Determination of constant α force-free solar magnetic fields from magnetograph data

At first it is shown that a magnetic field being force-free, i.e. satisfying × B = B, with = constant ( 0) in the whole exterior of the Sun cannot have a finite energy content and cannot be determined uniquely from only one magnetic field component given at the photosphere. Then the boundary value problem for a semi-infinite column of arbitrary cross section is solved by a Green's function method.     

Calculation of force-free magnetic field with non-constant α

A numerical method is developed for solving the force-free magnetic field equation, × B = B, with spatially-varying . The boundary conditions required are the distribution of B _n (viz. normal component of the field on the photosphere) as well as the value of in the region of positive (or negative) B _n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of . The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.On leave of absence from Department of Astronomy, University of Tokyo.     

The roots of coronal structure in the Sun's surface

We have compared the structures seen on X-ray images obtained by a flight of the NIXT sounding rocket payload on July 11, 1991 with near-simultaneous photospheric and chromospheric structures and magnetic fields observed at Big Bear. The X-ray images reflect emission of both Mgx and Fexvi, formed at 1 × 10⁶ K and 3 × 10⁶ K, respectively. The brightest H sources correspond to a dying sub-flare and other active region components, all of which reveal coronal enhancements situated spatially well above the H emission. The largest set of X-ray arches connected plages of opposite polarity in a large bipolar active region. The arches appear to lie in a small range of angle in the meridian plane connecting their footpoints. Sunspots are dark on the surface and in the corona. For the first time we see an emerging flux region in X-rays and find the emission extends twice as high as the H arches. Many features which we believe to correspond to X-ray bright points (XBPs) were observed. Whether by resolution or spectral band, the number detected greatly exceeds that from previous work. All of the brighter XBPs correspond to bipolar H features, while unipolar H bright points are the base of more diffuse comet-like coronal arches, generally vertical. These diverge from individual features by less than 30°, and give a good measure of what the canopies must do. The H data shows that all the H features were present the entire day, so they are not clearly disappearing or reappearing. We find a new class of XBPs which we call satellite points, elements of opposite polarity linked to nearby umbrae by invisible field lines. The satellite points change rapidly in X-ray brightness during the flight. An M1.9 flare occurred four hours after the flight; examination of the pre-flare structures reveals nothing unusual.     

Interferometric study of the Milky Way between Carina and Aquila

Large field H observations of the Milky Way between Carina and Aquila were made through a narrow interference filter 15 wide. Characteristic large-scale features of the observed region are extended emission areas in Carina, Norma-Scorpius and Scutum-Sagittarius and some weak isolated nebulosities near the Coal Sac, Centauri and Normae. H photographs, a chart mapping the emission, and a list of identified emission regions are given.     

Iron Kα-fluorescence in solar flares: A probe of the photospheric iron abundance

The X-ray line at 6.4 keV has been observed from solar flares. It is found that K-fluorescence of neutral iron in the photosphere due to thermal (T 10⁷ K) X-rays of the gradual phase is its dominant production mechanism. For a given flux and energy spectrum of incident X-rays, the flux at 1 AU of iron K-photons depends on the photospheric iron abundance, the height of the X-ray source, and the helio-centric angle between the flare and the observer. Therefore, the flux of iron K-photons, when measured simultaneously with the flux and energy spectrum of the X-ray continuum and the flare location, can give us information on the height of the X-ray source and the photospheric iron abundance. Here we present our Monte Carlo calculations of iron K-fluorescence efficiencies, so that they might be useful for interpretations of future measurements of the 6.4 keV line (e.g., by a detector to be flown on the Solar Maximum Mission).     

Studies of solar flares using optical,X-ray and radio data

I have studied a number of flares for which good X-ray and optical data were available. An average lag of 5.5 s between hard X-ray (HXR) start and H start, and HXR peak and Ha peak was found for 41 flares for which determination was possible. Allowing for time constants the time lag is zero. The peak H lasts until 5–6 keV soft X-ray (SXR) peak. The level of H intensity is determined by the SXR flux.Multiple spikes in HXR appear to correspond to different occurrences in the flare development. Flares with HXR always have a fast H rise. Several flares were observed in the 3835 band; such emission appears when the 5.1–6.6 keV flux exceeds 5 × 10⁴ ph cm^-2 s^-1 at the Earth. Smaller flares produce no 3835 emission; we conclude that coronal back conduction cannot produce the bright chromospheric network of that wavelength.The nearly simultaneous growth of H emission at distant points means an agent travelling faster than 5 × 10³ km s^-1 is responsible, presumably electrons.In all cases near the limb an elevated Ha source is seen with the same time duration as HXR flux; it is concluded that this H source is almost always an elevated cloud which is excited by the fast electrons. A rough calculation is given. Another calculation of H emission from compressed coronal material shows it to be inadequate.In several cases homologous flares occur within hours with the same X-ray properties.Radio models fit, more or less, with field strengths on the order of 100G. A number of flares are discussed in detail.     

The neutral interface adjoining theHII region DR21

Observations of C100 and C125 atomic carbon recombination lines were made at the Algonquin Radio Observatory, towards the neutral interface separating theHii region DR21 (at RA=20^h37^m14^s, Dec=+42°0900) from its associated molecular cloud. An analysis of the Cn observations in conjunction with a simple model of a neutral interface enabled the derivation of the following parameters: electron density of 300 cm^–3, electron temperature of 30 K, microturbulent velocity of 2.3 km s^–1, and depth of the neutral interface of 0.01 pc. A single,stimulated emission model is sufficient to reproduce the Cn observations in the wavelength range from 4.6 cm (C100) to 21 cm (C166). All the known Cn data do support a pressure equilibrium between the neutral interface and theHii region, after the usual allowance is made for carbon depletion on grains.     

The ionization mechanism in low level emission galaxy nuclei: Shocks

We analyze the emission component of galaxy nuclei at very low intensity levels (W(H)2Å). This emission level is considerably lower than that of classical LINERS like NGC 1052. We have access to weaker emission lines by averaging spectra with similar line ratios for H [NII], and [SII]. From the resulting spectrum for very low level emission nuclei, the [SII] 6717, 6731/[SIII] 9069, 9532 line ratio criterion (Diazet al., 1985a) unambiguously shows that shock-wave heating is the mechanism responsible for the ionization in such objects.     

Fine structure of the Solar Chromosphere: Arch-Shaped Mottles

We analyze a time series of high resolution observations near the solar limb, obtained in H and the Mg b1 line. We identified arch-shaped dark mottles, which are thin, faint H structures observable under very good seeing conditions, best seen in H +0.75 Å. Their mean length is about 15, their mean height about 6 and indicative lifetimes is of the order of 5 min. They show negative (away from the observer) line-of-sight velocities. A possible interpretation is that material flows from the apex towards the feet of the arches.     

The orientation of magnetic fields in quiescent prominences

We have measured the longitudinal component, B, of the magnetic field in quiescent prominences and obtained a relationship between B and , where is the angle between the long axis of the prominence and the north-south direction on the sun. From this relationship we deduce a distribution function for the magnetic field vector in quiescent prominences in terms of the angle between the field and the long axis of the prominence. The mean angle, , for our data is small, - 15°, indicating that the magnetic field traverses quiescent prominences under a small, but finite angle.On leave from Max-Planck Institut für Physik und Astrophysik, München.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Theory of the Trojan asteroids

In the previously published Parts I and II of the paper, the author has constructed a formal long-periodic solution for the case of 11 resonance in the restricted problem of three bodies to 0(m ^3/2), wherem is the small mass parameter of the system. The time-dependencet(, ,m), where is the mean synodic longitude and is related to the Jacobi constant, has been expressed by ahyperelliptic integral. It is shown here that with the approximationm=0 in the integrand, the functiont(, , 0) can be expanded in a series involving standardelliptic functions. Then the problem of inversion can be formally solved, yielding the function (t, , 0).Similarly, the normalized period (,m) of the motion can be approximated by theHagihara hyperelliptic integral (, 0), corresponding tom=0. This integral is also expanded into elliptic functions. Asymptotic forms for (, 0) are derived for 0 and for 1, corresponding to the extreme members of thetadpole branch of the family of orbits.     

Linearly expanding universes in JBD-theory

The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.     

An example for solar flares caused by magnetic field non-equilibrium

Using a photospheric magnetogram of the solar activity complex HR 16862, 16863, 16864 at the end of May 1980 as boundary data a sequence of three-dimensional force-free magnetic fields with spatially constant ( defined by the equation × B = B) is calculated, including numerical field-line tracing. The field is assumed not to be frozen-in and ¦¦, which is a measure of the magnetic free energy, is assumed to increase with time due to some dynamo mechanism. Variation of , starting from = 0, produces a catastrophe-like change of the topology of a field-line system corresponding to an arch filament system connecting the leading spot of HR 16863 with the trailing spot of HR 16862. This topological change is interpreted as causing a series of large homologous flares with synchronous flaring in the two spots. The catastrophe-like behaviour of the field topology is attributed to the nonlinear field-line equations.     

Lα measurements during the solar eclipse of 12 November 1966

Rocket measurements of the solar L (1216 Å) flux during various phases of the total eclipse of 12 November, 1966 confirm that the radiation emanates from the chromosphere. A significant difference between two portions of the photosphere limb is attributed to enhanced emission in the region of a Ca K plage. The average size of the L disk is found to be approximately 4000 km above the photosphere, and a brightening is observed at the limb.     

Hα Doppler brightening and Lyman-α Doppler dimming in moving Hα prominences

We consider the effect that coherent motion has on the observed brightness of moving clouds above the photosphere. We find that steady state clouds (constant N _e and T _e ) that are moving perpendicular to the line of sight will appear brighter in H for speeds between 8 and 100 km/sec and dimmer for speeds greater than 135 km/sec. The brightening and dimming are due to apparent Doppler shifts of the respective H absorption and the Lyman- emission profiles seen by the absorption profile of the moving cloud.We apply this analysis, along with optical depth and geometrical considerations, to the observed brightness variations of the 1 March 1969 limb eruptive prominence. We find that all of the observed brightening and dimming can be explained by the motions, and that no significant change in the prominence N _e or T _e was necessary during the observed H event. This conclusion is significant in interpreting an X-ray burst that began as the prominence velocity increased abruptly at the time of maximum H intensity. The thermal X-ray peak occurred 150 sec later when the prominence had become faint again. There was no associated flare that was visible in H. We discuss the relative brightness of H and D ₃ in a specific moving prominence knot.We note that the observed range of limb speeds (30–150 km/sec) may be due to the combined H Doppler brightening and Lyman- dimming effects. We also discuss generally the H brightness of disk surges (bright and dark) and flares, and sprays and puffs that occur at or near the limb.Now at the Dept. of Physics and Astrophysics, University of Colorado, and High Altitude Observatory (NCAR) Boulder, Colo., U.S.A.     

The spectral indices in the optical continuum of the QSOs,BL Lacertae objects and the nuclei of Seyfert,N and normal galaxies

The hypothesis that the optical continua of QSOs, BL Lac objects and the nuclei of Seyfert, N and normal galaxies arise due to incoherent synchrotron radiation from electrons and consequently the flux of radiation in the optical continua of these objects is given by the power law:F(v)v is examined. Following Kinman, spectral indices _B–V and _U–B in(B-V) and(U-B) colours as well as their average and difference have been defined and calculated for samples of 227 QSOs, 32 BL Lac objects and nuclei of 62 Seyfert, 12 N and 7 normal galaxies. Here has been assumed to be an estimate of the spectral index . On the other hand, has been regarded as a measure of departure from the power law. On the basis of this, the distributions of and in QSOs, BL Lac objects and the nuclei of Seyfert, N and normal galaxies have been studied. The value of depends mainly on the balance of the energy loss due to synchrotron radiation and the rate of replenishment of energy by injection of high energy electrons in the radiating region. The increase in the value of and therefore that of indicates that the activity in the object is slowing down and the object is growing older. Assuming that the QSOs, BL Lac objects and the nuclei of Seyfert, N and normal galaxies essentially represent different phases in the evolutionary sequence of extragalactic objects, we suggest that they may be arranged in the sequence: QSOsBL Lac objects Seyferts 1N galaxies Seyferts 2 Normal galaxies in the decreasing order of activity in the core or nuclei of these objects.On leave of absence from the Government Science College, Rajpur, M.P., India.     

Limb Prominence Eruption on 11 August 2000 as Seen From Ground- and Space-Based Observations

We report on a prominence eruption as seen in H with the Crimean Lyot coronagraph, the global H network, and coronal images from the LASCO C2 instrument on board SOHO. We observed an H eruption at the northwest solar limb between 07:38:50 UT and 07:58:29 UT on 11 August 2000. The eruption originated in a quiet-Sun region and was not associated with an H filament. No flare was associated with the eruption, which may indicate that, in this case, a flux rope was formed prior to the eruption of the magnetic field. The H images and an H Dopplergram show a helical structure present in the erupted magnetic field. We suggest that the driving mechanism of the eruption may be magnetic flux emergence or magnetic flux injection. The limb H observations provide missing data on CME speed and acceleration in the lower corona. Our data show that the prominence accelerated impulsively at 5.5 km s^–2 and reached a speed slightly greater than 800 km s^–1 in a narrow region (h<0.14 R ) above the solar surface. The observations presented here also imply that, based only on a CME's speed and acceleration, it cannot be determined whether a CME is the result of a flare or an eruptive prominence.     

Spatial correlation of Hα filaments and photospheric velocity

The location of H filaments is compared with maps of the photospheric line of sight velocity V and the magnetic field H . It is found that (1) H filaments are associated with regions of ¦V ¦ 300m s^–1, (2) always both positive as well as negative velocities are present under H structures, (3) stable (long lasting) portion of filaments frequently occur at the position of H = 0 as well as V = 0 lines, (4) this association remains valid for the longitudes less than 50° from central meridian.     

Polarization of Lyman-alpha lines from hydrogen-like ions

The Oppenheimer-Penney theory to calculate the polarization of L lines from hydrogen-like ions, when the impact electrons are distributed such that their probability is more in the regions close to the magnetic field (f(cos ⁿ ), is applied by Chandra and Joshi (1984). The work of Chandra and Joshi (1984) has been reinvestigated for the pitch-angle distributionf()sin ⁿ . The degrees of polarization are still found to be independent of the atomic number of a hydrogen-like ion.     

Time delay between Hα and hard X-ray emissions during impulsive solar flares

This investigation shows that statistically there are significant time delays between H and hard X-ray (HXR) emissions during solar flares; most impulsive flares produce HXR emissions up to 1 min before and up to 2 min after the onset of H emission. HXR emissions are also found to be peaked up to 2 min before the H emissions.