Coronal Seismology and the Propagation of Acoustic Waves Along Coronal Loops

We use a combination of analytical theory, numerical simulation, and data analysis to study the propagation of acoustic waves along coronal loops. We show that the intensity perturbation of a wave depends on a number of factors, including dissipation of the wave energy, pressure and temperature gradients in the loop atmosphere, work action between the wave and a flow, and the sensitivity properties of the observing instrument. In particular, the scale length of the intensity perturbation varies directly with the dissipation scale length (i.e., damping length) and the scale lengths of pressure, temperature, and velocity. We simulate wave propagation in three different equilibrium loop models and find that dissipation and pressure and temperature stratification are the most important effects in the low corona where the waves are most easily detected. Velocity effects are small, and cross-sectional area variations play no direct role for lines-of-sight that are normal to the loop axis. The intensity perturbation scale lengths in our simulations agree very well with the scale lengths we measure in a sample of loops observed by TRACE. The median observed value is 4.35x10^9 cm. In some cases the intensity perturbation increases with height, which is likely an indication of a temperature inversion in the loop (i.e., temperature that decreases with height). Our most important conclusion is that thermal conduction, the primary damping mechanism, is accurately described by classical transport theory. There is no need to invoke anomalous processes to explain the observations.Comment: To appear in the Dec. 1, 2004 issue of the Astrophysical Journa

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 (Antiochos & Klimchuk 1991). Using a new adaptive grid code, we simulate the complete growth of a condensation, and find that after approx. 5,000 s it reaches a quasi-steady state. We show that the size and the growth time of the condensation are in good agreement with data, and discuss the implications of the model for coronal heating and SOHO/TRACE observations.Comment: Astrophysical Journal latex file, 20 pages, 7 b-w figures (gif files

Post-flare UV light curves explained with thermal instability of loop plasma

In the present work we study the C8 flare occurred on September 26, 2000 at 19:49 UT and observed by the SOHO/SUMER spectrometer from the beginning of the impulsive phase to well beyond the disappearance in the X-rays. The emission first decayed progressively through equilibrium states until the plasma reached 2-3 MK. Then, a series of cooler lines, i.e. Ca x, Ca vii, Ne vi, O iv and Si iii (formed in the temperature range log T = 4.3 - 6.3 under equilibrium conditions), are emitted at the same time and all evolve in a similar way. Here we show that the simultaneous emission of lines with such a different formation temperature is due to thermal instability occurring in the flaring plasma as soon as it has cooled below ~ 2 MK. We can qualitatively reproduce the relative start time of the light curves of each line in the correct order with a simple (and standard) model of a single flaring loop. The agreement with the observed light curves is greatly improved, and a slower evolution of the line emission is predicted, if we assume that the model loop consists of an ensemble of subloops or strands heated at slightly different times. Our analysis can be useful for flare observations with SDO/EVE.Comment: 24 pages, 7 figures, accepted for publicatio

Self-Organization of Reconnecting Plasmas to Marginal Collisionality in the Solar Corona

We explore the suggestions by Uzdensky (2007) and Cassak et al. (2008) that coronal loops heated by magnetic reconnection should self-organize to a state of marginal collisionality. We discuss their model of coronal loop dynamics with a one-dimensional hydrodynamic calculation. We assume that many current sheets are present, with a distribution of thicknesses, but that only current sheets thinner than the ion skin depth can rapidly reconnect. This assumption naturally causes a density dependent heating rate which is actively regulated by the plasma. We report 9 numerical simulation results of coronal loop hydrodynamics in which the absolute values of the heating rates are different but their density dependences are the same. We find two regimes of behavior, depending on the amplitude of the heating rate. In the case that the amplitude of heating is below a threshold value, the loop is in stable equilibrium. Typically the upper and less dense part of coronal loop is collisionlessly heated and conductively cooled. When the amplitude of heating is above the threshold, the conductive flux to the lower atmosphere required to balance collisionless heating drives an evaporative flow which quenches fast reconnection, ultimately cooling and draining the loop until the cycle begins again. The key elements of this cycle are gravity and the density dependence of the heating function. Some additional factors are present, including pressure driven flows from the loop top, which carry a large enthalpy flux and play an important role in reducing the density. We find that on average the density of the system is close to the marginally collisionless value.Comment: accepted for publication in The Astrophysical Journal, 33 pages, 12 figure

Structure of solar coronal loops: from miniature to large-scale

We will use new data from the High-resolution Coronal Imager (Hi-C) with unprecedented spatial resolution of the solar corona to investigate the structure of coronal loops down to 0.2 arcsec. During a rocket flight Hi-C provided images of the solar corona in a wavelength band around 193 A that is dominated by emission from Fe XII showing plasma at temperatures around 1.5 MK. We analyze part of the Hi-C field-of-view to study the smallest coronal loops observed so far and search for the a possible sub-structuring of larger loops. We find tiny 1.5 MK loop-like structures that we interpret as miniature coronal loops. These have length of the coronal segment above the chromosphere of only about 1 Mm and a thickness of less than 200 km. They could be interpreted as the coronal signature of small flux tubes breaking through the photosphere with a footpoint distance corresponding to the diameter of a cell of granulation. We find loops that are longer than 50 Mm to have a diameter of about 2 arcsec or 1.5 Mm, consistent with previous observations. However, Hi-C really resolves these loops with some 20 pixels across the loop. Even at this greatly improved spatial resolution the large loops seem to have no visible sub-structure. Instead they show a smooth variation in cross-section. The fact that the large coronal loops do not show a sub-structure at the spatial scale of 0.1 arcsec per pixel implies that either the densities and temperatures are smoothly varying across these loops or poses an upper limit on the diameter of strands the loops might be composed of. We estimate that strands that compose the 2 arcsec thick loop would have to be thinner than 15 km. The miniature loops we find for the first time pose a challenge to be properly understood in terms of modeling.Comment: Accepted for publication in A&A (Jun 19, 2013), 11 pages, 10 figure

A Contemporary View of Coronal Heating

Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades the problem has been known as the coronal heating problem, but it is now clear that `coronal heating' cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult

How to use magnetic field information for coronal loop identification?

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible e.g. in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g. potential fields (current free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.Comment: 14 pages, 3 figure

Shocks and Thermal Conduction Fronts in Retracting Reconnected Flux Tubes

We present a model for plasma heating produced by time-dependent, spatially localized reconnection within a flare current sheet separating skewed magnetic fields. The reconnection creates flux tubes of new connectivity which subsequently retract at Alfv\'enic speeds from the reconnection site. Heating occurs in gas-dynamic shocks which develop inside these tubes. Here we present generalized thin flux tube equations for the dynamics of reconnected flux tubes, including pressure-driven parallel dynamics as well as temperature dependent, anisotropic viscosity and thermal conductivity. The evolution of tubes embedded in a uniform, skewed magnetic field, following reconnection in a patch, is studied through numerical solutions of these equations, for solar coronal conditions. Even though viscosity and thermal conductivity are negligible in the quiet solar corona, the strong gas-dynamic shocks generated by compressing plasma inside reconnected flux tubes generate large velocity and temperature gradients along the tube, rendering the diffusive processes dominant. They determine the thickness of the shock that evolves up to a steady-state value, although this condition may not be reached in the short times involved in a flare. For realistic solar coronal parameters, this steady-state shock thickness might be as long as the entire flux tube. For strong shocks at low Prandtl numbers, typical of the solar corona, the gas-dynamic shock consists of an isothermal sub-shock where all the compression and cooling occur, preceded by a thermal front where the temperature increases and most of the heating occurs. We estimate the length of each of these sub-regions and the speed of their propagation.Comment: 39 pages (AASTeX: 29 pages of text, 10 figures), accepted for publication in the Astrophysical Journa

Profiles of heating in turbulent coronal magnetic loops

Context: The location of coronal heating in magnetic loops has been the subject of a long-lasting controversy: does it occur mostly at the loop footpoints, at the top, is it random, or is the average profile uniform? Aims: We try to address this question in model loops with MHD turbulence and a profile of density and/or magnetic field along the loop. Methods: We use the ShellAtm MHD turbulent heating model described in Buchlin & Velli (2006), with a static mass density stratification obtained by the HydRad model (Bradshaw & Mason 2003). This assumes the absence of any flow or heat conduction subsequent to the dynamic heating. Results: The average profile of heating is quasi-uniform, unless there is an expansion of the flux tube (non-uniform axial magnetic field) or the variation of the kinetic and magnetic diffusion coefficients with temperature is taken into account: in the first case the heating is enhanced at footpoints, whereas in the second case it is enhanced where the dominant diffusion coefficient is enhanced. Conclusions: These simulations shed light on the consequences on heating profiles of the complex interactions between physical effects involved in a non-uniform turbulent coronal loop.Comment: 9 pages, 8 figure