the physical properties of the transiting cometary tails (e.g. size, temperature, and column density). We show that the absorption depth of a comet in a set of lines arising from similar excitation levels of a given chemical species follows a simple curve as a function of g·f, where f is the line oscillator strength and g its lower level multiplicity. This curve is the analogue of the curve of growth for interstellar absorption lines, where equivalent widths are replaced by absorption depths. To fit this exocomet curve of growth, we introduced a model where the cometary absorption is produced by a homogeneous cloud, covering only a limited fraction of the stellar disc. This model is defined by two parameters: α, characterising the size of the cloud relative to the star, and β, related to the optical depth of the absorbing gas. This model was tested on two comets observed with the Hubble Space Telescope in December 1997 and October 2018, in a set of lines of ionised iron (Fe II) at 2750 Ã. The measured absorption depths are found to satisfactory match the two-parameter curve of growth model, indicating that both comets cover roughly 40% of the stellar disc (α = 0.4) and have optical thicknesses close to unity in those lines (β ~ 1). Then, we show that if we consider a set of lines arising from a wider range of energy levels, the absorbing species seems to be populated at thermodynamical equilibrium, causing the cometary absorption to follow a curve of growth as a function of g f âe^{â E_l/k_BT} (where T is the temperature of the absorbing medium). For the comet observed on December 6, 1997, we derive a temperature of T = 10 500 ± 500 K and a total Fe II column density of N_FeII = (1.11 ± 0.09) Ã- 10¹⁵ cm^{â 2}.