Less than the sum of its parts: the dust-corrected H$\alpha$ luminosity
  of star-forming galaxies explored at different spatial resolutions with MaNGA
  and MUSE
  The H$\alpha$ and H$\beta$ emission line luminosities measured in a single
integrated spectrum are affected in non-trivial ways by point-to-point
variations in dust attenuation in a galaxy. This work investigates the impact
of this variation when estimating global H$\alpha$ luminosities corrected for
the presence of dust by a global Balmer decrement. Analytical arguments show
that the dust-corrected H$\alpha$ luminosity is always underestimated when
using the global H$\alpha$/H$\beta$ flux ratio to correct for dust attenuation.
We measure this effect on 156 face-on star-forming galaxies from the Mapping
Nearby Galaxies at APO (MaNGA) survey. At 1-2 kpc spatial resolution, the
effect is small but systematic, with the integrated dust-corrected H$\alpha$
luminosity underestimated by $2$-$4$ per cent (and typically not more than by
$10$ per cent), and depends on the specific star formation rate of the galaxy.
Given the spatial resolution of MaNGA, these are lower limits for the effect.
From Multi Unit Spectroscopic Explorer (MUSE) observations of NGC 628 with a
resolution of 36 pc we find the discrepancy between the globally and the
point-by-point dust-corrected H$\alpha$ luminosity to be $14 \pm 1$ per cent,
which may still underestimate the true effect. We use toy models and
simulations to show that the true difference depends strongly on the spatial
variance of the H$\alpha$/H$\beta$ flux ratio, and on the slope of the relation
between H$\alpha$ luminosity and dust attenuation within a galaxy. Larger
samples of higher spatial resolution observations are required to quantify the
dependence of this effect as a function of galaxy properties.
