Coronal force-free magnetic field: Source-surface model

Models of the magnetic field in the solar chromosphere and corona are still mainly based on theoretical extrapolations of photospheric measurements. For the practical calculation of the global field, the so-called source-surface model has been introduced, in which the influence of the solar wind is described by the requirement that the field be radial at some exterior (source) surface. Then the assumption that the field is current-free in the volume between the photosphere and this surface allows for its determination from the photospheric measurement. In the present paper a generalization of the source-surface model to force-free fields is proposed. In the generalized model the parameter( = ×B·B/B ²)must be non-constant (or vanish identically) and currents are restricted to regions with closed field lines. A mathematical algorithm for computing the field from boundary data is devised.     

The geometrical height-scale and the pressure equilibrium in the sunspot umbra

Spectra of spots very near to the solar limb (limb distance 8) are used to determine the height difference between the levels of formation of the continuum and the line cores of 60 medium-strong Fraunhofer lines. For all lines (with Rowland Intensity < 10), this difference is < 1 (= 725 km) and well correlated with the Rowland intensity. The line absorption coefficient is calculated for some lines with known oscillator strength. This gives a possibility to deduce a value for the scale height of the umbra, which is found to be about 100 km, thus being equal to the photospheric scale height. Pure hydrostatic equilibrium exists, therefore, in the umbra, and vertical magnetic forces are negligible. Other methods for determining the scale height are discussed for comparison.The horizontal pressure equilibrium is discussed by taking into account the Wilson effect, and by neglecting dynamic terms (flow of matter). The magnetic field is confirmed to be force-free in higher layers (chromosphere). The pressure difference umbra-photosphere increases towards deeper layers, having a maximum at ^* - 1 which corresponds to about two times the magnetic pressure H ²/8. If rotational symmetry of the field is assumed, this can be explained by a minimum radius of curvature of the field lines of 1/4 spot radius.Mitteilungen aus dem Fraunhofer Institut Nr. 90.     

The stationary post-flare arch of May 21/22, 1980

On May 21/22, 1980 the Hard X-Ray Imaging Spectrometer aboard the SMM imaged an extensive coronal structure after the occurrence of a two-ribbon flare on May 21, 20:50 UT. The structure was observed from 22:20 UT on May 21 until its disappearence at 09:00 UT on May 22.At 22:20 UT the brightest pixel in the arch was located at a projected altitude of 95 000 km above the zero line of the longitudinal magnetic field. At 23:02 UT the maximum of brightness shifted to a neighbouring pixel with approximately the same projected altitude. This sudden shift indicates that the X-ray structure consisted of (at least) two separate arches at approximately the same altitude, one of which succeeded the other as the brightest arch in the structure at 23:02 UT.From 23:02 UT onwards the maximum of brightness did not change its position in the HXIS coarse field of view. With a spatial resolution of 32 this places an upper limit of 1.1 km s^-1 on the rise velocity of the arch. Thus, contrary to a similar arch observed on November 6/7, where rise velocities of the order of 10 km s^-1 were measured in the same phase of development, the May 22 arch was a stationary structure at an altitude of 145000 km.The following values were estimated for the physically relevant quantities of the May 21/22 arch at the time of its maximum brightness (23:00 UT): temperature T 6.3 × 10⁶ K, electron density n _e 1.1 × 10⁹ cm^-3, total emitting volume V 5 × 10²⁹ cm³, energy density 2.9 erg cm^–3, total energy contents E 1.4 × 10³⁰ erg, total mass M 9 × 10¹⁴ g.The top of the arch was observed at 145 000 km altitude within 1.5 hr after the flare occurrence. Since it seems unlikely that the structure already existed prior to the flare at 20:50 UT, the arch must have risen to its stationary position with an average velocity exceeding 17 km s^–1 (possibly much faster). We speculate that the arch was formed very fast at the flare onset, when (part of) the active region loop system was elevated within minutes to the observed altitude.     

The formation of flare loops by magnetic reconnection and chromospheric ablation

Slow-mode shocks produced by reconnection in the corona can provide the thermal energy necessary to sustain flare loops for many hours. These slow shocks have a complex structure because strong thermal conduction along field lines dissociates the shocks into conduction fronts and isothermal subshocks. Heat conducted along field lines mapping from the subshocks to the chromosphere ablates chromospheric plasma and thereby creates the hot flare loops and associated flare ribbons. Here we combine a non-coplanar compressible reconnection theory with simple scaling arguments for ablation and radiative cooling, and predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G the temperature of the hot flare loops decreases from 1.2 × 10⁷ K to 4.0 × 10⁶ K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0% to 86% of the total field. When the perpendicular component exceeds 86% of the total field or when the altitude of the reconnection site exceeds 10⁶km, flare loops no longer occur. Shock enhanced radiative cooling triggers the formation of cool H flare loops with predicted densities of 10¹³ cm^–3, and a small gap of 10³ km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons.     

Average photospheric poloidal and toroidal magnetic field components near solar minimum

Average (over longitude and time) photospheric magnetic field components are derived from 3 Stanford magnetograms made near the solar minimum of cycle 21. The average magnetograph signal is found to behave as the projection of a vector for measurements made across the disk. The poloidal field exhibits the familiar dipolar structure near the poles, with a measured signal in the line Fe i 5250 Å of 1 G. At low latitudes the poloidal field has the polarity of the poles, but is of reduced magnitude ( 0.1 G). A net photospheric toroidal field with a broad latitudinal extent is found. The polarity of the toroidal field is opposite in the nothern and southern hemispheres and has the same sense as subsurface flux tubes giving rise to active regions of solar cycle 21.These observations are used to discusse large-scale electric currents crossing the photosphere and angular momentum loss to the solar wind.Now at Kitt Peak National Observatory, Tucson, Ariz. 85726, U.S.A.     

Polar coronal plumes

Polar coronal plumes are modeled using concentrations of magnetic flux at 1.01R , and assuming the field is current-free, or a potential field. Identifying the density enhancement of plumes with magnetic flux concentration produces good agreement between 1.01R and 1.10R , for model conditions of a large background magnetic field and a plume separation of 50 000 to 70 000 km at the base. Beyond 1.10R , both plumes and the potential field diverge very nearly as r ².Also Department of Astrogeophysics, University of Colorado, Boulder, Colo. 80309, U.S.A. Presently visiting Stanford University Institute for Plasma Research, Via Crespi, Stanford, Calif. 94303, U.S.A.     

On the physical conditions in the photospheric network: An improved model of solar faculae

Semi-empirical models of solar faculae, cospatial with strong photospheric magnetic fields, have been constructed from continuum observations. The center-to-limb contrast of the various models was computed taking into account their geometrical shape. The adopted model whose horizontal size was taken to be 750 km, indicates that, in field regions, the temperature begins to rise outwards at z -125 km (above ₅₀₀₀ = 1) and that the extrapolated temperature at z -400 km is about 1500 K above that of the undisturbed atmosphere; the electron density is higher by a factor of about 30.     

Non-inductive current driven by Alfvén waves in solar coronal loops

It has been shown that Alfvén waves can drive non-inductive current in solar coronal loops via collisional or collisionless damping. Assuming that all the coronal-loop density of dissipated wave power (W= 10–3 erg cm^–3 s^–1), which is necessary to keep the plasma hot, is due to Alfvén wave electron heating, we have estimated the axial current density driven by Alfvén waves to be jz 10³–10⁵ statA cm^–2. This current can indeed support the quasi-stationary equilibrium and stability of coronal loops and create the poloidal magnetic field up to B 1–5 G.     

Magnetosonic waves in structured atmospheres with steady flows

The magnetosonic modes of magnetic plasma structures in the solar atmosphere are considered taking into account steady flows of plasma in the internal and external media and using a slab geometry. The investigation brings nearer the theory of magnetosonic waveguides, in such structures as coronal loops and photospheric flux tubes, to realistic conditions of the solar atmosphere. The general dispersion relation for the magnetosonic modes of a magnetic slab in magnetic surroundings is derived, allowing for field-aligned steady flows in either region. It is shown that flows change both qualitatively and quantitatively the characteristics of magnetosonic modes. The flow may lead to the appearance of a new type of trapped mode, namelybackward waves. These waves are the usual slab modes propagating in the direction opposite to the internal flow, but advected with the flow. The disappearance of some modes due to the flow is also demonstrated.The results are applied to coronal and photospheric magnetic structures. In coronal loops, the appearance of backward slow body waves or the disappearance of slow body waves, depending upon the direction of propagation, is possible if the flow speed exceeds the internal sound speed ( 300 km s^–1). In photospheric tubes, the disappearance of fast surface and slow body waves may be caused by an external downdraught of about 3 km s^–1.     

Coronal Mass Ejection of 15 May 2001: I. Evolution of Morphological Features of the Eruption

We study the initiation and development of the limb coronal mass ejection (CME) of 15 May 2001, utilizing observations from Mauna Loa Solar Observatory (MLSO), the Solar and Heliospheric Observatory (SOHO), and Yohkoh. The pre-eruption images in various spectral channels show a quiescent prominence imbedded in the coronal void, being overlaid by the coronal arch. After the onset of rapid acceleration, this three-element structure preserved its integrity and appeared in the MLSO MK-IV coronagraph field of view as the three-part CME structure (the frontal rim, the cavity, and the prominence) and continued its motion through the field of view of the SOHO/LASCO coronagraphs up to 30 solar radii. Such observational coverage allows us to measure the relative kinematics of the three-part structure from the very beginning up to the late phases of the eruption. The leading edge and the prominence accelerated simultaneously: the rapid acceleration of the frontal rim and the prominence started at approximately the same time, the prominence perhaps being slightly delayed (4 – 6 min). The leading edge achieved the maximum acceleration a_max 600 ± 150 m s^–2 at a heliocentric distance 2.4 –2.5 solar radii, whereas the prominence reached a_max 380± 50 m s^–2, almost simultaneously with the leading edge. Such a distinct synchronization of different parts of the CME provides clear evidence that the entire magnetic arcade, including the prominence, erupts as an entity, showing a kind of self-similar expansion. The CME attained a maximum velocity of v_max 1200 km s^–1 at approximately the same time as the peak of the associated soft X-ray flare. Beyond about 10 solar radii, the leading edge of the CME started to decelerate at a–20 m s^–2, most likely due to the aerodynamic drag. The deceleration of the prominence was delayed for 10 –30 min, which is attributed to its larger inertia.     

Coronal streamers

This work extends a previous analysis of helmet streamers into the somewhat higher range of coronal temperature where streamer geometries are shown to be open, in the sense that there is solar wind expansion everywhere. It is shown that, for a given photospheric field distribution, a certain minimum temperature is required for this type of streamer - this minimum temperature coinciding with the maximum temperature compatible with a helmet streamer. Near this minimum temperature, the streamer is very constricted and the critical point in the streamer core lies at the point of minimum cross-section. Hence the throat, under these conditions, becomes a true geometrical throat rather than the conventional gravitational throat. As the temperature is increased, the streamer shape becomes correspondingly more radial and the location of the throat becomes asymptotically more gravitationally determined. Residual manifestations of coronal streamers at large distances are investigated. It is found that lateral density variations at the earth's orbit tend to be small but velocity variations can become appreciable (100–200 km/sec) for streamers originating in regions where the photospheric magnetic field is strong. At large distances, either streamer or interstreamer regions can dominate, the former occurring at high temperature (2 × 10⁶K) and the latter being favored at lower temperature (1.5 × 10⁶K). In all cases the cross-section becomes essentially radial just above the point where it is a minimum. The marked sensitivity of these shapes to coronal temperature is pointed out - computations indicating that streamers can vary from helmet configurations to almost radial filaments for a very slight increase in temperature. This behavior suggests a strong solar cycle influence upon coronal form.     

Time variation of the spectrum of Gyro-synchrotron emission from the Sun

The emission spectra and their time variations of gyro-synchrotron emission from an ensemble of energetic electrons are computed for some initial power-law distributions of the electron energies N()d= ^– with =2 or 4. The spectra and decay curves of the emission are compared with solar microwave bursts in order to separately estimate the magnetic field H and . From a limited number of observations, we have 3 and H 10³ gauss for the microwave impulsive bursts, and 2 and H (500–1000) gauss for the microwave type-IV bursts.     

Coronal magnetic fields from microwave polarization observations

The solar active region (AR) 7530 was observed at 6 cm on July 3 and 4, 1993 with the Westerbork Synthesis Radio Telescope, using a multi-channel receiver with very narrow bandwidth. We compare the radio data with Yohkoh SXT observations and with the magnetic field extrapolated from the Marshall vector magnetograms in the force-free and current-free approximations. The comparison with soft X-rays shows that, although a general agreement exists between the shape of the radio intensity map and the X-ray loops, the brightness temperature, T _b, obtained using the parameters derived from the SXT is much lower than that observed. The comparison with the extrapolated photospheric fields shows instead that they account very well for the observed T _b above the main sunspots, if gyroresonance emission is assumed. In the observation of July 4 an inversion and strong suppression of the circular polarization was clearly present above different portions of the AR, which indicates that particular relationships exist between the electron density and the magnetic field in the region where the corresponding lines of sight cross the field quasi-perpendicularly. The extrapolated magnetic field at a much higher level ( 10¹⁰ cm), satisfies the constraints required by the wave propagation theory all over the AR. However, a rather low electron density is derived.     

Interplanetary acceleration of energetic particles at 1 and 5 AU

Energetic particle (0.1 to 100 MeV protons) acceleration is studied by using high resolution interplanetary magnetic field and plasma measurements at 1 AU (HEOS-2) and at 5 AU (Pioneer 10). Energy changes of a particle population are followed by computing test particle trajectories and the energy changes through the particle interaction with the time varying magnetic field. The results show that considerable particle acceleration takes place throughout the interplanetary medium, both in the corotating interaction regions (CIR) (5 AU), and in quiet regions (1 AU). Although shocks may contribute to acceleration we suggest statistical acceleration within the CIRs is sufficient to explain most energetic particle observations (e.g., McDonaldet al., 1975; Barnes and Simpson, 1976).The first and second order statistical acceleration coefficients which include transit time damping and Alfvén resonance interactions, are found to be well represented byD _T 8.5×10^–6 T ^0.5 MeV s^–1 andD _TT 4×10^–6 T ^1.5 MeV² s^–1 at 5 AU.By comparison, Fisk's estimates (1976), based on quasi-linear theory for transit-time damping, gaveD _TT 5×10^–7 T MeV² s^–1 at 1 AU.     

Loss of equilibrium in coronal loops

The loss of equilibrium in coronal magnetic field structures is a possible source of energy for coronal heating and solar flares. We investigate whether such a loss of equilibrium occurs when a coronal loop is progressively twisted by photospheric motions. In studies of 2-D cylindrical equilibria, long loops have been found to be of constant cross-sectional area along most of their length, with axial variations being confined to narrow boundary layers. We use this information to develop a 1-D line-tied model, for a 2-D coronal loop. We specify the twist in terms of the azimuthal field and more physically, in terms of the photospheric footpoint displacement. In the former case we find a loss of equilibrium, but not in the latter. We also examine a twisted loop with a non-zero plasma pressure. The loss of equilibrium is only found at high-plasma . It is conjectured that such high- can occur in flare loops and prior to a prominence eruption. However, when the plasma evolves adiabatically, there is no loss of equilibrium.     

Quasi-stationary solar wind in ray structures of the streamer belt

It is shown on the basis of analyzing the LASCO/SOHO data that the main quasi-stationary solar wind (SW), with a typical lifetime of up to 10 days, flows in the rays of the streamer belt. Depending on R, its velocity increases gradually from V3 km s^–1 at R1.3 R to V170 km s^–1 at R15 R . We have detected and investigated the movement of the leading edge of the main solar wind at the stage when it occupied the ray, i.e., at the formative stage of a quasi-stationary plasma flow in the ray. It is shown that the width of the leading edge of the main SW increases almost linearly with its distance from the Sun. It is further shown that the initial velocity of the inhomogeneities (`blobs') that travel in the streamer belt rays increases with the distance from the Sun at which they originate, and is approximately equal to the velocity of the main solar wind which carries them away. The characteristic width of the leading edge of the `blob' R , and remains almost unchanging as it moves away from the Sun. Estimates indicate that the main SW in the brightest rays of the streamer belt to within distances at least of order R3 R represents a flow of collisional magnetized plasma along a radial magnetic field.     

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.     

Measurements of magnetic fields in solar corona as based on the radio observations of the inversion of polarization of local sources at microwaves

The possibility of measuring magnetic fields of solar active regions at coronal heights up to 10¹⁰ cm by observing the inversion of circular polarization of local sources at microwaves is demonstrated. The observations by the radiotelescope RATAN-600 were accomplished with the angular resolution 17–34 in the wavelength range 2–4 cm. It is found that the inversion of polarization occured within a core of local source situated above the largest sunspot of Mc Math 14822. The inversion was followed during the period of June 30–July 3, 1977. The measured coronal magnetic field of 16 G is found to be at the height 12 × 10⁹ cm. This measured field proves to agree with a simulated potential structure of Mc Math 14822 coronal magnetic field. Our analysis of the inversion has been based on the theory of interaction (coupling) of the ordinary and extraordinary wave modes in the region of quasi-transverse propagation.     

Two Unusual Episodes of ≈ 13-Day Variations

Fourier analysis (DFT/CLEAN) of the international sunspot number (R) series since 1932 has revealed two long (250–500 days) and distinct episodes of solar activity exhibiting persistent 13 -day variations. The first episode lasts 500 days near the maximum of solar cycle 20, and the second, 250 days near the end of the current solar cycle 22. The solar radio flux density (F _{10_7cm}) series since 1947 has also been analyzed. During the first episode both solar indices exhibit distinct 27- and 13-day variations (the first report of 13-day variations in F _{10_7cm}). During the second episode neither index exhibits distinct 27-day variations and only R exhibits 13-day variations. Conditions affecting the appearance of 13-day variations in F _{10_7cm} are discussed.