Computation of inner coronal magnetic fields from longitudinal field components on a spherical photosphere

A method is developed which for a certain day permits the approximate calculation of closed small and large scale magnetic field lines. From the photospheric longitudinal components of the magnetic field measured at this day normal components are derived taking into account the curvature of the solar surface. The magnetic fields are assumed to be potential or force-free fields.The method is applied to observations of September 5 and September 7, 1973. The projected magnetic field lines are compared with the loop structures which are visible in XUV pictures taken on these days. In the cases where no good agreement could be obtained for potential fields, force-free fields are calculated and fitted to the observed structures.     

Location of energy source for coronal heating on the photosphere

It is reported that ultra-fine dynamic ejections along magnetic loops of an active region originate from intergranular lanes and they are associated with subsequent heating in the corona. As continuing work, we analyze the same set of data but focus on a quiet region and the overlying EUV/UV emission as observed by the Atmospheric Imaging Assembly(AIA) on board Solar Dynamics Observatory(SDO). We find that there appear to be dark patches scattered across the quiet region and the dark patches always stay along intergranular lanes. Over the dark patches, the average UV/EUV emission at 131, 171, 304 and 1600 (middle temperature) is more intense than that of other regions and EUV brightness is negatively correlated with 10830  intensity, though, such a trend does not exist for high temperature lines at 94, 193, 211 and 335 . For the same quiet region, where both Ti O 7057  broad band images and 10830  filtergrams are available, contours for the darkest lane areas on Ti O images and dark patches on 10830  filtergrams frequently differ in space. The results suggest that the dark patches do not simply reflect the areas with the darkest lanes but are associated with a kind of enhanced absorption(EA) at 10830 . A strict definition for EA with narrow band 10830  filtergrams is found to be difficult. In this paper, we define enhanced absorption patches(EAPs) of a quiet region as the areas where emission is less than ~90% of the mean intensity of the region. The value is equivalent to the average intensity along thin dark loops connecting two moss regions of the active region. A more strict definition for EAPs, say 88%, gives even more intense UV/EUV emission over those in the middle temperature range. The results provide further observational evidence that energy for heating the upper solar atmosphere comes from the intergranular lane area where the magnetic field is constantly brought in by convection motion in granules.     

The resistances of the photosphere and of a flaring coronal loop

Solar Physics - We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called “dynamo models”, which invoke an analogy between the...     

The resistances of the photosphere and of a flaring coronal loop

We consider two aspects of solar flares from the point of view of circuit theory. First, we show that the so-called dynamo models, which invoke an analogy between the Earth's magnetosphere-ionosphere circuit and the solar corona-photosphere circuit, are illfounded. Second, we consider the rate of coronal energy release in the impulsive phase of a modest flare, and show that, if the energy going into mass motion can be neglected, the corona must present a resistance of about 10^–3 . Classical resistivity, even in a highly filamented circuit, cannot provide so high a resistance. Anomalous resistivity due to ion sound turbulence can provide the required resistance in this case, but is insufficient to explain the very high power levels inferred in some fast spikes.     

The evolution of line-tied coronal arcades including a converging footpoint motion

It has been demonstrated in the past that single, two-dimensional coronal arcades are very unlikely driven unstable by a simple shear of the photospheric footpoints of the magnetic field lines. By means of two-dimensional, time-dependent MHD simulations, we present evidence that a resistive instability can result if in addition to the footpoint shear a slow motion of the footpoints towards the photospheric neutral line is included. Unlike the model recently proposed by van Ballegooijen and Martens (1989), the photospheric footpoint velocity in our model is nonsingular and the shear dominates everywhere. Starting from a planar potential field geometry for the arcade, we find that after some time a current sheet is formed which is unstable with respect to the tearing instability. The time of its onset scales with the logarithm of the magnetic diffusivity assumed in our calculation. In its nonlinear phase, a quasi-stationary situation arises in the vicinity of the x-line with an almost constant reconnection rate. The height of the x-line above the photosphere and the distance of the separatrix footpoints remain almost constant in this phase, while the helical flux tube, formed above the neutral line, continuously grows in size.     

The evolution of a coronal streamer and the photospheric magnetic field

A large equatorial coronal streamer observed in the outer corona (3R ) grew in brightness and size during successive limb passages between October 6, 1973 and January 10, 1974 (solar rotations 1606–1611). Unlike previous studies of streamers and their photospheric associations, no definite surface feature could be identified in the present case. This suggests that the streamer is associated with the large scale photospheric magnetic field. Comparison of the streamer growth with observed underlying photospheric magnetic flux changes indicated that as the streamer increased in brightness, areal extent, and density, the photospheric magnetic flux decreased. Three possible explanations for the streamer's growth are presented; the conceptually simplest being that the decrease in photospheric field results in an opening of the flux tubes under the streamer which permits an increased mass flux through the streamer.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The study of toroidal magnetic configurations in a spherically symmetric gravitational field with applications to coronal loops and transients

One procedure for solving MHD equations is to search for a solution in an area that is restricted by boundary surfaces. This procedure requires the magnetic field to be truncated on the boundary. As a result, boundary current sheets appear. This approach is certainly acceptable for laboratory plasma experiments in which these surfaces are made of metal. For astrophysically relevant plasma, an alternative approach has been formulated by the author. We require the total magnetic energy,W, to be finite and, simultaneously, the magnetic fieldB to be continuous. The proposed approach leads to an eigenvalue problem that is treated analytically. The complete set of exact MHD solutions with multi-toroidal structure is obtained. These solutions are applied to coronal loops and transients, using the similarity assumption for time-dependent solutions.The derived pressure and density excess distributions are discussed. The estimation of the total mass excess, as well as the minimum value of the magnetic field intensity, is demonstrated. An indirect way of obtaining magnetic field measurements for transients, based on the developed model, is proposed.     

Evidence linking coronal transients to the evolution of coronal holes

The positions of X-ray coronal transients outside of active regions observed during Skylab were superposed on H synoptic charts and coronal hole boundaries for seven solar rotations. We confirmed a detailed spatial association between the transients and neutral lines. We found that most of the transients were related to large-scale changes in coronal hole area and tended to occur on the borders of evolving equatorial holes.Skylab Solar Workshop Post-Doctoral Appointee, 1975–1977.     

Solar force-free magnetic fields on and above the photosphere

If the problem of a magnetic field being force-free with = constant ( 0) is solved by some previously published methods, then the field obtained in the whole exterior of the Sun cannot have a finite energy content and the solution cannot be determined uniquely from only one magnetic field component given at the photosphere. A magnetic field in the volume between two parallel planes has been investigated by us (Chen and Wang, 1986).Based on observational data we present in this paper a suitable physical model for a half-space and adopted an integral transform established by us (Chen, 1980, 1983) to solve this problem. We then obtain a unique analytical solution of the problem from only one magnetic field component (longitudinal field observed) given at the photosphere. Not only the uniqueness of the solution has been proved but also the finiteness of magnetic energy content in the half-space considered has been verified. We have demonstrated that there is no singular point in the solution. It enables us to describe analytically the configurations of magnetic fields on and above the photosphere.     

Investigation of the evolution of coronal bright points and magnetic field topology

Our investigation has been carried using the instruments onboard the Solar Dynamics Observatory (SDO) providing a high resolution of images (AIA photographs and HMI magnetograms). We have investigated the structure and magnetic evolution of several coronal bright points and small scale N-S polarity magnetic fluxes closely associated with them. We also compare the evolution of the magnetic polarities of elementary isolated sources of positive and negative fluxes (magnetic bipoles) and coronal bright points. Tiny (“elementary”) coronal bright points have been detected. A standard coronal bright point is shown to be a group of “elementary” coronal bright points that flare up sequentially. Our investigation shows that a change in the magnetic fluxes of opposite polarities is observed before the flare of a coronal bright point. We show that not all cases of the formation of coronal bright points are described by the magnetic reconnection model. This result has not been considered previously and has not been pointed out by other authors.     

Meridional motions of magnetic features in the solar photosphere

We cross-correlate pairs of Mt. Wilson magnetograms spaced at intervals of 24–38 days to investigate the meridional motions of small magnetic features in the photosphere. Our study spans the 26-yr period July 1967–August 1993, and the correlations determine longitude averages of these motions, as functions of latitude and time. The time-average of our results over the entire 26-yr period is, as expected, antisymmetric about the equator. It is poleward between 10° and 60°, with a maximum rate of 13 m s^–1, but for latitudes below ±10° it is markedly equatorward, and it is weakly equatorward for latitudes above 60°. A running 1-yr average shows that this complex latitude dependence of the long-term time average comes from a pattern of motions that changes dramatically during the course of the activity cycle. At low latitudes the motion is equatorward during the active phase of the cycle. It tends to increase as the zones of activity move toward the equator, but it reverses briefly to become poleward at solar minimum. On the poleward sides of the activity zones the motion is most strongly poleward when the activity is greatest. At high latitudes, where the results are more uncertain, the motion seems to be equatorward except around the times of polar field reversal. The difference-from-average meridional motions pattern is remarkably similar to the pattern of the magnetic rotation torsional oscillations. The correspondence is such that the zones in which the difference-from-average motion is poleward are the zones where the magnetic rotation is slower than average, and the zones in which it is equatorward are the zones where the rotation is faster.Our results suggest the following characterization: there is a constant and generally prevailing motion which is perhaps everywhere poleward and varies smoothly with latitude. On this is superimposed a cycle-dependent pattern of similar amplitude in which the meridional motions of the small magnetic features are directed away from regions of magnetic flux concentration. This is suggestive of simple diffusion, and of the models of Leighton (1964) and Sheeley, Nash, and Wang (1987). The correspondence between the meridional motions pattern and the torsional oscillations pattern in the magnetic rotation suggests that the latter may be an artifact of the combination of meridional motion and differential rotation.     

Energy equilibrium in a coronal magnetic loop

Temperature distribution in the cylindrically symmetric coronal magnetic loop, (i) with constant pressure and (ii) with the pressure varying along the radial distance, of the (a) hotter apex and (b) cooler apex than base is investigated analytically by considering the equilibrium between the heat conduction and radiation loss. If the temperature of the loop does not lie within one of the specified temperature ranges, then the distribution is calculated numerically.The effect of the inclusion of heating due to an external source is studied and found that it increases the length of the loop. On the basis of the observed phenomenon, that the magnetic field varies along the loop, the temperature distribution in the loop is investigated for the loop-geometries proposed by Antiochos and Sturrock (1976). It is concluded that for the larger compression in the area of cross section, the height of the loop decreases.Present investigation shows that no loop with equal apex and base temperatures can exist, but a small variation between the two temperatures supports the existence of the loop, which can be observed in nature.     

On the appearance of magnetic flux in the solar photosphere

Ideas and models for the appearance of photospheric magnetic structure are confronted with observational data. Some findings are: The magnetic flux emerging in an active region consists of a bundle of flux tubes which were already concentrated before penetrating into the photosphere. A model of a rising bunch of flux tubes joining into a few strands at larger depths describes the coalescence of spots near the leading and following edges of the active region while more flux may surface near the center of the region. There is no observational evidence for appreciable helical twists in the flux bundles.Throughout the region's lifetime the magnetic elements move coherently, the whole magnetic structure rotates faster than the quiet photosphere. In active regions the convective flow at scales larger than the granulation is arrested by the magnetic structure. The long-lived supergranular cells around spots and in the enhanced network in turn determine the decay properties of spots and facular clusters. The modulation of the convective flow by the magnetic structure explains the slow dispersal of faculae.The hierarchy of magnetic elements (sunspots-pores-knots-facular clusters-facular points) may be explained by a set of magnetostatic flux tube models in the top of the convection zone. The underlying assumptions are that the heat flow along the magnetic field is reduced and that there is no heat exchange across the field except by radiation.A tentative model is proposed to account for the amplification, ascent and emergence of intense flux bundles. The assumptions are: (i) the field is concentrated in toroidal bundles by differential rotation, (ii) in the deep convection zone flux bundles are contained by the external turbulent pressure, and (iii) for field strengths up to the equipartition value efficient lateral heat exchange is possible. After a loop has surfaced radiative cooling and subsequent convective downflow reduce the temperature in the top of the flux tubes which then contract to field strengths well above the local equipartition value. There the heat flow is channelled along the field, which creates the conditions for the magnetostatic flux tube models without requiring a blocking of the heat flow somewhere within the tubes.The paper contains a brief review on the evolution of the magnetic field from the emergence in active regions up to the enigmatic disappearance, and a list of topics for further observational investigation.     

Filigree,magnetic fields,and flows in the photosphere

The interaction between small-scale magnetic fields and horizontal photospheric flows has been studied from observations of high angular resolution obtained with the Lockheed narrowband filter in the Swedish Vacuum Solar Telescope at La Palma. The measured magnetic flux density (B ) is in the range from a detection limit of 10 G to about 500 G, showing a good correspondence with the filigree. The magnetic flux elements take part in the local flows towards downdrafts at the supergranulation cell boundaries. The measured flux density, as well as the associated filigree intensity, decrease as the structures approach the downdrafts, presumably as a result of increased tilting and possibly submergence of flux into the downdrafts.     

Numerical studies of the Kelvin-Hemholtz instability in a coronal jet

Kelvin-Hemholtz(K-H)instability in a coronal EUV jet is studied via 2.5D MHD numerical simulations.The jet results from magnetic reconnection due to the interaction of the newly emerging magnetic field and the pre-existing magnetic field in the corona.Our results show that the Alfv e′n Mach number along the jet is about 5–14 just before the instability occurs,and it is even higher than 14 at some local areas.During the K-H instability process,several vortex-like plasma blobs with high temperature and high density appear along the jet,and magnetic fields have also been rolled up and the magnetic configuration including anti-parallel magnetic fields forms,which leads to magnetic reconnection at many X-points and current sheet fragments inside the vortex-like blob.After magnetic islands appear inside the main current sheet,the total kinetic energy of the reconnection outflows decreases,and cannot support the formation of the vortex-like blob along the jet any longer,then the K-H instability eventually disappears.We also present the results about how the guide field and flux emerging speed affect the K-H instability.We find that a strong guide field inhibits shock formation in the reconnecting upward outflow regions but helps secondary magnetic islands appear earlier in the main current sheet,and then apparently suppresses the K-H instability.As the speed of the emerging magnetic field decreases,the K-H instability appears later,the highest temperature inside the vortex blob gets lower and the vortex structure gets smaller.     

Large scale magnetic dipole and multipole progressive waves in the photosphere

The physical meaning of the photospheric short-period magnetic variation is interpreted. The motion of progressive waves along the equator with a 4.12 year circulation period may explain the basic feature of the variation. These waves have only one wavelength along the equator. The field distribution of one constituent of these waves is similar to that of a rotating dipole. The subharmonics of this dipole-wave are multipole terms circulating with periods of multiples of 4.12 years and the wave-lengths along the equator contain the same multiplying factor. The interference of the dipole and the multipole waves with a background rotation and with the 27-day Bartels rotation time results in a series of periods recorded by the earlier published analysis. The relevant linear relationship for the angular velocities has also been proved based on the magnetic observation.     

Observations of the longitudinal magnetic field in the transition region and photosphere of a sunspot

The Ultraviolet Spectrometer and Polarimeter on the Solar Maximum Mission spacecraft has observed for the first time the longitudinal component of the magnetic field by means of the Zeeman effect in the transition region above a sunspot. The data presented here were obtained on three days in one sunspot, have spatial resolutions of 10 arc sec and 3 arc sec, and yield maximum field strengths greater than 1000 G above the umbrae in the spot. The method of analysis, including a line-width calibration feature used during some of the observations, is described in some detail in an appendix; the line width is required for the determination of the longitudinal magnetic field from the observed circular polarization.The transition region data for one day are compared with photospheric magnetograms from the Marshall Space Flight Center. Vertical gradients of the magnetic field are computed from the two sets of data; the maximum gradients of 0.41 to 0.62 G km^–1 occur above the umbra and agree with or are smaller than values observed previously in the photosphere and low chromosphere.     

Studies of magnetic fields in the solar photosphere using the line-ratio method

The longitudinal magnetic field measured using the Fe I λ 525 and Fe I λ 524.7 nm lines and global magnetic field of the sun differ depending on the observatory. To study the cause of these discrepancies, we calculate the H _‖(525)/H _‖(524.7) ratios for various combinations of magnetic elements and compare them with the corresponding observed values. We use the standard quiet model of the solar photosphere suggesting that there are magnetic fields of different polarities in the range between zero and several kilogauss. The magnetic element distribution is found as a function of magnetic field strength and the parameters of this distribution are determined for which the calculated H _‖(525)/H _‖(524.7) ratio agrees with the observed one. The sigma-components are found to be shifted differently for various points of the Fe I λ 525 nm profile calculated for the inhomogeneous magnetic field. The farther the point is from the line center, the larger the sigma-components shift. Such a peculiarity of the profiles may be responsible for the discrepancies in the measured values of the global magnetic field obtained at different observatories. The increase in modulus of the global magnetic field during the maxima of solar activity can be due to a larger fraction of magnetic elements with kilogauss magnetic fields.     

The current sheet and Joule heating of a slender magnetic tube in the upper photosphere

Joule heating in a slender magnetic flux tube is investigated. The distribution of the magnetic field and electric sheet current encircling a vertical cylindrical magnetic tube is determined by equating the converging magnetic flux, which results from the converging and downward flow of the granulation, and the dissipative expanding magnetic flux due to Ohmic decay. Here, to ensure the mass flux conservation, an overshooting convective flow pattern resembling recent simulations was assumed. Even with the electrical resistivity from neutral hydrogen, the width of the current sheet was found to be 2 km, being much smaller than the tube diameter of 150 km, either from an exact or approximate (Gaussian) field distribution.The resultant energy flux density due to Joule heating averaged over the cylindrical cross sectional area, is 1 × 10⁹ erg cm^-2 s^-1 for an assumed photospheric magnetic field of 1500 G. This amount may supply enough energy to heat the temperature minimum region of the flux tube by T = 300 K in accord with observations, though our estimation of the excess radiation loss which should be supplied by the Joule heating to keep T = 300 K is rather uncertain.A possible role of the Joule heating on spicule formation is briefly discussed together with discussions on the slab geometry, general flow patterns, and non-constant field distributions inside the flux tube.     

Prominence condensation and magnetic levitation in a coronal loop

We describe the results of a model dynamic simulation of the formation and support of a narrow prominence at the apex of a coronal magnetic loop or arcade. The condensation process proceeds via an initial radiative cooling and pressure drop, and a secondary siphon flow from the dense chromospheric ends. The anti-buoyancy effect as the prominence forms causes a bending of the confining magnetic field, which propagates toward the semi-rigid ends of the magnetic loop. Thus, a wide magnetic hammock or well (of the normal-polarity Kippenhahn-Schlüter-type) is formed, which supports the prominence at or near the field apex. The simplicity of this 1.5-dimensional model, with its accompanying diagnostics, allows one to comprehend the various contributions to the nonlinear dynamics of prominence condensation and levitation.