Optimal fitting of gaussian-apodized or under-resolved emission lines in
  Fourier Transform spectra providing new insights on the velocity structure of
  NGC 6720
  An analysis of the kinematics of NGC 6720 is performed on the commissioning
data obtained with SITELLE, the Canada-France-Hawaii Telescope's new imaging
Fourier transform spectrometer. In order to measure carefully the small
broadening effect of a shell expansion on an unresolved emission line, we have
determined a computationally robust implementation of the convolution of a
Gaussian with a sinc instrumental line shape which avoids arithmetic overflows.
This model can be used to measure line broadening of typically a few km/s even
at low spectral resolution (R less than 5000). We have also designed the
corresponding set of Gaussian apodizing functions that are now used by ORBS,
the SITELLE's reduction pipeline. We have implemented this model in ORCS, a
fitting engine for SITELLE's data, and used it to derive the [SII] density map
of the central part of the nebula. The study of the broadening of the [NII]
lines shows that the Main Ring and the Central Lobe are two different shells
with different expansion velocities. We have also derived deep and spatially
resolved velocity maps of the Halo in [NII] and Halpha and found that the
brightest bubbles are originating from two bipolar structures with a velocity
difference of more than 35 km/s lying at the poles of a possibly unique Halo
shell expanding at a velocity of more than 15 km/s.
