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

Aim. We study the magnetohydrostatic equilibrium of magnetic flux tubes with circular cross sections embedded in a magnetic surrounding atmosphere. Methods. We solve the static momentum equation in 2.5D to obtain the thermodynamics that are consistent with a prescribed velocity and magnetic fields. Results. We show that force balance is roughly satisfied if the flux tube's magnetic field is aligned with its axis. Equilibrium is guaranteed if this magnetic field possesses a transverse component. Several forms of this transverse field are investigated. The resulting magnetic field configurations are critically reviewed in terms of the results from spectropolarimetric observations. The thermodynamic structure that allows the flux tube to be in mechanical equilibrium is also calculated. We show that the inferred pressure, density, and temperature stratification reproduce intensity features similar to dark core penumbral filaments and penumbral grains.