Fitting pseudo-Sérsic (Spergel) light profiles to galaxies in interferometric data: The excellence of the uυ-plane

¹ Purple Mountain Observatory, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, PR China
e-mail: qhtan@pmo.ac.cn
² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
³ Institut de Radioastronomie Millimétrique, 300 Rue de la Piscine, 38406 Saint-Martin-d’Hères, France
⁴ National Radio Astronomy Observatory, 800 Bradbury Dr., SE Ste 235, Albuquerque, NM 87106, USA
⁵ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 75014 Paris, France
⁶ Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa, 277-8583, Japan
⁷ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, PR China
⁸ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
⁹ Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
¹⁰ School of Physics and Astronomy, University of Southampton, Highfield SO17 1BJ, UK
¹¹ Center for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
¹² National Astronomical Research Institute of Thailand, Don Kaeo, Mae Rim, Chiang Mai 50180, Thailand
¹³ Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Pathumwan, Bangkok 10330, Thailand
¹⁴ European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching bei Munchen, Germany
¹⁵ Cosmic Dawn Center (DAWN), Denmark

Received: 22 June 2023
Accepted: 7 December 2023

Abstract

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 uυ-plane, which has been recently implemented in the IRAM software GILDAS (uv_fit). Spergel profiles provide an alternative to the Sérsic profile, with the advantage of having an analytical Fourier transform, making them ideal for modeling visibilities in the uυ-plane. We provide an approximate conversion between the Spergel index and the Sérsic 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 uυ-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 uυ-plane is likely driven by the difficulty of accounting for a correlated signal in interferometric images. Even in the uυ-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.