Parametric generation of magnetoacoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal solar model atmosphere permeated by a horizontal magnetic field whose strength is proportional to the square root of the plasma density and in the approximation of a specified field for vertically propagating and nonpropagating magnetoacoustic-gravity waves, we consider the nonlinear interaction between the corresponding disturbances, to within quantities of the second order of smallness. We investigate the efficiency of the nonlinear generation of waves at difference and sum frequencies and of an acoustic flow (wind) as a function of the magnetic-field strength and the excitation frequency of the initial disturbances at the lower atmospheric boundary.     

The heating of solar magnetic flux tubes II. Nonadiabatic longitudinal tube waves

The formation of shocks and shock heating by radiatively damped longitudinal waves in solar magnetic flux tubes of different filling factors is studied. We consider three flux tubes of filling factors: 1%, 20%, and exponentially spreading which represent normal, enhanced network regions and the interior of supergranulation cells respectively. Monochromatic waves with periods 60 s and energy fluxes of 4.0 · 10⁸ erg cm^?2 s^?1 are assumed to propagate in the tubes. We find that the H^?-continuum losses and the Mg II line emission are much reduced in the tube of small filling factor while the mean temperatures are roughly similar in both tubes. The exponential flux tube shows little or no shock heating and no radiation damping. Shocks form earlier in the tube of high filling factor, and have larger strength.     

On heating of solar active regions by magnetic energy dissipation

The Tucker's proposal of heating of active regions by magnetic energy dissipation has been found to be unsatisfactory in its present form because it predicts unacceptably high values of the twisting velocity for the magnetic field.     

On the chromospheric velocity field in sunspot regions

The wavelength shifts of approximately 8000 absorption elements in the H-line from spectra of 66 different sunspot regions have been measured.The average velocity field in the chromosphere close to sunspots is determined. Inside 15000 km from the spot's penumbral rim the average velocity vector is directed towards the spot and downwards in the chromosphere; the angle with the horizontal direction is on the average equal to 20°. The magnitude of the average velocity vector shows a maximum of 6.8 ± 1.2 km/sec just outside the penumbral rim and decreases quickly with increasing distance from the spot. Outside 15000 km from the penumbral rim the average velocity vector is small (-0.7 km/sec) and directed nearly vertically outwards from the sun. No significant tangential component of the average velocity field is found.The deviations of the individual elements from the average velocity field are on the average larger than the value of the average velocity. The total rms deviation in the line of sight velocity is equal to 6.8 km/sec. Thus, a large number of elements, as used in this investigation, is required to give significant values of the average velocity vector.We have also observed velocities in the penumbra. The average velocity vector is here probably small and its direction uncertain. The rms deviation in the line of sight velocities observed in the penumbra is equal to 7.5 km/sec.     

Small-scale magnetic flux tube diagnostics in a solar flare

I ±V profiles of the Fei 5247 and 5250 lines in the 2B flare of June 16, 1989 have been analyzed. A bright knot of the flare outside the sunspot where the central intensity of H reached a peak value of 1.4 (relative to the continuum) has been explored. The Fei 5250/Fei 5247 magnetic line ratio based on the StokesV peak separations of these lines at five evolutionary phases of the flare (including the start of the flare, the flash phase, the peak and 16 min after the peak) has been analyzed. It was found that the StokesV peak separation for the Fei 5250 line was systematically larger than that of the Fei 5247 line. This is evidence for the presence in the flare of small-scale flux tubes with kG fields. The flux tube magnetic field strength was about 1.1 kG at the start of the flare and during the flash phase, 1.55 kG during the peak, and 1.38 kG 16 min after the peak. The filling factor,, appears to decrease monotonically during the flare.     

On the possibility of a bimodal solar dynamo

A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analogous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4–5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a possible explanation of chromospheric line asymmetries of solar flares

We discuss the relationship between the chromospheric downward motions and the line asymmetries in solar flares by using a simple model. It is found that both the blue asymmetry and red asymmetry of the H line can be caused by downward motions, as long as the moving material is confined to different heights in the chromosphere. The Ca ii K line, however, mainly shows a red asymmetry. The results can qualitatively explain some observations.     

Magneto-gravity waves and the heating of the solar corona

It is generally believed that the heating of the solar corona is caused by waves originating in the photosphere and propagating into the corona where their energy is dissipated. The medium through which these waves propagate is in general permeated by magnetic fields complicating the behaviour of this propagation considerably. We have therefore analysed the wave motions in a plasma permeated by constant magnetic and gravitational fields. In general, three waves modes were found, which we called the + mode, –mode, and the Alfvén mode. Each mode was found to be strongly coupled to each of the three kinds of motion; acoustic, gravity, and hydromagnetic. However, the Alfvén mode was found to be separable from the dispersion relation, and therefore independent of compressibility and gravity. The local dispersion relation is derived and expressed in nondimensional form independent of the constants that describe a particular atmosphere. From the dispersion relation one can show that rising waves propagate either with a constant or a growing wave amplitude depending on the magnitudes and directions of the gravitational field, magnetic field, and the wave vector. The variation of the density with height is taken into account by a generalized W.K.B. method. Equations are found which give the height at which wave reflection occurs, giving the upper bound for possible wave propagation.Work supported by the National Aeronautics and Space Administration under Research Grant NGR-29-001-016.On leave of absence from the Desert Research Institute and Department of Physics, University of Nevada, Reno, Nevada, U.S.A.     

Propagation of magnetoacoustic-gravity waves in a horizontally-stratified medium: IV. kinematics

A model magneto-atmosphere is used to discuss the behavior of the group velocity for magnetoacoustic-gravity (MAG) waves as a function of their angular frequency. The qualitative frequency/time history of a signal generated by a source differs significantly from the case where the magnetic field is zero, for which a clear distinction may be made between the acoustic and gravity components of the signal.     

Comments on the heating of solar active regions by magnetic energy dissipation

The method of Kumar and Narain (1985) to calculate the twisting velocity of magnetic field appears to be erroneous. Hence, their conclusion about Tucker's proposal for the heating of active regions by magnetic energy dissipation may not be correct.     

X-ray heating of a low-temperature region in chromospheric flares

Part of the proper X-ray emission of a flare is absorbed in the chromosphere and heats the region which creates an optical (in particular Hα) flare emission. The heating of chromosphere by X-ray emission may be responsible for the diffuse halo around the flare kernels. The optical emission of flare kernels, whose main sources of heating are energetic particles and/or thermal fluxes, may be also increased. By simple model calculations the present paper discusses the possibility of such effects for the large flare of 1972 August 7.     

On the propagation of chromospheric condensations in solar flares (I)

We simulate dynamically the downward propagation of the chromospheric condensation, which originates following the chromospheric evaporation during solar flares. Our attention is concentrated on the lower part of the atmosphere. The top of the chromosphere (base of the transition region) is regarded as the top boundary. The condensation is mimicked by assuming an impulsive pressure increase at the top boundary. Using such a method, we compute in detail the evolution process of a condensation. The results show that the condensation can penetrate into the deeper atmosphere, though it becomes very weak at the later phase. Moreover, we also discuss the possibility that the mass motions in the condensation may cause the asymmetries of some spectral lines as observations have indicated.     

Dual chromospheric flows in the vicinity of a solar pore

Chromospheric line-of-sight velocities are investigated in a small pore and its vicinity on the part of the active region NOAA 11024 with a size of 5″. We used H_α spectra of the active region and undisturbed atmosphere obtained with the French–Italian solar telescope THEMIS (Tenerife, Spain). Significant line-of-sight velocity time variations are found. At the beginning of the observations, the investigated region consisted of two areas of oppositely directed flows. The first area had a bright point in the vicinity of the pore and the second area covered the pore. There were upflows in the former and downflows in the latter. Oppositely directed flows appeared in both areas 2.7 min after the start of observations. In the part of the active region with a length of 2Mm, two oppositely directed flows within the same resolution elements, the so-called dual flows, were observed. The size of the area occupied by the dual flows varied quickly. The area shifted toward the pore. The velocity of upflows and downflows reached 25 km/s. The downflows in the first area lasted only for approximately 1 min. Upflows in the second area gradually covered the pore and lasted for 2 min. The resulting velocity field distribution can be due to a new small-scale magnetic flux emergence.     

On the propagation of chromospheric condensations in solar flares (II)

We study the evolution of the mass motion velocity in the chromospheric condensation, when it propagates into the deeper atmosphere. The condensation is represented by a shock-like structure. Its momentum equation can be solved after some approximations. The computations are carried out for two cases, i.e., the case that the gas pressure just behind the condensation front is constant and the case that the pressure increase at the top of the condensation is constant. The results show that the duration of the condensation in the second case is considerably longer than that in the first case. The most evident difference of the velocity evolution between the two cases appears in their later phase. A comparison of the results in this paper with the dynamic simulations indicates that the second case may be closer to the real situation.     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.     

Initial phase of chromospheric evaporation in a solar flare

In this paper we discuss the initial phase of chromospheric evaporation during a solar flare observed with instruments on the Solar Maximum Mission on May 21, 1980 at 20:53 UT. Images of the flaring region taken with the Hard X-Ray Imaging Spectrometer in the energy bands from 3.5 to 8 keV and from 16 to 30 keV show that early in the event both the soft and hard X-ray emissions are localized near the footpoints, while they are weaker from the rest of the flaring loop system. This implies that there is no evidence for heating taking place at the top of the loops, but energy is deposited mainly at their base. The spectral analysis of the soft X-ray emission detected with the Bent Crystal Spectrometer evidences an initial phase of the flare, before the impulsive increase in hard X-ray emission, during which most of the thermal plasma at 10⁷ K was moving toward the observer with a mean velocity of about 80 km s^-1. At this time the plasma was highly turbulent. In a second phase, in coincidence with the impulsive rise in hard X-ray emission during the major burst, high-velocity (370 km s^-1) upward motions were observed. At this time, soft X-rays were still predominantly emitted near the loop footpoints. The energy deposition in the chromosphere by electrons accelerated in the flare region to energies above 25 keV, at the onset of the high-velocity upflows, was of the order of 4 × 10¹⁰ erg s^-1 cm^-2. These observations provide further support for interpreting the plasma upflows as the mechanism responsible for the formation of the soft X-ray flare, identified with chromospheric evaporation. Early in the flare soft X-rays are mainly from evaporating material close to the footpoints, while the magnetically confined coronal region is at lower density. The site where upflows originate is identified with the base of the loop system. Moreover, we can conclude that evaporation occurred in two regimes: an initial slow evaporation, observed as a motion of most of the thermal plasma, followed by a high-speed evaporation lasting as long as the soft X-ray emission of the flare was increasing, that is as long as plasma accumulation was observed in corona.     

The universally growing mode in the solar atmosphere: coronal heating by drift waves

N -body simulations are an important tool in the study of formation of large-scale structures. Much of the progress in understanding the physics of galaxy clustering and comparison with observations would not have been possible without N -body simulations. Given the importance of this tool, it is essential to understand its limitations as ignoring these can easily lead to interesting but unreliable results. In this paper, we study the limitations due to the finite size of the simulation volume. In an earlier work, we proposed a formalism for estimating the effects of a finite box size on physical quantities and applied it to estimate the effect on the amplitude of clustering, mass function. Here, we extend the same analysis and estimate the effect on skewness and kurtosis in the perturbative regime. We also test the analytical predictions from the earlier work as well as those presented in this paper. We find good agreement between the analytical models and simulations for the two-point correlation function and skewness. We also discuss the effect of a finite box size on relative velocity statistics and find the effects for these quantities scale in a manner that retains the dependence on the averaged correlation function     .     

On a possible mechanism of solar faculae heating

A new mechanism of solar faculae heating is suggested. Interaction of the convective motion with the magnetic field results in decrease of its scale down to values providing for an ohmic dissipation and leading to heating at the photospheric level. Photospheric magnetic fields, faculae and granulation are considered as a combined problem. The heating mechanism causes the observed correlation of faculae brightness with the velocity field. Some points of observation are proposed for examining the action of the suggested mechanism. The effective decreasing of the magnetic field scale may be responsible for the origin of the fine structure. The model does not contradict generally accepted ideas on the active region development.     

Acceleration of pickup interstellar protons by shock waves in corotating solar wind regions

It follows from numerous measurements of the differential fluxes of energetic charged particles in corotating interaction regions between solar wind streams with different speeds that the spectra of particles accelerated by reverse shocks are harder than those of particles accelerated by forward shocks. The measurements cannot be explained in terms of the theory of diffusive acceleration (first-order Fermi acceleration). We show that the measurements can be easily explained in terms of the theory of drift acceleration of charged particles by shock waves with allowance made for their multiple scattering from the front.     

Temperature minimum heating in solar flares by resistive dissipation of Alfvén waves

We examine the possibility that the strong heating produced at temperature-minimum levels during solar flares is due to resistive dissipation of Alfvén waves generated by the primary energy release process in the corona. It is shown how, for suitable parameters, these waves can carry their energy essentially undamped into the temperature-minimum layers and can then produce a degree of heating consistent with observations.Also Department of Applied Physics, Stanford University.