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We study the magnetohydrostatic equilibrium of magnetic flux tubes withcircular cross sections embedded in a magnetic surrounding atmosphere. We solvethe static momentum equation in 2.5D to obtain the thermodynamics that areconsistent with a prescribed velocity and magnetic fields. We show that forcebalance is roughly satisfied if the flux tube's magnetic field is aligned withits axis. Equilibrium is guaranteed if this magnetic field possesses atransverse component. Several forms of this transverse field are investigated.The resulting magnetic field configurations are critically reviewed in terms ofthe results from spectropolarimetric observations. The thermodynamic structurethat allows the flux tube to be in mechanical equilibrium is also calculated.We show that the inferred pressure, density and temperature stratificationreproduce intensity features similar to dark core penumbral filaments andpenumbral grains.

The structure of sunspot penumbrae IV. MHS equilibrium for penumbral flux tubes and the origin of dark core penumbral filaments and penumbral grains