Towards Precision Cosmology With Improved PNLF Distances Using VLT-MUSE
  I. Methodology and Tests
  The [O III ] 5007 Planetary Nebula Luminosity Function (PNLF) is an
established distance indicator that has been used for more than 30 years to
measure the distances of galaxies out to ~15 Mpc. With the advent of the
Multi-Unit Spectroscopic Explorer on the Very Large Telescope (MUSE) as an
efficient wide-field integral field spectrograph, the PNLF method is due for a
renaissance, as the spatial and spectral information contained in the
instrument's datacubes provides many advantages over classical narrow-band
imaging. Here we use archival MUSE data to explore the potential of a novel
differential emission-line filter (DELF) technique to produce spectrophotometry
that is more accurate and more sensitive than other methods. We show that DELF
analyses are superior to classical techniques in high surface brightness
regions of galaxies and we validate the method both through simulations and via
the analysis of data from two early-type galaxies (NGC 1380 and NGC 474) and
one late-type spiral (NGC 628). We demonstrate that with adaptive optics
support or under excellent seeing conditions, the technique is capable of
producing precision (< 0.05 mag) [O III ] photometry out to distances of 40 Mpc
while providing discrimination between planetary nebulae and other
emission-line objects such as H II regions, supernova remnants, and background
galaxies. These capabilities enable us to use MUSE to measure precise PNLF
distances beyond the reach of Cepheids and the tip of the red giant branch
method, and become an additional tool for constraining the local value of the
Hubble constant.
