Potential of the Surface Brightness Fluctuations method to measure distances to dwarf elliptical galaxies in nearby clusters

The potential of the Surface Brightness Fluctuations (SBF) method to determine the membership of dwarf elliptical galaxies (dEs) in nearby galaxy clusters is investigated. Extensive simulations for SBF measurements on dEs in the I band for various combinations of distance modulus, seeing and integration time are presented, based on average VLT FORS1 and FORS2 zero points. These show that for distances up to 20 Mpc (Fornax or Virgo cluster distance), reliable membership determination of dEs can be obtained down to very faint magnitudes $-10>M_{V}>-12$ mag ($\mu_0({V})\simeq 25$ mag arcsec -2 ) within integration times of the order of 1 hour and with good seeing. Comparing the limiting magnitudes of the method for the different simulated observing conditions we derive some simple rules to calculate integration time and seeing needed to reach a determined limiting magnitude at a given distance modulus for observing conditions different to the ones adopted in the simulations. Our simulations show a small offset of the order of 0.15 mag towards measuring too faint SBF. It is shown that this is due to loss of fluctuation signal when recovering pixel-to-pixel fluctuations from a seeing convolved image. To check whether our simulations represent well the behaviour of real data, SBF measurements for a real and simulated sample of bright Centaurus Cluster dEs are presented. They show that our simulations are in good agreement with the achievable $S/N$ of SBF measurements on real galaxies.