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.
