On the inability of magnetically constricted transition regions to account for the 105 to 106 K plasma in the quiet solar atmosphere

Abstract

Although ‘back conduction’ from the corona has been shown to be inadequate for powering EUV emission below T ≈ 2 × 105 K, it is thought to be adequate in the temperature range 2 × 105 K < T < 106 K. No models to date, however, have included the large magnetic constriction which should occur in the legs of coronal loops where conductive ‘transition regions’, hitherto thought to contain the bulk of the plasma in this higher temperature range, are located. On the basis of fine scale magnetograms, Dowdy et al. (1986) have estimated that these magnetic flux tubes are constricted from end to end by an areal factor of approximately 100. Furthermore, on the basis of simple steady-state conductive models, Dowdy et al. (1985) have shown that the large constriction can inhibit the conductive flow of heat by an order of magnitude. We are thus led to re-examine static models of this region of the atmosphere which incorporate not only conduction and radiation but also the effects of large magnetic constrictions. We find that the structure of this plasma depends not only on the magnitude of the constriction but also on the tube's shape. Our results show that no model with a constriction of order 100 can simultaneously (a) produce the variation of differential emission measure with temperature derived from measured line intensities and (b) satisfy the observed constraint (Reeves, 1976) that EUV emission from below T ≈ 7 × 105 K be confined to the supergranular network, covering no more than 0.45 of the solar surface. The failure of the models suggests that the bulk of the 105–106 K plasma in the quiet solar atmosphere is not in ‘transition region’ structures, but is instead magnetically isolated from the corona and heated internally. Even though the ‘transition region’ component of 105–106 K plasma in the legs of coronal loops should exist, it comprises only a small fraction of the total 105–106 K plasma and, hence, produces only a small fraction of the observed EUV emission from this temperature range. We also find that for any permitted tube shape, constriction factors of order 100 reduce the coronal conductive energy losses to the transition region to a value which is less than a third of the value for an unconstricted field, i.e., to less than 2 × 105 erg cm −2 s −1. In particular, if the magnetic geometry of the upper transition region is extremely concave (i.e., ‘horn’-shaped geometry with most of the areal divergence near the hot end), then a constriction of order 100 results in a conductive loss of less than 1 × 104 erg cm−2 s−1 and, hence, much less than the coronal radiative energy loss. For such geometries, the constriction in the magnetic field hence provides an effective thermal insulation of the corona from the cooler parts of the solar atmosphere.