  It is well known that gas in galaxy discs is highly turbulent, but there is
much debate on which mechanism can energetically maintain this turbulence.
Among the possible candidates, supernova (SN) explosions are likely the primary
drivers but doubts remain on whether they can be sufficient in regions of
moderate star formation activity, in particular in the outer parts of discs. In
this paper, we measure the SN efficiency $\eta$, namely the fraction of the
total SN energy needed to sustain turbulence in galaxies, and verify that SNe
can indeed be the sole driving mechanism. The key novelty of our approach is
that we take into account the increased turbulence dissipation timescale
associated to the flaring in outer regions of gaseous discs. We analyse the
distribution and kinematics of HI and CO in 10 nearby star-forming galaxies to
obtain the radial profiles of the kinetic energy per unit area, for both the
atomic gas and the molecular gas. We use a theoretical model to reproduce the
observed energy with the sum of turbulent energy from SNe, as inferred from the
observed star formation rate (SFR) surface density, and the gas thermal energy.
We find that the observed kinetic energy is remarkably well reproduced by our
model across the whole extent of the galactic discs, assuming $\eta$ constant
with the galactocentric radius. Taking into account the uncertainties on the
SFR surface density and on the atomic gas phase, we obtain that the median SN
efficiencies for our sample of galaxies are $\langle \eta_\mathrm{atom}
\rangle=0.015_{-0.008}^{+0.018}$ for the atomic gas and $\langle
\eta_\mathrm{mol} \rangle = 0.003_{-0.002}^{+0.006}$ for the molecular gas. We
conclude that SNe alone can sustain gas turbulence in nearby galaxies with only
few percent of their energy and that there is essentially no need for any
further source of energy.
