We describe a scenario for the topology of
the magnetic field in penumbrae that accounts for
recent observations showing upflows, downflows, and
reverse magnetic polarities. According to our conjecture,
short narrow magnetic loops fill the penumbral
photosphere. Flows along these arched field lines are
responsible for both the Evershed effect and the convective
transport. This scenario seems to be qualitatively
consistent with most existing observations, including
the dark cores in penumbral filaments reported by
Scharmer et al. Each bright filament with dark core would
be a system of two paired convective rolls with the dark core
tracing the common lane where the plasma sinks down.
The magnetic loops would have a hot footpoint in one of
the bright filament and a cold footpoint in the dark core.
The scenario fits in most of our theoretical prejudices
(siphon flows along field lines, presence of overturning
convection, drag of field lines by downdrafts, etc).
If the conjecture turns out to be correct, the mild upward
and downward velocities observed in penumbrae must
increase upon improving the resolution. This and other
observational tests to support or disprove the scenario
are put forward.