  Vela X-1 is a runaway X-ray binary system hosting a massive donor star, whose
strong stellar wind creates a bow shock as it interacts with the interstellar
medium. This bow shock has previously been detected in H$\alpha$ and IR, but,
similar to all but one bow shock from a massive runaway star (BD+43$^{\rm
o}$3654), has escaped detection in other wavebands. We report on the discovery
of $1.3$ GHz radio emission from the Vela X-1 bow shock with the MeerKAT
telescope. The MeerKAT observations reveal how the radio emission closely
traces the H$\alpha$ line emission, both in the bow shock and in the
larger-scale diffuse structures known from existing H$\alpha$ surveys. The Vela
X-1 bow shock is the first stellar-wind-driven radio bow shock detected around
an X-ray binary. In the absence of a radio spectral index measurement, we
explore other avenues to constrain the radio emission mechanism. We find that
thermal/free-free emission can account for the radio and H$\alpha$ properties,
for a combination of electron temperature and density consistent with earlier
estimates of ISM density and the shock enhancement. In this explanation, the
presence of a local ISM over-density is essential for the detection of radio
emission. Alternatively, we consider a non-thermal/synchrotron scenario,
evaluating the magnetic field and broad-band spectrum of the shock. However, we
find that exceptionally high fractions ($\gtrsim 13$%) of the kinetic wind
power would need to be injected into the relativistic electron population to
explain the radio emission. Assuming lower fractions implies a hybrid scenario,
dominated by free-free radio emission. Finally, we speculate about the
detectability of radio bow shocks and whether it requires exceptional ISM or
stellar wind properties.
