  Many past studies have predicted the steady-state production and maintenance
of abiotic O$_2$ and O$_3$ in the atmospheres of CO$_2$-rich terrestrial
planets orbiting M dwarf stars. However, the time-dependent responses of these
planetary atmospheres to flare events - and the possible temporary production
or enhancement of false positive biosignatures therein - has been comparatively
less well studied. Most past works that have modeled the photochemical response
to flares have assumed abundant free oxygen like that of the modern or
Proterozoic Earth. Here we examine in detail the photochemical impact of the UV
emitted by a single flare on abiotic O$_2$/O$_3$ production in prebiotic,
CO$_2$-dominated atmospheres of M dwarf planets with CO$_2$ levels ranging from
10% to 90% of 1 bar. We find that a single flare generally destroys O$_2$ while
modestly enhancing O$_3$ column densities. We simulate the spectral observables
of both the steady-state atmosphere and time-dependent spectral response over
the flare window for both emitted and transmitted light spectra. Over the
course of the flare, the O$_3$ UV Hartley band is modestly enhanced by a
maximum of 6 ppm while the CO$_2$ molecular transit depths modestly decline by
7 ppm. In both emitted and transmitted light spectra, the 9.65 $\mu$m O$_3$
band is hidden by the overlapping 9.4 $\mu$m CO$_2$ band for all scenarios
considered. Overall, we find that the possible enhancements of abiotic O$_3$
due to a single flare are small compared to O$_3$'s sensitivity to other
parameters such as CO$_2$ and H$_2$O abundances or the availability of reducing
gases such as H$_2$.
