Resolving stellar populations with crowded field 3D spectroscopy
  (Abridged) We describe a new method to extract spectra of stars from
observations of crowded stellar fields with integral field spectroscopy (IFS).
Our approach extends the well-established concept of crowded field photometry
in images into the domain of 3-dimensional spectroscopic datacubes. The main
features of our algorithm are: (1) We assume that a high-fidelity input source
catalogue already exists and that it is not needed to perform sophisticated
source detection in the IFS data. (2) Source positions and properties of the
point spread function (PSF) vary smoothly between spectral layers of the
datacube, and these variations can be described by simple fitting functions.
(3) The shape of the PSF can be adequately described by an analytical function.
Even without isolated PSF calibrator stars we can therefore estimate the PSF by
a model fit to the full ensemble of stars visible within the field of view. (4)
By using sparse matrices to describe the sources, the problem of extracting the
spectra of many stars simultaneously becomes computationally tractable. We
present extensive performance and validation tests of our algorithm using
realistic simulated datacubes that closely reproduce actual IFS observations of
the central regions of Galactic globular clusters. We investigate the quality
of the extracted spectra under the effects of crowding. The main effect of
blending between two nearby stars is a decrease in the S/N in their spectra.
The effect increases with the crowding in the field in a way that the maximum
number of stars with useful spectra is always ~0.2 per spatial resolution
element. This balance breaks down when exceeding a total source density of ~1
significantly detected star per resolution element. We close with an outlook by
applying our method to a simulated globular cluster observation with the
upcoming MUSE instrument at the ESO-VLT.
