Fitting Pseudo-Sérsic (spergel) Light Profiles to Galaxies in Interferometric Data: the Excellence of the Uυ-Plane

Modern (sub)millimeter interferometers, such as ALMA and NOEMA, offer high angular resolution and unprecedented sensitivity. This provides the possibility to characterize the morphology of the gas and dust in distant galaxies. To assess the capabilities of the current software in recovering morphologies and surface brightness profiles in interferometric observations, we tested the performance of the Spergel model for fitting in the u upsilon-plane, which has been recently implemented in the IRAM software GILDAS (uv_fit). Spergel profiles provide an alternative to the Sersic profile, with the advantage of having an analytical Fourier transform, making them ideal for modeling visibilities in the u upsilon-plane. We provide an approximate conversion between the Spergel index and the Sersic index, which depends on the ratio of the galaxy size to the angular resolution of the data. We show through extensive simulations that Spergel modeling in the u upsilon-plane is a more reliable method for parameter estimation than modeling in the image plane, as it returns parameters that are less affected by systematic biases and results in a higher effective signal-to-noise ratio. The better performance in the u upsilon-plane is likely driven by the difficulty of accounting for a correlated signal in interferometric images. Even in the u upsilon-plane, the integrated source flux needs to be at least 50 times larger than the noise per beam to enable a reasonably good measurement of a Spergel index. We characterized the performance of Spergel model fitting in detail by showing that parameter biases are generally low (<10%) and that uncertainties returned by uv_fit are reliable within a factor of two. Finally, we showcase the power of Spergel fitting by reexamining two claims of extended halos around galaxies from the literature, showing that galaxies and halos can be successfully fitted simultaneously with a single Spergel model.