Spectral signature of uncombed penumbral magnetic fields

The uncombed penumbral model proposed by Solanki & Montavon (1993) is used to understand some recent observational results found in penumbrae. This model uses a penumbral magnetic field structured into horizontal flux tubes embedded in a more vertical background field. A modified version of this model, with a weaker field strength in the horizontal tubes, is used to explain the gradient with height of field strength and inclination found in studies using inversion techniques. These studies have found that over a range of 300 km, the field strength of the outer penumbra increases with height by more than 500 G. Similarly, the field inclination decreases with height by 30◦ in the same range of heights. We show that spectra generated by the uncombed model can give rise to these two effects as long as the horizontal tubes (of ∼100 km diameter) remain unresolved. We also study the linear, quadratic and rms fluctuations of the inclination gradients that can be generated by the uncombed model. These gradients are found to be compatible with those obtained from the null divergence condition and those derived from observations of net circular polarization. A key ingredient to explain these gradients is the contribution of the two boundary layers that enclose the horizontal magnetic tubes as seen by the line-of-sight. Our realization of the uncombed model also predicts values of the net circular polarization observed with the Advanced Stokes Polarimeter. The existence of a pure background penumbral field as proposed by the model is, however, put into question.