Motions in solar magnetic tubes

The line-centre-magnetogram technique has been used to measure the average velocity in magnetic elements in plages and isolated magnetic elements (including dipoles) in Ca ii 8542, Mg i 5183, Fe i 8688 and C i 9111. The velocities vary from 0.6 km s^–1 downflow in the line of deepest origin to zero in the highest. The smooth curve obtained by combining these with the results of other investigators is in conformity with Giovanelli's (1977) theory of inflow in the neighborhood of the temperature minimum.This material is based upon research supported by the National Science Foundation under its contract No. AST 74-04129 with the Association of Universities for Research in Astronomy, Inc., for management, operation and maintenance of the Kitt Peak National Observatory.Visiting Astronomer, Kitt Peak National Observatory.     

The magnetic non-equilibrium of buoyant flux tubes in the solar corona

The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field.The path of an untwisted tube in an atmosphere with an ambient magnetic field is calculated. For a given footpoint separation, the height of the tube is lowered by increasing the strength of the external magnetic field. If the footpoints are slowly moved apart, the tube rises, until a threshold separation is reached beyond which there is no possible equilibrium height. This threshold width does not depend on the strength of the external field.The effects of twisting up a curved loop are studied, using an extension of results obtained for slender curved tubes with a straight axis. It is shown that for a twisted tube of given width, there can be two possible values of the equilibrium height. If, however, the tube is twisted more than a certain amount or if the footpoints are too widely separated there is no equilibrium. The critical footpoint separation for non-equilibrium is smaller for a twisted tube that an untwisted one.Twisting a tube or moving its feet apart is thus likely to result in non-equilibrium, causing the tube to rise indefinitely under the influence of the unbalanced buoyant force. It is suggested that this phenomenon could be important in the preflare stage of a large two-ribbon solar flare, by causing the initial slow rise of an active region filament. As well as being involved in the onset of an erupting prominence, this non-equilibrium may also be relevant to the formation of coronal loop transients.     

The time-delayed solar cycle luminosity modulation by sub-surface magnetic flux tubes

In order to explore the mechanism of the solar cycle luminosity change observed by the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of the spacecraft Solar Maximum Mission, we examined running mean time profiles of the daily ACRIM data from the declining phase of solar cycle 21 to the rising phase of solar cycle 22. By comparing them with those of the daily sunspot number, integrated surface magnetic field flux, integrated He I 10830 Å line equivalent width data, and two kinds of data sets of the daily integrated Ca II K line index as indices of the surface magnetic activities, we found (i) that the running mean time profiles of the six independent data sets have several peaks and valleys in common in one solar cycle with time intervals on the order of a few hundreds of days, and (ii) that the peaks and valleys of the ACRIM data profiles followed the peaks and valleys of all the other five indices of the surface activities by 40 to 60 days. This time delay phenomenon suggests (i) that the luminosity modulation was not directly caused by dark and bright features of the surface magnetic activities that the other five indices represent, and (ii) that the missing sunspot radiative flux which was blocked by sub-surface magnetic flux tubes of sunspots and sunspot groups should be re-radiated 40 to 60 days after the surface emergence of the magnetic flux tubes. The concept of the time delay resolves the enigma of the missing sunspot radiative flux and the enigma of the ACRIM experiment that the luminosity dropped when a sunspot or a sunspot group appeared on the surface while the yearly mean of the luminosity decreased and increased along with the decrease and increase of the yearly sunspot number of the 11-year solar cycle. A model of the mechanism to understand these phenomena is presented and its application to other stars is suggested.     

Motions and magnetic fields in filaments

Based on the developed method of jointly using data on the magnetic fields and brightness of filaments and coronal holes (CHs) at various heights in the solar atmosphere as well as on the velocities in the photosphere, we have obtained the following results:

The upward motion of matter is typical of filament channels in the form of bright stripes that often surround the filaments when observed in the HeI 1083 nm line.

The filament channels observed simultaneously in Hα and HeI 1083 nm differ in size, emission characteristics, and other parameters. We conclude that by simultaneously investigating the filament channels in two spectral ranges, we can make progress in understanding the physics of their formation and evolution.

Most of the filaments observed in the HeI 1083 nm line consist of dark knots with different velocity distributions in them. A possible interpretation of these knots is offered.

The height of the small-scale magnetic field distribution near the individual dark knots of filaments in the solar atmosphere varies between 3000 and 20000 km.

The zero surface separating the large-scale magnetic field structures in the corona and calculated in the potential approximation changes the inclination to the solar surface with height and is displaced in one or two days.

The observed formation of a filament in a CH was accompanied by a significant magnetic field variation in the CH region at heights from 0 to 30000 km up to the change of the predominant field sign over the entire CH area. We assume that this occurs at the stage of CH disappearance.

     

Radiative heating and the buoyant rise of magnetic flux tubes in the solar interior

We study the effect of radiative heating on the evolution of thin magnetic flux tubes in the solar interior and on the eruption of magnetic flux loops to the surface. Magnetic flux tubes experience radiative heating because (1) the mean temperature gradient in the lower convection zone and the overshoot region deviates substantially from that of radiative equilibrium, and hence there is a non-zero divergence of radiative heat flux; and (2) the magnetic pressure of the flux tube causes a small change of the thermodynamic properties within the tube relative to the surrounding field-free fluid, resulting in an additional divergence of radiative heat flux. Our calculations show that the former constitutes the dominant source of radiative heating experienced by the flux tube.In the overshoot region, the radiative heating is found to cause a quasi-static rising of the toroidal flux tubes with an upward drift velocity 10^-3|| cm s^-1, where _e – _ad < 0 describes the subadiabaticity in the overshoot layer. The upward drift velocity does not depend sensitively on the field strength of the flux tubes. Thus in order to store toroidal flux tubes in the overshoot region for a period comparable to the length of the solar cycle, the magnitude of the subadiabaticity (< 0) in the overshoot region must be as large as 3 × 10^–4. We discuss the possibilities for increasing the magnitude of and for reducing the rate of radiative heating of the flux tubes in the overshoot region.Using numerical simulations we study the formation of -shaped emerging loops from toroidal flux tubes in the overshoot region as a result of radiative heating. The initial toroidal tube is assumed to be non-uniform in its thermodynamic properties along the tube and lies at varying depths beneath the base of the convection zone. The tube is initially in a state of neutral buoyancy with the internal density of the tube plasma equal to the local external density. We find from our numerical simulations that such a toroidal tube rises quasi-statically due to radiative heating. The top portion of the nonuniform tube first enters the convection zone and may be brought to an unstable configuration which eventually leads to the eruption of an anchored flux loop to the surface. Assuming reasonable initial parameters, our numerical calculations yield fairly short rise times (2–4 months) for the development of the emerging flux loops. This suggests that radiative heating is an effective way of causing the eruption of magnetic flux loops, leading to the formation of active regions at the surface.The National Solar Observatory is one of the National Optical Astronomy Observatories by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.     

Motions and magnetic fields in quiescent prominences

An observed relation between line-of-sight velocities and the longitudinal component of the magnetic field in quiescent prominences is discussed. Weak fields in quiescent prominences are associated with large velocities determined from Doppler shifts of resolved emission knots and Doppler line widths measured in Ca ii K line. It is suggested that the observed irregular motions in prominences are driven by photospheric horizontal convection coupled by the prominence magnetic field. An energy flux of 3 × 10⁵ ergs cm^–2 sec^–1 present in the form of Alfvén waves in quiescent prominences is consistent with the observations.     

Dependence of the canopy height of solar magnetic flux tubes on its definition

By analyzing a canopy tube described by Athay, we point out the possibility that the different canopy heights given by different authors are caused by different definitions of canopy heights. For the same canopy tube, those heights where the magnetic field has horizontal components, where neighboring magnetic tubes meet each other and where the magnetic field becomes uniform or vertical range from near the solar photosphere to the solar corona.     

Basic properties of magnetic flux tubes and restrictions on theories of solar activity

It is shown that the mean longitudinal field in a magnetic flux tube is reduced, rather than enhanced, by twisting the tube to form a rope. It is shown that there is no magnetohydrostatic equilibrium when one twisted rope is wound around another. Instead there is rapid line cutting (neutral point annihilation). It is shown that the twisting increases, and the field strength decreases, along a flux tube extending upward through a stratified atmosphere.These facts are at variance with Piddington's recent suggestion that solar activity is to be understood as the result of flux tubes which are enormously concentrated by twisting, which consist of several twisted ropes wound around each other, and which came untwisted where they emerge through the photosphere.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.     

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.     

Radio and soft X-ray evidence for dense non-potential magnetic flux tubes in the solar corona

The source positions of solar radio bursts of spectral types I, III(U) and III(J) and V observed by the Culgoora radioheliograph are found to lie almost radially above soft X-ray loops on pictures taken by the S-056 telescope aboard Skylab. The radio source positions and the X-ray loops occur near magnetic loops on computed potential field maps. However, the magnetic induction required to explain the radio observations is much greater than the computed potential field value at that height. Dense current-carrying magnetic flux tubes emanating from active regions on the Sun and extending to 1.5R above the photosphere provide a satisfactory model for the radio bursts.     

The lack of chemical separation during the diffusion of gas into solar magnetic tubes

At a temperature well above T _min, so that hydrogen is mainly ionized and diffuses negligibly into magnetic tubes, helium can still be mainly neutral so that chemical differentiation could occur. Calculation shows that the rate is too small to acccount for variations in chemical abundance found in the solar wind.     

Dynamical effects in solar photospheric flux tubes

The interaction of an intense flux tube, extending vertically through the photosphere, with p-modes in the ambient medium is modelled by solving the time dependent MHD equations in the thin flux tube approximation. It is found that a resonant interaction can occur, which leads to the excitation of flux tube oscillations with large amplitudes. The resonance is not as sharp as in the case of an unstratified atmosphere, but is broadened by a factor proportional toH ^–2, whereH is the local pressure scale height. In addition, the inclusion of radiative transport leads to a decrease in the amplitude of the oscillations, but does not qualitatively change the nature of the interaction.     

Motions of Hα-spicules along the solar limb

A series of H-spectrograms obtained with the 21 in. Lyot coronagraph has been examined. Measurements of relative distances between spicules (nearly 50 features) embrace the time interval of about 21 min (38 pictures). It is found out that spicules oscillate along the limb with a characteristic time interval (period) about 1 min, characteristic amplitude of 1 arc sec and velocities about 10–15 km/s. The oscillations show no correlation for distant spicules.     

Gas entry into non-spot magnetic tubes

Gas penetration into twisted magnetic tubes can occur by the inward diffusion of neutral atoms in the neighbourhood of the temperature minimum between photosphere and chromosphere, where the degree of ionization is low. Again, turbulent buffeting indents tubes in the convection zone and, in particular near the photosphere, provides a larger area where the overall diffusion rate may be enhanced. These processes do not contribute rapidly to the gas content of magnetic tubes, but diffusion near the temperature minimum may well be the source of the observed downflow in magnetic points.     

Leaky and non-leaky oscillations in magnetic flux tubes

An extensive analysis, both analytic and numerical, of waves in flux tubes imbedded in (possibly) magnetic surroundings is given. It is shown that any wave confined to the tube and its neighbourhood can be put into one of seven categories. Simple criteria for deciding the existence of each type in any particular case are derived. Many other (leaky) modes are found which excite waves in the external medium and thereby lose energy to the surroundings. A number of asymptotic analyses allow much information to be gained about these without the need for numerical solution of the complicated equations involved. Three particular cases, pertaining to photospheric flux tubes, H fibrils, and coronal loops, are considered in detail.     

Magnetosonic waveguide model of solar wind flow tubes

We consider solar wind flow tubes as a magnetosonic wave-guide. Assuming a symmetric expansion in edges of slab-modelled wave-guide, we study the propagation characteristics of magnetosonic wave in the solar wind flow tubes. We present the preliminary results and discuss their implications.     

Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.