Alfvén waves in the solar atmosphere

The nonlinear propagation of Alfvén waves on open solar magnetic flux tubes is considered. The flux tubes are taken to be vertical and axisymmetric, and they are initially untwisted. The Alfvén waves are time-dependent axisymmetric twists. Their propagation into the chromosphere and corona is investigated by solving numerically a set of nonlinear time-dependent equations, which couple the Alfvén waves into motions parallel to the initial magnetic field (motion in the third coordinate direction is artificially suppressed). The principal conclusions are: (1) Alfvén waves can steepen into fast shocks in the chromosphere. These shocks can pass through the transition region into the corona, and heat the corona. (2) As the fast shocks pass through the transition region, they produce large-velocity pulses in the direction transverse to B _o. The pulses typically have amplitudes of 60 km s^–1 or so and durations of a few tens of seconds. Such features may have been observed, suggesting that the corona is in fact heated by fast shocks. (3) Alfvén waves exhibit a strong tendency to drive upward flows, with many of the properties of spicules. Spicules, and the observed corrugated nature of the transition region, may therefore be by-products of magnetic heating of the corona. (4) It is qualitatively suggested that Alfvén waves may heat the upper chromosphere indirectly by exerting time-dependent forces on the plasma, rather than by directly depositing heat into the plasma.     

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.     

On an efficient shock wave generation mechanism in the quiet solar transition region

Two competing fundamental hypotheses are usually postulated in the solar coronal heating problem: heating by nanoflares and heating by waves. In the latter it is assumed that acoustic and magnetohydrodynamic disturbances whose amplitude grows as they propagate in a medium with a decreasing density come from the convection zone. The shock waves forming in the process heat up the corona. In this paper we draw attention to yet another very efficient shock wave generation process that can be realized under certain conditions typical for quiet regions on the Sun. In the approximation of stationary dissipative hydrodynamics we show that a shock wave can be generated in the quiet solar chromosphere–corona transition region by the fall of plasma from the corona into the chromosphere. This shock wave is directed upward, and its dissipation in the corona returns part of the kinetic energy of the falling plasma to the thermal energy of the corona. We discuss the prospects for developing a quantitative nonstationary model of the phenomenon.     

The solar wind velocity in the eleven-year cycle no. 20 and the solar radar cross-section

The annual average values of the solar wind velocity over the period 1962–1972 were investigated on the basis of data obtained from different space probes. The comparison of the pattern of the annual average solar wind velocities observed by the Vela and Pioneer 6 satellites indicates that the pattern presented by Gosling et al. (1971) is realistic. The long-range trend in the solar wind velocity during the 11-year cycle is governed by the number and intensity of irregularities occurring in the corona. These irregularities may represent motions of mass or some types of MHD shock waves and they are responsible for the increased heating of the corona which then in turn causes an increase in the values of the solar radar cross-section and of the solar wind velocity. A close relation is demonstrated between the monthly and annual average values of the solar wind velocity and of the cross-section.     

Coronal Flux Recycling Times

High-cadence, high-resolution magnetograms have shown that the quiet-Sun photosphere is very dynamic in nature. It is comprised of discrete magnetic fragments which are characterized by four key processes – emergence, coalescence, fragmentation and cancellation. All of this will have consequences for the magnetic field in the corona above. The aim of this study is to gauge the effect of the behavior of the photospheric flux fragments on the quiet-Sun corona. By considering a sequence of observed magnetograms, photospheric flux fragments are represented by a series of point sources and the resulting potential field arising from them is examined. It is found that the quiet-Sun coronal flux is generally recycled on time scales considerably shorter than the corresponding time scales for the recycling of photospheric flux. From the motions of photospheric fragments alone, a recycling time of coronal flux of around 3 h is found. However, it is found that the amount of reconnection driven by the motions of fragments is comparable to the amount driven by emergence and cancellation of flux, resulting in a net flux replacement time for the corona of only 1.4 h. The technique used in this study was briefly presented in a short research letter (R. M. Close et al., Astrophys. J., 612, L81, 2004); here the technique is discussed in far greater depth. Furthermore, an estimate is made of the currents required to flow along separator field lines in order to sustain the observed heating rates (assuming separator reconnection is the key mechanism by which the solar corona is heated).     

Role of 3d-dispersive Alfven waves in coronal heating

Coronal heating is one of the unresolved puzzles in solar physics from decades. In the present paper we have investigated the dynamics of vortices to apprehend coronal heating problem. A three dimensional (3d) model has been developed to study propagation of dispersive Alfvén waves (DAWs) in presence of ion acoustic waves which results in excitation of DAW and evolution of vortices. Taking ponderomotive nonlinearity into account, development of these vortices has been studied. There are observations of such vortices in the chromosphere, transition region and also in the lower solar corona. These structures may play an important role in transferring energy from lower solar atmosphere to corona and result in coronal heating. Nonlinear interaction of these waves is studied in view of recent simulation work and observations of giant magnetic tornadoes in solar corona and lower atmosphere of sun by solar dynamical observatory (SDO).     

Intermittent heating in a model of solar coronal loops

X-ray and EUV observations of the solar corona reveal a very complex and dynamic environment where there are many examples of structures that are believed to outline the Sun's magnetic field. In this present study, the authors investigate the temporal response of the temperature, density and pressure of a solar coronal plasma contained within a magnetic loop to an intermittent heating source generated by Ohmic dissipation. The energy input is produced by a one-dimensional MHD flare model. This model is able to reproduce some of the statistical properties derived from X-ray flare observations. In particular the heat deposition consists of both a sub-flaring background and much larger, singular dissipative events. Two different heating profiles are investigated: (a) the spatial average of the square of the current along the loop and (b) the maximum of the square of the current along the loop. For case (a), the plasma parameters appear to respond more to the global variations in the heat deposition about its average value rather than to each specific event. For case (b), the plasma quantities are more intermittent in their evolution. In both cases the density response is the least bursty signal. It is found that the time-dependent energy input can maintain the plasma at typical coronal temperatures. Implications of these results upon the latest coronal observations are discussed.     

Solar Wind and Chromospheric Network

A physical model of the transition region, including upflow of the plasma in magnetic field funnels that are open to the overlying corona, is presented. A numerical study of the effects of Alfvén waves on the heating and acceleration of the nascent solar wind originating in the chromospheric network is carried out within the framework of a two-fluid model for the plasma. It is shown that waves with reasonable amplitudes can, through their pressure gradient together with the thermal pressure gradient, cause a substantial initial acceleration of the wind (on scales of a few Mm) to locally supersonic flows in the rapidly expanding magnetic field trunks of the transition region network. The concurrent proton heating is due to the energy supplied by cyclotron damping of the high-frequency Alfvén waves, which are assumed to be created through small-scale magnetic activity. The wave energy flux of the model is given as a condition at the upper chromosphere boundary, located above the thin layer where the first ionization of hydrogen takes place.Among the new numerical results are the following: Alfvén waves with an assumed f ^-1 power spectrum in the frequency range from 1 to ⁴ Hz, and with an integrated mean amplitude ranging between 25 and 75 km s⁴, can produce very fast acceleration and also heating through wave dissipation. This can heat the lower corona to a temperature of 5× 10⁵ K at a height of h=12,000 km, starting from 5× 10⁴ K at h=3000 km. The resulting thermal and wave pressure gradients can accelerate the wind to speeds of up to 150 km s^-1 at h=12,000 km, starting from 20 km s^-1 at h=3000 km in a rapidly diverging flux tube. Thus the nascent solar wind becomes supersonic at heights well below the classical Parker-Type sonic point. This is a consequence of the fact that any large wave-energy flux, if it is to be conducted through the expanding funnel to the corona, implies the building-up of an associated wave-pressure gradient. Because of the diverging field geometry, this might lead to a strong initial acceleration of the flow. There is a multiplicity of solutions, depending mainly on the coronal pressure. Here we discuss two new (as compared with a static transition region model) possibilities, namely that either the flow remains supersonic or slows down abruptly by shock formation, which then yields substantial coronal heating up to the canonical 10⁶ K for the proton temperature.     

Relating White-Light Coronal Images to Magnetic Fields and Plasma Flow

The solar magnetic field is key to a detailed understanding of the Sun's atmosphere and its transition to the solar wind. However, the lack of detailed magnetic field measurements everywhere except at the photosphere has made it challenging to determine its topology and to understand how it produces the observed plasma properties of the corona and solar wind. Recent progress based on the synthesis of diversified observations has shown that the corona is highly filamentary, that the coronal magnetic field is predominantly radial, and that the ability of closed fields to trap plasma at the base of the corona is a manifestation of how the solar field controls the solar wind. In this paper, we explain how these results are consistent with the relationship between density structure of white-light images and fields and flow. We point out that the ‘shape’ of the corona observed in white-light images is a consequence of the steep fall-off in density with radial distance, coupled with the inherent limitation in the sensitivity of the observing instrument. We discuss how the significant variation in radial density fall-off with latitude leads to a coronal shape that is more precisely revealed when a radial gradient filter is used, but which also gives a false impression of the tracing of highly non-radial fields. Instead, the coronal field is predominantly radial, and the two magnetic features that influence the shape of the corona are the closed fields at the base of the corona, and the polarity reversal forming the heliospheric current sheet in the outer corona. An erratum to this article is available at .     

Coronal MHD perturbation field generated by localized perturbers in a photospheric active region

We investigate the two-dimensional boundary value problem of the linear wave excitation in the solar corona by a pair of periodic perturbers localized at the photosphere. The physical properties of the corona allow us to consider a magnetic configuration such as a potential arcade which is in a magneto-hydrostatic equilibrium with the surrounding plasma. The model excludes the A1fvén mode and since the slow mode is absent in a potential arcade, the excited waves are then the fast magneto-acoustic modes. The characteristic magnetic field scale length is twice the scale height of the coronal plasma, assumed isothermal and the induced fluid motions are in the direction perpendicular to the magnetic field, in the cross-sectional plane of the arcade.A particular example of two localized perturbers in a photospheric active region is given, pointing out the effects produced in the perturbed fields by the variation of the different parameters involved. Such example shows that, while a modification of the linear size or the horizontal wave number of the perturbers does not affect significantly the propagating disturbances, the variation of the perturbers' frequency produces important effects. Such effects can be summarized by saying that low-frequency perturbers are able to disturb the whole coronal magnetic configuration above the active region while high-frequency perturbers only disturb the coronal region just above them, producing a channeling feature. Moreover, for high frequencies the perturbations grow withz all the way from the photosphere while for very low frequencies evanescent waves are dominant, although thanks to the influence of the medium their amplitude starts to grow from somez on.     

TWO-FLUID MODEL FOR HEATING OF THE SOLAR CORONA AND ACCELERATION OF THE SOLAR WIND BY HIGH-FREQUENCY ALFVÉN WAVES

A model of the solar corona and wind is developed which includes for the first time the heating and acceleration effects of high-frequency Alfvén waves in the frequency range between 1 Hz and 1 kHz. The waves are assumed to be generated by the small-scale magnetic activity in the chromospheric network. The wave dissipation near the gyro-frequency, which decreases with increasing solar distance, leads to strong coronal heating. The resulting heating function is different from other artificial heating functions used in previous model calculations. The associated thermal pressure-gradient force and wave pressure-gradient force together can accelerate the wind to high velocities, such as those observed by Helios and Ulysses. Classical Coulomb heat conduction is also considered and turns out to play a role in shaping the temperature profiles of the heated protons. The time-dependent two-fluid (electrons and protons) model equations and the time-dependent wave-spectrum equation are numerically integrated versus solar distance out to about 0.3 AU. The solutions finally converge and settle on time-stationary profiles which are discussed in detail. The model computations can be made to fit the observed density profiles of a polar coronal hole and polar plume with the sonic point occurring at 2.4 R and 3.2 R , respectively. The solar wind speeds obtained at 63 R are 740 km s^-1 and 540 km s^-1; the mass flux is 2.1 and 2.2 × 10⁸ cm^-2 s^-1 (normalized to 1 AU), respectively. The proton temperature increases from a value of 4 × 10⁵ K at the lower boundary to 2 × 10⁶ K in the corona near 2 R .     

Energy balance of the corona and the origin of quasi-stationary high-speed solar wind streams

The energy balance of open-field regions of the corona and solar wind and the influence of the flow geometry in the corona upon the density and temperature, are analyzed. It is found that the energy flux arriving at the corona is constant for the corona's open regions with different flow geometries. For the waves heating the corona and solar wind, the dependence of the absorption coefficient on the corona's plasma density is found to be within the range of distances r=1.05–1.5R . It is shown that the wave absorption is more dependent on electron density than the coronal emission. It is this difference that causes lower-density coronal holes to be colder than quiet regions. It is found that the additional energy flux necessary for providing energy balance of the corona and for producing solar wind is a flux of Alfvén waves, which can provide the energy needed for producing quasi-stationary high-speed solar wind streams. Theoretical models of coronal holes and the question of why the high-speed solar wind streams are precisely flowing out of coronal holes, are discussed.     

The Effects of the Velocity Filtration Mechanism on the Minor Ions of the Corona

Due to their different mass and varying charge states, heavy solar ions provide invaluable information on the physical mechanisms responsible for the heating of the corona and the solar wind acceleration. It is shown in the present work that some key characteristics observed in the corona are straightforward features predicted by the velocity filtration effect. This mechanism originally proposed by Scudder (1992a,b) accounts for the heating of the corona by just assuming that the velocity distribution functions have enhanced supra-thermal tails. The apparent `heating' is then a natural consequence of the increasing ratio of supra thermal over thermal particles as a function of altitude. Applied to the minor ions, it offers a natural explanation for the high temperatures of the heavy ions compared to the protons. The kinetic filtration theory predicts temperatures more than proportional to the mass of the ions, with a small correction for the charge state. With sufficiently high temperatures, the ions flow faster than the protons. These characteristics are in good agreement with the most recent spectroscopic and in-situ solar wind observations.     

How Accurately Can We Determine the Coronal Heating Mechanism in the Large-Scale Solar Corona?

In recent papers by Priest et al., the nature of the coronal heating mechanism in the large-scale solar corona was considered. The authors compared observations of the temperature profile along large coronal loops with simple theoretical models and found that uniform heating along the loop gave the best fit to the observed data. This then led them to speculate that turbulent reconnection is a likely method to heat the large-scale solar corona. Here we reconsider their data and their suggestion about the nature of the coronal heating mechanism. Two distinct models are compared with the observations of temperature profiles. This is done to determine the most likely form of heating under different theoretical constraints. From this, more accurate judgments on the nature of the coronal heating mechanism are made. It is found that, due to the size of the error estimates in the observed temperatures, it is extremely difficult to distinguish between some of the different heat forms. In the initial comparison the limited range of observed temperatures (T>1.5 MK) in the data sets suggests that heat deposited in the upper portions of the loop, fits the data more accurately than heat deposited in the lower portions. However if a fuller model temperature range (T<1.0 MK) is used results in contridiction to this are found. In light of this several improvements are required from the observations in order to produce theoretically meaningful results. This gives serious bounds on the accuracy of the observations of the large-scale solar corona in future satellite missions such a Solar-B or Stereo.     

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.     

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     

Possible Role of mhd Waves in Heating the Solar Corona

Heating of the solar corona by MHD waves has been investigated. Taking account of dissipation mechanisms self-consistently, a new general dispersion relation has been derived for waves propagating in a homogeneous plasma. Solution of this sixth-order dispersion relation provides information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. Wave quantities with and without dissipation are presented. In particular, we consider one of the most important clues from space observations that viscosity of coronal plasma may be orders of magnitude different from its classical value in heating of the corona by MHD waves.     

The outflow of solar wind from the active regions

The numerical integration of hydrodynamics equations with an allowance for thermal conductivity was made using the temperature distribution in the corona situated above the active regions obtained from the damping time of solar radio bursts of Types III and V. It is essential that for the integration path serve the magnetic field lines along which exciters of bursts are moving and accelerated coronal plasma can move freely too.The main result is the discovery of such regions, where the high temperature gradient precludes the possibility of a continuous flow of coronal plasma. These regions, where intense heating and rapid acceleration of the coronal plasma take place, were situated at distances of about 2 R from the Sun's center. They probably possess the character of weak detonation waves. The waves of cooling can also be present in these regions of discontinuity of the flow. The observations of bursts of Type V at distances up to 6.3 R gives some evidence that discontinuities of flow of the solar wind of the same nature can possibly arise also in the more remote parts of the solar corona.It is important that the similar jumps of velocity and other parameters of coronal plasma were also discovered earlier in a quite independent way as a result of the interpretation of the solar radio echo data. It can be anticipated that the nonthermal heating of coronal plasma, which was postulated to remove discrepancies between the existing models and observations of solar wind, was localized mainly in these regions thus playing an important role in the formation of the fundamental properties of the interplanetary medium.The obtained results are of preliminary character since there are no reliable and homogeneous data on bursts of Types III and V especially at 20-10 MHz, where the work is difficult due to the man-made interference and also at still lower frequencies, observed by the cosmic probes. We can hope that the filling of this gap allows us to construct a realistic model of outflow of coronal plasma from active regions, which can be successfully compared with the results of direct measurement of parameters of solar wind.     

Mechanisms of coronal heating

The Sun is a mysterious star. The high temperature of the chromosphere and corona present one of the most puzzling problems of solar physics. Observations show that the solar coronal heating problem is highly complex with many different facts. It is likely that different heating mechanisms are at work in solar corona. Recent observations show that Magnetic Carpet is a potential candidate for solar coronal heating.     

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.