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

Abstract

Aims. 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. Methods. To perform all the experiments described above, 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. The uncertainty was evaluated through the accuracy, the precision, and the standard deviation of the fitting. Results. We demonstrate how the usual mathematical approximations taken in the SBF theoretical derivation have a negligible impact on the results and how modelling the instrumental noise reduces the uncertainty. We conducted various studies where we varied the size of the mask applied over the image, the surface and fluctuation brightness of the galaxy, its size and profile, its point spread function, and the sky background. It is worth highlighting that we find a strong correlation between having a high number of pixels within the studied mask and retrieving a low uncertainty result. We address how the standard deviation of the fitting underestimates the actual uncertainty of the measurement. Lastly, we find that, when studying SBF gradients, the result is a pixel-weighted average of all the SBFs present within the studied region. Retrieving an SBF gradient requires high-quality data and a sufficient difference in the fluctuation value through the different radii. We show how the SBF uncertainty can be obtained and we present a collection of qualitative recommendations for a safe SBF retrieval. Conclusions. Our main findings are as follows. 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. The uncertainty associated with the intrinsic variability of the system can be obtained using sets of Monte Carlo mock galaxy simulations. 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.