Modelling of surface brightness fluctuation measurements: Methodology, uncertainty, and recommendations

The goal of this work is to scrutinise the surface brightness fluctuation (SBF) calculation methodology. We analysed the SBF derivation procedure, measured the accuracy of the fitted SBF under controlled conditions, retrieved the uncertainty associated with the variability of a system that is inherently stochastic, and studied the SBF reliability under a wide range of conditions. Additionally, we address the possibility of an SBF gradient detection. We also examine the problems related with biased measurements of the SBF and low luminosity sources. All of this information allows us to put forward guidelines to ensure a valid SBF retrieval. To perform all these experiments, we carried out Monte Carlo simulations of mock galaxies as an ideal laboratory. Knowing its underlying properties, we attempted to retrieve SBFs under different conditions. We show how the SBF uncertainty can be obtained and we present a collection of qualitative recommendations for a safe SBF retrieval: it is important to model the instrumental noise, rather than fitting it; the target galaxies must be observed under appropriate observational conditions; in a traditional SBF derivation, one should avoid pixels with fluxes lower than ten times the SBF estimate to prevent biased results. We offer our computational implementation in the form of a simple code designed to estimate the uncertainty of the SBF measurement. This code can be used to predict the quality of future observations or to evaluate the reliability of those already conducted.