  The nebular recombination line H$\alpha$ is widely used as a star-formation
rate (SFR) indicator in the local and high-redshift Universe. We present a
detailed H$\alpha$ radiative transfer study of high-resolution isolated
Milky-Way and Large Magellanic Cloud simulations that include radiative
transfer, non-equilibrium thermochemistry, and dust evolution. We focus on the
spatial morphology and temporal variability of the H$\alpha$ emission, and its
connection to the underlying gas and star formation properties. The H$\alpha$
and H$\beta$ radial and vertical surface brightness profiles are in excellent
agreement with observations of nearby galaxies. We find that the fraction of
H$\alpha$ emission from collisional excitation amounts to $f_{\rm
col}\sim5-10\%$, only weakly dependent on radius and vertical height, and that
scattering boosts the H$\alpha$ luminosity by $\sim40\%$. The dust correction
via the Balmer decrement works well (intrinsic H$\alpha$ emission recoverable
within $25\%$), though the dust attenuation law depends on the amount of
attenuation itself both on spatially resolved and integrated scales. Important
for the understanding of the H$\alpha$-SFR connection is the dust and helium
absorption of ionizing radiation (Lyman continuum [LyC] photons), which are
about $f_{\rm abs}\approx28\%$ and $f_{\rm He}\approx9\%$, respectively.
Together with an escape fraction of $f_{\rm esc}\approx6\%$, this reduces the
available budget for hydrogen line emission by nearly half ($f_{\rm
H}\approx57\%$). We discuss the impact of the diffuse ionized gas, showing -
among other things - that the extraplanar H$\alpha$ emission is powered by LyC
photons escaping the disc. Future applications of this framework to
cosmological (zoom-in) simulations will assist in the interpretation of
spectroscopy of high-redshift galaxies with the upcoming James Webb Space
Telescope.
