J. A. Klimchuk

A model for solar coronal mass ejections

We propose a new model for the initiation of a solar coronal mass ejection (CME). The model agrees with two properties of CMEs and eruptive flares that have proved to be very difficult to explain with previous models: (1) very low-lying magnetic field lines, down to the photospheric neutral line, can open toward infinity during an eruption; and (2) the eruption is driven solely by magnetic free energy stored in a closed, sheared arcade. Consequently, the magnetic energy of the closed state is well above that of the posteruption open state. The key new feature of our model is that CMEs occur in multipolar topologies in which reconnection between a sheared arcade and neighboring flux systems triggers the eruption. In this magnetic breakout model, reconnection removes the unsheared field above the low-lying, sheared core flux near the neutral line, thereby allowing this core flux to burst open. We present numerical simulations that demonstrate our model can account for the energy requirements for CMEs. We discuss the implication of the model for CME/flare prediction.

Three-dimensional Stereoscopic Analysis of Solar Active Region Loops. I. SOHO/EIT Observations at Temperatures of (1.0-1.5) × 106 K

The three-dimensional structure of solar active region NOAA 7986 observed on 1996 August 30 with the Extreme-Ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory (SOHO) is analyzed. We develop a new method of dynamic stereoscopy to reconstruct the three-dimensional geometry of dynamically changing loops, which allows us to determine the orientation of the mean loop plane with respect to the line of sight, a prerequisite to correct properly for projection effects in three-dimensional loop models. With this method and the filter-ratio technique applied to EIT 171 and 195 A images we determine the three-dimensional coordinates [x(s), y(s), z(s)], the loop width w(s), the electron density ne(s), and the electron temperature Te(s) as a function of the loop length s for 30 loop segments. Fitting the loop densities with an exponential density model ne(h) we find that the mean of inferred scale height temperatures, Tλe=1.22 ± 0.23 MK, matches closely that of EIT filter-ratio temperatures, TEITe=1.21 ± 0.06 MK. We conclude that these cool and rather large-scale loops (with heights of h≈30-225 Mm) are in hydrostatic equilibrium. Most of the loops show no significant thickness variation w(s), but we measure for most of them a positive temperature gradient (dT/ds>0) across the first scale height above the footpoint. Based on these temperature gradients we find that the conductive loss rate is about 2 orders of magnitude smaller than the radiative loss rate, which is in strong contrast to hot active region loops seen in soft X-rays. We infer a mean radiative loss time of τrad≈40 minutes at the loop base. Because thermal conduction is negligible in these cool EUV loops, they are not in steady state, and radiative loss has entirely to be balanced by the heating function. A statistical heating model with recurrent heating events distributed along the entire loop can explain the observed temperature gradients if the mean recurrence time is 10 minutes. We computed also a potential field model (from SOHO/MDI magnetograms) and found a reasonable match with the traced EIT loops. With the magnetic field model we determined also the height dependence of the magnetic field B(h), the plasma parameter β(h), and the Alfven velocity vA(h). No correlation was found between the heating rate requirement EH0 and the magnetic field Bfoot at the loop footpoints.

The magnetic field of solar prominences

A model is presented which accounts for the formation of coronal magnetic field lines with the appropriate dipped structure to support prominences. The critical ingredients of the model are that the prominence magnetic field is a truly three-dimensional structure with significant variation along the prominence length, and the magnetic field is strongly sheared near the photospheric neutral line. Numerical calculations are presented which demonstrate that these two features lead to dip formation. In addition our model is able to account for the long-puzzling observation of inverse polarity in quiescent prominences.

The Dynamic Formation of Prominence Condensations

We present simulations of a model for the formation of a prominence condensation in a coronal loop. The key idea behind the model is that the spatial localization of loop heating near the chromosphere leads to a catastrophic cooling in the corona. Using a new adaptive grid code, we simulate the complete growth of a condensation and find that after ~5000 s it reaches a quasi-steady state. We show that the size and growth time of the condensation are in good agreement with data and discuss the implications of the model for coronal heating and for observations of prominences and the surrounding corona.

Nonthermal Spectral Line Broadening and the Nanoflare Model

A number of theoretical and observational considerations suggest that coronal loops are bundles of unresolved, impulsively heated strands. This ‘‘nanoflare’’ model, as it is sometimes called, predicts high-speed evaporative upflows, which might be revealed as nonthermal broadening of spectral line profiles. We have therefore generated synthetic line profile observations based on one-dimensional hydrodynamic simulations for comparison with actual observations. The predicted profiles for Ne viii (770.4 8), a transition region line, and Mg x (624.9 8), a warm coronal line, have modest broadening that agrees well with existingobservations. The predicted profiles for Fexvii(254.87 8), a hot line that will be observed by the Extreme Ultraviolet Imaging Spectrometer (EIS) on the Solar-B mission, are somewhat broader and are also consistent with the limited number of hot line observations that are currently available. Moreover, depending on the properties of the assumed nanoflare and other parameters of the simulation, the Fe xvii profile can have distinctive enhancements in the line wing. This indicates a powerful diagnostic capability that can be exploited once Solar-B is launched. Subject headingg hydrodynamics — Sun: corona Online material: color figures

Three-dimensional Stereoscopic Analysis of Solar Active Region Loops. II. SOHO/EIT Observations at Temperatures of 1.5-2.5 MK

In this paper we study the three-dimensional structure of hot MK) loops in solar active (T e B 1.5¨2.5 region NOAA 7986, observed on 1996 August 30 with the Extreme-ultraviolet Imaging Telescope (EIT ) on board the Solar and Heliospheric Observatory (SOHO). This complements a —rst study (Paper I) on cooler MK) loops of the same active region, using the same method of Dynamic Stereo- (T e B 1.0¨1.5 scopy to reconstruct the three-dimensional geometry. We reconstruct the three-dimensional coordinates x(s), y(s), z(s), the density and temperature pro—le of 35 individual loop segments (as a function n e (s), T e (s) of the loop coordinate s) using EIT 195 and 284 images. The major —ndings are as follows. (1) All Ae loops are found to be in hydrostatic equilibrium, in the entire temperature regime of MK. T e 1.0¨2.5 (2) The analyzed loops have a height of 2¨3 scale heights, and thus only segments extending over about one vertical scale height have sufficient emission measure contrast for detection. (3) The temperature gra- dient over the lowest scale height is of order dT /ds B 1¨ 10 Kk m~1. (4) The radiative loss rate is found to exceed the conductive loss rate by about two orders or magnitude in the coronal loop segments, implying that the loops cannot be in quasi-static equilibrium, since standard steady-state loop models show that radiative and conductive losses are comparable. (5) A steady state could only be maintained if the heating rate matches exactly the radiative loss rate in hydrostatic equilibrium, requiring a heat E H deposition length of the half density scale height j. (6) We —nd a correlation of p P L~1 between loop j H base pressure and loop length, which is not consistent with the scaling law predicted from steady-state models of large-scale loops. All observational —ndings indicate consistently that the energy balance of the observed EUV loops cannot be described by steady-state models. Subject headings: Sun: activitySun: coronaSun: magnetic —eldsSun: UV radiation ¨ techniques: image processing

The Origin of High-Speed Motions and Threads in Prominences

Prominences are among the most spectacular manifestations of both quiescent and eruptive solar activity, yet the origins of their magnetic-field and plasma structures remain poorly understood. We have made steady progress toward a comprehensive model of prominence formation and evolution with our sheared three-dimensional arcade model for the magnetic field and our thermal nonequilibrium model for the cool, dense material suspended in the corona. According to the thermal nonequilibrium model, condensations form readily along long, low-lying magnetic field lines when the heating is localized near the chromosphere. In most cases this process yields a dynamic cycle in which condensations repetitively form, stream along the field, and ultimately disappear by falling onto the nearest footpoint. Two key observed features were not adequately explained by our earlier simulations of thermal nonequilibrium, however: the threadlike (i.e., elongated) horizontal structure and high-speed motions of many condensations. In this paper we discuss how simple modifications to the radiative loss function, the heating scale, and the geometry of our model largely eliminate these discrepancies. In particular, condensations in nearly horizontal flux tubes are most likely to develop both transient high-speed motions and elongated threads. These results strengthen the case for thermal nonequilibrium as the origin of prominence condensations and support low-twist models of prominence magnetic structure.

Spectroscopic Diagnostics of Nanoflare-heated Loops

To evaluate the usefulness of spectroscopic techniques for diagnosing realistic solar plasmas and to better understand the physical origin of coronal heating, we have simulated observations of model coronal loops that are heated randomly and impulsively by nanoflares. We find that the emission measures, densities, and filling factors that are inferred from spectral line intensities (EMs, ns, and s, respectively) are generally an excellent representation of the properties of the nanoflare-heated plasma. To better than 25% in most cases, EMs indicates the amount of material present in the ? log T = 0.3 temperature interval centered on the peak of the line contribution function, ns indicates the average density of this material, and s indicates the fraction of the total volume that the material occupies. Measurements with lithium-like lines are much less accurate, however. We provide diagnostic values and line intensities for many different spectral lines that can be compared directly with observations from the Coronal Diagnostic Spectrometer and Solar Ultraviolet Measurements of Emitted Radiation instruments on SOHO and from the future Extreme Ultraviolet Imaging Spectrometer instrument on Solar-B. Such comparisons will provide the first ever rigorous test of the nanoflare concept, which has enormous implications for understanding the mechanism of coronal heating.

A Self-consistent Model for the Resonant Heating of Coronal Loops: The Effects of Coupling with the Chromosphere

We present the first model of resonant heating of coronal loops that incorporates the dependence of the loop density on the heating rate. By adopting the quasi-static equilibrium scaling law ρ ∝ Q5/7, where ρ is the density and Q is the volumetric heating rate, we are able to approximate the well-known phenomena of chromospheric evaporation and chromospheric condensation, which regulate the coronal density. We combine this scaling law with a quasi-nonlinear MHD model for the resonant absorption of Alfven waves in order to study the spatial and temporal dependence of the heating. We find that the heating is concentrated in multiple resonance layers, rather than in the single layer of previous models, and that these layers drift throughout the loop to heat the entire volume. These newfound properties are in much better agreement with coronal observations.

An Explanation for the “Switch-On” Nature of Magnetic Energy Release and Its Application to Coronal Heating

A large class of coronal heating theories postulate that the random mixing of magnetic footpoints by photospheric motions leads to the formation of current sheets in the corona and, consequently, to energy release there via magnetic reconnection. Parker pointed out that in order for this process to supply the observed energy flux into the corona, the stress in the coronal magnetic field must have a fairly specific value at the time that the energy is released. In particular, he argued that the misalignment between reconnecting flux tubes must be roughly 30° in order to match the observed heating. No physical origin for this number was given, however. In this paper we propose that secondary instability is the mechanism that switches on the energy release when the misalignment angle in the corona reaches the correct value. We calculate both the three-dimensional linear and fully nonlinear development of the instability in current sheets corresponding to various misalignment angles. We find that no secondary instability occurs for angles less than about 45°, but for larger angles the instability grows at a rapid rate, and there is an explosive release of energy. We compare our results with the observed properties of the corona and discuss the implications for future observations.