  Black widows are close binary systems in which a millisecond pulsar is
orbited by a companion a few per cent the mass of the sun. It has been
suggested that the pulsar's rotationally powered $\gamma$-ray luminosity
gradually evaporates the companion, eventually leaving behind an isolated
millisecond pulsar. The evaporation efficiency is determined by the temperature
$T_{\rm ch}\propto F^{2/3}$ to which the outflow is heated by the flux $F$ on a
dynamical time-scale. Evaporation is most efficient for companions that fill
their Roche lobes. In this case, the outflow is dominated by a cap around the
L1 point with an angle $\theta_g\sim (T_{\rm ch}/T_g)^{1/2}$, and the
evaporation time is $t_{\rm evap}=0.46(T_{\rm ch}/T_g)^{-2}\textrm{ Gyr}$,
where $T_g>T_{\rm ch}$ is the companion's virial temperature. We apply our
model to the observed black widow population, which has increased substantially
over the last decade, considering each system's orbital period, companion mass,
and pulsar spin-down power. While the original (Fruchter et al. 1988) black
widow evaporates its companion on a few Gyr time-scale, direct evaporation on
its own is too weak to explain the overall population. We propose instead that
the evaporative wind couples to the companion's magnetic field, removes angular
momentum from the binary, and maintains stable Roche-lobe overflow. While a
stronger wind carries more mass, it also reduces the Alfv\'en radius, making
this indirect magnetic braking mechanism less dependent on the flux $t_{\rm
mag}\propto t_{\rm evap}^{1/3}$. This reduces the scatter in evolution times of
observed systems, thus better explaining the combined black widow and isolated
millisecond pulsar populations.
