Knobs and dials of retrieving JWST transmission spectra. I. The importance of p-T profile complexity

We investigate the impact of using multipoint p-T profiles of varying complexity on the retrieval of synthetically generated hot Jupiter transmission spectra modelled after state-of-the-art observations of the hot Jupiter WASP-39~b with JWST. We perform homogenised atmospheric retrievals with the TauREx retrieval framework on a sample of synthetically generated transmission spectra, accounting for varying cases of underlying p-T profiles, cloud-top pressures, and expected noise levels. These retrievals are performed using a fixed-pressure multipoint p-T prescription with increasing complexity, ranging from isothermal to an eleven-point profile. We evaluate the performance of the retrievals based on the Bayesian model evidence, and the accuracy of the retrievals compared to the known input parameters. We find that performing atmospheric retrievals using an isothermal prescription for the pressure-temperature profile consistently results in wrongly retrieved atmospheric parameters when compared to the known input parameters. For an underlying p-T profile with a fully positive lapse rate, we find that a two-point profile is sufficient to retrieve the known atmospheric parameters, while under the presence of an atmospheric temperature inversion, we find that a more complex profile is necessary. Our investigation shows that, for a data quality scenario mirroring state-of-the-art observations of a hot Jupiter with JWST, an isothermal p-T prescription is insufficient to correctly retrieve the known atmospheric parameters. We find a model complexity preference dependent on the underlying pressure-temperature structure, but argue that a p-T prescription on the complexity level of a four-point profile should be preferred. This represents the overlap between the lowest number of free parameters and highest model preference in the cases investigated in this work.