The Size Dependence of Contrasts and Numbers of Small Magnetic Flux Tubes in an Active Region

Intensity contrasts and number densities of bright points, knots and pores ranging in size between 0″.15 and 4″ are studied using high resolution pictures in Mg b₁ of a young active region. On the average, the contrast in the wing of the line increases very strongly with decreasing size, while the continuum contrast increases more slowly. The ratio of contrast in the line to contrast in the continuum increases rapidly with decreasing size. The possibility is explored of using this contrast ratio as an indicator of size. The distribution of the contrast ratio in a part of the active region is used in this way to derive a size distribution of facular points. The resulting distribution has a limited accuracy, but is free from systematic distortion due to selection effects. Validity checks on the method are presented. We measure the size distribution of the pores in the same area, and combine the result with that for the facular points. The combined distribution shows that the surface area covered by magnetic elements with diameter δ has a maximum near δ = 0″.8. It increases roughly proportional to δ for δ < 0″.3 and falls off as δ for δ > 1″.5. It is inferred that elements with 0″.5 < δ < 1″.6, which show no conspicuous contrast in the line wing or in the continuum, occupy as much area as the pores, and twice as much as the facular points. We suggest that the changing appearance of a facular area with increasing height of formation reflects at least as much the increasing weight of the small elements in the contrast as a real change in intrinsic properties (such as the diameter) of individual elements. A spatial resolution better than 0″.1 may be needed to resolve the individual elements in plages and the chromospheric network.