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Context: Observations at 0.1" have revealed the existence of dark cores inthe bright filaments of sunspot penumbrae. Expectations are high that suchdark-cored filaments are the basic building blocks of the penumbra, but theirnature remains unknown.  Aims: We investigate the origin of dark cores in penumbral filaments and thesurplus brightness of the penumbra. To that end we use an uncombed penumbralmodel.  Methods: The 2D stationary heat transfer equation is solved in a stratifiedatmosphere consisting of nearly horizontal magnetic flux tubes embedded in astronger and more vertical field. The tubes carry an Evershed flow of hotplasma.  Results: This model produces bright filaments with dark cores as aconsequence of the higher density of the plasma inside the tubes, which shiftsthe surface of optical depth unity toward higher (cooler) layers. Ourcalculations suggest that the surplus brightness of the penumbra is a naturalconsequence of the Evershed flow, and that magnetic flux tubes about 250 km indiameter can explain the morphology of sunspot penumbrae.

Heat transfer in sunspot penumbrae. Origin of dark-cored penumbral filaments