  The question of possible small-scale dynamo action in the surface layers of
the Sun is revisited with realistic 3D MHD simulations. As in other MHD
problems, dynamo action is found to be a sensitive function of the magnetic
Prandtl number ${\rm P_{\rm m} }=\nu/\eta$; it disappears below a critical
value ${\rm P_{\rm c}}$ which is a function of the numerical resolution. At a
grid spacing of 3.5 km, ${\rm P_{\rm c}}$ based on the hyperdiffusivities
implemented in the code (STAGGER) is $\approx 1$, increasing with increasing
grid spacing. As in other settings, it remains uncertain whether small scale
dynamo action is present in the astrophysical limit where ${\rm P_{\rm m} }<<1$
and magnetic Reynolds number ${\rm R_m}\gg 1$. The question is discussed in the
context of the strong effect that external stray fields are observed to have in
generating and maintaining dynamo action in other numerical and laboratory
systems, and in connection with the type-II hypertransient behavior of dynamo
action observed in the absence of such external fields.
