In contrast to the dark umbrae of sunspots, penumbrae have a heat flux that is around 75% that of the normal quiet sun (see, e.g., Schmidt 1991). It is clear that convective motions that are only slightly less efficient than the normal granulation should be responsible for the penumbral brightness. The nature of these convective motions is not yet known. But recent models of interchange convection of magnetic flux tubes look promising (Schlichenmaier et al. 1998, Jahn & Schmidt 1994; see also Schlichenmaier et al. 1999). These theoretical models make use of the concept of penumbral flux tubes that act like convective bubbles carrying the energy upwards. In this model, the structuring of the penumbral magnetic field is directly related to the transport of energy by convection. A penumbral magnetic field structured in individual flux tubes is also used in the siphon flow models of Montesinos & Thomas 1997(and references therein) to explain the Evershed effect (for a review see Thomas 1996; Solanki 1997). This paper discusses some of the spectroscopic signatures of the uncombed penumbral model proposed by Solanki & Montavon (1993, SM hereinafter) that partially accounts for this magnetic field structuring.
Observations have shown for decades a filamentary structure of the penumbra in continuum images (see, e.g., Sobotka 1997). The Evershed flow is also known to be highly structured, with flow channels extending radially in the penumbra. Title et al. (1993) and Rimmele (1995) concluded that the Evershed channels were well correlated with the dark penumbral fibrils seen in filtergrams. The filamentary condition of the penumbral magnetic field has been more difficult to investigate. Clear evidence of azimuthal fluctuations of the magnetic field inclination were found by Title et al. (1993) using magnetograms and by Degenhardt & Wiehr (1991) from Stokes V spectra. A similar conclusion was reached by Rimmele (1995). Data from the Advanced Stokes Polarimeter (ASP, see Skumanich et al. 1997) in the visible range showed that these inclination fluctuations were highly correlated with field strength fluctuations in the sense that vertical fields were stronger than horizontal ones (Lites et al. 1993, Stanchfield et al. 1997). Also using data from the ASP, but with a different analysis technique, Westendorp Plaza et al. (2000a, hereinafter WESa) found the same correlation between magnetic field strength and inclination. Martínez Pillet (1997) discussed the organization of penumbral magnetic fields into flux tubes with fluctuating inclinations and field strengths as well as their association with the Evershed flow. This connection between the Evershed flow and horizontal weak penumbral flux tubes has received additional support from recent infrared (IR) measurements. Rüedi et al. (1999) have used TiI lines in the 2 µm region to find evidence for the existence of these concentrations. This work also shows how the low and horizontal field channels that carry the flow are associated with cooler temperatures (as shown by the strength of TiI line), at least in the outer penumbral regions.
This better understanding of the penumbral magnetic field organization is incorporated in this paper into the model of SM and its predictions are compared with recent observational findings that are not yet fully understood. In particular, we scrutinize some of the results of the inversions carried out by WESa and Westendorp Plaza et al. (2000b, hereinafter WESb, see also Fig. 1 in Westendorp Plaza et al., 1997). These authors find that almost everywhere in the outer penumbra (normalized radial distance larger than 0.7), the mean penumbral field strength increases with height (several hundreds of Gauss over the line-forming region) and that the field inclination decreases (over the same range) by as much as . These conclusions are somewhat puzzling. First, any single-component model of a flux tube that opens up with height predicts a penumbral magnetic field that decreases upwards (see, e.g., Pizzo 1986). Second, and more important, it is impossible to account for a decrease of in a range of heights of only 300 km (a typical line-forming region). That these inclination gradients are needed to explain the shapes of the circular polarization profiles observed in penumbrae is well known (Sánchez Almeida & Lites 1992; SM). The net circular polarization (NCP) observed in penumbrae (i.e., the integrated signal over the Stokes V profile) can only be satisfactorily explained with these large gradients (Sánchez Almeida & Lites 1992). But these gradients cannot be fitted into a single-component model of the penumbra (Solanki et al. 1993). Already Sánchez Almeida & Lites (1992) pointed out that the only way in which these gradients are realizable is as a result of the fine scale structure of the penumbra. The first model that explained the observed NCP taking into account the unresolved structured of the penumbral magnetic field was proposed by SM. In this model, horizontal tubes that carry most (but not all) of the Evershed flow, immersed in a more vertical background field, were able to predict the center-to-limb variation (CLV) of the observed NCP. This NCP was due to the fact that the line-of-sight (LOS) crossed the upper and lower boundaries of the horizontal tubes. The jumps in the field inclination seen by the LOS were of around and, thus, were able to generate the NCP. The tube used by SM was of 150 km diameter which is large enough to cover an important fraction of a typical line forming region. But, as mentioned by SM, a set of many thinner piled up flux tubes will work as well. Indeed, Sánchez Almeida (1998) has proposed that the deduced for the inclination gradient and the gradients derived from the condition applied to penumbral vector magnetic field data are only compatible with flux tubes with diameters of 1-15 km. These tubes are optically thin (for typical photospheric densities) and a large number of them are needed to generate the desired amount of NCP.
In this paper, we elaborate on SM model and introduce the above mentioned properties of the horizontal field channels (smaller field strength, lower temperatures; although hotter tubes are also considered for comparison). The NCP predicted from this model is then compared with recent ASP data (Sect. 2.1). We synthesize the Stokes spectra formed in this type of penumbral configuration and invert them with the SIR code (Ruiz Cobo & del Toro Iniesta 1992) to compare our results with the findings of WESa and WESb (including what they called "differential opacity effect", see Sect. 3). Similarly, we study how the SM model can be fine tuned to account for all the gradients as estimated from both, NCP and from the condition using one single flux tube. We also point out how this null divergence condition implies the existence of (reasonable) azimuthal magnetic fields.
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000