IMF-induced intrinsic uncertainties on measuring galaxy distances based on the number of giant stars: the case of the ultra-diffuse galaxy NGC 1052-DF2

The surface brightness fluctuation (SBF) technique is one of the distance measurement methods that has been applied on the low surface brightness galaxy NGC 1052-DF2 yielding a distance of about 20 Mpc implying it to be a dark matter deficient galaxy. We assume the number of giant stars above a given luminosity threshold to represent the SBF magnitude. The SBF magnitude depends on the distance, but this is degenerate with the star formation history (SFH). Using a stellar population synthesis model we calculate the number of giant stars for stellar populations with different galaxy-wide stellar initial mass functions (gwIMFs), ages, metallicities and SFHs. If the gwIMF is the invariant canonical IMF, the 1$\sigma$ (3$\sigma$) uncertainty in colour allows a distance as low as 12 Mpc (8 Mpc). If instead the true underlying gwIMF is the integrated galaxy-wide IMF (IGIMF) then overestimating distances for low-mass galaxies would be a natural result, allowing NGC 1052-DF2 to have a distance of 11 Mpc within the 1$\sigma$ colour uncertainty. Finally, we show that our main conclusion on the existence of a bias in the SBF distance estimation is not much affected by changing the luminosity lower limit for counting giant stars.