Radiative properties of magnetic elements - II. Center to limb variation of the appearance of photospheric faculae

For the understanding of more complex numerical simulation results, a basic facular model is created consisting of a magnetic flux sheet embedded in a plane parallel atmosphere. The atmosphere within the flux sheet is similar to the external one but shifted in the downward direction to result in a Wilson depression of 150 km. It is shown that the horizontal spatial extension of the contrast enhancement produced by this model increases from center to limb from a few tenths to up to 1 as a consequence of enhanced radiation from the limbward surface outside (behind) the magnetic flux concentration. For a conceivable explanation of this radiative effect it is noted that a plasma parcel on the solar surface sideways of the flux sheet sees a more transparent sky in the direction towards the flux sheet compared to a direction away from it because of the rarefied atmosphere within the flux sheet. This facular model also produces a dark lane at the disk-center side (in front) of the flux sheet even though no flow is present. It it is due to the deep layers of the flux sheet that have a lower temperature gradient and are cooler than the surrounding atmosphere at equal geometrical depth. This implies that limb observations offer a glimpse of the cool bottom of magnetic elements. The center-to-limb variation of the size and the dark-lane effect derived from this basic model is recovered in a self-consistent, two-dimensional non-stationary simulation of a magnetic flux concentration. These findings are in excellent agreement with and provide an interpretation of recent observations of faculae at very high resolution by Lites et al. (2004, Sol. Phys., 221,65).