The heating of the solar corona

The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona. Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed.Received: 6 February 2003, Published online: 14 November 2003 Correspondence to: R. W. Walsh     

Heating Events in the Quiet Solar Corona

Sensitive observations of the quiet Sun observed by EIT on the SOHO satellite in high-temperature iron-line emission originating in the corona are presented. The thermal radiation of the quiet corona is found to fluctutate significantly, even on the shortest time scale of 2 min and in the faintest pixels. The power spectrum of the emission measure time variations is approximately a power law with an exponent of 1.79±0.08 for the brightest pixels and 1.69±0.08 for the average and the faintest pixels. The more prominent enhancements are identified with previously reported X-ray network flares (Krucker et al., 1997) above the magnetic network of the quiet chromosphere. In coronal EUV iron lines they are amenable to detailed analysis suggesting that the brightenings are caused by additional plasma injected from below and heated to slightly higher temperature than the preexisting corona. Statistical investigations are consistent with the hypothesis that the weaker emission measure enhancements originate from the same parent population. The power input derived from the impulsive brightenings is linearly proportional to the radiative loss in the observed part of the corona. The absolute amount of impulsive input is model-dependent. It cannot be excluded that it can satisfy the total requirement for heating. These observations give strong evidence that a significant fraction of the heating in quiet coronal regions is impulsive.     

Very-Large-Array Observations of Evolving Type I Noise Storms and Nonthermal Bursts In Association With Flares And Coronal Mass Ejections

Very-Large-Array (VLA) observations of the Sun at 20, 91 and 400 cm have been combined with data from the SOHO, TRACE and Wind solar missions to study the properties of long-lasting Type I noise storms and impulsive metric and decimetric bursts during solar flares and associated coronal mass ejections. These radio observations provide information about the acceleration and propagation of energetic electrons in the low and middle corona as well as their interactions with large-scale magnetic structures where energy release and transport takes place. For one flare and its associated CME, the VLA detected impulsive 20 and 91 cm bursts that were followed about ten minutes later by 400 cm burst emission that appeared to move outward into the corona. This event was also detected by the Waves experiment on Wind which showed intense, fast-drifting interplanetary Type III bursts following the metric and decimetric bursts detected by the VLA. For another event, impulsive 91 cm emission was detected about a few minutes prior to impulsive bursts at 20.7 cm, suggesting an inwardly propagating beam of electrons that excited burst emission at lower levels and shorter wavelengths. We also find evidence for significant changes in the intensity of Type I noise storms in the same or nearby active region during impulsive decimetric bursts and CMEs. These changes might be attributed to flare-initiated heating of the Type I radio source plasma by outwardly-propagating flare ejecta or to the disruption of ambient magnetic fields by the passage of a CME.     

The solar corona as a minimum energy system?

This paper is an exploration of the possibility that the large-scale equilibrium of plasma and magnetic fields in the solar corona is a minimum energy state. Support for this conjecture is sought by considering the simplest form of that equilibrium in a dipole solar field, as suggested by the observed structure of the corona at times of minimum solar activity. Approximate, axisymmetric solutions to the MHD equations are constructed to include both a magnetically closed, hydrostatic region and a magnetically open region where plasma flows along field lines in the form of a transonic, thermally-driven wind. Sequences of such solutions are obtained for various degrees of magnetic field opening, and the total energy of each solution is computed, including contributions from both the plasma and magnetic field. It is shown that along a sequence of increasingly closed coronal magnetic field, the total energy curve is a non-monotonic function of the parameter measuring the degree of magnetic field opening, with a minimum occurring at moderate field opening.For reasonable choices of model parameters (coronal temperature, base density, base magnetic field strength, etc.), the morphology of the minimum energy solution resembles the observed quiet, solar minimum corona. The exact location energy minimum along a given sequence depends rather sensitively on some of the adopted parameter values. It is nevertheless argued that the existence of an energy minimum along the sequences of solutions should remain a robust property of more realistic coronal wind models that incorporate the basic characteristics of the equilibrium corona- the presence of both open and closed magnetic regions.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Coronal heating and solar wind acceleration; gyrotropic electron-proton solar wind

In coronal holes the electron (proton) density is low, and heating of the proton gas produces a rapidly increasing proton temperature in the inner corona. In models with a reasonable electron density in the upper transition region the proton gas becomes collisionless some 0.2 to 0.3 solar radii into the corona. In the collisionless region the proton heat flux is outwards, along the temperature gradient. The thermal coupling to electrons is weak in coronal holes, so the heat flux into the transition region is too small to supply the energy needed to heat the solar wind plasma to coronal temperatures. Our model studies indicate that in models with proton heating the inward heat conduction may be so inefficient that some of the energy flux must be deposited in the transition region to produce the proton fluxes that are observed in the solar wind. If we allow for coronal electron heating, the energy that is needed in the transition region to heat the solar wind to coronal temperatures, may be supplied by heat conduction from the corona.     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.     

An Impulsive Heating Model for the Evolution of Coronal Loops

It was suggested by Parker that the solar corona is heated by many small energy release events generally called microflares or nanoflares. More and more observations showed flows and intensity variations in nonflaring loops. Both theories and observations have indicated that the heating of coronal loops should actually be unsteady. Using SOLFTM (Solar Flux Tube Model), we investigate the hydrodynamics of coronal loops undergoing different manners of impulsive heating with the same total energy deposition. The half length of the loops is 110 Mm, a typical length of active region loops. We divide the loops into two categories: loops that experience catastrophic cooling and loops that do not. It is found that when the nanoflare heating sources are in the coronal part, the loops are in non-catastrophic-cooling state and their evolutions are similar. When the heating is localized below the transition region, the loops evolve in quite different ways. It is shown that with increasing number of heating pulses and inter-pulse time, the catastrophic cooling is weakened, delayed, or even disappears altogether.     

Study of two-stage coronal jet associated with a C1.4 class solar flare

We study an active region coronal jet that evolved from southward of a major sunspot of NOAA AR12178 on 04 October 2014. This jet is associated with an onset of the GOES C1.4 flare. We use SDO/AIA, SDO/HMI, GONG \(H\upalpha\) and GOES data for analysing the observed event. We term this jet as a two-stage confined eruption of the plasma. In the first stage, some plasma erupts above the compact flaring region. In the second stage, this eruptive jet plasma and associated magnetic field lines interact with another set of distinct magnetic field lines present in its south-east direction. This creates an X-point region, where the second stage of the jet eruption is deflected above it on a curvilinear path into overlying corona. The lower part of the jet is followed by a cool surge eruption, which is visible only in \(H{\upalpha}\) emissions. The magnetic flux cancellation at the footpoint causes the triggering of C-class flare eruption. This flare energy release further triggers first stage of the coronal jet eruption. The second stage of the jet eruption is a consequence of an interaction of two distinct sets of magnetic field lines in the overlying corona. The first stage of the coronal jet and co-spatial but lagging cool surge may have common origin due to the reconnection generated heating pulses. This complex evolution of the coronal jet involves flare heating induced first stage plasma eruption, guiding of jet’s material above a junction of two distinct sets of field lines in the corona, and intra-relationship with cool surge. In effect, it imposes rigid constraints on the existing jet models.     

Energy released by the interaction of coronal magnetic fields

Comparisons between coronal spectroheliograms and photospheric magnetograms are presented to support the idea that as coronal magnetic fields interact, a process of field line reconnection usually takes place as a natural way of preventing magnetic stresses from building up in the lower corona. This suggests that the energy which would have been stored in stressed fields is continuously released as kinetic energy of material being driven aside to make way for the reconnecting fields. However, this kinetic energy is negligible compared to the thermal energy of the coronal plasma. Therefore, it appears that these slow adjustments of coronal magnetic fields cannot account for even the normal heating of the corona, much less the energetic events associated with solar flares.Visiting Scientist, Kitt Peak National Observatory, Tucson Arizona.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

MHD waves and instabilities of a temperature-anisotropic plasma in the solar corona as a source of its heating

The MHD instabilities of a temperature-anisotropic coronal plasma are considered. We show that aperiodic mirror instabilities of slow MHD waves can develop under solar coronal conditions for weak magnetic fields (B < 1 G) and periodic ion-acoustic instabilities can develop for strong magnetic fields (B > 10 G). We have found the instability growth rates and estimated the temporal and spatial scales of development and decay of the periodic instability. We show that the instabilities under consideration can play a prominent role in the energy balance of the corona and may be considered as a large-scale energy source of the wave coronal heating mechanism.     

Role of magnetic carpet in coronal heating

One of the fundamental questions in solar physics is how the solar corona maintains its high temperature of several million Kelvin above photosphere with a temperature of 6000 K. Observations show that solar coronal heating problem is highly complex with many different facts. It is likely that different heating mechanisms are at work in the solar corona. The separate kinds of coronal loops may also be heated by different mechanisms. Using data from instruments onboard the Solar and Heliospheric Observatory (SOHO) and from the more recent Transition Region and Coronal Explorer (TRACE) scientists have identified small regions of mixed polarity, termed magnetic carpet contributing to solar activity on a short time scale. Magnetic loops of all sizes rise into the solar corona, arising from regions of opposite magnetic polarity in the photosphere. Energy released when oppositely directed magnetic fields meet in the corona is one likely cause for coronal heating. There is enough energy coming up from the loops of the “magnetic carpet” to heat the corona to its known temperature.     

Very Large Array,SOHO, and RHESSI Observations of Magnetic Interactions and Particle Propagation across Large-Scale Coronal Loops

Very Large Array (VLA) observations at wavelengths of 20 and 91 cm have been combined with data from the SOHO and RHESSI solar missions to study the evolution of transequatorial loops connecting active regions on the solar surface. The radio observations provide information about the acceleration and propagation of energetic electrons in these large-scale coronal magnetic structures where energy release and transport take place. On one day, a long-lasting Type I noise storm at 91 cm was seen to intensify and shift position above the northern hemisphere region following an impulsive hard X-ray burst in the southern hemisphere footpoint region. VLA 20-cm observations as well as SOHO EIT EUV images showed evolving coronal plasma that appeared to move across the solar equator during this time period. This suggests that the transequatorial loop acted as a conduit for energetic particles or fields that may have triggered magnetic changes in the corona where the northern noise storm region was seen. On another day, a hard X-ray burst detected at the limb was accompanied by impulsive 20- and 91-cm burst emission along a loop connecting to an active region in the same hemisphere but about 5′ away, again suggesting particle propagation and remote flare triggering across interconnecting loops.     

Solar coronal heating by magnetosonic waves

Solar coronal heating by magnetohydrodynamic (MHD) waves is investigated. ultraviolet (UV) and X-ray emission lines of the corona show non-thermal broadenings. The wave rms velocities inferred from these observations are of the order of 25–60 km s⁻¹ . Assuming that these values are not negligible, we solved MHD equations in a quasi-linear approximation, by retaining the lowest order non-linear term in rms velocity. Plasma density distribution in the solar corona is assumed to be inhomogeneous. This plasma is also assumed to be permeated by dipole-like magnetic loops. Wave propagation is considered along the magnetic field lines. As dissipative processes, only the viscosity and parallel (to the local magnetic field lines) heat conduction are assumed to be important. Two wave modes emerged from the solution of the dispersion relation. The fast mode magneto-acoustic wave, if originated from the coronal base can propagate upwards into the corona and dissipate its mechanical energy as heat. The damping length-scale of the fast mode is of the order of 500 km. The wave energy flux associated with these waves turned out to be of the order of 2.5×10⁵ ergs cm⁻² s⁻¹ which is high enough to replace the energy lost by thermal conduction to the transition region and by optically thin coronal emission. The fast magneto-acoustic waves prove to be a likely candidate to heat the solar corona. The slow mode is absent, in other words cannot propagate in the solar corona.     

On the role of hydromagnetic waves in the corona and the base of the solar wind

Hydromagnetic waves are of interest for heating the corona or coronal loops and for accelerating the solar wind. This paper enumerates some of the limitations that must be considered before hydromagnetic waves are taken seriously. In the lowest part of the corona, waves interact so that a significant fraction of the coronal wave flux should have periods as 10 s. If the problem of interest determines either a flux of wave energy or a dissipation rate, the distance that each wave mode can travel can be specified, and for at least one mode it must be consistent with the size and location of the region where the waves are to act. Heating of coronal loops observed by X-rays can be explained if the strength of the magnetic field along the loop lies within a rather narrow range and if the wave period is sufficiently short. In general, Alfvén waves travel furthest and reach high into the corona and into the solar wind. The radial variation of the magnetic field is the most important parameter determining where the waves are dissipated. Heating of coronal helmets by Alfvén waves is probable.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Interpretation of the observed motions of hard X-ray sources in solar flares

In connection with the RHESSI satellite observations of solar flares, which have revealed new properties of hard X-ray sources during flares, we offer an interpretation of these properties. The observed motions of coronal and chromospheric sources are shown to be the consequences of three-dimensional magnetic reconnection at the separator in the corona. During the first (initial) flare phase, the reconnection process releases an excess of magnetic energy related predominantly to themagnetic tensions produced before the flare by shear plasma flows in the photosphere. The relaxation of a magnetic shear in the corona also explains the downward motion of the coronal source and the decrease in the separation between chromospheric sources. During the second (main) flare phase, ordinary reconnection dominates; it describes the energy release in the terms of the “standard model” of large eruptive flares accompanied by the rise of the coronal source and an increase in the separation between chromospheric sources.     

DISCRETE RANDOM HEATING EVENTS IN CORONAL LOOPS

The response of the coronal plasma in a magnetic loop to the release of discrete, random amounts of energy quanta over fixed time intervals is investigated. Nanoflare heating (10²⁴ erg per event) with event lifetimes on a scale of 1–20 s are shown to be able to maintain a coronal loop at typical coronal temperatures, 2 x 10⁶ K (Parker, 1988; Kopp and Poletto, 1993). Microflare events (10²⁷ erg) observed by Porter et al. (1995) with a lifetime of approximately 1 min are also investigated and it is found that the loop apex temperature varies by at most 40% from its initial static condition. However, larger energy events of the order of 10²⁸ erg (Schmieder et al., 1994) occur too infrequently and the plasma cools to chromospheric values. The implications of time-dependent heating of the corona upon observations are also discussed.     

The rate of flux pile-up magnetic reconnection in reduced MHD

The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 10²⁵– 10²⁶ erg s^–1and heating of quiet coronal loops are within the compass of the model.     

Geometrical considerations in imaging the solar corona

X-ray observations of the solar corona show that it is comprised of three-dimensional magnetic structures which appear to be primarily in the form of fluxtubes or loops. Imaging the X-ray corona has led to a greater understanding of the dynamical behaviour of and the energy distribution in these magnetic structures. However, imaging observations, by their very nature, integrate along the line of sight resulting in a two-dimensional representation of the actual three-dimensional distribution. The optically thin nature of the solar corona to X-ray radiation makes the integrated images particularly difficult to interpret. The analysis of the two-dimensional observations must, therefore, inlcude the effect of the orientation of the coronal structure to the line-of-sight direction; a fact which is almost always ignored. In this paper we discuss the effect of loop orientation on the two-dimensional representation and argue that these effects may lead to a misinterpretation of the physics occurring in the structures observed. In particular, we discuss observations taken by the Soft X-ray Telescope (SXT) on board the Yohkoh satellite, taking account of the instrumental thermal response, spatial resolution, and point-spread-function.We test the effect of geometry on the determination of the loop pressure by considering equatorial loops at various longitudes and discuss the implications of this for studies of coronal soft X-ray loops.     

Relationship between CME dynamics and solar flare plasma

The relationship between the velocity of CMEs and the plasma temperature of the associated X-ray solar flares is investigated.The velocity of CMEs increases with plasma temperature(R=0.82)and photon index below the break energy(R=0.60)of X-ray flares.The heating of the coronal plasma appears to be significant with respect to the kinetics of a CME from the reconnection region where the flare also occurs.We propose that the initiation and velocity of CMEs perhaps depend upon the dominant process of conversion of the magnetic field energy of the active region to heating/accelerating the coronal plasma in the reconnected loops.Results show that a flare and the associated CME are two components of one energy release system,perhaps,magnetic field free energy.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.