A self-consistent model of a thermally balanced quiescent prominence in magnetostatic equilibrium in a uniform gravitational field

We present a theoretical model of quiescent prominences in the form of an infinite vertical sheet. Self-consistent solutions are obtained by integrating simultaneously the set of nonlinear equations of magnetostatic equilibrium and thermal balance. The basic features of the models are: (1) The prominence matter is confined to a sheet and supported against gravity by a bowed magnetic field. (2) The thermal flux is channelled along magnetic field lines. (3) The thermal flux is everywhere balanced by Low's (1975b) hypothetical heat sink which is proportional to the local density. (4) A constant component of the magnetic field along the length of the prominence shields the cool plasma from the hot surrounding. We assume that the prominence plasma emits more radiation than it absorbs from the radiation fields of the photosphere, chromosphere and corona, and we interpret the above hypothetical heat sink to represent the amount of radiative loss that must be balanced by a nonradiative energy input. Using a central density and temperature of 10¹¹ particles cm^–3 and 5000 K respectively, a magnetic field strength between 2 to 10 gauss and a thermal conductivity that varies linearly with temperature, we discuss the physical properties implied by the model. The analytic treatment can also be carried out for a class of more complex thermal conductivities. These models provide a useful starting point for investigating the combined requirements of magnetostatic equilibrium and thermal balance in the quiescent prominence.     

Flare-associated surge prominence on 1980 october 30

The Hα observations of a flare-associated surge prominence on 1980 October 30 have been described. Morphology and dynamics of the surge prominence have been presented. From our observations and analysis we have estimated the magnetic field associated with surge material to be about 35 gauss which is in good agreement with the earlier result of Tandberg-Hanssen & Malville (1974). It has been determined that coronal pressure is not acting as a resistive force on the outward expansion of the surge into the corona. The kinetic energy of the surge was about 10²⁸ erg, which is 2 orders less than required for the mass to escape the chromosphere. It appears that the flare-associated surge prominence was perhaps a result of kink instability in the flaring region.     

The formation of solar prominences by thermal instability in a current sheet

The energy balance equation for the upper chromosphere or lower corona contains a radiative loss term which is destabilizing, because a slight decrease in temperature from the equilibrium value causes more radiation and hence a cooling of the plasma; also a slight increase in temperature has the effect of heating the plasma. In spite of this tendency towards thermal instability, most of the solar atmosphere is remarkably stable, since thermal conduction is very efficient at equalizing any temperature irregularity which may arise. However, the effectiveness of thermal conduction in transporting heat is decreased considerably in a current sheet or a magnetic flux tube, since heat can be conducted quickly only along the magnetic field lines. This paper presents a simple model for the thermal equilibrium and stability of a current sheet. It is found that, when its length exceeds a certain maximum value, no equilibrium is possible and the plasma in the sheet cools. The results may be relevant for the formation of a quiescent prominence.     

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.     

Enhanced emission of Alfvén waves from sunspots during proton flares

Thomas (1978) has shown that, if Alfvén waves exist in a sunspot umbra, they are normally reflected so strongly by the temperature minimum as to be essentially undetectable in the upper solar atmosphere. However, it is known that in many proton flares, chromospheric emission overlies the umbra of a sunspot, indicating that the transition region (TR) between chromosphere and corona in the umbral flux tube has moved down to lower altitudes. As a result of this lowering, umbral Alfvén waves have readier access to the corona: the coronal leakage depends exponentially on the altitude of the TR. We find that the Alfvén wave flux which leaks out of the umbra into the corona can exceed 10⁷ ergs cm^-2 s^-1. A flux of this magnitude is expected to dissipate rapidly in the corona, thereby contributing to a positive feedback loop which ensures prolonged (1 hr) leakage of the umbral Alfvén waves into the corona. We propose that these Alfvén waves may contribute significantly to prolonged energization of proton flares in which umbral coverage occurs.     

Numerical Simulations of Torsional Alfvén Waves in Axisymmetric Solar Magnetic Flux Tubes

We numerically investigate Alfvén waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of the physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated and used to determine regions in the solar chromosphere where strong wave reflection may occur.     

The “FIP Effect” and the Origins of Solar Energetic Particles and of the Solar Wind

We find that the element abundances in solar energetic particles (SEPs) and in the slow solar wind (SSW), relative to those in the photosphere, show different patterns as a function of the first ionization potential (FIP) of the elements. Generally, the SEP and SSW abundances reflect abundance samples of the solar corona, where low-FIP elements, ionized in the chromosphere, are more efficiently conveyed upward to the corona than high-FIP elements that are initially neutral atoms. Abundances of the elements, especially C, P, and S, show a crossover from low to high FIP at \({\approx}\,10~\mbox{eV}\) in the SEPs but \({\approx}\,14~\mbox{eV}\) for the solar wind. Naively, this seems to suggest cooler plasma from sunspots beneath active regions. More likely, if the ponderomotive force of Alfvén waves preferentially conveys low-FIP ions into the corona, the source plasma that eventually will be shock-accelerated as SEPs originates in magnetic structures where Alfvén waves resonate with the loop length on closed magnetic field lines. This concentrates FIP fractionation near the top of the chromosphere. Meanwhile, the source of the SSW may lie near the base of diverging open-field lines surrounding, but outside of, active regions, where such resonance does not exist, allowing fractionation throughout the chromosphere. We also find that energetic particles accelerated from the solar wind itself by shock waves at corotating interaction regions, generally beyond 1 AU, confirm the FIP pattern of the solar wind.     

A model of solar flares and faculae

Theories of solar flares based on the storage of energy (usually as magnetic energy) in the solar atmosphere are shown to be incompatible with observational data.The sunspot energy deficit and the photospheric faculae both involve energy fluxes comparable with the flare requirement ( 3 × 10²⁹ erg s^–1). Both also require a subsurface system of waves or oscillations, perhaps those discussed by Danielson and Savage and by Wilson. The flare model proposed is based on a temporary diversion of this energy carried by Alfvén waves through spots and magnetic elements or micro-pores; the calculated plasma perturbation velocity in the umbra is about 6 km s^–1 for a major flare.In the atmosphere the wave energy divides into two parts to produce the cool, stationary optical flare and the particle flare. The first part is dissipated around flux tubes which are mainly horizontal in the chromosphere and which tend to concentrate along the magnetic neutral line (B = 0). Each tube vibrates individually as a taut wire in a viscous fluid, to excite the fluid just outside the tube. The second part of the energy emerges along tubes mainly vertical in the chromosphere and is converted to shock waves in the corona and then to particle energy for the radio and X-ray flare and the blast wave.The model includes white-light faculae, quasi-permanent X-ray and fast-particle emissions, sympathetic flares and surges. An unambiguous test would be provided by observations of plasma motions of a few kilometres per second in spots and micro-pores.     

Propagation of magnetically guided acoustic shocks in the solar chromosphere

We study the propagation of a train of acoustic shocks guided by diverging magnetic fields through a static model of the solar chromospheric network and transition region. Our results show that for initial flux densities of the order 10⁶ ergs cm^–2 s^–1 in the lower chromosphere, the local efficiency of acoustic transmission into the corona can be much higher than calculated for a plane parallel atmosphere. Thus acoustic energy will tend to be deposited at higher chromospheric levels in diverging magnetic fields, and magnetic guiding may well influence the temperature profile of the network and plages. But the total flux that can be transmitted into the corona along such diverging fields is severely limited, since the magnetic elements occupy a small fractional area of the photosphere, and the transmission efficiency is a rapidly decreasing function of initial acoustic flux density. We conclude that diverging magnetic fields and a varying ratio of specific heats are not likely to allow high frequency shocks to dissipate high enough in a static atmosphere, to contribute significantly to the coronal energy balance. This result strengthens the view that acoustic waves do not heat the solar corona. However, the conclusion may be sensitive to the influence of observed mass motions, such as spicules.     

Role of plasma flow in determining structure of the chromosphere-corona transition zone of the sun

Transfer of material between the chromosphere and corona of the Sun must occur whenever the geometry of any interconnecting magnetic structure changes, and there will also be a flow of plasma along field lines caused by any pressure difference between the two feet of each arch. Part of the energy conducted downwards towards the chromosphere is required to heat plasma rising into the corona, whereas material falling back towards the solar surface gives up energy to reinforce the conducted flow.This study shows that the term associated with flow is comparable to the radiation-loss term in the energy budget of the transition zone if the plasma speed at the base of the corona reaches about 3 km s^–1. This value is probably exceeded within most flux tubes during some period of their development, and speeds an order of magnitude higher can occur in favourable regions.This paper also examines limits to the temperature gradient of the transition zone set by the requirement of continuity of plasma flow.     

Physical properties of the quiet solar chromosphere–corona transition region

The physical properties of the quiet solar chromosphere–corona transition region are studied. Here the structure of the solar atmosphere is governed by the interaction of magnetic fields above the photosphere. Magnetic fields are concentrated into thin tubes inside which the field strength is great. We have studied how the plasma temperature, density, and velocity distributions change along a magnetic tube with one end in the chromosphere and the other one in the corona, depend on the plasma velocity at the chromospheric boundary of the transition region. Two limiting cases are considered: horizontally and vertically oriented magnetic tubes. For various plasma densities we have determined the ranges of plasma velocities at the chromospheric boundary of the transition region for which no shock waves arise in the transition region. The downward plasma flows at the base of the transition region are shown to be most favorable for the excitation of shock waves in it. For all the considered variants of the transition region we show that the thermal energy transfer along magnetic tubes can be well described in the approximation of classical collisional electron heat conduction up to very high velocities at its base. The calculated extreme ultraviolet (EUV) emission agrees well with the present-day space observations of the Sun.     

The Evaporation Regime in a Confined Flare

We studied the evolution of a small eruptive flare (GOES class C1) from its onset phase using multi-wavelength observations that sample the flare atmosphere from the chromosphere to the corona. The main instruments involved were the Coronal Diagnostic Spectrometer (CDS) aboard SOHO and facilities at the Dunn Solar Tower of the National Solar Observatory/Sacramento Peak. Transition Region and Coronal Explorer (TRACE) together with Ramaty High-Energy Spectroscopic Imager (RHESSI) also provided images and spectra for this flare. Hα and TRACE images display two loop systems that outline the pre-reconnection and post-reconnection magnetic field lines and their topological changes revealing that we are dealing with an eruptive confined flare. RHESSI data do not record any detectable emission at energies ≥25 keV, and the observed count spectrum can be well fitted with a thermal plus a non-thermal model of the photon spectrum. A non-thermal electron flux F ≈ 5 × 10¹⁰ erg cm⁻² s⁻¹ is determined. The reconstructed images show a very compact source whose peak emission moves along the photospheric magnetic inversion line during the flare. This is probably related to the motion of the reconnection site, hinting at an arcade of small loops that brightens successively. The analysis of the chromospheric spectra (Ca II K, He I D₃ and Hγ, acquired with a four-second temporal cadence) shows the presence of a downward velocity (between 10 and 20 km s⁻¹) in a small region intersected by the spectrograph slit. The region is included in an area that, at the time of the maximum X-ray emission, shows upward motions at transition region (TR) and coronal levels. For the He I 58.4 and O v 62.97 lines, we determine a velocity of ≈−40 km s⁻¹ while for the Fe XIX 59.22 line a velocity of ≈−80 km s⁻¹ is determined with a two-component fitting. The observations are discussed in the framework of available hydrodynamic simulations and they are consistent with the scenario outlined by Fisher (1989). No explosive evaporation is expected for a non-thermal electron beam of the observed characteristics, and no gentle evaporation is allowed without upward chromospheric motion. It is suggested that the energy of non-thermal electrons can be dissipated to heat the high-density plasma, where possibly the reconnection occurs. The consequent conductive flux drives the evaporation process in a regime that we can call sub-explosive.     

On the solar tsunami

Some problems of qualitative theory of solar tsunami caused by rapid magnetic disturbances are discussed. The energy of tsunami is found sufficient to produce oscillations of quiescent prominences, facular brightenings after flares and also some flares and also some flares of moderate intensity. Coronal plasma satisfied the condition of incompressibility, but in the chromosphere the effects of incompressibility, but in the chromosphere the effects of compressibility generally must be taken into account. Long gravity waves with the wave-length of 10⁵ km can propagate on distances comparable with solar radius without sensible damping and dissipation. The solution of tsunami problem for a model of two-component ocean consists of two long gravity waves moving with different velocity in the chromosphere and corona. The effect of encounter of tsunami with magnetic fields are discussed.     

Magnetic reconnection in the temperature minimum region and prominence formation

Magnetic reconnection at the photospheric boundary is an essential part of some theories for prominence formation. We consider a simple model for reconnection in this region. Parameters of the reconnecting current sheet are expressed in terms of the concentration and temperature of the outside dense and cold plasma, magnetic field intensity, and velocity of convective flows at the photosphere. The reconnection process is shown to be most efficient in a layer several hundred kilometers thick coinciding with the temperature minimum region of the solar atmosphere. The calculated upward flux of matter through the current sheet ( 10¹¹–10¹² g s^–1) is amply sufficient for prominence formation in the upper chromosphere or lower corona.     

Solar flares as resulting from the temporary interruption of energy flow to the corona: A case of hydromagnetic resonance

The hypothesis that solar flares may be caused by a choking off of the normal energy flux to the corona by the strong closed magnetic fields of a plage is examined. If the energy flux into a plage from the photosphere is of the order of 10⁸ ergs/cm² sec, and if a substantial fraction of this energy is carried in the form of Alfvén waves, then the rate of dissipation of the waves is slower than the rate at which energy is injected. Since the waves must propagate along the magnetic field and cannot reenter the photosphere, they must remain within the plage; hence, the magnetic and kinetic energy in a small-scale motion (either waves, turbulence, or high-energy particles) must increase with time, eventually causing disruption of the volume when the small-scale energy density exceeds the energy in the mean field. It is believed that the unusually broad wings in the emission lines represent evidence of this phenomenon. The accumulation of waves is manifested as a resonance which occurs initially only at discrete locations in the magnetic field, but later is expected to involve the whole flare volume. The response of a typical volume of flare dimensions due to a trapping of the normal wave supply to the corona is studied through use of the virial equation. For magnetic fields typical of a plage, the region expands in a time scale of 10²–10³ sec, with a velocity in the neighborhood of 10–20 km/sec. Small-scale velocities within the region, however, have reached 100–300 km/sec, indicating that almost all the energy in the flare resides in small-scale forms. The energy density of the flare region exhibits a behavior much more explosive than the expansion rate. There is a rapid rise to maximum in 10² sec or less, and a slow subsequent decline taking about 10³–10⁴ sec due to the dilution of energy caused by expansion of the region. The predicted temporal behavior of the energy density coincides qualitatively with the light curves observed during flares, and it is suggested that the rise and decline of the energy density is to be associated with the optical flare. The total flare is defined as the time required for the energy density of the chromosphere and corona to return to the pre-flare state. During this time (about one hour) a large flare can derive the necessary 10³² ergs from normal photospheric energy output.     

Purely coronal flare-like variations

A detailed study of the quasi-periodical post-flare variations on November 6, 1980 in X-rays, UV lines, microwaves, and metric waves confirms that these variations were predominantly thermal phenomena and occurred solely in the corona. Only the short-lived impulsive components that preceded all or most of the individual variations were of non-thermal character and penetrated down to the transition layer. The chromosphere (in Hα) did not participate in any part of these events, in contrast to a flare that appeared at the same place a few hours later. However, the X-ray emission of these variations was so strong that the transition layer and the chromosphere definitely should have been enhanced through heat conduction along the magnetic field lines. The expected heat flux at the top of the chromosphere coming from some of these coronal brightenings was 60–80% of the flux expected in the flare at 17:26 which gave rise to a 2B flare in Hα (Figure 8). Therefore, we suggest that the variations were produced in a coronal plasmoid with closed field lines completely detached from the lower atmospheric layers (Figure 9b). We also give reasons why such a detached plasmoid can be expected to be formded in the very late phase (some 4–5 hr after the onset) of a major two-ribbon flare.     

Eruptive prominence and associated CME observed with SUMER, CDS and LASCO (SOHO)

Observations of an eruptive prominence were obtained on 1 May 1996, with the SUMER and CDS instruments aboard SOHO during the preparatory phase of the Joint Observing Programme JOP12. A coronal mass ejection observed with LASCO is associated temporally and spatially with this prominence. The main objective of JOP12 is to study the dynamics of prominences and the prominence–corona interface. By analysing the spectra of Oiv and Siiv lines observed with SUMER and the spectra of 15 lines with CDS, Doppler shifts, temperatures and electron densities (ratio of Oiv 1401 to 1399Å) were derived in different structures of the prominence. The eruptive part of the prominence consists of a bubble (plasmoid) of material already at transition region temperatures with red shifts up to 100 km s^-1 and an electron density of the order of 10¹⁰cm^-3. The whole prominence was very active. It developed both a large helical loop and several smaller loops consisting of twisted threads or multiple ropes. These may be studied in the SUMER movie (movie 2). The profiles of the SUMER lines show a large dispersion of velocities (±50 km s^-1) and the ratio of the Oiv lines indicates a large dispersion in electron density (3 x 10⁹cm^-3 to 3x 10¹¹cm^-3). The CME observed by LASCO left the corona some tens of minutes before the prominence erupted. This is evidence that the prominence eruptions are probably the result of the removal of the restraining coronal magnetic fields which are in part responsible for the original stability of the prominence.     

Transverse oscillations in solar spicules induced by propagating Alfvénic pulses

The excitation of Alfvénic waves in solar spicules by localized Alfvénic pulses is investigated. A set of incompressible MHD equations in the two-dimensional x–z plane with steady flows and sheared magnetic fields is solved. Stratification due to gravity and transition region between chromosphere and corona is taken into account. An initially localized Alfvénic pulse launched below the transition region can penetrate from transition region into the corona. We show that the period of the transversal oscillations is in agreement with those observed in spicules. Moreover, it is found that the excited Alfvénic waves spread during propagation along the spicule length, and suffer efficient damping of the oscillations amplitude. The damping time of the transverse oscillations increased with decreasing k _b values.     

Heat transfer in the corona and transition region

Thermal transfer in closed magnetic tubes in the corona and transition region is described on the basis of a static model in which all heat generated is radiated away, though conduction transfers much of the heat to the transition region prior to emission. The rate of conductive transfer depends on the cross-section of the magnetic tube as it passes through the chromosphere and transition region. This is derived from the pressure in the normal chromosphere. There is then only one main parameter to establish conditions in the corona and transition region, viz. the heating per unit area of the Sun's surface, which must equal the observed radiation from corona and transition region. The density adjusts itself so as to radiate away all heat generated within the tube; conditions in the tube below the transition region have little influence other than to decide where the base of the transition region lies and the width of the region particularly in its lower parts. For the observed rate of heating, the computed densities (or pressures), the ratio of coronal to transition region emissions, and the distribution of radiation in the EUV spectrum agree closely with those observed. The optimum maximum temperatures are found with heating concentrated in the highest regions of the flux tubes. It is only in the lowest 20–40 km of the transition region, where T<10⁵K, that any additional heating is needed to explain EUV line intensities. The equation of heat transfer also has solutions in which the temperature is oscillatory with disance. These do not apply to the normal corona, but may be relevant to prominences.     

The Ly α and Ly β Profiles in Solar Prominences and Prominence Fine Structure

Ly α and Ly β line profiles in a solar prominence were observed with high spatial and spectral resolution with SOHO/SUMER. Within a 60-arcsec scan, we measure a very large variety of profiles: not only reversed and nonreversed profiles but also red-peaked and blue-peaked ones in both lines. Such a spatial variability is probably related to both the fine structure in prominences and the different orientations of mass motions. The usage of integrated-intensity cuts along the SUMER slit allowed us to categorize the prominence in three regions. We computed average profiles and integrated intensities in these lines in the range 2.36 – 42.3 W m⁻² sr⁻¹ for Ly α and 0.027 – 0.237 W m⁻² sr⁻¹ for Ly β. As shown by theoretical modeling, the Ly α/Ly β ratio is very sensitive to geometrical and thermodynamic properties of fine structure in prominences. For some pixels, and in both lines, we found agreement between observed intensities and those predicted by one-dimensional models. But a close examination of the profiles indicated a rather systematic disagreement concerning their detailed shapes. The disagreement between observations and thread models (with ambipolar diffusion) leads us to speculate about the importance of the temperature gradient between the cool and coronal regions. This gradient could depend on the orientation of field lines as proposed by Heinzel, Anzer, and Gunár (Astron. Astrophys. 442, 331, 2005).