On the A-transform of the exponential integrals

In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE _n which is denoted as _n (). The main result of this analysis enables us to establish a two-term recurrence formula for _n (0) and a three-term recurrence formula for _n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.     

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.     

The blanketing in the rocket ultraviolet from 225.2 to 319.6 nm

The blanketing effect for the solar disc center and its value near the limb (cos = 0.23) are obtained for the rocket ultraviolet region using the Harvard center and limb spectra. The value of for the disc center appears to be 0.67 (on average) relative to the quasicontinuum. The essential decrease of towards the limb is also revealed.     

Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.     

Determination of Optical Spectra by a Modified Kramers Kronig Integral

A new modified Kramers Kronig Integral is derived and shown to produce excellent results when k data is only known over a limited range. By considering the effect of resonance features simulated using the Dirac-Delta function, the new integral is shown to be more rapidly converging than both the conventional Kramers Kronig integral and a modified (Subtractive Kramers Kronig – SKK) integral introduced by Ahrenkiel (1971). The new integral does not require extensive extrapolation of reflectance data outside the measured region in order to produce reliable results. By extending the above procedure to include n data points, it is shown that at wavelength ₀, \[ n(_0)=\sum_{i=1}^{\rm n}(-1)^{\rm n+1}\prod_{\stackrel{j=1}{j \not=i}}^{\rm n} \frac{(_j^2-_0^2)}{(_i^2- _j^2)}n(_i)+\frac{2}{\pi}P\int_{0}^{\infty}(-1)^{\rm n+1} \frac{\prod_{i=1}^{\rm n}(_i^2-_0^2)}{\prod_{i=0}^{\rm n}(^2-_i^2)} k()d \] with relative error given by, \[ R_n(_0)=\prod_{i=1}^{\rm n}\frac{_i^2- _0^2}{_^2-_i^2} . \] This n^th order expression should prove useful in establishing the internal self-consistency of data sets for which both optical coefficients have been theoretically derived.     

The asymptotic behavior of the supersonic solutions of the two-fluid solar wind equations

Three different asymptotic branches of the two-fluid equations are found with _e ^m , _p ⁿ , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The behaviour of the infrared lines of neutral oxygen and the balmer lines of hydrogen in the spectra of early-type stars with emission lines

The equivalent widths of the oxygen lines at 7774 and 8446 and of H (and some H) have been measured for 22 early-type, emission-line stars. A strong correlation between H and 8446 intensities has been found, although there is no such correlation between H and 7774. This confirms the probability that Bowen's mechanism is operative (the neutral oxygen 3³ D state is overpopulated because the excitation energy of Ly- nearly coincides with that of theOi 1025 line). The possibility of using 8446 and H equivalent widths for a comparison of oxygen to hydrogen abundances in these stars is discussed.     

On symmetrical planetary corotations

Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) _jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– _jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev ₅-resonance. This paper presents the symmetric solutions =0 (mod ), = _jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.     

On verification of the asymptotic model of the first kind

For the case of closed Friedmann models with the cosmological constant, an N - dependence is plotted, whereN is the conformal time of existence of the Universe, and is the ratio of the cosmological constant to its Einstein's value. The observational properties of the asymptotic model of the first kind (the so-called Al model) corresponding to the maximum of this dependence are analyzed. For the matter-dominated models, the maximum is achieved at the point = 1. Formulae for the calculation of the age of the Universe and for that of the photometric distance in the Al model are deduced. The observational properties of the A1 model are compared to the corresponding properties of the standard cosmological model ( = 0) which does not occupy any special distinguished position on the N - diagram. It is shown that from the standpoint of the modern observational cosmology these two models cannot be told one from another. However, the A1 model has better standing from the viewpoint of the strong wordings of the anthropic cosmological principle.     

A spectroscopic study of the microorganism model of interstellar grains

The microorganism model of interstellar grains is investigated by spectroscopy from the infrared (IR), visible to the ultraviolet (UV) wave regions.E. coli, yeast and spores ofBacillus subtilis exhibit absorption bands at =3.1 and 9.7 m; they also exhibit several absorptions at 68 m which are in agreement with the observed IS extinction curves.To obtain the extinction curves in the visible and UV regions, dry films of microorganism are prepared on a MgF₂ plate or synthesized quartz plate and their spectra measured. In the wavelength region 190400 nm, conventional spectrophotometers are adopted for the measurement. The extinction curve of the film ofE. coli is similar to the observed IS curve.For the wave-range 100<<400 nm, a vacuum UV spectrometer is adopted to avoid absorptions due to O₂ in the atmosphere. The extinction spectra by this method are in agreement with the result obtained by the conventional method where comparison is possible. The extinction curves ofE. coli and yeast are such that they incrase towards the short wavelength and exhibit a peak at -190 nm, which is different from the well-known IS peak at =220 nm. It remains to be seen whether interstellar low temperatures (1040 K) can shift the peak position in the extinction curve of biochemical materials.     

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.     

Scanner observations of comet P/Crommelin 18181

Spectral scans of the coma of comet P/Crommelin 1818. I have been obtained in the wavelength range 3200–6500 Å. Strong emission features of CN(3883 Å) and C₂ Swan bands (4695, 5165, and 5538 Å) have been identified. Some weak emission features of CH(3890 Å), C₃(4050 Å), CN(4200 »), and C₂ + CH(4358 ») were also detected. Sodium was found to be absent in this comet. An estimate of CN and C₂ abundances has been made and their production rate have been derived.     

EUV arcades: Signatures of filament instability

We have examined seven active regions of the Skylab period in the EUV (Harvard College Observatory), and in H and K₃ (Observatoire de Meudon, spectroheliograms and patrols) in order to elucidate the magnetic geometry in the coronal environment of filaments. We have also looked for signatures of magnetic reconfigurations associated with instabilities (i.e. velocities or disappearances) of filaments. Out of sixteen H filaments observed, six were stable (lifetime 48^h). All the filaments lay within coronal cavities as seen in lines formed above 1.5 × 10⁶ K (Mgx 625, Sixii 521, Fexvi 417, Fexv 361). None of the stable filaments had arcades or arches spanning the cavities except (sometimes) at the ends of the filaments. On the other hand, most (8/10) of the unstable filaments (having concurrent Doppler shifts or a subsequent DB within 24^h) had arcades or single arches spanning their cavities. The arches were observed in EUV lines with formation temperatures as low as 2–4 × 10⁵ K (Oiv 554, Ovi 1032, Ne vii 465), as well as in hotter lines. A statistical test shows that the arcade/instability vs non-arcade/stability association is significant at the 99% confidence level. We suggest 2 types of scenario relating arcades to instabilities. The more preferable scenario is closely related to the Kuperus/Van Tend model of filament disruptions.     

Spectroscopic Data for the 6it s6it p 3 P1 level of Lu+ for the Determination of the Solar Lutetium Abundance

We report spectroscopic measurements on the 6s6p ³P₁ level of Lu⁺ at 28503.16 cm^-1. The radiative lifetime of this level was measured to be 37.4 ± 1.9 ns using time-resolved laser-induced fluorescence of a slow ion beam. Branching fractions were determined from Lu spectra recorded using the 1.0 m Fourier transform spectrometer at the National Solar Observatory. Thelog(gf) values determined by combining the radiative lifetime and branching fractions for the 3507.39, 5983.90, and 6221.87 (air wavelengths) lines are - 1.16 ± 0.03, - 1.16 ± 0.06, and -0.76 ± 0.04, respectively. The 6221.87 line has been identified by Bord, Cowley, and Mirijanian (1997) as the best candidate for the determination of the solar lutetium abundance because it is only slightly blended in the solar spectrum. The present 6221.87 transition probability measurement brings their solar lutetium abundance into good agreement with the CI chondrite abundance.     

Multi-cloud model (MCM) method and its applications to the study on asymmetric spectral profiles

A method of multi-cloud model (MCM) is proposed in this paper in order to research asymmetric profiles of spectral line formed by solar discrete active objects aligned along the line-of-sight difection. Based on the MCM method, under the conditions of certain assumptions and approximations, the line-of-sight velocityV and three other physical parameter approximation values, (i.e. Doppler width _D , source functionS and optical depth at line center ₀) within different clouds may be derived simultaneously by fitting both profiles theoretical and observational. An application example of the method withm=3 shows that MCM method is suitable to measure the velocity fields of multi-object at the same time from their non-Gaussian profiles of complex. TheV and _D derived from the method are reliable,S and ₀ are approximation. An influence of the variations of initial values in the parameter on the solution is given as well.     

Simultaneous measurements of magnetic fields and brightness fields using a 4-image spectroheliograph

The use of an auxiliary beamsplitter with the Kitt Peak 15-foot spectroheliograph permits spectroheliograms to be taken simultaneously in 4 identical images of the sun. By using two of these images for a Zeeman spectroheliogram, a third image for a Fei 4071 spectroheliogram, and the fourth image for a 6107Å continuum spectroheliogram, simultaneous measurements of magnetic fields and brightness fields have been obtained. Within the limits of intensity variations imposed by doppler shifts and brightness fluctuations of the continuum, a quantitative relation does exist between the measured values of brightness and magnetic field strength of the photospheric network. For intensities measured +0.12 Å from the core of Fei 4071, this relation is ln(1 +I/I) = ¦B ¦, whereB refers to the component of magnetic field normal to the solar surface,I/I is the fractional excess of brightness of the magnetic regions relative to the brightness of non-magnetic regions, and = (6±2)%/100 gauss.Kitt Peak National Observatory Contribution No. 538.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.Visiting Astronomer, Solar Division, Kitt Peak National Observatory.     

The observed limb effect in Fraunhofer lines,I

The absolute limb effect is presented for Fei lines 3767 and 3969; for five Tii lines of multiplet 42 near 4535 and one Tiii line at 4534; two lines of Mgi, 4571 and 5172; two lines of Baii at 5854 and 6497. The scattered light of the McMath solar telescope is illustrated by several figures but not applied to the limb-effect observations. It is suggested that the supergravity shift at the limb is the result of scattering of the atoms in anisotropic velocity field.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.     

Oxygen abundances in old disc and halo stars of the Galaxy

Intermediate resolution (/ 25 000) CCD spectra of the oxygen triplet at 7770 Å have been analyzed to determine oxygen abundances in a sample of metal-deficient stars with metallicities covering the range –2.5[Fe/H]–0.2. Important oxygen overabundances ([O/Fe]1) are found in the more metal deficient stars of the sample. We briefly discuss the information that these observations provide about the early nucleosynthesis history and chemical evolution of the Galaxy.     

On polarimetry in solar active regions

The usefulness of magnetically sensitive iron lines Fe 5250.2, 6173.3 and 6302.3 for solar polarimetry is investigated. The line-to-continuum absorption coefficient ₀ for Fe 5250.2 depends strongly on temperature variations. Thus a photospheric calibration of polarimeter signals cannot be used for the different parts of an active region. This is also true for the Doppler calibration of longitudinal magnetographs.Fe 6302.5 is shown to be useful for polarimetry in active regions. A Milne-Eddington approximation is possible so that Unno's formulae are sufficient for the interpretation of polarimetric data.The ambiguity of the azimuth of the linear polarization prevents the determination of the true field structure with respect to the solar surface. The magnetic flux cannot be determined outside the disc centre without making assumptions for the unknown field structure. This determination is possible only for single stable sunspots; for irregular active regions the field configuration remains ambiguous even at the disc centre.     

A generalized method for deriving mass-loss rates: The first order moment of unsaturated P Cygni line profiles

For the case of optically thin lines, we show that the relation existing between the first order momentW ₁ (E()/E _c –1)(–₁₂)d of a P Cygni profile and the quantityMn(level), whereM is the mass-loss rate of the central star andn(level) the fractional abundance of the ion under study, is in fact independent of any Sobolev-type approximations used for the transfer of line radiation, contrary to what has been assumed in some previous works (Castoret al., 1981; Surdej, 1982). Consequently, all results established in the context of very rapidly expanding atmospheres and mainly referring to the non-dependence ofW ₁ vs various physical (underlying photospheric absorption line, limb darkening, etc.) and geometrical (velocity fieldv(r), etc.) effects remain unchanged for arbitrary (e.g non-Sobolev type) outward-accelerating velocity laws.Whenever applied with caution, Equation (50) thus provides a very powerful means of deriving mass-loss rates—with a total uncertainty less than 60 percent—from the measurementW ₁ of unsaturated P Cygni profiles observed in the spectrum of early—as well as late—type stars, quasars, etc.