J. T. Karpen

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.

Constraints on Active Region Coronal Heating

We derive constraints on the time variability of coronal heating from observations of the so-called active region moss by the Transition Region and Coronal Explorer (TRACE). The moss is believed to be due to million-degree emission from the transition regions at the footpoints of coronal loops whose maximum temperatures are several million degrees. The two key results from the TRACE observations discussed in this paper are that in the moss regions one generally sees only moss, not million-degree loops, and that the moss emission exhibits only weak intensity variations, � 10% over periods of hours. TRACE movies showing these results are presented. We demonstrate, using both analytic and numerical calculations, that the lack of observable million-degree loops in the moss regions places severe constraints on the possible time variability of coronal heating in the loops overlying the moss. In particular, the heating in the hot moss loops cannot be truly flarelike with a sharp cutoff, but instead must be quasi-steady to an excellent approximation. Furthermore, the lack of significant variations in the moss intensity implies that the heating magnitude is only weakly varying. The implications of these conclusions for coronal heating models will be discussed. Subject headings: Sun: corona — Sun: transition region — Sun: UV radiation On-line material: mpg animation

Structure and Dynamics of the Sun’s Open Magnetic Field

The solar magnetic field is the primary agent that drives solar activity and couples the Sun to the heliosphere. Although the details of this coupling depend on the quantitative properties of the field, many important aspects of the corona-solar wind connection can be understood by considering only the general topological properties of those regions on the Sun where the field extends from the photosphere out to interplanetary space, the so-called open field regions that are usually observed as coronal holes. From the simple assumptions that underlie the standard quasi-steady corona-wind theoretical models, and that are likely to hold for the Sun as well, we derive two conjectures as to the possible structure and dynamics of coronal holes: (1) coronal holes are unique in that every unipolar region on the photosphere can contain at most one coronal hole, and (2) coronal holes of nested polarity regions must themselves be nested. Magnetic reconnection plays the central role in enforcing these constraints on the field topology. From these conjectures we derive additional properties for the topology of open field regions, and propose several observational predictions for both the slowly varying and transient corona/solar wind.

A Transient Heating Model for Coronal Structure and Dynamics

A wealth of observational evidence for flows and intensity variations in nonflaring coronal loops leads to the conclusion that coronal heating is intrinsically unsteady and concentrated near the chromosphere. We have investigated the hydrodynamic behavior of coronal loops undergoing transient heating with one-dimensional numerical simulations in which the timescale assumed for the heating variations (3000 s) is comparable to the coronal radiative cooling time and the assumed heating location and scale height (10 Mm) are consistent with the values derived from TRACE studies. The model loops represent typical active region loops: 40-80 Mm in length, reaching peak temperatures up to 6 MK. We use ARGOS, our state-of-the-art numerical code with adaptive mesh refinement, in order to resolve adequately the dynamic chromospheric-coronal transition region sections of the loop. The major new results from our work are the following: (1) During much of the cooling phase, the loops exhibit densities significantly larger than those predicted by the well-known loop scaling laws, thus potentially explaining recent TRACE observations of overdense loops. (2) Throughout the transient heating interval, downflows appear in the lower transition region (T ~ 0.1 MK) whose key signature would be persistent, redshifted UV and EUV line emission, as have long been observed. (3) Strongly unequal heating in the two legs of the loop drives siphon flows from the more strongly heated footpoint to the other end, thus explaining the substantial bulk flows in loops recently observed by the Coronal Diagnostic Spectrometer and the Solar Ultraviolet Measurement of Emission Radiation instrument. We discuss the implications of our studies for the physical origins of coronal heating and related dynamic phenomena.

Dynamic Responses to Magnetic Reconnection in Solar Arcades

We present a numerical simulation of the interaction between two line dipoles through magnetic reconnection in the lower solar atmosphere, a process believed to be the origin of many manifestations of solar activity. This work differs from previous studies in that the field is sheared asymmetrically and that the dipoles have markedly unequal field strengths. This calculation already yielded one key discovery, denoted reconnection driven current filamentation, as described in a previous Astrophysical Journal letter. In this paper we focus on the chromospheric and coronal dynamics resulting from the shear-driven reconnection of unequal dipoles, discuss the important implications for chromospheric eruptions, compare our calculation with high-resolution Normal Incidence X-Ray Telescope observations of a surge, and contrast our results with the predictions of fast reconnection models.

Condensation Formation by Impulsive Heating in Prominences

Our thermal nonequilibrium model for prominence formation provides an explanation for the well-observed presence of predominantly dynamic, cool, dense material suspended in the corona above filament channels. According to this model, condensations form readily along long, low-lying magnetic field lines when heating is localized near the chromosphere. Often this process yields a dynamic cycle in which condensations repeatedly form, stream along the field, and ultimately disappear by falling onto the nearest footpoint. Our previous studies employed only steady heating, as is consistent with some coronal observations, but many coronal heating models predict transient episodes of localized energy release (e.g., nanoflares). Here we present the results of a numerical investigation of impulsive heating in a model prominence flux tube and compare the outcome with previous steady-heating simulations. We find that condensations form readily when the average interval between heating events is less than the coronal radiative cooling time (~2000 s). As the average interval between pulses decreases, the plasma evolution more closely resembles the steady-heating case. The heating scale and presence or absence of background heating also determine whether or not condensations form and how they evolve. Our results place important constraints on coronal heating in filament channels and strengthen the case for thermal nonequilibrium as the process responsible for the plasma structure in prominences.

Constraints on the Magnetic Field Geometry in Prominences

This paper discusses constraints on the magnetic field geometry of solar prominences derived from one-dimensional modeling and analytic theory of the formation and support of cool coronal condensations. In earlier numerical studies we identified a mechanism—thermal nonequilibrium—by which cool condensations can form on field lines heated at their footpoints. We also identified a broad range of field line shapes that can support condensations with the observed sizes and lifetimes: shallowly dipped to moderately arched field lines longer than several times the heating scale. Here we demonstrate that condensations formed on deeply dipped field lines, as would occur in all but the near-axial regions of twisted flux ropes, behave significantly differently than those on shallowly dipped field lines. Our modeling results yield a crucial observational test capable of discriminating between two competing scenarios for prominence magnetic field structure: the flux rope and sheared-arcade models.

Prominence Formation by Thermal Nonequilibrium in the Sheared-Arcade Model

The existence of solar prominences—cool, dense, filamented plasma suspended in the corona above magnetic neutral lines—has long been an outstanding problem in solar physics. In earlier numerical studies we identified a mechanism, thermal nonequilibrium, by which cool condensations can form in long coronal flux tubes heated locally above their footpoints. To understand the physics of this process, we began by modeling idealized symmetric flux tubes with uniform cross-sectional area and a simplified radiative-loss function. The present work demonstrates that condensations also form under more realistic conditions, in a typical flux tube taken from our three-dimensional MHD simulation of prominence magnetic structure produced by the sheared arcade mechanism. We compare these results with simulations of an otherwise identical flux tube with uniform cross-sectional area, to determine the influence of the overall three-dimensional magnetic configuration on the condensation process. We also show that updating the optically thin radiative loss function yields more rapidly varying, dynamic behavior in better agreement with the latest prominence observations than our earlier studies. These developments bring us substantially closer to a fully self-consistent, three-dimensional model of both magnetic field and plasma in prominences.

CORONAL MAGNETIC FIELD RELAXATION BY NULL-POINT RECONNECTION

We derive the minimum energy state resulting from complete magnetic reconnection in a translationally or axisymmetric MHD system, in the limit of a low plasma beta and high magnetic Reynolds number—conditions appropriate to the solar corona. The results are necessary for determining the amount of energy that can be liberated by reconnection and, hence, are important for understanding coronal heating and other forms of solar activity. The key difference between our approach and previous work is that because of line tying at the high-beta photosphere, reconnection is limited to occur only at magnetic null points initially present in the system. We find that under these circumstances the minimum energy state is not the usual linear force-free field but a state in which the nonpotential component of the field is distributed uniformly on equal flux surfaces. We discuss the implications of our results for the Suns corona and for laboratory plasmas.

A Transient Heating Model for the Structure and Dynamics of the Solar Transition Region

Understanding the structure and dynamics of the Suns transition region has been a major challenge to scientists since the Skylab era. In particular, the characteristic shape of the emission measure distribution and the Doppler shifts observed in EUV emission lines have thus far resisted all theoretical and modeling efforts to explain their origin. Recent observational advances have revealed a wealth of dynamic fine-scale structure at transition-region temperatures, validating earlier theories about the existence of such cool structure and explaining in part why static models focusing solely on hot, large-scale loops could not match observed conditions. In response to this newly confirmed picture, we have investigated numerically the hydrodynamic behavior of small, cool magnetic loops undergoing transient heating spatially localized near the chromospheric footpoints. For the first time we have successfully reproduced both the observed emission measure distribution over the entire range log T = 4.7-6.1 and the observed temperature dependence of the persistent redshifts. The closest agreement between simulations and observations is obtained with heating timescales of the order of 20 s every 100 s, a length scale of the order of 1 Mm, and energy deposition within the typical range of nanoflares. We conclude that small, cool structures can indeed produce most of the quiet solar EUV output at temperatures below 1 MK.