Short-Period Waves That Heat the Corona Detected at the 1999 Eclipse

As a part of a study of the cause of solar coronal heating, we searched for high-frequency (1 Hz) intensity oscillations in coronal loops in the [Fexiv] coronal green line. We summarize results from observations made at the 11 August 1999 total solar eclipse from Râmnicu-Vâlcea, Romania, through clear skies. We discuss the image reduction and analysis through two simultaneous series of coronal CCD images digitized at 10 Hz for a total time of about 140 s. One series of images was taken through a 3.6 Å filter isolating the 5303 Å[Fexiv] coronal green line and the other through a 100 Å filter in the nearby K-corona continuum. Previous observations, described in Pasachoff et al. (2000), showed no evidence for oscillations in the [Fexiv] green line at a level greater than 2% of coronal intensity. We describe several improvements made over the 1998 eclipse that led to increased image clarity and sensitivity. The corona was brighter in 1999 with the solar maximum, further improving the data. We use Fourier analysis to search in the [Fexiv] channel for intensity oscillations in loops at the base of the corona. Such oscillations in the 1-Hz range are predicted as a result of density fluctuations from the resonant absorption of MHD waves. The dissipation of a significant amount of mechanical energy from the photosphere into the corona through this mechanism could provide sufficient energy to heat the corona. A Monte Carlo model of the data suggests the presence of enhanced power, particularly in the 0.75–1.0 Hz range, and we conclude that MHD waves remain a viable method for coronal heating.     

The solar wind and the temperature-density structure of the solar corona

The influence of the solar wind on large-scale temperature and density distributions in the lower corona is studied. This influence is most profoundly felt through its effect upon the geometry of coronal magnetic fields since the presence of expansion divides the corona into magnetically open and closed regions. Each of these regions is governed by entirely different energy transport processes. This results in significant temperature differences since only the open field regions suffer outward conductive heat losses. Because the temperature influences the density in an exponential manner, large density inhomogeneities are to be expected.An approximate method for calculating the temperature and density distribution in a known magnetic field geometry is outlined and numerical estimates are carried out for representative coronal conditions. These estimates show that temperature differences of a factor of about two and density differences of ten can be expected in the lower corona even for uniform base conditions. As a result, we do not regard the so-called coronal holes necessairly as locations of reduced mechanical heating. Alternatively, we suggest that they are regions of open magnetic field lines being continuously drained of energy contert by the solar wind expansion and outward thermal conduction.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Tunneling and interference of Alfvén waves

The propagation and interference of Alfvén waves in magnetic regions is studied. A multilayer approximation of the standard models of the solar atmosphere is used. In each layer, there is a linear law of temperature variation and a power law of Alfvén velocity variation. The analytical solutions of a wave equation are stitched at the layer boundaries. The low-frequency Alfvén waves (P > 1 s) are able to transfer the energy from sunspots into the corona by tunneling only. The chromosphere is not a resonance filter for the Alfvén waves. The interference and resonance of Alfvén waves are found to be important to wave propagation through the magnetic coronal arches. The transmission coefficient of Alfvén waves into the corona increases sharply on the resonance frequences. To take into account the wave absorption in the corona, a method of equivalent schemes is developed. The heating of a coronal arch by Alfvén waves is discussed.     

Dissipating waves in a hot,compressible, magnetic,structured atmosphere

The damping of ducted, fast, magnetohydrodynamic (MHD) waves by ion viscosity and electron heat conduction in a radiating, optically thin, warm, structured atmosphere has been evaluated. Dissipation is more effective in a warm plasma than in a cold one but, for waves ducted by solar coronal loops, dissipation is only efficient if the periods of the waves are shorter than a few tens of seconds and only if the background magnetic field is less than about 15 G. It appears that MHD waves of longer periods and in stronger magnetic fields will survive the dissipative mechanisms considered here and may be manifest as observable coronal oscillations.     

LASCO observations of the coronal rotation

The near-rigid rotation of the corona above the differential rotation of the photosphere has important implications for the form of the global coronal magnetic field. The magnetic reconfiguring associated with the shear region where the rigidly-rotating coronal field lines interface with the differentially-rotating photospheric field lines could provide an important energy source for coronal heating. We present data on coronal rotation as a function of altitude provided by the Large Angle Spectrometric Coronagraph (LASCO) instrument aboard the Solar and Heliospheric Observatory (SOHO) spacecraft. LASCO comprises of three coronagraphs (C1, C2, and C3) with nested fields-of-view spanning 1.1 R to 30 R. An asymmetry in brightness, both of the Fexiv emission line corona and of the broad-band electron scattered corona, has been observed to be stable over at least a one-year period spanning May 1996 to May 1997. This feature has presented a tracer for the coronal rotation and allowed period estimates to be made to beyond 15R, up to 5 times further than previously recorded for the white-light corona. The difficulty in determining the extent of differential motion in the outer corona is demonstrated and latitudinally averaged rates formed and determined as a function of distance from the Sun. The altitude extent of the low latitude closed coronal field region is inferred from the determined rotation periods which is important to the ability of the solar atmosphere to retain energetic particles. For the inner green line corona (<2 R) we determine a synodic rotation period of (27.4±0.1) days, whereas, for the outer white- light corona, (>2.5 R) we determine a rotation period of (27.7±0.1) days.     

Observations of quasiperiodic variations in the solar flux at 10.7 GHz

Observations of the continuum microwave flux at 2.8 cm from quiet regions of the solar disc reveal low amplitude, quasiperiodic fluctuations at periods of 234 s and 150 s. For oscillating elements 10 arc seconds in extent, the corresponding peak to peak temperature variations are 230 K and 190 K. The energy flux in the oscillations is estimated to be 2.5x10² ergs cm² s^–1, assuming they are caused by acoustic waves. If the oscillating elements are 1 arc second in extent, the energy flux is comparable to that required for coronal heating.No evidence is found for strong oscillations at periods greater than 250 s, although other authors have claimed microwave detection of strong fluctuations at periods of 280 s and 400 s.     

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.     

On the quality of resonant absorption as a coronal loop heating mechanism

The qualityQ of a resonance is defined as the ratio of the total energy contained in the system to the dissipation per driving cycle. Hence, a good quality resonance is one with little losses, i.e., little dissipation per driving cycle. However, for heating coronal plasmas by means of resonant absorption of waves, bad quality resonances are required. Here, the quality of the MHD resonances that occur when an inhomogeneous coronal loop is excited by incident waves is investigated for typical coronal loop parameter values in the frame work of linear, resistive MHD. It is shown that the resonances in coronal loops have bad quality and, hence, yield a lot of Ohmic heating per driving cycle compared to the total energy stored in the loop. As a consequence, the time scales of the heating process are relatively short and resonant absorption turns out to be a viable candidate for the heating of the magnetic loops observed in the solar corona.     

Космическое черенковское излучение

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Magnetic Dips in Prominences

Magnetic dips are generally assumed to be basic equilibrium configurations in quiescent solar prominences. Here we discuss two types of the magnetic dips which were considered in the literature: (1) dips resulting from a force-free magnetic equilibrium in the corona, and (2) magnetic dips which are formed in situations where the Lorentz force balances the weight of the prominence plasma. An important parameter which decides between these two cases is the plasma . For 1, the effect of the prominence material on the equilibrium structure is quite negligible and the case (1) holds. If, however, is larger, say between 0.1 and 1 or even higher, magnetic dips of the second kind are formed and they can be characterized by the angle 1 between the vertical and the direction of the field lines at the surface of the prominence structure. A simple and illustratory formula is derived to relate this angle to the plasma at the prominence center, namely ccot21. c=1 thus corresponds to 1=45°. Finally, we discuss the range of values of both c and 1 as deduced from various observations and conclude that the dips of the second kind are important for the prominence equilibria. We also suggest a new method for determination of the field-line inclination.     

Numerical simulation of coronal heating by resonant absorption of Alfvén waves

The heating of coronal loops by resonant absorption of Alfvén waves is studied in compressible, resistive magnetohydrodynamics. The loops are approximated by straight cylindrical, axisymmetric plasma columns and the incident waves which excite the coronal loops are modelled by a periodic external driver. The stationary state of this system is determined with a numerical code based on the finite element method. Since the power spectrum of the incident waves is not well known, the intrinsic dissipation is computed. The intrinsic dissipation spectrum is independent of the external driver and reflects the intrinsic ability of the coronal loops to extract energy from incident waves by the mechanism of resonant absorption.The numerical results show that resonant absorption is very efficient for typical parameter values occurring in the loops of the solar corona. A considerable part of the energy supplied by the external driver, is actually dissipated Ohmically and converted into heat. The heating of the plasma is localized in a narrow resonant layer with a width proportional to ^1/3. The energy dissipation rate is almost independent of the resistivity for the relevant values of this parameter. The efficiency of the heating mechanism and the localization of the heating strongly depend on the frequency of the external driver. Resonant absorption is extremely efficient when the plasma is excited with a frequency near the frequency of a so-called collective mode.     

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 .     

Impulsive phenomena in a small active region

The temporal and spatial variations of EUV emission from a small growing active region were investigated. Frequent localized short term ( few minutes) fluctuations in EUV emission were observed throughout the 7.2 hr interval when the most continuous observations were acquired. Approximately 20% of the 5 x 5 pixels had intensity variations exceeding a factor of 1.3 for the chromospheric L line, a factor of 1.5 for lines formed in the chromospheric-coronal transition region and a factor of 1.4 for the coronal Mg x line. A subflare in the region produced the largest intensity enhancements, ranging from a factor of 2.3 for the chromospheric L line to 8 for the transition region and coronal lines. The EUV fluctuations in this small active region are similar to those observed in coronal bright points, suggesting that impulsive heating is an important, perhaps dominant form of heating the upper chromospheric and lower coronal plasmas in small magnetic bipolar regions. The responsible mechanism most likely involves the rapid release of magnetic energy, possibly associated with the emergence of magnetic flux from lower levels into the chromosphere and corona.     

Solar flare activity and the structure of the coronal neutral line

In this study we analyse the positions of major flares from 1978 and 1979, with respect to the magnetic structure of the solar corona, as described by a potential field model. We find that major flares exhibit no strong association with the neutral line at the chromospheric level. However, when we calculate the neutral line's position at higher and higher altitudes in the corona, we find that major flares show an increasing tendency to be found close to these high-altitude coronal neutral lines. The correlation between flares and higher-altitude coronal neutral lines reaches a maximum at an altitude of 0.35R , and thereafter decreases as the neutral line is moved out to the source surface at an altitude of 1.50R . This indicates that major flares are strongly associated with coronal structure at the 0.35R level ( 250 000 km) - an altitude surprisingly high in the corona. This reinforces the idea that flares are associated with large-scale coronal magnetic fields and also indicates that the region of coronal magnetic topology important to solar flare processes may be larger than previously thought.     

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.     

High coronal structure of high velocity solar wind stream sources

When solar wind plasma in the trailing (eastern) edge of a high-speed stream is mapped back to its estimated source in the high corona using the constant radial velocity (EQRH) approximation, a large range of velocities appears to come from a restricted range in longitude, often only a few degrees. This actually constitutes a sharp eastern coronal boundary for the solar wind stream source, and demands that the boundary have a three-dimensional structure. Using interplanetary data, we infer a systematic variation in source altitude (identified approximately with the Alfvén point), with faster solar wind attaining its interplanetary characteristics at lower altitudes. This also affects the accuracy of the source longitude estimates, so that we infer a width in the high corona of 4–6° for the source of the trailing edges of streams which appear to originate from a single longitude. We demonstrate that the possible systematic interplanetary effects (in at least some cases) are not large ( 2° in heliocentric longitude). The relatively sharp boundaries imply that high-speed streams are well-defined structures all the way down to their low coronal sources, and that the magnetic field structure controls the propagation of the plasma through the corona out to the vicinity of the Alfvén point ( 20 R ).     

Forerunners: Outer rims of solar coronal transients

The large loop or blob-like transient events viewed in the white-light corona are rimmed by broad regions where the density is slightly enhanced above the pre-transient corona. Every one of the Skylab events studied for which sufficiently good Skylab coronagraph coverage is available shows this effect. The upper boundaries of these forerunners blend gradually into the background corona 1 to 2R above the transients' leading edges. In any single event, the coronal mass enhancement represented by the forerunner comprises up to 25% of the total excess mass present in the coronagraph's field of view and includes a much larger volume of the corona than previously attributed to the underlying transient. We have not yet seen a forerunner without an accompanying transient. Clearly, forerunners must be reckoned with in any proposed models of discrete outward coronal mass motions, because they indicate the presence of disturbed corona far ahead of the denser portions of the event.Skylab Solar Workshop Postdoctoral Appointee 1975–78. The Skylab Solar Workshops are sponsored by NASA and NSF and managed by the High Altitude Observatory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Characteristics of Coronal Alfvén Waves Deduced from Helios Faraday Rotation Measurements

A statistical study of Faraday rotation fluctuations (FRF) has been performed using polarization angle data of S-band (f = 2.3 GHz) radio spacecraft signals. The measurements were recorded during the recurring superior conjunctions of the Helios probes, during which the solar proximate point of the radio ray path reached heliocentric distances between 3 and 34 R. The most commonly found temporal FRF spectra are power laws with an average spectral index 1.5 over the frequency range from 1 mHz < v < 10 mHz. The FRF variance decreases with heliocentric distance, the falloff exponent being 8 for R < 6 R and 3 for distances 8 < R < 6 R < 16 R. The results are interpreted under the assumption that the FRF are produced by Alfvén waves propagating in the coronal plasma. For the applicable range of heliocentric distances it is shown that Alfvén waves are in a regime of free propagation and probably transfer much of their energy to the kinetic energy of the solar wind. The spatial power spectrum of magnetic field fluctuations is inferred to be strongly anisotropic, the irregularities extending along the background magnetic field with axial ratios of the order of 10.     

General-relativistic hierarchical cosmology: An exact model

An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R ^–2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R ^–, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.