Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

Large-scale solar velocity fields

Daily observations of Doppler line shifts made with very low spatial resolution (3) with the Stanford magnetograph have been used to study the equatorial rotation rate, limb effect on the disk, and the mean meridonial circulation. The equatorial rotation rate was found to be approximately constant over the interval May 1976–January 1977 and to have the value 2.82 rad s^–1 (1.96 km s^–1). This average compares favorably with the results of Howard (1977) of 2.83 rad s^–1 for the same time period. The RMS deviation of the daily measurements about the mean value was 1% of the rate (20 m s^–1), much smaller than the fluctuations reported by Howard and Harvey (1970) of several per cent. These 1% fluctuations are uncorrelated from day-to-day and may be due to instrumental problems. The limb effect on the disk was studied in equatorial scans (after suppressing solar rotation). A redshift at the center of the disk relative to a position 0.60R from the center of 30 m s^–1 was found for the line Fe i 5250 Å. Central meridian scans were used (after correcting for the limb effect defined in the equatorial scans) to search for the component of mean meridonial circulation symmetric across the equator. A signal is found consistent with a polewards flow of 20 m s^–1 approximately constant over the latitude range 10–50°. Models of the solar differential rotation driven by an axisymmetric meridonial circulation and an anisotropic eddy viscosity (Kippenhahn, 1963; Cocke, 1967; Köhler, 1970) predict an equatorwards flow at the surface. However, giant cell convection models (Gilman, 1972, 1976, 1977) predict a mean polewards flow (at the surface). The poleward-directed meridonial flow is created as a by-product of the giant cell convection and tends to limit the differential rotation. The observation of a poleward-directed meridonial circulation lends strong support to the giant cell models over the anisotropic eddy viscosity models.Now at Kitt Peak National Observatory, Tucson, Ariz., U.S.A.     

Differential rotation and giant cell circulation of solar Ca+-network

We report new results obtained from high precision computer controlled tracings of ca. 400 bright Ca⁺-mottles made during summer 1975 in continuation of our 1974 program (Schröter and Wöhl, 1975). In particular, we looked in 1975 for the existence of a giant circulation pattern in the equatorial zone. We find for the differential rotation: = 13.93 – 2.90 sin² B (deg/day, sidereal) when combining the new measurements with those obtained in 1974. Observations from 26th April until June 19th give strong evidence that at that time four giant circulation cells, crossing the solar equator, (i.e. a nonaxisymmetric velocity field pattern with respect to the solar equator) did exist. This yields two more rapid and two slower rotating sectors with v = ±80 m s^–1. These giant cells transport angular momentum towards the equator.     

Upper limit on the steady emission of the 2.223 MeV neutron capture γ-ray line from the Sun

Data accumulated by the Solar Maximum Mission Gamma Ray Spectrometer (GRS) have been searched for evidence of the 2.223 MeV neutron capture line from the Sun, outside the times of -ray-emitting solar flares. Background-corrected spectra accumulated over 3-day intervals between 1980 and 1989 show no evidence of the line. Upper limits are reported separately for periods of high and low solar activity.A conservative 3 upper limit of 5.7 × 10^–5 (cm² s)^–1 is placed on the steady flux in the 2.223 MeV line during inactive periods, which is nearly two orders of magnitude lower than previously published results. After correction for limb darkening of the line emission from off-center positions, this upper limit becomes 7.1 × 10^–5 (cm²s)^–1. Our 3 upper limit on the steady flux in the line during periods of high solar activity is 6.9 × 10^–5 (cm² s)^–1, or 8.6 × 10^–5 (cm² s)^–1 after correction for limb darkening. Our results imply that the quiescent solar corona cannot be heated by ions accelerated above 1 MeV in microflares (or a continuous acceleration process), so long as the ion energy spectrum is similar to that measured in large flares. We also use our results to derive the rate of tritium production at the solar surface; our upper limit of 9 nuclei (cm² s)^–1 is about a factor of 9 below the upper limit from searches for ³H in the solar wind. We place upper limits of the order 10³³ on the number of energetic (> 30 MeV) protons which can be stored in active regions prior to being released in solar flares, which imply that the strongest observed flares cannot be produced by such a mechanism.     

Solar Activity and Deep Convection Modeling

We suggest from synoptic charts of radial magnetic field and intensities of spectral lines (Fe?i, He?ii, and Fe?ix/x) over Carrington rotations 1942??C?2050 that deep convective layers control the pattern of large-scale solar activity. A new result is a Kolmogorov-type energy spectrum of the longitudinal variations of solar activity. This spectrum for nonphotospheric scales of convection (harmonic number m<100) is a new ??fingerprint?? of turbulence in the deep layers of the solar convection zone (CZ). The manifestation of one source of convective turbulence in the deep CZ is revealed as the excess in the power spectrum over the Kolmogorov spectrum. This source may be identified with giant convection cells at the CZ bottom. The convective cascade of the turbulence starts at the vortex size corresponding to the trans-CZ convective cells with the turnover time which the mixing length theory (MLT) predicts. This connection between the MLT formalism and real features in the Sun could account for the success of the MLT in stellar modeling.     

Diagnostic application of highly ionized iron lines in the XUV spectrum of a solar flare

Recent atomic data have been used to analyze a solar flare spectrum obtained with the Goddard Space Flight Center's grating spectrometer on the OSO-5 satellite. There exist in the wavelength region 90–200 Å strong lines from each of the ions Fe xviii-Fe xxiv. The Fe xxi lines can be used as an electron density diagnostic for the 10⁷ K plasma. From our analysis of a particular flare, we find a steep positive slope in the emission measure between 10^6.5 and 10^7.2 K and an electron density of 4 × 10¹¹ cm^–3 at 10⁷ K. We emphasise the need for high spectral and spatial resolution observations of solar flares in this wavelength region, which has to date been largely neglected.     

Variability in the power spectrum of solar five-minute oscillations

Two-dimensional power spectra of solar five-minute oscillations display prominent ridge structures in (k, ω) space, where k is the horizontal wavenumber and ω is the temporal frequency. The positions of these ridges in k and ω can be used to probe temperature and velocity structures in the subphotosphere. We have been carrying out a continuing program of observations of five-minute oscillations with the diode array instrument on the vacuum tower telescope at Sacramento Peak Observatory (SPO). We have sought to establish whether power spectra taken on separate days show shifts in ridge locations; these may arise from different velocity and temperature patterns having been brought into our sampling region by solar rotation. Power spectra have been obtained for six days of observations of Doppler velocities using the Mgi λ5173 and Fei λ5434 spectral lines. Each data set covers 8 to 11 hr in time and samples a region 256″ × 1024″ in spatial extent, with a spatial resolution of 2″ and temporal sampling of 65 s. We have detected shifts in ridge locations between certain data sets which are statistically significant. The character of these displacements when analyzed in terms of eastward and westward propagating waves implies that changes have occurred in both temperature and horizontal velocity fields underlying our observing window. We estimate the magnitude of the velocity changes to be on the order of 100 m s^-1; we may be detecting the effects of large-scale convection akin to giant cells.     

The effect of Kelvin-Helmholtz instability on rising flux tubes in the convection zone

If the solar dynamo operates at the bottom of the convection zone, then the magnetic flux created there has to rise to the surface. When the convection zone is regarded as passive, the rising flux is deflected by the Coriolis force to emerge at rather high latitudes, poleward of typical sunspot zones (Choudhuri and Gilman, 1987; Choudhuri, 1989). Choudhuri and D'Silva (1990) included the effects of convective turbulence on the rising flux through (a) giant cell drag and (b) momentum exchange by small-scale turbulence. The momentum exchange mechanism could enable flux tubes of radii not more than a few hundred km to emerge radially at low latitudes, but the giant cell drag mechanism required unrealistically small flux tube radii (a few meters for a reasonable giant cell upflow) to counteract the Coriolis force. We now include the additional effect of Kelvin-Helmholtz instability in a symmetrical flux ring caused by the azimuthal flow induced during its rise. The azimuthal flow crosses the threshold for the instability only if there is a giant cell upflow to drag the flux tubes appreciably. In the absence of such a drag, as in the case of a passive convection zone or in the case of momentum exchange by small-scale turbulence, the azimuthal velocity never becomes large enough to cause the instability, leaving the results of the previous calculations unaltered. The giant cell drag, aided by Kelvin-Helmholtz instability, however, becomes now a viable mechanism for curbing the Coriolis force - 10⁴ G flux tubes with radii of a few hundred km being dragged radially by upflows of 70 m s^-1.     

On the initial phase of interaction between expanding stellar envelopes and surrounding medium

The initial stages of deceleration in the circumstellar medium of a stellar envelope, thrown off by a shock wave, are investigated. The equations of spherical-symmetric adiabatic hydrodynamics are shown to have a similarity solution in the case of the density of the expanding envelope being approximated by a reasonable power law. The overall flow pattern has such a form that the stellar material is decelerated in the internal shock wave while another shock propagates through the circumstellar matter. Between the shocks there is a contact discontinuity separating the circumstellar and stellar matter. The characteristics of the similarity solution are calculated for various exponents in the density laws of an expanding envelope and circumstellar matter and for two values of the adiabatic index (=5/3, 4/3). Some parts of the flow exhibit Rayleigh-Taylor instability.Special attention is paid to the validity of the hydrodynamics. In full agreement with D'yachenkoet al. (1969), we conclude that the kinetic and collisionless processes are of great importance if the initial stages of stellar envelope deceleration are to be properly monitored.The results obtained can also be employed to describe the interaction between the exploding core of a red giant star and its rarefied envelope. This is of interest for explosive nucleosynthesis.The similarity solution is applied to the envelopes expelled both by type-II supernovae and by rapid novae. In particular, the thermalization time-scale of circumstellar plasma is estimated. For SNii this time-scale proves to be of the order of 60 yr. This confirms with the observational data on the moment of the maximum radio-emission of young SNRs. In the case of rapid novae, this time is less by a factor of 10. Therefore, the peak radio and X-ray (2 keV) lumnosity may occur several years after the rapid nova outburst. The explosion of a degenerate carbon core is found to result in the heating of the hydrogen-helium envelope of a red giant star up to 3×10⁶ K.     

Solar abundances of light nuclei and mixing of the Sun

Radial profiles of the light nuclei (A 15) are calculated in the non-mixing Sun, taking into account the changes of solar structure with time. The results are discussed in relation to models of solar mixing and compared with abundance determinations at the solar surface or in the solar wind. B cannot be depleted in the outer convective zone without producing a large increase in the He³/He⁴ ratio. A decrease in He³/He⁴ would be accompanied by changes in C¹³/C¹² and N¹⁵/N¹⁴ of a magnitude which is not observed.It is shown that boron could be depleted in the pre-main sequence period of the Sun, if mixing was on a time-scale of 10⁶ yr. The simultaneous small increase in He³/He⁴ does not contradict observation. However, Be would be depleted more strongly than B.A He³/He⁴ decrease is always accompanied by large changes in N¹⁵/N¹⁴ and C¹³/C¹². Since such changes are not observed, it is concluded that the He³/He⁴ ratio in the outer convective zone is a reliable upper limit for (He³ + D)/He⁴ in the solar nebula. Thus the D/H ratio in the protosolar material was much lower than it is in sea water or in carbonaceous chondrites.     

Contribution to the observation of the photospheric oscillations

Observations of the 300 s photospheric oscillation on large solar surfaces (up to 520 in diameter) using a sodium optical resonance cell seem to show that the power at long horizontal wavelengths is larger than previous results would indicate. In order to get more information about the spatial distribution of the energy, a new observational method has been perfected, which will allow us to obtain the spatiotemporal power spectrum.In some of our observations, a long-period oscillation (about 40 min) appears, with an amplitude comparable to that of the 300-s oscillation, and which seems to be correlated with the occurence of chromospheric flares.     

The impulsive and gradual phases of a solar limb flare as observed from the solar maximum mission satellite

Simultaneous observations of a solar limb flare in the X-ray and ultraviolet regions of the spectrum are presented. Temporal and spectral X-ray observations were obtained for the 25–300 keV range while temporal, spectral, and spatial X-ray observations were obtained for the 30–0.3 keV range. The ultraviolet observations were images with a 10 spatial resolution in the lines of O v (T _e 2.5 × 10⁵ K) and Fe xxi (T _e 1.1 × 10⁷ K). The hard X-ray and O v data indicate that the impulsive phase began in the photosphere or chromosphere and continued for several minutes as material was ejected into the corona. Impulsive excitation was observed up to 30 000 km above the solar surface at specific points in the flare loop. The Fe xxi observations indicate a preheating before the impulsive phase and showed the formation of hot post-flare loops. This later formation was confirmed by soft X-ray observations. These observations provide limitations for current flare models and will provide the data needed for initial conditions in modeling the concurrent coronal transient.     

Short-Term Periodicities in Solar Indices

The purpose of the present communication is to identify the short-term (few tens of months) periodicities of several solar indices (sunspot number, Caii area and K index, Lyman , 2800 MHz radio emission, coronal green-line index, solar magnetic field). The procedure used was: from the 3-month running means (3m) the 37-month running means (37m) were subtracted, and the factor (3m – 37m) was examined for several parameters. For solar indices, considerable fluctuations were seen during the ± 4 years around sunspot maxima of cycles 18–23, and virtually no fluctuations were seen in the ± 2 years around sunspot minima. The spacings between successive peaks were irregular but common for various solar indices. Assuming that there are stationary periodicities, a spectral analysis was carried out which indicated periodicities of months: 5.1–5.7, 6.2–7.0, 7.6–7.9, 8.9–9.6, 10.4–12.0, 12.8–13.4, 14.5–17.5, 22–25, 28 (QBO), 31–36 (QBO), 41–47 (QTO). The periodicities of 1.3 year (15.6 months) and 1.7 years (20.4 months) often mentioned in the literature were seen neither often nor prominently. Other periodicities occurred more often and more prominently. For the open magnetic flux estimated by Wang, Lean, and Sheeley (2000) and Wang and Sheeley (2002), it was noticed that the variations were radically different at different solar latitudes. The open flux for < 45 solar latitudes had variations very similar (parallel) to the sunspot cycle, while open flux for > 45 solar latitudes had variations anti-parallel to the sunspot cycle. The open fluxes, interplanetary magnetic field and cosmic rays, all showed periodicities similar to those of solar indices. Many peaks (but not all) matched, indicating that the open flux for < 45 solar latitudes was at least partially an adequate carrier of the solar characteristics to the interplanetary space and thence for galactic cosmic ray modulation.     

On the interpretation of Fraunhofer line Doppler shifts at supergranule boundaries

We have used the SPO tower telescope and echelle spectrograph to study differences in the profiles of three Fei lines, between magnetic network and cells. Ca K slit-jaw pictures were used to identify the network and cell areas, and mean network and cell profiles were computed from digitized spectra for the g = 0 lines 4065, 5434, and the g = 1.5 line 5233. The profile bisectors show that the wings of all three lines are red-shifted in the network by between 75–200 m s^–1 relative to the cell profiles. But the redshift decreases in the line core and becomes less than the standard error of 20 m s^–1 near the line core minimum. This disappearance of the redshift at the cores of all 3 lines formed over the height range 250–500 km above _0.5 = 1, argues against a steady downflow at supergranule boundaries. We show that such red-shifted wings and a relatively unshifted core can result if granular convection is suppressed near the network flux tubes, without implying any downflow in the vicinity of these flux tubes. Our results also indicate that searches for large-scale convective velocity patterns should measure shifts of the line core, rather than the line wings which appear to be very sensitive to inhomogeneities in granule structure.Visiting Astronomers, Sacramento Peak Observatory.     

High spatial resolution microwave observations of the Sun

Over the past decade two large arrays — the Westerbork Synthesis Radio Telescope (WSRT) and the Very Large Array (VLA) built primarily for sidereal radio astronomy have been used for solar radio astronomical studies with spatial resolution of a few seconds of arc. In this review, we discuss some results obtained at Maryland using these instruments.The quiet Sun observations made with the WSRT have premitted us to produce synthesized maps of supergranulation network at 6 cm wavelength. The brightness temperatures of typical network elements and cells are respectively 2.5 × 10⁴ K and 1.5 × 10⁴ K; thus the contrast is 1.71 which compares with 1.31 for Ca ⁺ K and 20 for L networks. Limb profiles in both equatorial and polar directions have been obtained; limb brightening is observed at both west and south limbs, peak limb temperature being about 40% higher than disk temperature. We have produced synthesized maps of disk filaments which correspond well to H disk filaments and regions of reduced emission in He i 10 830 Å spectroheliograms. Using the WSRT synthesized maps at 6 cm, we have compared the structure of a sunspot associated source with model computations. Using a new method of analysis we have been able to map the vertical as well as the horizontal component of the sunspot magnetic field at specific locations in the low corona. Using the VLA, we have mapped coronal loops at 20 cm; the radio emission is attributed to bremsstrahlung near the loop footpoints whereas gyroresonance process dominates near the loop top. Using the VLA, we have carried out simultaneous observations of a microwave burst at 2 and 6 cm. The 6 cm burst source is apparently located near the top of a flaring loop, while the 2 cm emission originates from the loop footpoints. The 6 cm emission is attributed to gyrosynchrotron radiation of thermal electons in the bulk heated plasma at 4 × 10⁷ K, while the 2 cm emission is due to nonthermal particles released and accelerated during the flare process. A DC electric field flare model appears to explain the observed delay between the peaks at the two wavelengths. From the delay, the strength of the electric field in the flaring region is estimated.     

The relationship between r.m.s. doppler velocities and temperature in the solar transition region

An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 10⁵ K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T ^1/2. Also, for all temperatures less than 10⁵ K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Sunspots: Their rotation,their expansion in the activity zone,their links with the giant convective cells

The rotational properties of sunspots during the time interval 1977–1986 (solar cycle 21) are studied; only sunspot groups older than 4 days have been the object of this research. We have looked systematically for any kind of anomaly or fine structure in the differential rotation latitudinal profile and any significant change occurring during the course of the solar cycle.Some latitudinal bands are found where the angular rotation rate, rather than decreases according to its overall tendency, increases or is constant with the latitude. The differential rotation profile is, therefore, finely structured. The whole fine-structure pattern is affected by a slow equatorward shift. It is suggested that these fine structure features are due to the Coriolis forces acting on the meridional motions associated with giant toroidal convective cells. Some of the properties of such cells are inferred.Moreover, while the spot zone shifts equatorward, it is found to expand poleward; this expansion occurs by the addition of new belts of activity on the poleward side of the pre-existing active zone. The active zone is therefore found to consist, at the maximum activity epoch, of three different belts of spot production, each of them being centered around a local maximum-activity latitude; each of these centroids of activity is hypothesized to lie where a couple of meridional streams - associated with giant cells - converge. The activity belts are independent of each other as far as their activation, maximum, and end time, as well as their lifetime and level of activity are concerned. The angular rotation rate is correlated, in each belt, with the local level of activity.     

Upper limits for the microwave pulsed emission from supernova explosions in clusters of galaxies

Between 1972 and 1975 an international collaborative search was carried out for prompt 10 GHz emission at the onset of supernovae. The motivations and techniques involved in this effort are described, and the results of the three years' work are summarized. No pulses from supernovae were detected, the best upper limit being 4×10⁴³ ergs in a 40 MHz band at 10 GHz for a pulse time-scale 0.5 s. Methods for improving this limit are briefly described.     

Large-scale structure of background fields and active regions

An attempt is made to study the relations between emergence of active regions and the solar background large-scale structures on the basis of Solar Geophysical Data, including Kitt-Peak magnetograms, H filtergrams, and Ca images.The emergence of 217 active regions (a.r.s) that have appeared on the solar disk not farther than ± 60° from the central meridian is studied. The a.r.s are divided into two classes A and B according to their birth location. Class A contains a.r.s emerged far (8–10°) from the background field boundaries, and class B- those emerged near to (55°) or just at the boundaries.It was found that a.r.s of class A differ appreciably from those of class B; in particular, the dimensions and the intensity (S, I) of class B a.r.s are nearly twice as large as those of class A. For class A a.r.s some alterations of the solar large-scale structure boundaries were found in 15% of all the cases, whereas for those of class B in 60%.     

Further considerations on contracting solar nebula

Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant - 1.69. This serves to provide a physical understanding of the Titius-Bode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R _p= Ra^p, where R _pare the radii of the solar nebula at various halts during the collapse, R the radius of the present Sun and a = 1.442. a is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T _p = T ₀(a^3/2)^p, where T _p are the orbital periods at the radii R _p, T ₀ - 0.1216d - 3 h, and a the Roche constant. We are inclined to interpret T ₀' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T _pcorresponding to the radii R _psubmit themselves to the Laplace's resonance relation.