Charles C. Kankelborg

Time Variability of the “Quiet” Sun Observed with TRACE. II. Physical Parameters, Temperature Evolution, and Energetics of Extreme-Ultraviolet Nanoflares

We present a detailed analysis of the geometric and physical parameters of 281 EUV nanoflares, simultaneously detected with the TRACE telescope in the 171 and 195 A wavelengths. The detection and discrimination of these flarelike events is detailed in the first paper in this series. We determine the loop length l, loop width w, emission measure EM, the evolution of the electron density ne(t) and temperature Te(t), the flare decay time τdecay, and calculate the radiative loss time τloss, the conductive loss time τcond, and the thermal energy Eth. The findings are as follows: (1) EUV nanoflares in the energy range of 1024-1026 ergs represent miniature versions of larger flares observed in soft X-rays (SXR) and hard X-rays (HXR), scaled to lower temperatures (Te 2 MK), lower densities (ne 109 cm-3), and somewhat smaller spatial scales (l ≈ 2-20 Mm). (2) The cooling time τdecay is compatible with the radiative cooling time τrad, but the conductive cooling timescale τcond is about an order of magnitude shorter, suggesting repetitive heating cycles in time intervals of a few minutes. (3) The frequency distribution of thermal energies of EUV nanoflares, N(E) ≈ 10-46(E/1024)-1.8 (s-1 cm-2 ergs-1) matches that of SXR microflares in the energy range of 1026-1029, and exceeds that of nonthermal energies of larger flares observed in HXR by a factor of 3-10 (in the energy range of 1029-1032 ergs). Discrepancies of the power-law slope with other studies, which report higher values in the range of a = 2.0-2.6 (Krucker & Benz; Parnell & Jupp), are attributed to methodical differences in the detection and discrimination of EUV microflares, as well as to different model assumptions in the calculation of the electron density. Besides the insufficient power of nanoflares to heat the corona, we find also other physical limits for nanoflares at energies 1024 ergs, such as the area coverage limit, the heating temperature limit, the lower coronal density limit, and the chromospheric loop height limit. Based on these quantitative physical limitations, it appears that coronal heating requires other energy carriers that are not luminous in EUV, SXR, and HXR.

The Relationship Between X-Ray Radiance and Magnetic Flux

We use soft X-ray and magnetic field observations of the Sun (quiet Sun, X-ray bright points, active regions, and integrated solar disk) and active stars (dwarf and pre-main-sequence) to study the relationship between total unsigned magnetic flux, � , and X-ray spectral radiance, LX. We find thatand LX exhibit a very nearly linear relationship over 12 orders of magnitude, albeit with significant levels of scatter. This suggests a universal relationship between magnetic flux and the power dissipated through coronal heating. If the relationship can be assumed linear, it is consistent with an average volumetric heating rate � Q � �=L, where � B is the average field strength along a closed field line and L is its length between footpoints. The �- LX relationship also indicates that X-rays provide a useful proxy for the magnetic flux on stars when magnetic measurements are unavailable. Subject headings: stars: coronae — stars: magnetic fields — Sun: corona — Sun: magnetic fields — Sun: X-rays, gamma rays

A new view of the solar corona from the transition region and coronal explorer (TRACE)

The TRACE Observatory is the first solar-observing satellite in the National Aeronautics and Space Administration’s (NASA) Small Explorer series. Launched April 2, 1998, it is providing views of the solar transition region and low corona with unprecedented spatial and temporal resolution. The corona is now seen to be highly filamented, and filled with flows and other dynamic processes. Structure is seen down to the resolution limit of the instrument, while variability and motions are observed at all spatial locations in the solar atmosphere, and on very short time scales. Flares and shock waves are observed, and the formation of long-lived coronal structures, with consequent implications for coronal heating models, has been seen. This overview describes the instrument and presents some preliminary results from the first six months of operation.

Prevalence of small-scale jets from the networks of the solar transition region and chromosphere

As the interface between the Sun’s photosphere and corona, the chromosphere and transition region play a key role in the formation and acceleration of the solar wind. Observations from the Interface Region Imaging Spectrograph reveal the prevalence of intermittent small-scale jets with speeds of 80 to 250 kilometers per second from the narrow bright network lanes of this interface region. These jets have lifetimes of 20 to 80 seconds and widths of ≤300 kilometers. They originate from small-scale bright regions, often preceded by footpoint brightenings and accompanied by transverse waves with amplitudes of ~20 kilometers per second. Many jets reach temperatures of at least ~105 kelvin and constitute an important element of the transition region structures. They are likely an intermittent but persistent source of mass and energy for the solar wind.

Hot explosions in the cool atmosphere of the Sun

The solar atmosphere was traditionally represented with a simple one-dimensional model. Over the past few decades, this paradigm shifted for the chromosphere and corona that constitute the outer atmosphere, which is now considered a dynamic structured envelope. Recent observations by the Interface Region Imaging Spectrograph (IRIS) reveal that it is difficult to determine what is up and down, even in the cool 6000-kelvin photosphere just above the solar surface: This region hosts pockets of hot plasma transiently heated to almost 100,000 kelvin. The energy to heat and accelerate the plasma requires a considerable fraction of the energy from flares, the largest solar disruptions. These IRIS observations not only confirm that the photosphere is more complex than conventionally thought, but also provide insight into the energy conversion in the process of magnetic reconnection.

On the prevalence of small-scale twist in the solar chromosphere and transition region

The solar chromosphere and transition region (TR) form an interface between the Sun’s surface and its hot outer atmosphere. There, most of the nonthermal energy that powers the solar atmosphere is transformed into heat, although the detailed mechanism remains elusive. High-resolution (0.33–arc second) observations with NASA’s Interface Region Imaging Spectrograph (IRIS) reveal a chromosphere and TR that are replete with twist or torsional motions on sub–arc second scales, occurring in active regions, quiet Sun regions, and coronal holes alike. We coordinated observations with the Swedish 1-meter Solar Telescope (SST) to quantify these twisting motions and their association with rapid heating to at least TR temperatures. This view of the interface region provides insight into what heats the low solar atmosphere.

Evidence of Separator Reconnection in a Survey of X-Ray Bright Points

X-ray bright points are among the simplest coronal structures hypothesized to be powered by magnetic reconnection. Their magnetic field appears to consist of a simple loop of field lines connecting positive to negative photospheric sources. Quantitative three-dimensional models of reconnection in this geometry are therefore expected to apply directly to X-ray bright points. We assemble a survey from archival Solar and Heliospheric Observatory data of 764 X-ray bright points (EUV Imaging Telescope) along with their associated photospheric magnetic fields (Solar Oscillation Imager/Michelson Doppler Imager). Measurements are made of each quantity relevant to the simple three-dimensional reconnection model. These data support several predictions of a magnetic reconnection model providing further evidence in favor of the hypothesis that magnetic reconnection supplies heating power to the quiet solar corona.

The Unresolved Fine Structure Resolved: IRIS Observations of the Solar Transition Region

The heating of the outer solar atmospheric layers, i.e., the transition region and corona, to high temperatures is a long-standing problem in solar (and stellar) physics. Solutions have been hampered by an incomplete understanding of the magnetically controlled structure of these regions. The high spatial and temporal resolution observations with the Interface Region Imaging Spectrograph (IRIS) at the solar limb reveal a plethora of short, low-lying loops or loop segments at transition-region temperatures that vary rapidly, on the time scales of minutes. We argue that the existence of these loops solves a long-standing observational mystery. At the same time, based on comparison with numerical models, this detection sheds light on a critical piece of the coronal heating puzzle.The heating of the outer solar atmospheric layers, i.e., the transition region and corona, to high temperatures is a long-standing problem in solar (and stellar) physics. Solutions have been hampered by an incomplete understanding of the magnetically controlled structure of these regions. The high spatial and temporal resolution observations with the Interface Region Imaging Spectrograph (IRIS) at the solar limb reveal a plethora of short, low-lying loops or loop segments at transition-region temperatures that vary rapidly, on the time scales of minutes. We argue that the existence of these loops solves a long-standing observational mystery. At the same time, based on comparison with numerical models, this detection sheds light on a critical piece of the coronal heating puzzle.

Coronal Heating by Collision and Cancellation of Magnetic Elements

A model is proposed for the coronal response to the interaction between randomly moving photospheric magnetic flux elements. In this model the collision between two elements of opposing signs results in reconnection and the appearance of an X-ray bright point. A section of quiet Sun on which elements are distributed and moving randomly will contain a number of X-ray bright points. The model combines a distribution of element sizes, random velocities of the elements, and a model for pair-wise collisions. This results in quantitative predictions for surface density of X-ray bright points, the distribution of their luminosities, and their contribution to the total heat flux in the quiet Sun. The predictions depend principally on the densities of flux elements of each sign + and -, the average element size , and the random velocity v0. The predicted heat flux, FXBP = 0.1 + -v0, is in rough agreement with published observational studies of X-ray bright points but well below the flux required to supply heat to the quiet Sun corona. Other predictions of the model are similarly consistent with published studies.

Fast Differential Emission Measure Inversion of Solar Coronal Data

We present a fast method for reconstructing differential emission measures (DEMs) using solar coronal data. The method consists of a fast, simple regularized inversion in conjunction with an iteration scheme for removal of residual negative emission measure. On average, it computes over 1000 DEMs s{sup -1} for a sample active region observed by the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory, and achieves reduced chi-squared of order unity with no negative emission in all but a few test cases. The high performance of this method is especially relevant in the context of AIA, which images of order one million solar pixels per second. This paper describes the method, analyzes its fidelity, compares its performance and results with other DEM methods, and applies it to an active region and loop observed by AIA and by the Extreme-ultraviolet Imaging Spectrometer on Hinode.