Curvature effects in extended stellar atmospheres-absorption and scattering

The numerical solution of radiative transfer equation including curvature with both absorption and scattering has been developed in the frame work of Discrete Space Theory. Two cases have been considered: (A) irradiation of the atmosphere at =T and (B) no irradiation on either side of the atmosphere. Isotropic scattering has been assumed. It is found that the emergent luminosities (defined by r ² I(r, ) ) from scattering dominated atmospheres are smaller than those from absorption dominated atmospheres.     

On transfer equation in a semi-infinite atmosphere with albedo ω>1

In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH ⁰-functionH ⁰() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases.     

Large-scale structure of a sunspot and its surrounding photosphere

Preliminary results of a study of photographic and photometric properties of the large-scale ( 3) structure of a sunspot and its surrounding photosphere are given. Stratospheric direct frames of the solar photosphere were used in the study. Isophotes located immediately beyond the outer edge of the penumbra were of an irregular form and reflected bright and dark regions. No presence of either a sunspot bright outer ring or inner ring was detected. The photospheric structure and its behaviour with time were, in fact, unchanged up to the very boundary of the penumbra.A distribution of the smeared intensity in a sunspot has been derived. The mean brightness of the penumbra is I _PU 0.62 I and umbra I _U < 0.15 I . An analysis of the obtained results allowed us to make a conclusion that the area of the dark penumbral regions exceeds that of the bright penumbral regions, and the condition S _BR/S _DR < 1 should be fulfilled in the penumbrae of sunspots.     

Mgix emission lines in an active region spectrum obtained with the Solar EUV Rocket Telescope and Spectrograph (SERTS)

Theoretical electron-temperature-sensitive Mgix emission line ratios are presented forR _I =I(443.96 )/I(368.06 ),R ₂ =I(439.17 )/I(368.06 ),R ₃ =I(443.37 )/I(368.06 ),R ₄ =I(441.22 )/I(368.06 ), andR ₅ =I(448.28 )/I(368.06 ). A comparison of these with observational data for a solar active region, obtained during a rocket flight by the Solar EUV Rocket Telescope and Spectrograph (SERTS), reveals excellent agreement between theory and observation forR ₁ throughR ₄, with discrepancies that average only 9%. This provides experimental support for the accuracy of the atomic data adopted in the line ratio calculations, and also resolves discrepancies found previously when the theoretical results were compared with solar data from the S082A instrument on boardSkylab. However in the case ofR ₅, the theoretical and observed ratios differ by almost a factor of 2. This may be due to the measured intensity of the 448.28 line being seriously affected by instrumental effects, as it lies very close to the long wavelength edge of the SERTS spectral coverage (235.46–448.76 ).     

Observations of stray-light and sunspot intensities during the Mercury transit of 1970 May 9

In order to test the usual method for correcting sunspot intensity measurements for stray light, we have measured, during the Mercury transit of 1970 May 9, the intensities of Mercury, a sunspot umbra, and the aureole. The direct observations result in Mercury intensities < 0.06 I and aureole intensities <0.01 I . The stray light correction to the spot intensities has been <(0.03 ± 0.01) I . The main contribution to the stray light on the solar disc is shown to be produced by a spread-function with a half width of 10 arc sec. Consequently, for stray light corrections the range R R + + 20 in the aureole has to be measured very precisely; furthermore, a remarkable fraction of the stray light in the center of an umbra originates from the surrounding penumbra.Mitteilungen aus dem Fraunhofer Institut, Nr. 102.     

ON THE WAVELENGTH DEPENDENCY (AND ITS VARIATIONS) OF THE RATIO DISK-AVERAGED TO DISK-CENTER INTENSITY,F/I 0 (λλ0.385 TO 10 µm)

In the whole wavelength range, 0.385 to 10.0 µm, the ratios F/I ₀ of disk-averaged intensity F to disk-center intensity I ₀ follow very closely the simple relation F/I ₀ = 0.975 - 0.091^-1 - 0.00024^-5. The residuals exhibit a well-defined structure with minima and maxima in the order of± 5 × 10^-3 , which reflect the wavelength-dependency of the source function B(,) and the continuous absorption coefficient . The fact that the scatter of the coefficients of the relevant limb-darkening functions is usually much larger than the scatter of the F/I ₀ ratios seems to confirm the occurrence of limb-darkening variations, which however leave the F/I ₀ ratios almost unchanged. Nevertheless, minor differences between different observations, which concern the details in the wavelength-dependency of the F/I ₀ residuals, seem to indicate that even the F/I ₀ ratios undergo minor variations.     

Ca X line ratios in solar flares

Theoretical Ca X electron temperature sensitive emission line ratios, derived using electron excitation rates interpolated from accurateR-matrix calculations, are presented forR ₁ =I(419.74 )/I(574.02 ,),R ₂ =I(411.65 )/I(574.02 ),R ₃ =I(419.74 )/I(557.75 ), andR ₄ =I(411.65 )/I(557.75 ). A comparison of these with observational data for three solar flares, obtained by the Naval Research Laboratory's S082A slitless spectrograph on boardSkylab, reveals good agreement between theory and observation forR ₁ andR ₃ in one event, which provides limited support for the accuracy of the atomic data adopted in the analysis. However, in the other flares the observed values ofR ₁ –R ₄ are much larger than the theoretical high-temperature limits, which is probably due to blending of the 419.74 line with Civ 419.71 , and 411.65 with possibly Ciii 411.70 .     

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.     

Ar XIII line ratios in solar flares

Theoretical ArXIII electron-density-sensitive emission line ratios, derived using electron impact excitation rates interpolated from accurateR-matrix calculations, are presented forR ₁ =I(242.22 )/I(236.27 ),R ₂ =I(210.46 )/I(236.27 ), andR ₃ =I(248.68 )/I(236.27 ). Electron densities deduced from the observed values ofR ₁,R ₂, andR ₃ for solar flares obtained with the NRL S082A slitless spectrograph on boardSkylab are in excellent agreement, and furthermore compare favorably with those determined from line ratios in CaXV, which is formed at a similar electron temperature to that of ArXIII. These results provide experimental support for the accuracy of the atomic data adopted in the analysis, as well as for the techniques used to calculate the line ratios.     

Dynamical behavior of nuclear reaction systems disturbed by fluid motion in the solar core

Using Euler's equation of motion, the equation for disturbed fluid motion against a hydrostatic equilibrium has been derived, and the nonequilibrium dynamical equation of a P-PI nuclear reaction system driven by He³ has been analysed using developed nonequilibrium theory. We find that the system in the solar core is unstable in the layer extending from about 0.2R to 0.4R if the core is disturbed by fluid motion; this instability may be related to thermal diffusion.     

Evidence for leading spiral arm formation in NGC 7479

Azimuthal profiles of the spiral NGC 7479 in theB andI passbands have been analyzed using a subset of the azimuthal parameters proposed by Beckman and Cepa (1989), to look for the presence of shock fronts in the arms, as predicted by the density wave theory. The sign of the skewness parameter, showing that beyond the corotation radius the concave side of the southern arm shows steeper profiles in both colours, is an indicator that the arm studied is a leading structure. We also measure a colour gradient in the arm, with theB intensity peak of the profile nearer to the shock front than theI peak. The measured angular shift, when converted to time drift assuming that the bar ends near the corotation radius, is consistent with the drift expected for an ageing stellar population.     

The effect of oblateness of the bigger primary on collinear libration points in the restricted problem of three bodies

In the restricted problem of three bodies, the effect of oblateness of the bigger primary appears as an additional term in the potential. As a result, the location of libration points and the roots of the characteristic equation at these points depend not only upon the mass parameter but also on the oblateness termI of the bigger primary. Series solutions are developed in terms of andI which are used for locating the collinear libration points and for determining the mean motions and characteristic exponents at these points.The work is supported by a fellowship awarded to the second author by University Grant Commission, India.     

Symmetry in hierarchical cosmology

An idealized model of a hierarchy of clusters is considered, and the number-count asymmetry measure in two different directions,R ₁ |N ⁺-N ^-|/(N ⁺+N ^-), is evaluated, for values ofl _I /c _I =(distance between cluster centres)/(cluster diameter). Providedl _I /c _I 10, theory predictsR _I 0.1, in agreement with the symmetry of high-redshift radio sources.     

Comparison between some Hα and X-ray flares

In the present paper, H-evolutive curves of chromospheric events are compared with flux evolutive curves of X-ray events observed at the same time in different spectral regions. A correspondence between the emissions E(I _H/I _chr)'s at higher and higher H-intensity levels, and the X-ray fluxes F()'s in harder and harder -ranges is shown. Further, the present observations seem to indicate the existence of a single triggering mechanism during the flash-phase of a flare. It is also shown that these results may be in agreement with Brown's model for chromospheric flares.     

Zeeman-doppler imaging: A new option for magnetic field study of Ap and solar-type stars

In the task of studying stellar magnetic fields, polarimetric methods have been intensively used in Ap stars. But the observational material classically used to reconstruct stellar magnetic structures (average longitudinal magnetic field as a function of rotational phase) is not rich enough in spatial information to derive geometries more complex than centered or decentered dipoles.In solar-type stars, all evidences of activity recently detected on their surfaces (starspots, flares, ...) indicate they are most likely magnetic stars. But polarimetric methods have always failed in these stars, probably due to the complex magnetic topologies encountered which even prevented until now a simple detection (Borra, Edwards, and Mayor, 1984). With the Zeeman broadening measurement technique proposed by Robinson (1980), no reliable results can be derived for rapid rotators, which are otherwise presumed to be the best candidates for magnetic detections. Once more, if temperature inhomogeneity charts are already available for solar-type stars (Vogt, 1987), spatial information on their magnetic distributions has conversely not yet been obtained.The new option, recently proposed by Semel (1989) and qualified by Donati, Semel, and Praderie (1989), is based on the rotational modulation study of a rapid rotator Stokes parameter V(), obtained with both high spectral resolution R, and high signal-to-noise ratio S/N. Since the magnetic information used refers to localized strips on the stellar disc (as a consequence of the star rotation), multipolar structures can thus be resolved.A new instrumentation and observing procedure have been defined for ZDI, in order to obtain very high S/N data. The method has been successfully tested on two bright magnetic Ap stars: a magnetic detection was obtained on UMa and a 15-point phase coverage of ² CVn is available for the reconstruction of complete 2D abundance and magnetic mappings of its photosphere.Concerning solar-type stars, a numerical simulation was carried out in order to determine the observational constraints required for the detection of typical magnetic field similar to those reported in slow rotators with the Robinson method (Saar, 1988). The specifications needed are S/N 400 per 40 mÅ pixel and R - 6 × 10⁴.     

A note on variable-G cosmologies

An example of a cosmological model with variable gravitational couplingG and a time-dependent cosmological term , has recently been presented. It has been shown that there is no creation of matter and that the rest mass of particles stays constant in this model. In this paper we will generalize the field equations to the case where bothG and depend both on time and position. It is shown that even in this case there may be no creation.     

Coronagraphic observations of an enhanced coronal region

Ratios of emission line intensities are used to calculate the variation of temperature and the variation of electron density as a function of ion class for differing paths through a coronal enhancement. The data indicate (a) a peak mean electron density of 2.3 × 10⁹ cm^–3, (b) a temperature maximum greater than 2.3 × 10⁶ K, and (c) the non-coincidence of the peak temperature and peak mean electron density. The latter demonstrates the invalidity of the assumption of symmetric models for coronal enhancements.The abundance of Ni was found to be equal to 0.045 that of Fe from the line ratio I( 6702)/ /I( 7059) and a density model based on the variation of the ratio I( 8024)/I( 6702).     

Genericity of the non-periodic solutions of the central force problem

We study the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. for negative energy and (0, 2), each energy levelI _h is foliated by the invariant toriI _hc of constant angular momentumc and, by Liouville-Arnold's theorem, the flow on eachI _hc is conjugated to a linear flow of rotation number _h (c).A well-known result asserts that if we require _h (c) to be rational for every value ofh andc, the, must be equal to one (Kepler's problem). In this paper we prove that for almost every (0, 2) _h (c) is a non-constant continuous function ofc, for everyh<0. In particular, we deduce that motion under central potentials is generically non-periodic.Partially supported by CIRIT under grant No. EE88/2.     

Activity in the quiet Sun

Macrospicules have been observed in H and He i D₃, on the disk and above the limb. In 1975, a rate of 1400 (A day)^–1 is inferred, and the ratio of equatorial to polar rates 2. D₃ intensities are a few × 10^–3 of the disk center, and do not decrease in coronal holes. The ratio of H to D₃ intensities is 10. The integral number of macrospicules with D₃ intensity I ₀ is proportional to I ₀ ^–1.     

The stability of motion in a periodic cubic force field

The non-linear differential equation , wherep(t) is a periodic square wave function of time with period , has been integrated by using a table of Jacobian elliptic functions. In the neighborhood of a typical elliptic fixed point, namely that for 11, 12-decimal accuracy has been used to determine a region which is stable.