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.
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