A. Skumanich

Optical Tomography of a Sunspot. II. Vector Magnetic Field and Temperature Stratification

An observational determination of the three-dimensional magnetic and thermal structure of a sunspot is presented. It has been obtained through the application of the SIR inversion technique (Stokes Inversion based on Response functions) on a low-noise, full Stokes profile two-dimensional map of the sunspot as observed with the Advanced Stokes Polarimeter. As a result of the inversion, maps of the magnetic field strength, B, zenith angle, γ, azimuth, χ, and temperature, T, over 25 layers at given optical depths (i.e., an optical tomography) are obtained, of which those between log τ5 = 0 and log τ5 = -2.8 are considered to provide accurate information on the physical parameters. All over the penumbra γ increases with depth, while B is larger at the bottom layers of the inner penumbra (as in the umbra) but larger at the top layers of the outer penumbra (as in the canopy). The corrugation of the penumbral magnetic field already observed by other authors has been confirmed by our different inversion technique. Such a corrugation is especially evident in the zenith angle maps of the intermediate layers, featuring the presence of the so-called spines that we further characterize: spines are warmer and have a less inclined magnetic field than the spaces between them and tend to have a smaller gradient of γ with optical depth over the entire penumbra, but with a field strength which is locally stronger in the middle penumbra and locally weaker in the outer penumbra and beyond in the canopy. In the lower layers of these external parts of the sunspot, most of the field lines are seen to return to the solar surface, a result that is closely connected with the Evershed effect (e.g., Westendorp et al., the third paper in this series). The Stokes V net area asymmetry map as well as the average B, γ, and T radial distributions (and that of the line-of-sight velocities; see the third paper in this series) show a border between an inner and an outer penumbra with different three-dimensional structure. We suggest that it is in this middle zone where most of a new family of penumbral flux tubes (some of them with Evershed flow) emerge interlaced (both horizontally and vertically) among themselves and with the background magnetic field of the penumbra. The interlacing along the line of sight is witnessed by the indication of many points in the outer penumbra showing rapid transitions with height between two structures, one with very weak and inclined magnetic field at the bottom of the photosphere and the other with a stronger and less inclined magnetic field. Over the whole penumbra, and at all optical layers, a constant but weak deviation from radiality of some 5° is detected for the azimuth of the vector magnetic field, which may be in agreement with former detections but which is not significantly higher than the size of the errors for this parameter.

Evidence for a downward mass flux in the penumbral region of a sunspot

Sunspots were the first extraterrestrial phenomenon found to harbour magnetic fields. But the physical nature of sunspots and their relationship to the Suns global magnetic field are still poorly understood. Perhaps the largest uncertainty is related to the outermost region of sunspots (the penumbra) and, in particular, the nature of the so-called Evershed flow-a stream of material emanating radially from sunspots at velocities of up to ∼ 6 km s -1 (ref. 5), before vanishing abruptly at the outer penumbral edges. Here we make use of a recently developed optical tomographic technique to obtain a three-dimensional model of the magnetic field and mass flow in the vicinity of a sunspot. We find that some of the magnetic field lines, together with a significant part of the Evershed mass flux, flow back towards the Sun in the deepest atmospheric layers at the outer edge of the sunspot and its surroundings. This observation should provide an important clue to our understanding of the appearance, stability and decay of sunspots, the most conspicuous tracers of the solar activity cycle.

On the value of 'αAR' from vector magnetograph data

This investigation centers upon the quantifying magnetic twist by the parameter α, commonly defined as (∇×Bh)z/Bz=μ0Jz/Bz, and its derivation from vector magnetograph data. This parameter can be evaluated at each spatial point where the vector B is measured, but one may also calculate a single value of α to describe the active region as a whole, here called αAR. We test three methods to calculate such a parameter, examine the influence of data noise on the results, and discuss the limitations associated with assigning such a quantity. The three methods discussed are (1)xa0to parameterize the distribution of α(x,y) using moments of its distribution, (2)xa0to determine the slope of the function Jz(x,y)=αARBz(x,y) using a least-squares fit and (3)xa0to determine the value of α for which the horizontal field from a constant-α force-free solution most closely matches the observed horizontal magnetic field. The results are qualitatively encouraging: between methods, the resulting value of the αARparameter is often consistent to within the uncertainties, even though the resulting αARcan differ in magnitude, and in some cases in sign as well. The worst discrepancies occur when a minimal noise threshold is adopted for the data. When the calculations are restricted to detections of 3σ or better, there is, in fact, fair quantitative agreement between the three methods. Still, direct comparison of different active regions using disparate methods must be carried out with caution. The discrepancies, agreements, and overall robustness of the different methods are discussed. The effects of instrumental limitations (spatial resolution and a restricted field-of-view) on an active-region αAR, and quantifying the validity of αAR, are addressed in Paperxa0II (Leka, 1999).

A quantitative comparison of vector magnetic field measurement and analysis techniques

We make a quantitative comparison between spectral vs filter measurement and analysis techniques for extraction of solar vector magnetic fields from polarimetric data using as a basis the accurately calibrated, high angular resolution Stokes profile data from the Advanced Stokes Polarimeter. It is shown that filter-based measurements deliver qualitative images of the field alignment for sunspots that are visually similar to images derived from the more detailed analysis of the Stokes profiles. However, quantitative comparison with least-squares fits to the full Stokes profiles show that both the strength of the field predicted by the filter-based analysis and its orientation contain substantial errors. These errors are largest for plage regions outside of sunspots, where the field strengths are inferred to be only a fraction of their true values, and errors in the orientation of 40–50° are common. Within sunspots, errors of 20° are commonplace. The greatest source of these errors is the inability of the filter-based measurements to account for the small fill fraction of magnetic fields or, equivalently, scattered light in the instrument, which reduce the degree of polarization. The uncertainties of the full profile fitting methods are also discussed, along with the errors introduced by coarser wavelength sampling of the observed Stokes profiles. The least-squares fitting procedure operates best when the profiles are sampled at least as frequently as one Doppler width of the line.

Emission cores in H and K lines

Calculations are made for the center-limb variations of the K2 and K3 components of the solar Ca ii K line using an optically thick model of the chromosphere. The center-limb variations are shown to require an increase of Doppler width with height in the chromosphere and to depend critically upon the location of the point where ΔλD has increased by a factor e. Good agreement with observations is found when, and only when, the increase in ΔλD occurs nearly simultaneously with the increase in chromospheric temperature.