Comparative analysis of photometric variability of TT ARI in the years 1994–1995 and 2001, 2004

We present the results of photometric observations of a bright cataclysmic variable TT Ari with an orbital period of 0.13755 days. CCD observations were carried out with the Russian-Turkish RTT 150 telescope in 2001 and 2004 (13 nights). Multi-color photoelectric observations of the system were obtained with the Zeiss 600 telescope of SAO RAS in 1994–1995 (6 nights). In 1994–1995, the photometric period of the system was smaller than the orbital one (0 _. ^d 132 and 0 _. ^d 134), whereas it exceeded the latter (0 _. ^d 150 and 0 _. ^d 148) in 2001, 2004. An additional period exceeding the orbital one (0 _. ^d 144) is detected in 1995 modulations. We interpret it as indicating the elliptic disc precession in the direction of the orbital motion. In 1994, the variability in colors shows periods close to the orbital one (0 _. ^d 136, b-v), as well as to the period indicating the elliptic disk precession (0 _. ^d 146, w-b). We confirm that during the epochs characterized by photometric periods shorter than the orbital one, the quasi-periodic variability of TT Ari at time scales about 20 min is stronger than during epochs with long photometric periods. In general, the variability of the system can be described as a “red” noise with increased amplitudes of modulations at characteristic time scales of 10–40 min.     

Physical properties of X-ray gas in galaxy cluster CL0024+17

We analyzed the X-ray data obtained by the Chandra telescope for the galaxy cluster CL0024+17 (z = 0.39). The mean temperature of the cluster is estimated (kT = 4.35 _?0.44 ^+0.51 keV) and the surface brightness profile is derived. We generated the mass and density profiles for dark matter and gas using numerical simulations and the Navarro-Frenk-White dark matter density profile (Navarro et al., 1995) for a spherically symmetric cluster in which gas is in hydrostatic equilibrium with the cluster field. The total mass of the cluster is estimated to be M ₂₀₀ = 3.51 _?0.47 ^+0.38 × 10 _Sun ¹⁴ within a radius of R ₂₀₀ = 1.24 _?0.17 ^+0.12 Mpc of the cluster center. The contribution of dark matter to the total mass of the cluster is estimated as ${{M_{200_{DM} } } \mathord{\left/ {\vphantom {{M_{200_{DM} } } {M_{tot} }}} \right. \kern-0em} {M_{tot} }} = 0.89$ .     

Fourier analysis of light curves of eclipsing variable stars

The photometric perturbationsB _h ^(l) arising from both tidal and rotational distortion of a close eclipsing binary have been given in two previous papers (Livaniou, 1977; Rovithis-Livaniou, 1977). The aim of the present paper will be to find the eclipse perturbationsB _2m =B _{2m, tid} +B _{2m, rot} of a close binary exhibiting partial eclipses. This will be done giving the suitable combinations of theB _h ^(l) 's and will make easier the application to real stars. After a very brief introduction, Section 2 gives both theB _{2m, tid} andB _{2m, rot} for uniformly bright discs; while in Sections 3 and 4 they are given for linear and quadratic limb-darkening, respectively. Finally, Section 5 gives a brief discussion of the results.     

Heat and mass transfer of an oscillatory flow with Hall current

In the first part of these notes new expressions—simpler than any previously obtained—are presented in integral form for the derivatives of the α _n ⁰ -functions (required for an interpretation of the observed light changes of eclipsing variables) with respect to the fractional radiir _{1, 2} and projected separation δ of their centres in terms of the modified Bessel functionsK _{0, 1} (x) of the second kind; and utilized for establishing new asymptotic formulae for the computation of ‘boundary integrals’ of the formJ _?1 ⁰ ,n(μ). In the second part of this paper, by a resort to bi-polar coordinates, we shall establish a new type of expansions for the α _n ⁰ -functions valid for any type of eclipses, and converging faster than the expansions of the cross-correlation integral of the form (1) for α _n ⁰ that have so far been established.     

Fourier analysis of the light curves of eclipsing variables,XXIII

The method of evaluating the photometric perturbationsB _2m of eclipsing variables in the frequency domain, developed by Kopal (1959, 1975e, 1978) for an interpretation of mutual eclipses in systems whose components are distorted by axial rotation and mutual tidal action. The aim of the present paper has been to establish explicit expressions for the photometric perturbationB _2m in such systems, regardless of the kind of eclipses and non-integral values ofm. Recently, Kopal (1978) introduced two different kinds of integrals with respect to associated α-functions andI-integrals which have been expressed in terms of certain general types of series that can be easily programmed for automatic computation within seconds of real time on highspeed computers. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Section 3 we shall deduce the integral $$\int_0^{\theta \prime } {\tfrac{{\alpha _n^\prime }}{\delta }} d(sin^{2m} \theta )$$ in terms of a certain general type of series and also β-function, which should enable us to evaluate explicit expressions forf _* ^(h) ,f ₁ ^(h) ,f ₂ ^(h) as well asB _2m .     

Photometric elements and apsidal motion of the eclipsing binary NSV 18773

The photometric elements of the eclipsing binary NSV 18773 (HD 99898) have been determined for the first time by analyzing its V-and I-band light curves from the ASAS-2 and ASAS-3 catalogs. Based on these elements and using other published spectroscopic and photometric data, we constructed a consistent system of geometrical and physical parameters for the system that consists of two stars (M ₁ = 20M _⊙, Sp₁=B0V, R ₁ = 5.0R _⊙ and M ₂ = 14M _⊙, Sp₂ = B1V, R ₂ = 6.5R _⊙) in elliptical orbits (P = 5 _. ^d 049, e = 0.365, a = 40.1R _⊙). The distance to the system is d = 3.3 kpc, the interstellar extinction is A _V = 2 _. ^m 0, and the age is t = 2.8 × 10⁶ yr. NSV 18773 is a visual binary with components V _A = 9 _. ^m 9 and V _B = 10 _. ^m 3 separated by 0 _. ^" 8. The third light (L ₃ = 0.61) that we found by analyzing the light curves shows that the eclipsing binary is the system’s fainter component B. We confirmed the rapid apsidal motion of the star detected by Otero and Wils (2006) and refined its observed period: U _obs = 150 ± 6 yr. Our photometric elements and physical parameters allowed the apsidal parameter $\bar k_2^{obs} = 0.0135(14)$ , which reflects the density distribution along the radii of the component stars, to be determined. Within the error limits, the derived parameter agrees with its theoretically expected value, $\bar k_2^{th} = 0.0119(8)$ , from current evolutionary models of stars of the corresponding masses and ages.     

Variability and possible rapid evolution of the hot post-AGB stars Hen 3-1347, Hen 3-1428, and LSS 4634

We present the results of spectroscopic and photometric observations for three hot southern-hemisphere post-AGB objects, Hen 3-1347 = IRAS 17074-1845, Hen 3-1428 = IRAS 17311-4924, and LSS 4634 = IRAS 18023-3409. In the spectrograms taken with the 1.9-m telescope of the South African Astronomical Observatory (SAAO) in 2012, we have measured the equivalent widths of the most prominent spectral lines. Comparison of the new data with those published previously points to a change in the spectra of Hen 3-1428 and LSS 4634 in the last 20 years. Based on ASAS data, we have detected rapid photometric variability in all three stars with an amplitude up to 0 _· ^m 3-0 _· ^m 4 in the V band. A similarity between the patterns of variability for the sample stars and other hot protoplanetary nebulae is pointed out. We present the results of UBV observations for Hen 3-1347, according to which the star undergoes rapid irregular brightness variations with maximum amplitudes ΔV = 0 _· ^m 25, ΔB = 0 _· ^m 25, and ΔU = 0 _· ^m 30 and shows color-magnitude correlations. Based on archival data, we have traced the photometric history of the stars over more than 100 years. Hen 3-1347 and LSS 4634 have exhibited a significant fading on a long time scale. The revealed brightness and spectrum variations in the stars, along with evidence for their enhanced mass, may be indicative of their rapid post-AGB evolution.     

Étude morphologique et cinématique des structures fines d'une tache solaire

A sequence of 34 photographs of the main spot of the group H 26 (Daily Maps of the Sun, Freiburg 1970, Rome number 5847) has been obtained with the 38 cm refractor of the Pic-du-Midi Observatory, showing throughout a resolution very close or equal to 0′'.3. An interval of 3 hr is covered. The pictures taken at intervals of 6 min approximately permit to study the fine structure of the penumbra and associated phenomena:

1. The penumbra appears to consist of bright grains, generally lined up in the form of filaments, showing up against a dark background (see Figure 1).
2. The bright grains form all over the penumbra (see Figure 5).
3. They move toward the umbra of the spot. Their horizontal velocity is zero at the border penumbra-photosphere and maximum at the umbral border (0.5 km s^?1) (see Figures 3,4 and 8). Therefore, the grains never originate in the photosphere nor do they enter it.
4. They disappear in the penumbra proper or, if they form near enough to the umbra and live long enough, they can enter the umbra and their appearance becomes similar to that of umbral dots.
5. The life time of the grains is a function of their place of origin within the penumbra: It is maximum and of the order of 3 hr or more for those forming in the middle part of the penumbra, and 50 and 40 min respectively for the points formed in the inner and outer part of the penumbra.

     

Sur un formalisme explicitant la loi des distances des planetes

The well-known Titius-Bode law (T-B) giving distances of planets from the Sun was improved by Basano and Hughes (1979) who found: $$a_n = 0.285 \times 1.523^n ;$$ a _n being the semi-major axis expressed in astronomical units, of then-th planet. The integern is equal to 1 for Mercury, 2 for Venus etc. The new law (B-H) is more natural than the (T-B) one, because the valuen=?∞ for Mercury is avoided. Furthermore, it accounts for distances of all planets, including Neptune and Pluto. It is striking to note that this law:

1. does not depend on physical parameters of planets (mass, density, temperature, spin, number of satellites and their nature etc.).
2. shows integers suggesting an unknown, obscure wave process in the formation of the solar system.

In this paper, we try to find a formalism accounting for the B-H law. It is based on the turbulence, assumed to be responsible of accretion of matter within the primeval nebula. We consider the function $$\psi ^2 (r,t) = |u^2 (r,t) - u_0^2 |$$ , whereu ²(r, t) stands for the turbulence, i.e., the mean-square deviation velocities of particles at the pointr and the timet; andu ₀ ² is the value of turbulence for which the accretion process of matter is optimum. It is obvious that Ψ²(r _n,t₀) = 0 forr _n=0.285×1.523 ⁿ at the birth timet ₀ of proto-planets. Under these conditions, it is easily found that $$\psi ^2 (r,t_0 ) = \frac{{A^2 }}{r}\sin ^2 [\alpha log r - \Phi (t_0 )]$$ With α=7.47 and Φ(t ₀)=217.24 in the CGS system, the above function accounts for the B-H law. Another approach of the problem is made by considering fluctuations of the potentialU(r, t) and of the density of matter ρ(r, t). For very small fluctuations, it may be written down the Poisson equation $$\Delta \tilde U(r,t_0 ) + 4\pi G\tilde \rho (r,t_0 ) = 0$$ , withU(r, t)=U ₀(r)+?(r, t ₀ ) and \(\tilde \rho (r,t_0 )\) . It suffices to postulate \(\tilde \rho (r,t_0 ) = k[\tilde U(r,t_0 )/r^2 ](k = cte)\) for finding the solution $$\tilde U(r,t_0 ) = \frac{{cte}}{{r^{1/2} }}\cos [a\log r - \zeta (t_0 )]$$ . Fora=14.94 and ζ(t ₀)=434.48 in CGS system, the successive maxima of ?(r,t ₀) account again for the B-H law. In the last approach we try to write Ψ(r, t) under a wave function form $$\Psi ^2 (r,t) = \frac{{A^2 }}{r}\sin ^2 \left[ {\omega \log \left( {\frac{r}{v} - t} \right)} \right].$$ It is emphasized that all calculations are made under mathematical considerations.     

Exotic ion H 3 ++ in strong magnetic fields

1. The exotic system H ₃ ⁺⁺ (which does not exist without magnetic field) exists in strong magnetic fields:
   1. In triangular configuration for B≈10⁸–10¹¹?G (under specific external conditions)
   2. In linear configuration for B>10¹⁰?G
2. In the linear configuration the positive z-parity states 1σ _g , 1π _u , 1δ _g are bound states
3. In the linear configuration the negative z-parity states 1σ _u , 1π _g , 1δ _u are repulsive states
4. The H ₃ ⁺⁺ molecular ion is the most bound one-electron system made from protons at B>3×10¹³?G

Possible application: The H ₃ ⁺⁺ molecular ion may appear as a component of a neutron star atmosphere under a strong surface magnetic field B=10¹²–10¹³?G.     

Sur un modele explicitant les differents types morphologiques des galaxies

In the now classical Lindblad-Lin density-wave theory, the linearization of the collisionless Boltzmann equation is made by assuming the potential functionU expressed in the formU=U ₀ + \(\tilde U\) +... WhereU ₀ is the background axisymmetric potential and \(\tilde U<< U_0 \) . Then the corresponding density distribution is \(\rho = \rho _0 + \tilde \rho (\tilde \rho<< \rho _0 )\) and the linearized equation connecting \(\tilde U\) and the component \(\tilde f\) of the distribution function is given by $$\frac{{\partial \tilde f}}{{\partial t}} + \upsilon \frac{{\partial \tilde f}}{{\partial x}} - \frac{{\partial U_0 }}{{\partial x}} \cdot \frac{{\partial \tilde f}}{{\partial \upsilon }} = \frac{{\partial \tilde U}}{{\partial x}}\frac{{\partial f_0 }}{{\partial \upsilon }}.$$ One looks for spiral self-consistent solutions which also satisfy Poisson's equation $$\nabla ^2 \tilde U = 4\pi G\tilde \rho = 4\pi G\int {\tilde f d\upsilon .} $$ Lin and Shu (1964) have shown that such solutions exist in special cases. In the present work, we adopt anopposite proceeding. Poisson's equation contains two unknown quantities \(\tilde U\) and \(\tilde \rho \) . It could be completelysolved if a second independent equation connecting \(\tilde U\) and \(\tilde \rho \) was known. Such an equation is hopelesslyobtained by direct observational means; the only way is to postulate it in a mathematical form. In a previouswork, Louise (1981) has shown that Poisson's equation accounted for distances of planets in the solar system(following to the Titius-Bode's law revised by Balsano and Hughes (1979)) if the following relation wasassumed $$\rho ^2 = k\frac{{\tilde U}}{{r^2 }} (k = cte).$$ We now postulate again this relation in order to solve Poisson's equation. Then, $$\nabla ^2 \tilde U - \frac{{\alpha ^2 }}{{r^2 }}\tilde U = 0, (\alpha ^2 = 4\pi Gk).$$ The solution is found in a classical way to be of the form $$\tilde U = cte J_v (pr)e^{ - pz} e^{jn\theta } $$ wheren = integer,p =cte andJ _v (pr) = Bessel function with indexv (v ² =n ² + α²). By use of the Hankel function instead ofJ _v (pr) for large values ofr, the spiral structure is found to be given by $$\tilde U = cte e^{ - pz} e^{j[\Phi _v (r) + n\theta ]} , \Phi _v (r) = pr - \pi /2(v + \tfrac{1}{2}).$$ For small values ofr, \(\tilde U\) = 0: the center of a galaxy is not affected by the density wave which is onlyresponsible of the spiral structure. For various values ofp,n andv, other forms of galaxies can be taken into account: Ring, barred and spiral-barred shapes etc. In order to generalize previous calculations, we further postulateρ ₀ =kU ₀/r ², leading to Poisson'sequation which accounts for the disc population $$\nabla ^2 U_0 - \frac{{\alpha ^2 }}{{r^2 }}U_0 = 0.$$ AsU ₀ is assumed axisymmetrical, the obvious solution is of the form $$U_0 = \frac{{cte}}{{r^v }}e^{ - pz} , \rho _0 = \frac{{cte}}{{r^{2 + v} }}e^{ - pz} .$$ Finally, Poisson's equation is completely solvable under the assumptionρ =k(U/r ². The general solution,valid for both disc and spiral arm populations, becomes $$U = cte e^{ - pz} \left\{ {r^{ - v} + } \right.\left. {cte e^{j[\Phi _v (r) + n\theta ]} } \right\},$$ The density distribution along the O _z axis is supported by Burstein's (1979) observations.     

Some identities for spheroidal harmonics

The spheroidal harmonics expressions $$\left[ {P_{2k}^{2s} \left( {i\xi } \right)P_{2k - 2r}^{2s} \left( \eta \right) - P_{2k - 2r}^{2s} \left( {i\xi } \right)P_{2k}^{2s} \left( \eta \right)} \right]e^{i2s\theta } $$ and $$\left[ {\eta ^2 P_{2k}^{2s} \left( {i\xi } \right)P_{2k - 2r}^{2s} \left( \eta \right) + \xi ^2 P_{2k - 2r}^{2s} \left( {i\xi } \right)P_{2k}^{2s} \left( \eta \right)} \right]e^{i2s\theta } $$ , have ξ²+η² as a factor. A method is presented for obtaining for these two expressions the coefficient of ξ²+η² in the form of a linear combination of terms of the formP _2m ^2s (iξ)P _2n ^2s (η)e ^i2sθ. Explicit formulae are exhibited for the casesr=1, 2, 3 and any positive or zero integersk ands. Such identities are useful in gravitational potential theory for ellipsoidal distributions when matching Legendre function expansions are employed.     

A few observations of and remarks on V1500 Cygni

The development of the post-nova light curve of V1500 Cyg inUBV andHβ, for 15 nights in September and October 1975 are presented. We confirm previous reports that superimposed on the steady decline of the light curve are small amplitude cyclic variations. The times of maxima and minima are determined. These together with other published values yield the following ephemerides from JD 2 442 661 to JD 2 442 674: $$\begin{gathered} {\text{From}} 17 {\text{points:}} {\text{JD}}_{ \odot \min } = 2 442 661.4881 + 0_{^. }^{\text{d}} 140 91{\text{n}} \hfill \\ \pm 0.0027 \pm 0.000 05 \hfill \\ {\text{From}} 15 {\text{points:}} {\text{JD}}_{ \odot \max } = 2 442 661.5480 + 0_{^. }^{\text{d}} 140 89{\text{n}} \hfill \\ \pm 0.0046 \pm 0.0001 \hfill \\ \end{gathered} $$ with standard errors of the fits of ±0 _. ^d 0052 for the minima and ±0 _. ^d 0091 for the maxima. Assuming V1500 Cyg is similar to novae in M31, we foundr=750 pc and a pre-nova absolute photographic magnitude greater than 9.68.     

New activity cycle of the classical symbiotic star V1413 Aql

We present the results of our photometric UBV JHKLM observations in 2008?C2011 for the classical symbiotic star V1413 Aql. At the end of 2008, the hot component of V1413 Aql experienced the next strong outburst (??V > 2 _· ^m 5). According to the photometric criterion (B-V ?? 0 _· ^m 9 ± 0 _· ^m 2), the star was in an active state even in the period preceding the strong 2008 outburst. Two eclipsing minima of the same amplitude were observed for V1413 Aql in 2010 and 2011. Our analysis of the 2011 eclipse has allowed us to estimate the sizes of the components with respect to the orbital semimajor axis if the system is seen edge-on: the radius of the cool component is R _g/a = 0.28 and the radius of the hot component is R _h/a = 0.17. However, judging by the B-V color index, the eclipse may be noncentral.     

Perturbations of a geo-centric synchronous satellite with resonance

We have investigated the resonances due to the perturbations of a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity. The resonances at the points resulting from (i) the commensurability between \(\dot{\theta}_{0}\) (steady-state orbital angular rate of the satellite) and \(\dot{\theta}_{m}\) (angular velocity of the moon around the earth) and (ii) the commensurability between \(\dot{\theta}_{0}\) and \(\dot{\psi}_{0}\) (steady-state regression rate of the synchronous satellite) are analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure as given in Brown and Shook (Planetary Theory, Cambridge University Press, Cambridge, 1933). We have observed that as θ _m (0^°≤θ _m ≤45^°) and ψ (0^°≤ψ≤135^°) increase, the amplitude decreases and the time period also decreases. We have also shown the effect of ψ on amplitude and time period for 0^°≤Γ≤45^°, where Γ is the angle measured from the minor axis of the earth’s equatorial ellipse to the projection of the satellite on the plane of the equator.     

Kinematics of stars in the northern and southern galactic hemispheres

We use vector spherical harmonics for a kinematic analysis of the proper motions of stars from the Hipparcos, Tycho-2, and UCAC3 catalogues in the northern and southern Galactic hemispheres. We have found that the statistically reliable values of the Ogorodnikov-Milne model parameters M ₃₂ ⁺ and M ₃₂ ^? have different signs in different hemispheres. This is a consequence of the Galaxy??s rotational retardation with distance from the principal Galactic plane. Based on various samples of stars from the above catalogues, we have obtained the following estimate for the magnitude of the vertical gradient of Galactic rotation velocity in the solar neighborhoods: (20.1 ± 2.9) < |?V_??/?z| < (49.2 ± 0.8) km s^?1 kpc^?1. Another result that is revealed by our analysis of the parameters M ₁₃ ^? and M ₁₃ ⁺ in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ?V _R /? _z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocity V _R increases with distance fromthe Galactic plane. We show that both these gradients give rise to an apparent acceleration of the solar motion along the x and y axes of the rectangular Galactic coordinate system. Our analysis of the parameters M ₂₁ ^? and M ₁₂ ⁺ shows no significant differences in both hemispheres and has allowed us to determine the Oort parameters, to estimate the Galactic rotation velocity and period in the solar neighborhood, and to calculate the ratio of the epicyclic frequency to the angular velocity of Galactic rotation in the solar neighborhood. The derived diagonal elements of the velocity field deformation tensor suggest that the orientation of the rectangular Galactic coordinate system in space must be determined by taking into account not only the geometrical factors but also the dynamical ones. All these results agree well with these quantities estimated over the entire sphere by various authors.     

Investigation of properties of galaxy clusters in the Hercules supercluster region

We investigated the properties of galaxy clusters in the region of the Hercules supercluster using observational data from the SDSS and 2MASS catalogs and the NED. We have selected 13 galaxy clusters with a total dynamical mass of 4.82 × 10¹⁵ M _⊙ in a 100 × 45 Mpc supercluster region in the plane of the sky (0.030 < z < 0.041). In addition, our sample includes eight clusters from the immediate neighborhoods of the superclusters and ten field clusters at the same z. The derived properties of the rich Hercules supercluster are shown in comparison with the data for the poor Leo supercluster. The main parameters of the virialized galaxy cluster regions in the near infrared (K _s ) for the Hercules supercluster differ from those for the Leo supercluster: the number of galaxies and the total luminosity (to a limiting magnitude of ?21 _· ^m 5) increase with cluster mass (L _K,200 ∝ M ₂₀₀ ^0.91±0.07 and N ₂₀₀ ∝ M ₂₀₀ ^0.94±0.07 ), but the dependences are steeper by 0.28 and 0.22. In the virialized cluster regions, the fraction of early-type galaxies selected by the bulge contribution, concentration index, and u t= r color is, on average, 66% (60% in Leo, 70% in the field) among the galaxies brighter than ?23 _· ^m 3 and 54% (51% in Leo, 61% in the field) among the galaxies brighter than ?22 _· ^m 3. The fraction of early-type galaxies in the superclusters does not change with galaxy cluster mass and luminosity. The composite luminosity function of the rich Hercules supercluster is described by a Schechter function and does not differ from the luminosity function of the poor Leo supercluster for the luminosity interval [?26 ^m , ?21 _· ^m 5] but differs from the field luminosity function at the same z determined from ten galaxy clusters.     

Redetermination of galactic spiral density wave parameters based on spectral analysis of masers radial velocities

To redetermine the Galactic spiral density wave parameters, we have performed a spectral (Fourier) analysis of the radial velocities for 44 masers with known trigonometric parallaxes, proper motions, and line-of-sight velocities. The masers are distributed in awide range of Galactocentric distances (3.5 kpc < R < 13.2 kpc) and are characterized by a wide scatter of position angles ?? in the Galactic XY plane. This has required an accurate allowance for the dependence of the perturbation phase both on the logarithm of the Galactocentric distances and on the position angles of the objects. To increase the significance of the extraction of periodicities from data series with large gaps, we have proposed and implemented a spectrum reconstruction method based on a generalized maximum entropy method. As a result, we have extracted a periodicity describing a spiral density wave with the following parameters from the maser radial velocities: the perturbation amplitude f _R = 7.7 _?1.5 ^+1.7 km s^?1, the perturbation wavelength ?? = 2.2 _?0.1 ^+0.4 kpc, the pitch angle of the spiral density wave i = ?5 _?0.9° ^+0.2° , and the phase of the Sun in the spiral density wave ?? _?? = ?147 _?17° ^+3° .     

Discrete frequency scattering in spherical layers surrounding a point source

The scattered radiation field in homogeneously absorbing and isotropically scattering spherical layers is studied, when the isotropic point source is at the centre. A complete frequency redistribution is assumed. It is shown, that on the inner boundaryr=R ₀ of the cavity, whenR ₀?1 (all radii are expressed in the path lengths), the source functionB～R ₀ ^?1 ln ^?1/2 R ₀ for the Doppler profile andB～R ₀ ^?3/2 for the Voigt and Lorentz profiles. The asymptotical behaviour of the source functionB(r) significantly differs from the analogous behaviour of solution for an infinite medium.     

Ultraviolet solar identifications based on extended absorption series observed in the laboratory spectrum of Sii

The absorption spectrum of Sii in the wavelength region 1500–1900 Å has been photographed at high resolution. The silicon vapour was produced in a 122 cm long King furnace at 1800–2300°C. Forty-two Rydberg series have been observed from the ground state terms 3p ^{2 3} P and¹ D to terms associated with the 3pns and 3pnd configurations. All of the series from these configurations withJ<4 have been extended with the 3pnd ³ D ₃ ^o levels reachingn=56. Numerous perturbations have been observed. This laboratory work has provided the basis for extending the identification of silicon lines in the solar spectrum. Nearly all lines found in the laboratory spectrum are also found in rocket spectrograms of the solar chromosphere. More than 300 lines have been attributed to Sii. The excellent correlation between laboratory and solar Sii lines will be illustrated.