  In this Letter, we explore the hypothesis that the smooth appearance of bow
shocks around some red supergiants (RSGs) might be caused by the ionization of
their winds by external sources of radiation. Our numerical simulations of the
bow shock generated by IRC-10414 (the first-ever RSG with an optically detected
bow shock) show that the ionization of the wind results in its acceleration by
a factor of two, which reduces the difference between the wind and space
velocities of the star and makes the contact discontinuity of the bow shock
stable for a range of stellar space velocities and mass-loss rates. Our best
fit model reproduces the overall shape and surface brightness of the observed
bow shock and suggests that the space velocity and mass-loss rate of IRC-10414
are $\approx$50 ${\rm km} \, {\rm s}^{-1}$ and $\approx$$10^{-6}$ $M_\odot \,
{\rm yr}^{-1}$, respectively, and that the number density of the local ISM is
$\approx$3 ${\rm cm}^{-3}$. It also shows that the bow shock emission comes
mainly from the shocked stellar wind. This naturally explains the enhanced
nitrogen abundance in the line-emitting material, derived from the spectroscopy
of the bow shock. We found that photoionized bow shocks are $\approx$15$-$50
times brighter in optical line emission than their neutral counterparts, from
which we conclude that the bow shock of IRC-10414 must be photoionized.
