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.