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.     

Formation of the solar system

Prentice (1978a, b), in his modern Laplacian theory of the origin of the solar system, has established a scenario in which he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant 1.69. In an attempt to understand this law in an alternative way, Rawal (1984a) assumes that during the collapse of the solar nebula the halts at various radii are brought about by the supersonic turbulent convection and arrives at the relation of the formR _p=Ra^p, whereR is the radius of the present Sun anda=1.422, is referred to, here, as the Roche constant. Kepler's third law assumes the form:T _p=T₀(a ^3/2) ^p ,T ₀ being the rotational period of the Sun at the time it attained its present radius.R _p satisfy Laplace's resonance relation without any exception. The present paper investigates inter-relations among the concepts of supersonic turbulent convection, rotational instability, and Roche limit.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Type III solar radio burst storms observed at low frequencies

The analysis of a storm of type III solar radio bursts observed in August 1968 between 5 and 0.2 MHz by the RAE-1 satellite has yielded the storm morphology, a possible relation to meter and decameter storms, and an average exciter speed of 0.37 c between 10 and 40 R (Fainberg and Stone, 1970a, b). A continuation of the analysis, based on the apparent dependence of burst drift rate on heliographic longitude of the associated active region, now provides a distance scale between plasma levels in the streamer, an upper limit to the scale size of coronal streamer density inhomogeneities, and an estimate of the solar wind speed. By fixing one level the distance scale is utilized to determine the electron density distribution along the streamer between 10 and 40 R . The streamer density is found to be 16 times that expected for the solar minimum quiet solar wind. An upper limit to the scale size of streamer density inhomogeneities is estimated to be of the order of 1 or 2 solar radii over the same height range. From the progressive delay of the central meridian passage (CMP) of the lower frequency emission, a streamer curvature is inferred which in turn implies an average solar wind speed of 380 km/sec between 14 and 36 R within the streamer.     

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.     

The properties of plasma flows in fine ray structures of the streamer belt

We show that within distances from the Sun's surface less than the height of a streamer helmet, each of two neighboring rays of the streamer belt, as they approach the solar surface, bends around the helmet on either side of it. Also, a minimum angular diameter of the rays of d2°–3° remains virtually constant within R=1.2–6.0 R . A density inhomogeneity (`blob') can be produced above the helmet top visible to at least R6 R . In this case the initial velocity of the `blob' increases with solar distance from where it is generated to something like the velocity of the bulk solar wind with which the `blob' is carried away.     

Latitude dependence of auroral frequency in relation to solar — Terrestrial and interplanetary parameters

The auroral frequency of occurrences (A) for the 20th solar cycle and for the geomagnetic latitudes 54–63 N has been investigated in relation to sunspot numbers (R _z), number of flares (F), the solar wind streams derived from the coronal holes (H) and the geomagnetic index (A _p). The relationship between A and the other indices were found to be strongly latitude dependent. At around 57–58 N, a drastic change in this relationship occurs, and an attempt is made qualitatively to evaluate this latitudinal variation.     

On the polarization of the solar coronal emission lines

The results of the spectrophotometrical measurements of the polarization in the coronal lines Fe xiv 5303 Å and Fe × 6374 Å are given. Polarization spectrograms were obtained by two spectrographs (prism and echelle types) during the solar eclipse in Mexico on 7 March, 1970 near the region of the second contact at the heights 0.06 to 0.12 R above the limb. The polarization in the green line is about 30% (for averaged height 1.08 R ). The polarization in the red line is close to the errors of the measurement and does not exceed 6%. A brief discussion of the results is also given.     

On a relation between the indices of solar activity in the photosphere and the corona

In the first part a new index of solar activity in the photosphere is introduced i.e. the areas index I _a defined with the help of the relation, where A and f are the total areas of the sunspots and faculae respectively corrected for foreshortening.In the second part a relation of the form: is proposed, where S represents the intensity of solar radio-emission in the frequency range 1000 f < 10000 MHz, i _f is the index of solar flares, S ₀o is the corresponding value of s for I _a = 0 and K is a constant.In the third part a relation of the form: is proposed, where I 5303 is the mean intensity of the coronal line 5303 Å for each quarter of the years 1954–1964, n _pf is the corresponding number of proton flares, I ₀ is the value of I ₅₃₀₃ corresponding to I = 0 and K is a constant.     

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 transfer of polarized radiation in spectral lines: Solar-type stellar atmospheres

The polarization structure in several spectral lines in solar type stars is computed using the method described by McKenna (1981, 1984a). The frequency redistribution function used for these calculations is a linear combination ofR _II andR _III. The line profiles and polarization structures have been computed for several weak solar resonance lines includingKi 7664 Å, Sri 4607 Å, Baii 4554 Å, for various polar angles along the stellar disk. Both the line profiles and polarization structures as well as the center to limb behavior of the line center polarization agree well with observations.The somewhat stronger resonance line Cai 4227 Å shows a different polarization structure when compared to the weaker solar resonance lines. It is found that for strong resonance lines the proper redistribution function to be used is a linear combination ofR _III andR _v (see McKenna, 1981, 1984b; Heinzel, 1981). The major reason for this is that for strong resonance lines both the upper and lower levels are broadened by collisions. This violates the assumptions upon which the redistribution functionsR _II andR _III are based.     

Abundance calibration and evolution of GiantHii Regions

We present a self-consistent method to determine abundance and evolutionary status for GiantHii Regions (GHR) as well as the nominal temperature of the ionizing cluster and the ionization parameter. We define the ionization parameter-free plane [,R ₂₃] (Vilchez and Pagel, 1988) where observations are compared with the prediction of photoionization models, in order to obtain the abundance and evolutionary status for a given GHR. This new method allows us to re-calibrate the empirical relationship (R ₂₃, O/H) by Pagelet al. (1979) up to abundances three times solar. The effects of evolution of GHR on their observed spectra are explained in terms of the cooling down of the ionizing population and some evolutionary tracks are presented.     

Anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R , the major axis scattering angle is 0.7 at =6 cm and it varies with heliocentric distance asR ^–1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to =20 cm, has a value 20±7 at 5R and varies with heliocentric distance asR ^–3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scales sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R and 4 km at 13R . These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Coronal sources at meter and optical wavelengths during the declining phase of the solar cycle

We present observations of the corona at 169 MHz with the Nançay Radioheliograph during the summer of 1984. We compare synoptic maps of the metric radio emission on the solar disk with synoptic charts of the K-corona as well as of the green and the red lines. Local sources of radio emission are not located near regions of enhanced green or red line emission which, in turn, are in general above chromospheric faculae. Thus the radio emissions located in the surroundings of faculae are apparently related to different loop systems, with lower density. The comparison of the radio data with the K-corona showed one radio source associated with enhanced emission both at 1.3 and at 1.7 R , apparently a streamer. Other radio sources did not show any clear associations, but were nevertheless located within the coronal plasma sheet, delineated by the large-scale K-corona emission. Moreover the large-scale structure of the corona at 169 MHz was quite similar to the coronal plasma sheet observed at 1.3 R above the limb. The extent of the radio emission in latitude is very similar to that of the K-corona, while the coronal line emission is more concentrated near the solar equator.     

The interaction effect of fast and slow solar wind streams in interplanetary space on wind characteristics at the Earth's orbit

By analyzing observational data, it has been possible to determine quantitative relationships that represent the role of the interaction of fast and slow solar wind (SW) streams in the formation of characteristic SW properties at the Earth's orbit.It is shown that maximum values of magnetic field B _M and density n _M peaks in the neighbourhood of the sector boundary (SB) at the base of the high-speed stream front are associated with solar wind characteristics such as the SW minimum velocity near the SB, V _m, the maximum velocity in the central part of the fast stream, V _M, and the slope of the magnetic field neutral line to the solar equatorial plane at R = 2.5 R (R is the solar radius).It is concluded that enhancements of absolute values of the z-component of the magnetic field, ¦B _z¦, recorded at the Earth's orbit, are largely attributable, at sufficiently large values of , to the interaction of different-velocity SW streams.     

The even-odd systematics inR-process nuclide abundances

We report and discuss solar systemN _R abundances for nuclidesA>70, obtained as differences between measured solar system abundances and calculatedS-process contributions. The abundance peak atA163 in the rare Earth element region reveals properties which are similar to those of theR-process peaks corresponding to magic neutron numbersN=82 andN=126. We observe that systematic differences in theN _R abundances of even-A and odd-A nuclides are restricted to specific mass regions. We discuss possible interpretations and conclude that these differences are most probably related to the properties of nuclear species during _– to the stability valley.... A genesis of the elements such as is sketched out would not be confined to our little Solar System, but would probably follow the same general sequence of events in every center of energy now visible as a Star. Sir William Crookes (1886)Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

The existence of long-lived rays of the coronal streamer belt – Radial density and velocity distributions of the solar wind flowing in them

A technique is proposed for separating the rays of the streamer belt with quasi-stationary and non-stationary solar wind (SW) flows. It is shown that the lifetime of rays with a quasi-stationary SW can exceed 20 days. A new method has been developed for measuring the relative density distribution of a quasi-stationary slow SW flowing along the streamer belt's ray of increased brightness, based on the LASCO/SOHO data. It is shown that the density n for such SW flows varies with the radius R according to the relationship nR ^–, where =₁3.3–3.9 within 4 R ₀ R 6 R ₀ (here R ₀ is the solar radius), and decreases gradually further away. It is also shown that the V(R)-profiles in some rays of the streamer belt differ little from each other, although the value of the mass flow density, j _E, at the Earth's orbit in them can vary more than by a factor of 4. This distinguishes in a crucial respect a slow SW in the streamer belt's rays from a fast SW originating in coronal holes, for which j _Econstant and the dependences V(R) in different fast flows can differ greatly.     

Solar flare activity and the structure of the coronal neutral line

In this study we analyse the positions of major flares from 1978 and 1979, with respect to the magnetic structure of the solar corona, as described by a potential field model. We find that major flares exhibit no strong association with the neutral line at the chromospheric level. However, when we calculate the neutral line's position at higher and higher altitudes in the corona, we find that major flares show an increasing tendency to be found close to these high-altitude coronal neutral lines. The correlation between flares and higher-altitude coronal neutral lines reaches a maximum at an altitude of 0.35R , and thereafter decreases as the neutral line is moved out to the source surface at an altitude of 1.50R . This indicates that major flares are strongly associated with coronal structure at the 0.35R level ( 250 000 km) - an altitude surprisingly high in the corona. This reinforces the idea that flares are associated with large-scale coronal magnetic fields and also indicates that the region of coronal magnetic topology important to solar flare processes may be larger than previously thought.     

Dependence of the aurora borealis occurrences on the solar-terrestrial parameters

The recent measurements made by satellites of the aurorae in connection with solar phenomena have increased interest in auroral research. In the present investigation, we establish that, for the 20th solar cycle, the occurrence of visual discrete aurorae A, deduced from a complete set of data, is significantly related to the sunspot numbers R _z, the number of flares F (of importance 1) the solar wind streams derived from solar coronal holes H, and the geomagnetic index A _p.By employing the theory of residues it has been found that A correlates significantly well with the above indices. Accuracies of the order of 75–94% were found for geomagnetic latitudes in the range of 54 –63 N.The A-R _zrelationship was investigated in particular for the period 1897–1951. For this period spectrum analysis of A annual values revealed the existence of 3–4 yr and 8–10 yr periodicities of significances 95% and 99%; respectively.Research Associate.     

Brightness variations of the white light corona during the years 1964–67

Observations of the white light corona were made on over 900 days during the years 1964–67 at heights between 1.125 and 2.0 R with the K-coronameter at Mount Haleakala and Mauna Loa, Hawaii. The brightness distribution of the minimum corona was elliptical with average equatorial intensities three times the polar. Coronal features of the new cycle at 1.125 R occurred predominantly in the sunspot zones at 25–30° latitude and in a high latitude zone which migrated toward the North pole before solar maximum. The brightness of the inner corona doubled over this period and a close association is found between the average corona and 10.7-cm solar radio flux. Electron densities in the equatorial regions were nearly twice those of Van de Hulst's model corona, in agreement with the results of recent eclipse observations.At Hawaii Institute of Geophysics.     

Observations of the Solar Limb Shape Distortions

Two new campaigns devoted to the observation of the solar limb distortions were made at the Pic-du-Midi Observatory, in September 2000 and September 2001, by means of the scanning heliometer. This apparatus can be used now routinely to accurately determine solar limb profiles (at two wavelengths), at any heliographic latitudes. Each measurement is made within 44 milliseconds (of time) which permits to record a limb profile together with the seeing. Scans are automatically rejected for seeing larger than 1.3 arc sec. Such conditions are essential to perform high-quality observations necessary to obtain the quadrupole term (l=2) in the polynomial expansion of the radius contour R() _{= constant} = R ₀ left(1+_l c _l P _l()right). Exceptional meteorological conditions in September 2001 (seeing of the order of 18 cm, for a 50 cm clear aperture of the refractor) enabled us to determine c ₂ and c ₄ (see Table I) with an accuracy of a few milli-arc-sec. Results indicate a distorted solar shape, the departures from a pure spherical body not exceeding 20 milli-arc-sec. We propose a model to interpret such results (the combination of a nearly uniform rotating core with a prolate solar tachocline and an oblate surface), which is briefly discussed. Our results are confronted to those obtained from space. We conclude that measurements of the quadrupole term from the ground are possible, but of high difficulty and can be obtained only during excellent weather conditions. The hexadecapole term should be only obtained from space. We show that an astrometric satellite would be required, whose mission would be also to accurately determine the solar rotation profiles (both surface and in depth) in order to unambiguously determine the inertia moments of the Sun through the J _n terms. Such values are also briefly discussed.