Constant cross section of loops in the solar corona

Abstract

Context. The corona of the Sun is dominated by emission from loop-like structures. When observed in X-ray or extreme ultraviolet emission, these million K hot coronal loops show a more or less constant cross section. Aims. In this study we show how the interplay of heating, radiative cooling, and heat conduction in an expanding magnetic structure can explain the observed constant cross section. Methods. We employ a three-dimensional magnetohydrodynamics (3D MHD) model of the corona. The heating of the coronal plasma is the result of braiding of the magnetic field lines through footpoint motions and subsequent dissipation of the induced currents. From the model we synthesize the coronal emission, which is directly comparable to observations from, e.g., the Atmospheric Imaging Assembly on the Solar Dynamics Observatory (AIA/SDO). Results. We find that the synthesized observation of a coronal loop seen in the 3D data cube does match actually observed loops in count rate and that the cross section is roughly constant, as observed. The magnetic field in the loop is expanding and the plasma density is concentrated in this expanding loop; however, the temperature is not constant perpendicular to the plasma loop. The higher temperature in the upper outer parts of the loop is so high that this part of the loop is outside the contribution function of the respective emission line(s). In effect, the upper part of the plasma loop is not bright and thus the loop actually seen in coronal emission appears to have a constant width. Conclusions. From this we can conclude that the underlying field-line-braiding heating mechanism provides the proper spatial and temporal distribution of the energy input into the corona -at least on the observable scales.

What can large-scale magnetohydrodynamic numerical experiments tell us about coronal heating?

“…Loops in the model match observations in terms of diameter, or cross section [68,102]. In general, loop structures found in observations, such as thin or thick loops at constant cross section, or expanding envelopes of several thin loops, are also seen in the three-dimensional MHD models [103].…”

“…The loop in a particular EUV band reflects only a small range in temperature, so that a very high temperature at the top of an expanding magnetic tube will effectively cut off the top part and thus lead to a loop that looks like it has a constant cross section [102]. This scenario is also found with loops in a more dynamic situation of a model of an emerging active region [68].…”

“…The current models also produce EUV loops with roughly the correct width of about 2 Mm [68,102]. At this point, it is not yet clear if these models have a sufficient spatial resolution and a small enough (numeric) magnetic resistivity for solid conclusions.…”

The magnetic field in the solar atmosphere

“…Using TRACE 171 Å observations, already Zhang et al (1999) had found that the width of the emission associated to fibrils was nearly the same at different heights: at their photospheric root as well as ≈30 Mm higher up in the atmosphere. It was speculated as a possible explanation that, either the observed emission might not be sensitive to the detection of the desired canopy structure-as recently supported by Peter and Bingert (2012), see Sect. 1.4.2 for details-or that network fields in the QS could, by some mechanism, be prevented from fanning out (Zhang 2005).…”

“…Peter and Bingert (2012) used an MHD model to investigate the temporal evolution of the corresponding synthesized coronal emission. They were able to show how emission of seemingly constant width may arise from an expanding flux tube.…”