One way of revealing the nature of the coronal heating mechanism is by comparing simple theoretical one dimensional hydrostatic loop models with observations at the temperature and/or density structure along these features. The most well-known method for dealing with comparisons like that is the $χ^2$ approach. In this paper we consider the restrictions imposed by this approach and present an alternative way for making model comparisons using Bayesian statistics. In order to quantify our beliefs we use Bayes factors and information criteria such as AIC and BIC. Three simulated datasets are analyzed in order to validate the procedure and assess the effects of varying error bar size. Another two datasets (Ugarte-Urra et al., 2005; Priest et al., 2000) are re-analyzed using the method described above. In one of these two datasets (Ugarte-Urra et al., 2005), due to the error estimates in the observed temperature values, it is not posible to distinguish between the different heating mechanisms. For this we suggest that both Classical and Bayesian statistics should be applied in order to make safe assumptions about the nature of the coronal heating mechanisms.
This article assesses the current state of understanding of coronal heating, outlines the key elements of a comprehensive strategy for solving the problem, and warns of obstacles that must be overcome along the way.
Context : We present a self-consistent model of solar coronal heating, originally developed by Heyvaert & Priest (1992), in which we include the dynamical effect of the background magnetic field along a coronal structure by using exact results from wave MHD turbulence (Galtier et al. 2000). Aims : We evaluate the heating rate and the microturbulent velocity for comparison with observations in the quiet corona, active regions and also coronal holes. Methods :The coronal structures are assumed to be in a turbulent state maintained by the slow erratic motions of the magnetic footpoints. A descrip…
I present a novel view on the problem of solar coronal heating. In my picture, coronal heating should be viewed as a self-regulating process that works to keep the coronal plasma marginally collisionless. The self-regulating mechanism is based on the interplay between two effects: (1) Plasma density controls coronal energy release via the transition between the slow collisional Sweet-Parker regime and the fast collisionless reconnection regime; (2) In turn, coronal energy release through reconnection leads to an increase in the ambient plasma density via chromospheric evaporation, which tempor…
We point out the priority of our paper (Mahajan et al. 2001, Phys. Plasmas, 8, 1340) over (Aschwanden et al. 2007, Astrophys J., 659, 1673) in introducing the term "Formation and primary heating of the solar corona" working out explicit models (theory as well as simulation) for coronal structure formation and heating. On analyzing the Aschwanden et al. (2007) scenario of coronal heating process (shifted to the chromospheric heating) we stress, that for efficient loop formation, the primary upflows of plasma in chromosphere/transition region should be relatively cold and fast (as opposed to hot…
The heating of the lower solar corona is examined using numerical simulations and theoretical models of magnetohydrodynamic turbulence in open magnetic regions. A turbulent energy cascade to small length scales perpendicular to the mean magnetic field can be sustained by driving with low-frequency Alfven waves reflected from mean density and magnetic field gradients. This mechanism deposits energy efficiently in the lower corona, and we show that the spatial distribution of the heating is determined by the mean density through the Alfven speed profile. This provides a robust heating mechanism …
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 s…
The bulk of solar coronal radiative loss consists of soft X-ray emission from quasi-static loops at the cores of Active Regions. In order to develop diagnostics for determining the heating mechanism of these loops from observations by coronal imaging instruments, I have developed analytical solutions for the temperature structure and scaling laws of loop strands for a wide range of heating functions, including footpoint heating, uniform heating, and heating concentrated at the loop apex. Key results are that the temperature profile depends only weakly on the heating distribution -- not suffici…
A theory for the heating of coronal magnetic flux ropes is developed. The dissipated magnetic energy has two distinct contributions: (1) energy injected into the corona as a result of granule-scale, random footpoint motions, and (2) energy from the large-scale, nonpotential magnetic field of the flux rope. The second type of dissipation can be described in term of hyperdiffusion, a type of magnetic diffusion in which the helicity of the mean magnetic field is conserved. The associated heating rate depends on the gradient of the torsion parameter of the mean magnetic field. A simple model of an…
I propose a new paradigm for solar coronal heating viewed as a self-regulating process keeping the plasma marginally collisionless. The mechanism is based on the coupling between two effects. First, coronal density controls the plasma collisionality and hence the transition between the slow collisional Sweet-Parker and the fast collisionless reconnection regimes. In turn, coronal energy release leads to chromospheric evaporation, increasing the density and thus inhibiting subsequent reconnection of the newly-reconnected loops. As a result, statistically, the density fluctuates around some crit…
Shock heating and particle acceleration processes are some of the most fundamental physical phenomena of plasma physics with countless applications in laboratory physics, space physics, and astrophysics. This study is motivated by previous observations of non-thermal heating of heavy ions in astrophysical shocks (Korreck et al. 2004). Here, we focus on shocks driven by Interplanetary Coronal Mass Ejections (ICMEs) which heat the solar wind and accelerate particles. This study focuses specifically on the heating of heavy ions caused by these shocks. Previous studies have focused only on the two…
Based on simultaneous observations of solar flares in hard and soft X-rays we studied several aspects of the Neupert effect. About half of 1114 analyzed events show a timing behavior consistent with the Neupert effect. For these events, a high correlation between the soft X-ray peak flux and the hard X-ray fluence is obtained, being indicative of electron-beam-driven evaporation. However, for about one fourth of the events there is strong evidence for an additional heating agent other than electron beams. We discuss the relevance of these findings with respect to Parker's idea of coronal heati…
There is currently no explanation of why the corona has the temperature and density it has. We present a model which explains how the dynamics of magnetic reconnection regulates the conditions in the corona. A bifurcation in magnetic reconnection at a critical state enforces an upper bound on the coronal temperature for a given density. We present observational evidence from 107 flares in 37 sun-like stars that stellar coronae are near this critical state. The model may be important to self-organized criticality models of the solar corona.
We present a series of models for the plasma properties along open magnetic flux tubes rooted in solar coronal holes, streamers, and active regions. These models represent the first self-consistent solutions that combine: (1) chromospheric heating driven by an empirically guided acoustic wave spectrum, (2) coronal heating from Alfven waves that have been partially reflected, then damped by anisotropic turbulent cascade, and (3) solar wind acceleration from gradients of gas pressure, acoustic wave pressure, and Alfven wave pressure. The only input parameters are the photospheric lower boundary …
Using recent data for the photosphere-chromosphere region of the solar atmosphere the magnetic reconnection in tripolar geometry has been investigated through the procedure of Sturrock (1999). Particular attention has been given to the width of the reconnecting region, wave number of the rapidly growing tearing mode, island length scales, frequency of MHD fluctuations, tearing mode growth rate, energy dissipation rate and minimum magnetic field strength required to heat chromospheric plasma to coronal temperatures. It is found that small length scales are formed in the upper chromosphere. The …
A magnetically-structured accretion disk corona, generated by buoyancy instability in the disk, can account for observations of flare--like events in Active Galactic Nuclei. We examine how Petschek magnetic reconnection, associated with MHD turbulence, can result in a violent release of energy and heat the magnetically closed regions of the corona up to canonical X-ray emitting temperatures. X-ray magnetic flares, the after effect of the energy released in slow shocks, can account for the bulk of the X-ray luminosity from Seyfert galaxies and consistently explain the observed short-timescale v…
We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations, used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum $E_k\simeq k^{-3/2}$ and heating rate levels compatible with the heating requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determi…
Popular models for the formation of X-ray spectra in AGN assume that a large fraction of the disk's angular momentum dissipation takes place in a hot corona that carries a small amount of the accreting mass. Here I discuss the formation of a magnetically-structured accretion disk corona, generated by buoyancy instability in the disk and the heating of localized flare regions up to the canonical X-ray emitting temperatures. I also examine the analogy between accreting disk-coronae and ADAFs and discuss the relevant emission mechanism in these two accretion models and how observational constrain…
We show that the coronal heating and the acceleration of the fast solar wind in the coronal holes are natural consequence of the footpoint fluctuations of the magnetic fields at the photosphere by one-dimensional, time-dependent, and nonlinear magnetohydrodynamical simulation with radiative cooling and thermal conduction. We impose low-frequency (<0.05Hz) transverse photospheric motions, corresponding to the granulations, with velocity <dv> = 0.7$km/s. In spite of the attenuation in the chromosphere by the reflection, the sufficient energy of the generated outgoing Alfven waves transmit into t…
We present an ab initio approach to the solar coronal heating problem by modelling a small part of the solar corona in a computational box using a 3D MHD code including realistic physics. The observed solar granular velocity pattern and its amplitude and vorticity power spectra, as reproduced by a weighted Voronoi tessellation method, are used as a boundary condition that generates a Poynting flux in the presence of a magnetic field. The initial magnetic field is a potential extrapolation of a SOHO/MDI high resolution magnetogram, and a standard stratified atmosphere is used as a thermal initi…
Two recent works have analyzed a solar large and steady coronal loop observed with Yohkoh/SXT in two filter passbands to infer the distribution of the heating along it. Priest et al. (2000) modelled the distribution of the temperature obtained from filter ratio method with an analytical approach, and concluded that the heating was uniform along the loop. Aschwanden (2001) found that a uniform heating led to an unreasonably large plasma column depth along the line of sight, and, using a two component loop model, that a footpoint-heated model loop (with a minor cool component) yields more accept…
We study the temporal evolution of coronal loops using data from the Solar X-ray Imager (SXI) on board of GOES-12. This instrument allows us to follow in detail the full lifetime of coronal loops. The observed light curves suggest three somewhat distinct evolutionary phases: rise, main, and decay. The durations and characteristic timescales of these phases are much longer than a cooling time and indicate that the loop-averaged heating rate increases slowly, reaches a maintenance level, and then decreases slowly. This suggests that a single heating mechanism operates for the entire lifetime of …
In preparation for lively debate at the May 2008 SPD/AGU Meeting in Fort Lauderdale, this document attempts to briefly lay out my own view of the evolving controversy over how the solar wind is accelerated. It is still unknown to what extent the solar wind is fed by flux tubes that remain open (and are energized by footpoint-driven wavelike fluctuations), and to what extent much of the mass and energy is input more intermittently from closed loops into the open-field regions. It may turn out that a combination of the two ideas is needed to explain the full range of observed solar wind phenomen…
Parker's initial insights from 1958 provided a key causal link between the heating of the solar corona and the acceleration of the solar wind. However, we still do not know what fraction of the solar wind's mass, momentum, and energy flux is driven by Parker-type gas pressure gradients, and what fraction is driven by, e.g., wave-particle interactions or turbulence. SOHO has been pivotal in bringing these ideas back to the forefront of coronal and solar wind research. This paper reviews our current understanding of coronal heating in the context of the acceleration of the fast and slow solar wi…
Using Particle-In-Cell simulations i.e. in the kinetic plasma description the discovery of a new mechanism of parallel electric field generation was recently reported. Here we show that the electric field generation parallel to the uniform unperturbed magnetic field can be obtained in a much simpler framework using the ideal magnetohydrodynamics (MHD) description. In ideal MHD the electric field parallel to the uniform unperturbed magnetic field appears due to fast magnetosonic waves which are generated by the interaction of weakly non-linear Alfvén waves with the transverse density inhomogene…
We solve numerically ideal, 2.5D, MHD equations in Cartesian coordinates, with a plasma beta of 0.0001 starting from the equilibrium that mimics a footpoint of a large curvature radius solar coronal loop or a polar region plume. On top of such an equilibrium, a purely Alfvénic, linearly polarised, plane wave is launched. In the context of the coronal heating problem a new two stage mechanism of plasma heating is presented by putting emphasis, first, on the generation of parallel electric fields within an ideal MHD description directly, rather than focusing on the enhanced dissipation mechanism…
Long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary different regimes of turbulence develop: strong turbulence is found for …
Cool stars like our Sun are surrounded by a million degree hot outer atmosphere, the corona. Since more than 60 years the physical nature of the processes heating the corona to temperatures well in excess of those on the stellar surface remain puzzling. Recent progress in observational techniques and numerical modeling now opens a new window to approach this problem. We present the first coronal emission line spectra synthesized from three-dimensional numerical models describing the evolution of the dynamics and energetics as well as of the magnetic field in the corona. In these models the cor…
We report on the first stereoscopic observations of polar coronal jets made by the EUVI/SECCHI imagers on board the twin STEREO spacecraft. The significantly separated viewpoints ($\sim$ 11$^\circ$) allowed us to infer the 3D dynamics and morphology of a well-defined EUV coronal jet for the first time. Triangulations of the jet's location in simultaneous image pairs led to the true 3D position and thereby its kinematics. Initially the jet ascends slowly at $\approx$10-20 $\mathrm{{km} {s}^{-1}}$ and then, after an apparent 'jump' takes place, it accelerates impulsively to velocities exceeding …
Recent measurements of quiet Sun heating events by Krucker and Benz (1998) give strong support to Parker's (1988) hypothesis that small scale dissipative events make the main contribution to the quiet heating. Moreover, combining their observations with the analysis by Priest et al. (2000), it can be concluded that the sources driving these dissipative events are also small scale sources, typically of the order of (or smaller than) 2000 km and the resolution of modern instruments. Thus arises the question of how these small scale events participate into the larger scale observable phenomena, a…
The Ultraviolet Coronagraph Spectrometer (UVCS) observed Doppler shifted material of a partial Halo Coronal Mass Ejection (CME) on December 13 2001. The observed ratio of [O V]/O V] is a reliable density diagnostic important for assessing the state of the plasma. Earlier UVCS observations of CMEs found evidence that the ejected plasma is heated long after the eruption. We have investigated the heating rates, which represent a significant fraction of the CME energy budget. The parameterized heating and radiative and adiabatic cooling have been used to evaluate the temperature evolution of the C…
We perform direct numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time to simulate the dynamics of a transverse section of a solar coronal loop. A stationary and large-scale magnetic forcing was imposed, to model the photospheric motions at the magnetic loop footpoints. A turbulent stationary regime is reached, which corresponds to energy dissipation rates consistent with the heating requirements of coronal loops. The temporal behavior of quantities such as the energy dissipation rate show clear indications of intermittency, whi…
A detailed study is presented of the decaying solar active region NOAA 10103 observed with the Coronal Diagnostic Spectrometer (CDS), the Michelson Doppler Imager (MDI) and the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO). Electron density maps formed using Si X (356.03A/347.41A) show that the density varies from ~10^10 cm^-3 in the active region core, to ~7x10^8 cm^-3 at the region boundaries. Over the five days of observations, the average electron density fell by ~30%. Temperature maps formed using Fe XVI(335.41A)/Fe XIV(334.18A) show ele…
We investigate a possibility of heating of the loops and other closed magnetic structures in active regions of the solar corona by the flow of solar wind (plus other flows that may be present) across the magnetic field lines (that are perpendicular to the flow), in a similar manner as a conventional MHD generator works. A simple model is formulated which allows to calculate the typical currents generated by this mechanism. This enables to make a judgement whether the loops in solar active regions can be heated by the proposed mechanism through the associated Ohmic dissipation. It is shown that…
I propose that solar coronal heating is a self-regulating process that keeps the coronal plasma roughly marginally collisionless. The self-regulating mechanism is based on the interplay of two effects. First, plasma density controls coronal energy release via the transition between the slow collisional Sweet-Parker regime and the fast collisionless reconnection regime. This transition takes place when the Sweet--Parker layer becomes thinner than the characteristic collisionless reconnection scale. I present a simple criterion for this transition in terms of the upstream plasma density (n_e), t…
The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled, nevertheless current sheets (corresponding to the original tangential discontinuities hypothesized by Parker)…
