  High-resolution observations of sunspots have revealed the existence of dark
cores inside the bright filaments of the penumbra. Here we present the
stationary solution of the heat transfer equation in a stratified penumbra
consisting of nearly horizontal magnetic flux tubes embedded in a stronger and
more vertical field. The tubes and the external medium are in horizontal
mechanical equilibrium. This model produces bright filaments with dark cores as
a consequence of the higher density of the plasma inside the flux tube, which
shifts the surface of optical depth unity toward higher (cooler) layers. Our
results suggest that the surplus brightness of the penumbra is a natural
consequence of the Evershed flow, and that magnetic flux tubes about 250 km in
diameter can explain the morphology of sunspot penumbra.
