Stellar structure with a Boltzmann factor: An extension to chemically heterogeneous H−He-stars

We present an attempt for an extension of the modified Boltzmann model, which was introduced by Callebautet al. (1982) as an improvement of the polytropic models, to the case of chemically-heterogeneous stars in equilibrium, containing H and He, by proposing a density profile of the formp=C ₁ T ^N exp (–_H m(–_*)/kT) +C ₂ T ^N exp (–_He m(–_*)/kT. Analytical properties are derived and numerical as well as analytical arguments are presented for the conclusion that this hypothesis for a density profile imposes an almost constant chemical profile to the model as a whole, thereby making it in this form unsuited for the study of heterogeneous stars. A comparison is made with the former Boltzmann model in the homogeneous limit.     

The latitude of filament bands at the sunspot minimum and the activity level in the two following 11-year solar cycles

The zonal structure of the distribution of filaments is considered. The mean latitudes of two filament bands are calculated in each solar hemisphere at the minima of the sunspot cycle in the period 1924–1986: middle latitude _{2, m} and low latitude _{1, m} . It is shown that the mean latitude of the filament band _{2, m} at the minimum -m of the cycle correlates, with = 0.94, with the maximum - M sunspot area S(M) and maximum Wolf number W(M) in the succeeding solar cycle M. It is shown that the mean latitude of the low-latitude filament band _{1, m} is linearly dependent on the mean latitude filament band _{2, m + 1} at the succeeding minimum. We found a correlation of the latitude of the low-latitude filament band _{1, m} with the maximum sunspot area in the M + 1 cycle. This enables us to predict the power of two succeeding 11-year solar cycles on the basis of the latitude of filament bands at the minimum of activity, 1985–1986: W(22) - 205 ± 10, W(23) - 210 ± 10. The importance of the relationships found for theory and applied aspects is emphasized. An attempt is made to interpret the relationships physically.     

Intensity fluctuations in Fraunhofer lines

An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z and if (z) and p(z) are not too rapidly varying, then (t) m (z , t)+N p(z , t) where m and N depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Dynamic phenomena in the chromospheric layer of a sunspot

We have studied running penumbral waves, umbral oscillations, umbral flashes and their interrelations from H observations of a large isolated sunspot. Using a subtraction image processing technique we removed the sharp intensity gradient between the umbra and the penumbra and enhanced the low contrast, fine features. We observed running penumbral waves which started in umbral elements with a size of a few arcseconds, covered the umbra and subsequently propagated through the penumbra. The period of the waves was 190 s and the mean propagation velocity was about 15 km s^–1. We detected intense brightenings, located between umbral elements from where waves started, which had the characteristics of umbral flashes. There are indications that umbral flashes are related to the propagation of the waves through the umbra and their coupling. The subtraction images also show considerable fine structure in the chromospheric umbra, with size between 0.3 and 0.8.     

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.     

Unsteady hydromagnetic free convection flow past an accelerated infinite vertical porous plate

Unsteady laminar free convection flow of a viscous incompressible and electrically conducting fluid past an accelerated vertical infinite porous plate subjected to a suction velocity proportional to (time)^–1/2 is studied in presence of a uniform horizontal magnetic field. Results are discussed with the effects of the Grashof number Gr, and the magnetic field parameterM for Pr (the Prandtl number)=0.71 and 7.0 representing air and water respectively at 20 °C.Nomenclature a suction/injection parameter - C _p specific heat at constant pressure - B ₀ magnetic induction - g acceleration due to gravity - Gr Grashof number (vg(T'_w-T')/U ₀ ³ ) - K thermal conductivity - M magnetic field parameter (B ₀ ² _e ² /U ₀ ² ) - Pr Prandtl number (C _p/K) - T' temperature of the fluid near the plate - T' _w temperature of the plate - T' temperature of the fluid at infinity - t' time variable - t dimensionless time (t' U ₀ ² /v) - u non-dimensional velocity (u'/U ₀) - U' velocity of the plate - U dimensionless velocity of the plate (U'/U _o) - U ₀ reference velocity - v' ₀ suction velocity - v ₀ nondimensional suction velocity (v' ₀/U ₀)=at^–1/2 - v' normal velocity component - v dimensionless normal velocity - Ec Eckert number ((vU ₀)^2/3/C _p(T' _w -T' )) - T dimensionless temperature of the fluid near the plate ((T'-T' )/T' _w –T' )) - x',y' coordinates along and normal to the plate - y dimensionless ordinate (=y' U _o/v) - v kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - similarity variable (y/2t) - _w density of the fluid at the plate - density of the fluid at infinity - ' skin-friction - dimensionless skin-friction - coefficient of viscosity - _e magnetic permeability     

Effect of Krein signatures on the stability of relative equilibria

We consider the linear stability of the equilibrium points of the generic rotating potentials U(r), U(r, ), U(r, and U(r, , . The stability analysis is performed using the concept of Krein's signature. This signature is calculated for all eigenvalues of the above potentials. Thereby, the Lagrangian points of the restricted three-body problem and the synchronous satellites of oblate and prolate planets are also studied. We find also the new positions of the eigenvalues for perturbations of the original L ₄ and L ₅ points of Mars, Jupiter, Saturn, Uranus and Neptune. Finally, we study the problem with the mass ratio µ close to the critical value and the stability of geostationary satellites perturbed by the Moon.     

Photospheric and chromospheric umbral dots in a decaying sunspot

Time-sequenced H filtergrams and narrow-band blue filtergrams (₀ = 4308 Å, = 10 Å) of umbral dots in a decaying sunspot were studied. The results are: (a) Photospheric umbral dots have lifetimes of about 40 min. (b) Two types of proper motion were found for photospheric umbral dots. Umbral dots born in the umbra or in the light bridge show virtually no proper motion. On the other hand, umbral dots of penumbral origin move inward to the umbra with speeds of about 0.4 km s ^–1. (c) Chromospheric umbral dots, which have dimensions of 0.6 × 1.2 in the mean, were more numerously found than photospheric umbral dots. (d) Photospheric umbral dots were observed to be associated with chromospheric umbral dots. Thus umbral dots are not phenomena confined to photospheric levels but also extend to chromospheric levels. (e) Some of the chromospheric umbral dots are unrelated to the photospheric umbral dots. They may be excited by the infalling matter from the umbral corona.Contribution from the Kwasan and Hida Observatories, University of Kyoto, No. 266.     

The prominence-corona interface compared with the chromosphere-corona transition region

The intensities of 52 EUV emission lines from each of 9 hedgerow prominences observed at the limb with the Harvard experiment on ATM-Skylab have been compared with intensities from the interior of network cells at the center of the disk, in order to compare the prominence-corona (P-C) interface with the chromosphere-corona (C-C) transition region. The intensity ratio I _cell/I _prominence for each line varies systematically (in all of the prominences observed), with the temperature of formation of the line as T ^–0.6. The density sensitive C iii (formed at T 9 × 10⁴ K) line ratio I ₁₁₇₅/I ₉₇₇ implies an average density 1.3 × 10⁹ electrons cm^–3 in the P-C interface and 4 times this value in the C-C transition of the cells. The total optical thickness at the head of the Lyman continuum is 10 in most of the prominences studied; in two of the prominences, however, we cannot reject the possibility that _o is large. Methods of analysis of these EUV data are developed assuming both a resolved and an unresolved internal prominence structure. Although the systematic differences between the P-C interface and the C-C transition are stressed, the similarities are probably more remarkable and may be a result of fine structure in the C-C transition.Currently on leave from the Institute of Astronomy, Hawaii; at the Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, 80309.     

Distribution of sunspots according to their magnetic fluxes

The occurrence frequency distribution of sunspots in different magnetic flux values has been examined. The number of sunspots decreases as ^-1.9 for sunspots with magnetic flux greater than 3 × 10²¹ Maxwell, where is the said flux of a sunspot.     

A new estimate of the solar meridional flow

We present a new method for measuring the solar magnetic meridional flow, and provide a comparison with other recent work. We have performed a least-squares fit to azimuthally averaged Mount Wilson Observatory synoptic data encompassing Carrington rotations 1722 to 1929 to produce an estimate of the solar meridional flow. A parametric fit to our results expresses the solar meridional flow as v() = 28.5 sin2.5 cos.     

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.     

Generalized polytropes: Stellar structure with a boltzmann factor

In order to study the structure of a chemically homogeneous star in equilibrium, a density profile of the form T ^N exp(–µm(–)/kT) is suggested. As for polytropes, qualitative aspects of the resulting stellar model can be discussed analytically. In particular it is shown that one reobtains forN=3 Eddington's standard model, whereas forN<3 nearly polytropic models result. WhenN>3, the effective polytropic index does vary appreciably over the star. Numerical results indicate that the proposed density profile is quite reasonable in view of the simplicity of the model. From a comparison of the degree of precision of a polytropic approximation with that of the newly proposed model it follows that the new approximation is definitely better than the polytropic one. It is suggested that the model may be useful to study the structure of stellar clouds, clusters and (spherical) galaxies.Now at Department of Applied Mathematics, Queen Mary College, University of London, England.     

On some characteristics of umbral fine structure

Photographic spectra of the umbra of a sunspot (1971, August 24, Rome No. 6205) around 6150 Å show fine bright threads which were identified as the spectra of a lightbridge, of the bright end of a penumbral filament and of umbral dots, respectively. It was found, in agreement with the results of other authors, that the magnetic field in bright structures is considerably weaker than in dark umbral material. Analysis of line profiles of Fe ii 6149.2 Å in umbral dots indicates (a) a fieldstrength reduced by a factor 2 compared to the surroundings, (b) an outflow with v3.0 km s^–1 relative to the penumbra and (c) possibly photospheric temperatures in umbral dots.Mitteilungen aus dem Fraunhofer Institut Nr. 115.     

On the relation of SPA measured at VLF to solar microwave burst energies

A surprisingly good correlation has been found for SPA measured at VLF propagation () and 7 GHz solar microwave burst energies (E ). The data are correlated in the form = a log E + b and include all kind of solar events, irrespectively from type, complexity or duration. Soft X-ray peak fluxes (I _x) have a known similar correlation to SPA, and a functional relationship of the form 479-01 can be established. As one practical application, the energies from solar events can be reasonably well inferred from SPA data, which are quite reliable and easily obtainable.     

Spectre continu dans le proche infrarouge de deux étoiles Be: HD 50138 et HD 51585

Continuous spectra of the Be objects HD 50138 and HD 51585 have been investigated between 1.6 and 1.2 ^-1. The infrared gradient _IR of HD 50138 (B5eV) is found to be 2.09±0.10, while the typical B5V star And indicates _IR=1.17. A B5V (HD 16219) star located at about the same distance as HD 50138 has _IR=1.29 and it is shown that interstellar reddening may account for _IR between HD 16219 and And. The difference in gradient between HD 50138 and HD 16219 ( _IR=0.8) may be explained by a continuous reemission in a lenticular envelope with a radius equal to 4R _*. The peculiar object HD 51585 exhibits a B0.5 continuous spectrum, for which the value d logI /d(1/) should be 1.13 according to model atmospheres computations. The distance as derived from color excess leads to disagreement between measured and computed (for a B0.5 star) values of d logI /d(1/). The reddening may be explained by reemission in an envelope the radius of which is smaller than 5R_*. In conclusion, the narrowness of the spectral range under consideration does not permit to decide whether the observed reddening is due to recombination to the third level of the hydrogen atom or whether it is part a thermal reemission in a circumstellar cloud at lower temperature, as it has been observed around 10 by various authors.

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Les spectres utilisés dans ce travail ont été obtenus à l'aide des téléscopes de 193 cm et 120 cm de l'Observatoire de Haute-Provence (CNRS).     

Early cosmological models in Lyra's geometry

A spatially homogeneous and isotropic Robertson-Walker model withzero-curvature of the universe is studied within the frame-work of Lyra'smanifold. The gauge-function in Lyra's manifold is taken to betime-dependent. Exact solutions of Einstein equations are obtained for twodifferent early phases of the universe viz. Inflationary phase andradiation-dominated phase by using `gamma-law' equation of statep = ( - 1) . The -index, describing the material content,varies continuously with cosmic time so that in the course of itsevolution, the universe goes through a transition from an inflationaryphase to a radiation-dominated phase. The physical properties of themodels are also discussed.     

High resolution EUV structure of the chromosphere-corona transition region above a sunspot

Ion emission line intensities between 1170 and 1700 Å allow one to determine the differential emission measure (DEM) and electron pressure of the plasma in the solar transition region (TR). These line intensities together with their Doppler shifts and line widths are measured simultaneously for the first time above a sunsport from data obtained with the NRL High Resolution Telescope and Spectrograph with 0.06 Å spectral and 1 spatial resolution.The Doppler shifts show both subsonic and supersonic flow in the same line of sight over the umbra. The temperature structure for 40 resolution elements in the sunspot umbra and penumbra is derived from the DEM and the observed electron pressures.Extrapolation of the emission measure curves supports the previous EUV and X-ray observations that coronal plasma above sunspots with T _e>10⁶ K is reduced while emission from TR plasma between 2×10⁵ and 10⁶ K is greatly enhanced relative to quiet or active regions. This enhancement shifts the minimum of the DEM to lower temperatures and increases the slope at 2×10⁵ K by a factor of two.New pressure diagnostics using the emission line intensity ratios of C iv to N iv are presented, and applied to the data.The energy balance in the TR for the sunspot umbra is dominated by radiative losses from the large amount of TR plasma.An estimate of the energy budget shows that an energy input is required to balance the radiative energy losses above the umbra. The observed divergence of the enthalpy flux for the umbral downflows can balance these radiative losses for T _e between 30000 and 200 000 K.A typical umbral model of T _e versus reduced mass column density is compared with one for chromospheric temperatures determined from the Ca H and K lines.Institute of Theoretical Astrophysics, University of Oslo, Norway.     

Linear analysis of the light curves of eclipsing variables

In this paper, general model analysis of the form c _{i i} () for the fractional loss of lightf() exhibited by a close binary system will be considered in the sense of the least-squares criterion. A general recursive method will be established for constructing the normal equations for the most useful functions _i (), and an economical storage of the method on a digital computer, with its computational steps, will also be given. Moreover, a full recursive computational algorithm for the least-squares approximation will also be established. By means of this algorithm, all the solution vectors, the variance for different orders of fit and the corresponding variance-covariance matrix could be computed once and for all and, moreover, recursively. The economical storage of the algorithm and its computational steps will be given. Finally, some of the practical difficulties encountered in the application of the least-squares criterion will be analysed, and some techniques for detecting and controlling these difficulties are also given. Numerical examples on the Algol system using a Fourier cosine series of the form c _i cos [(j - 1) /] will be given for illustration.     

Enhanced emission of Alfvén waves from sunspots during proton flares

Thomas (1978) has shown that, if Alfvén waves exist in a sunspot umbra, they are normally reflected so strongly by the temperature minimum as to be essentially undetectable in the upper solar atmosphere. However, it is known that in many proton flares, chromospheric emission overlies the umbra of a sunspot, indicating that the transition region (TR) between chromosphere and corona in the umbral flux tube has moved down to lower altitudes. As a result of this lowering, umbral Alfvén waves have readier access to the corona: the coronal leakage depends exponentially on the altitude of the TR. We find that the Alfvén wave flux which leaks out of the umbra into the corona can exceed 10⁷ ergs cm^-2 s^-1. A flux of this magnitude is expected to dissipate rapidly in the corona, thereby contributing to a positive feedback loop which ensures prolonged (1 hr) leakage of the umbral Alfvén waves into the corona. We propose that these Alfvén waves may contribute significantly to prolonged energization of proton flares in which umbral coverage occurs.