A new fitting concept for the robust determination of Sérsic model parameters^⋆

¹ Instituto de Astrofísica e Ciências do Espaço – Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
e-mail: Iris.Breda@astro.up.pt
² Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
³ University of Vienna, Department of Astrophysics, Türkenschanzstr. 17, 1180 Vienna, Austria
⁴ Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, OAL, Tapada da Ajuda, PT1349-018 Lisboa, Portugal
⁵ Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal

Received: 28 January 2019
Accepted: 30 September 2019

Abstract

Context. The Sérsic law (SL) offers a versatile, widely used functional form for the structural characterization of galaxies near and far. Whereas fitting this three-parameter function to galaxies with a genuine SL luminosity distribution (e.g., several local early-type galaxies–ETGs) yields a robust determination of the Sérsic exponent η and effective surface brightness μ_eff, this is not necessarily the case for galaxies whose surface brightness profiles (SBPs) appreciably deviate, either in their centers or over an extended radius interval, from the SL (e.g., ETGs with a “depleted” core and nucleated dwarf ellipticals, or most late-type galaxies-LTGs). In this general case of “imperfect” SL profiles, the best-fitting solution may significantly depend on the radius (or surface brightness) interval fit, the photometric passbands considered and the specifics of the fitting procedure (photometric uncertainties of SBP data points or image pixels, and corrections for point spread function (PSF) convolution effects). Such uncertainties may then affect, in a non-easily predictable manner, automated structural studies of large heterogeneous galaxy samples and introduce a scatter, if not a bias, in galaxy scaling relations and their evolution across redshift (z).

Aims. Our goal is to devise a fitting concept that permits a robust determination of the equivalent SL model for the general case of galaxies with imperfect SL profiles.

Methods. The distinctive feature of the concept proposed here (iFIT) is that the fit is not constrained through standard χ² minimization between an observed SBP and the SL model of it, but instead through the search for the best match between the observationally determined and theoretically expected radial variation of the mean surface brightness and light growth curve. This approach ensures quick convergence to a unique solution for both perfect and imperfect Sérsic profiles, even shallow and resolution-degraded SBPs. iFIT allows for correction of PSF convolution effects, offering the user the option of choosing between a Moffat, Gaussian, or user-supplied PSF. iFIT, which is a standalone FORTRAN code, can be applied to any SBP that is provided in ASCII format and it has the capability of convenient graphical storage of its output. The iFIT distribution package is supplemented with an auxiliary SBP derivation tool in python.

Results. iFIT has been extensively tested on synthetic data with a Sérsic index 0.3 ≤ η ≤ 4.2 and an effective radius 1 ≤ R_eff  (″)≤20. Applied to non PSF-convolved data, iFIT can infer the Sérsic exponent η with an absolute error of ≤ 0.2 even for shallow SBPs. As for PSF-degraded data, iFIT can recover the input SL model parameters with a satisfactorily accuracy almost over the entire considered parameter space as long as FWHM(PSF) ≤ R_eff. This study also includes examples of applications of iFIT to ETGs and local low-mass starburst galaxies. These tests confirm that iFIT shows little sensitivity on PSF corrections and SBP limiting surface brightness, and that subtraction of the best-fitting SL model in two different bands generally yields a good match to the observed radial color profile.

Conclusions. It is pointed out that the publicly available iFIT offers an efficient tool for the non-supervised structural characterization of large galaxy samples, as those expected to become available with Euclid and LSST.