Radial velocity measurements of the spectra of Zeta Aurigae outside eclipses

Radial velocities of both components of Zeta Aurigae have been measured on 39 grating spectra obtained in the interval February 1970-November 1981.The evaluation of the orbital elements of the primary component confirmed, the elements observed so far. The velocity variation of the secondary component has been determined according to the method described by Popper (1961) yieldingK _B=30.57±5.97 (m.e.) km s^–1. The masses of the components were found to beM _K sin³ i=6.4±1.7 andM _B sin³ i=4.5±0.9 solar masses. With the elements obtained a radial velocity curve of the B-star has been calculated. Comparison of the radial velocities derived from the hydrogen lines of the B-star with the calculated radial velocity curve shows systematic deviations which indicate that these lines originate partly in an expanding circumstellar envelope of the system. The main constituent of the envelope must be neutral hydrogen of high density. Variations of the radial velocities indicate density variations due to condensations inside this envelope.     

On the effect of collisional transitions on the cosmological hydrogen recombination spectrum

We study the effect of collisional 2s ? 2p transitions on the populations of the 2s and 2p states at the cosmological hydrogen recombination epoch and on the intensity of the recombination Hα line. Our calculations are based on a simple model hydrogen atom with four bound states (1s, 2s, 2p, and the n = 3 level with an equilibrium distribution in sublevels with different orbital quantum numbers l). We show that collisions do not lead to an equilibrium distribution in sublevels of the n = 2 level. The relative change in the cosmological Hα line intensity due to collisional transitions does not exceed 10^?3.     

General precession computed by numerical integration of ordinary differential equations

It is suggested that the effects of change in the celestial coordinates due to general precession be computed by solving numerically the differential equations for the instataneous rates of change in right ascension and declination. An approximate solution in closed from is given. Similar differential equations may be solved for the complete rotation matrix, requiring only the knowledge of the variations of the two function m and n with time. This suggests the existence of a relation between the classical precessional elements z, ζ₀ and Θ, and this relation is derived. Some numerical examples are also presented.     

Radial pulsations of massive main-sequence stars

The evolution of Population I stars (X = 0.7, Z = 0.02) with initial masses 40M _⊙ ≤ M _ZAMS ≤ 120M _⊙ until core hydrogen exhaustion has been computed. Models of evolutionary sequences have been used as the initial conditions in solving the equations of radiation hydrodynamics that describe the spherically symmetric motion of a self-gravitating gas. Stars with initial masses M _ZAMS ≥ 50M _⊙ are shown to become unstable against radial oscillations during the main-sequence evolution. The instability growth rate and the limit-cycle oscillation amplitude increase as the star evolves and as its initial mass increases. The pulsational instability is attributable to the iron Z-bump κ mechanism (T ∼ 2 × 10⁵ K). Convection that transfers from 20 to 50% of the total energy flux and, thus, reduces the efficiency of the κ mechanism emerges in the same layers. The periods of the radial oscillations of main-sequence stars lie within the range from 0.09 to 8 days. The boundaries of the instability region of radial pulsations in the Hertzsprung-Russell diagram have been determined and observational criteria for revealing pulsating variable main-sequence stars have been proposed.     

Stationary equations of hydrogen excitation and ionization in prominences

The statistical equilibrium equations for the continuum and first 10 levels of a hydrogen atom show that the radiation of a bright prominence (the brightness of the H line has attained 56 mÅ of the disc centre spectrum) is completely due to scattering of the Sun radiation. The basic unknowns are separated with certainty: electron concentration (n _e = 3.0 × 10¹⁰ cm^–3), effective thickness (l = 4.2 × 10⁸ cm) and electron temperature (T _e = 5000 K).Radiation of a very bright prominence (A (H) = 213 mÅ; T _e = 7300 K; n _e = 5.0 × 10¹¹ cm^–3; l = 1.3 × 10⁷ cm) is on account of electron impacts (40%) and the Sun radiation scattering (60%).The parameters are shown to depend greatly on the prominence optical thickness in the lines of the first subordinate series of a hydrogen atom. In the course of determination all the parameters and 100 interconnected integral equations of the radiation diffusion have been thickness-averaged; the population of levels has been calculated by observations using the self-absorption factors.     

Collisional excitation of interstellar molecules due to H2: Linear molecules CO,OCS, SiO,HCN and HC3N in1Σstate

Using a normalized perturbative, semi-classical approach, collision-induced rotational excitation rates of CO, OCS, SiO, HCN, HC₃N due to H₂ are computed. The calculated excitation rates for CO–H₂ and OCS–H₂ systems at 100 K are in good agreement with the results of close coupling approximation at low values ofJ, whereJ is the rotational quantum number. The rates are found to be very sensitive with respect to ortho and para states of H₂.     

The effect of UV stars on the intergalactic medium

We have investigated the effect of ionizing radiation from the UV stars (hot prewhite dwarfs) on the intergalactic medium (IGM). If the UV stars are powered only by gravitational contraction they radiate most of their energy at a typical surface temperature of 1.5×10⁵ K which produces a very highly ionized IGM in which the elements carbon, nitrogen and oxygen are left with only one or two electrons. This results in these elements being very inefficient coolants. The gas is cooled principally by free-free emission and the collisional ionization of hydrogen and helium. For a typical UV star temperature ofT=1.5×10⁵ K, the temperature of the ionized gas in the IGM isT _g =1.2×10⁵ K for a Hubble constantH _o=75 km s^–1 Mpc^–1 and a hydrogen densityn _H =10^–6 cm^–3. Heating by cosmic rays and X-rays is insignificant in the IGM except perhaps inHi clouds because when a hydrogen atom recombines in the IGM it is far more likely to be re-ionized by a UV-star photon than by of the other two types of particles due to the greater space density of UV-star photons and their appreciably larger ionization cross-sections. If the UV stars radiate a substantial fraction of their energy in a helium-burning stage in which they have surface temperatures of about 5×10⁴ K, the temperature of the IGM could be lowered to about 5×10⁴ K.     

The Radio Recombination Line Intensities Of Atoms And Ions: Helium,Carbon And Oxygen

The radio recombination line intensities of heavy elements of helium, carbon and oxygen are calculated with accounting for dielectronic recombination. Dielectronic recombination rates are determined accurate to the second order of a perturbation theory and the rates are described as function of principal quantum number for helium-like atom or ion. Balance equations are solved for the departure coefficients from LTE b_n. The collision and spontaneous transition rates are accounted for the balance equations, in which non-equilibrium distribution source is dielectronic recombination. Non-equilibrium amplification coefficients are found as functions of a medium temperature, density and ion charge z = 1–3 for radio recombination lines. Optical depths are calculated for the heavy element low-frequency lines with the numbers 300 > n > 1200. For the chosen electronic temperatures and densities T_e = 0.8× 10⁴–10× 10⁴ K, N_e = 0.05–0.1 cm⁻³ the line optical depth is determined by the values τ_L∼ 0.1× 10⁻⁴–100× 10⁻⁴. Calculated for free-free transition rates, the optical depth is given by using the value τ_ff∼ 10⁻²τ_L.     

A postulate leading to the Titius-Bode law

The revised Titius-Bode law (Balsano and Hughes, 1979) giving distances of planets from the Sun shows integers that recall the Bohr law in the early quantum theory of hydrogen atom. The author searchs for a formalism, similar to the Sommerfeld's one accounting for the planetary distribution of the solar system. It is shown that such a formalism might be started with the assumed relation $$\int_{r_0 }^{r_n } {U(r)dr = nk,} $$ whereU(r) stands for the gravitation potential created by the Sun at distancer,k=cte,r _o=cte,r _n=distance of then ^th planet andn=1, 2, 3... Although the inspiration of the present note came from the early quantum theory, it is emphasized that there is no connection between the above assumed equation and the Sommerfeld quantum rule, but a pure formal similarity. the true significance of that equation is still unknown. It is either a fortuitous coincidence leading to the T-B law or any possible unsuspected property of gravitation.     

Hydrogen ionization and n=2 population for model spicules and prominences

Using slab model atmospheres that are irradiated from both sides by photospheric, chromospheric, and coronal radiation fields we have determined the ionization and excitation equilibrium for hydrogen.The model atom consists of two bound levels (n = 1 and n = 2) and a continuum. Ly- was assumed to be optically thick with the transition in detailed radiative balance. The Balmer continuum was assumed to be optically thin with the associated radiative ionization dominated by the photospheric radiation field (T _rad = 5940 K). The ionization equilibrium was determined from an exact treatment of the radiative transfer problem for the internally generated Ly-c field and the impressed chromospheric and coronal field (characterized by T _rad = 6500K).Our calculations corroborate the hypothesis that N₂, the n = 2 population density, is uniquely determined by the electron density N _e. We also present ionization curves for 6000K, 7500K, and 10000K models ranging in total hydrogen density from 1 × 10¹⁰/cm³ to 3 × 10¹²/cm³. Using these curves it is possible to obtain the total hydrogen density from the n = 2 population density in prominences and spicules.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

MOL-D: A Collisional Database and Web Service within the Virtual Atomic and Molecular Data Center

MOL-D database is a collection of cross-sections and rate coefficients for specific collisional processes and a web service within the Serbian Virtual Observatory (SerVO) and the Virtual Atomic and Molecular Data Center (VAMDC). This database contains photo-dissociation cross-sections for the individual ro-vibrational states of the diatomic molecular ions and rate coefficients for the atom-Rydberg atom chemi-ionization and inverse electron–ion–atom chemi-recombination processes. At the moment it contains data for photodissociation cross-sections of hydrogen H\(_{2}^{+}\) and helium He\(_{2}^{+}\) molecular ions and the corresponding averaged thermal photodissociation cross-sections. The ro-vibrational energy states and the corresponding dipole matrix elements are provided as well. Hydrogen and helium molecular ion data are important for calculation of solar and stellar atmosphere models and for radiative transport, as well as for kinetics of other astrophysical and laboratory plasma (i.e. early Universe).     

Computation of the polarization characteristics of RATAN-600 in the “Southern sector with a flat reflector” mode with the diffraction effects considered

We report the Mueller matrix elements for RATAN-600 computed with the allowance for the diffraction effects in the space between the main, secondary, and flat mirrors in the Souther sector with a flat reflector (“South+flat”) observing mode and in the mode of single-sector observations at the horizon throughout the entire operating wavelength range. We show that the vertical size of the M ₄₁ and M ₃₂ elements decreases, the elements shift relative to the central horizontal section, and the lobe structure of the elements changes with increasing wavelength. In the “South+flat’ mode these changes, which are due to diffraction effects, begin to show up at shorter wavelength compared to the single-sector mode. We investigated the variation of the structure of the elements M ₄₁ and M ₃₂ with the elevation angle of the flat reflector and in the case of longitudinal and transversal off-focus offsets of the primary feed.     

Broadening and shift of Fe i lines perturbed by atomic hydrogen

The broadening and shift parameters for a number of Fei lines perturbed by atomic hydrogen are computed using the interatomic potential due to Hindmarsh et al. (1967, 1970). It is also shown that the rms radius and the effective radius of the radiating atom, which determine the force constants in the interatomic potential, can be simply related each other, depending on the orbital quantum number of the atomic level.Currently NAS/NRC Research Associate, on leave from the Università di Napoli.Operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation. Partial support for the NSO is provided by the USAF under a Memorandum of Understanding with the NSF.     

Gas,dust and molecules in the Galaxy

The relative abundances of cool neutral hydrogen, carbon monoxide and formaldehyde are studied using all the available observational data in the literature. The obtained mean valuesN _{H 1}/ ,N _{H 1}/N _CO,N _CO/ are approximately constant in the dark clouds of the solar neighbourhood and in the distant molecular clouds.The observed correlationsN _CO,A _v and ,A _v show that formaldehyde can also be used as an indicator of molecular hydrogen. The ratioN H₁/A _v depends on densities and decays considerably in the ranges of visual absorptions in which the molecules become detectable (A _v 2 mg); an average of /N _{H 1}10 is calculated for the dense dark clouds.Indications of systematic temperature gradiens T/A _v are found for formaldehyde and neutral hydrogen inside the dark clouds, and qualitative comparisons are made with theoretical quantum mechanics calculations.The observed carbon monoxide and formaldehyde abundances, the free electron layer in the Galaxy, the distribution of neutral hydrogen in different states are only compatible if an ionization rate of 10^–16 is accepted, provided presumably by 2 MeV protons of cosmic radiation.Three main states for neutral hydrogen and dust are identified from different kinds of observational data (21 cm line in emission, absorption in galactic radio sources and self-absorption in the hot gas background): (1) a homogeneous intercloud stratum of tenuous gas and dust with a galactic halfwidth of 350 pc and mean parametersn _H=0.2 atom cm^–3, spin temperatureT _s 10000 K andn _d 0.3 mg kpc^–1; (2) cool gas and dust concentrated in spiral features with a galactic half-width of less than 100 pc, probably forming clouds with diffuse and indefinite limits, with mean parametersn _H2 atom cm^–3,T _s <1100 K (probable average,T _s =135 K) andn _d 3 mg kpc^–1; (3) dense gas and dust clouds with a mean diameter of 7 pc and mean parametersn _H700 atom cm^–3 (90% in a molecular state),T _s 63 K andn _d 1 mg pc^–1 on which molecules as CO and H₂CO are formed.The application of the Jeans criteria for gravitational instability shows that the dense clouds are gravitationally bound while the gas in the intermediate state (2) can be protected against collapse by the total internal energy in the medium increasing due to cosmic rays and the magnetic field in the Galaxy.The observed velocity halfwidths and galacticZ-halfwidths in states (1) and (2) are compatible with a total mass density in the galactic layer of 90M pc^–2 (gas plus stars) according to the barometric equation.The relative abundancesN _{H 1}/N _CO, calculated from C¹²O and C¹³O data and comparisons with studies in the 21 cm emission line, show that the antenna temperatureT _A ⁺ in the 2.6 mm line of C¹²O is a good indicator of the cool gas densities in the Galaxy. The possible application of this for studies in galactic structure is discussed and hypothetical distributions of carbon monoxide in the zones outside the galactic planeB=0° are presented.From a synthesis based on the results obtained, a cycle is postulated for the neutral hydrogen in the Galaxy: condensation and cooling of gas molecular formation gravitational collapse and star formation gas dissipation and heating by cosmic rays and UV radiation.     

General model of depolarization and transfer of polarization of singly ionized atoms by collisions with hydrogen atoms

Simulations of the generation of the atomic polarization is necessary for interpreting the second solar spectrum. For this purpose, it is important to rigorously determine the effects of the isotropic collisions with neutral hydrogen on the atomic polarization of the neutral atoms, ionized atoms and molecules. Our aim is to treat in generality the problem of depolarizing isotropic collisions between singly ionized atoms and neutral hydrogen in its ground state. Using our numerical code, we computed the collisional depolarization rates of the p-levels of ions for large number of values of the effective principal quantum number n^* and the Unsöld energy E_p. Then, genetic programming has been utilized to fit the available depolarization rates. As a result, strongly non-linear relationships between the collisional depolarization rates, n^* and E_p are obtained, and are shown to reproduce the original data with accuracy clearly better than 10%. These relationships allow quick calculations of the depolarizing collisional rates of any simple ion which is very useful for the solar physics community. In addition, the depolarization rates associated to the complex ions and to the hyperfine levels can be easily derived from our results. In this work we have shown that by using powerful numerical approach and our collisional method, general model giving the depolarization of the ions can be obtained to be exploited for solar applications.     

Letter to the Editor: The collisional broadening of carbon radio recombination lines

The density matrix equations of highly excited carbon are analytically solved as functions of line number and temperature. Allowing for the series of the impact approximation theory and quadrupole interaction potential, the line widths are found with the theoretical error less than 0.06 in the range of temperatures T _e = 25 − 100 K. To determine the medium temperature and density by using the experimental values of line widths, the Doppler, radiational and impact broadening are calculated for the lines with the principal quantum numbers n > 300. This revised version was published online in July 2006 with corrections to the Cover Date.     

Small Fe bearing ring molecules of possible astrophysical interest: molecular properties and rotational spectra

A number of small, cyclic molecules containing several carbon atoms in their ring structure has been identified in different astrophysical environments. It is the aim of this work to study important molecular properties of such heterocyclic species bearing an iron atom, which is one of the most abundant cosmic elements. Quantum theoretical calculations based on a density functional approach have been employed to investigate physical properties of six small cyclic carbon and hydrocarbon molecules containing iron as a hetero atom, viz. FeC₂H _n and FeC₃H _n (n=0,2,4). The full geometry optimisation at the chosen level of electronic structure theory (B3LYP/6-31G(d)) including vibrational anharmonicities and non-rigidity, has furnished values for the rotational constants of these species to an expected accuracy of about one per cent. We present structural, electronic, vibrational, and rotational molecular properties including line frequencies, line strengths, and transition probabilities. These results may be helpful for identifying these molecules in future laboratory experiments in view of tentative astronomical observations.     

Multi-density models of the Broad Line Region in Active Galactic Nuclei: a comparative study with single-cloud models

Nearly ten years ago Kwan and Krolik (1979, 1981) published the firstsuccessful photoionization model of the Broad Line Region of Active Galactic Nuclei, the so-called ‘Standard Model’. Since then several efforts have been made to obtain better results using more sophisticated models. Anopen issue is that photoionization models are generally computed startingfrom the assumption that the emission line spectrum is produced by a single-slab cloud with a ‘standard’ hydrogen density n_H = 10^9.5 cm^-3, but it seems more likely that a range of densities is present in the Broad Line Region. Purpose of this paper is to review the results given by single-cloud models using the most recent photoionization code, Cloudy 84, and to investigate if the addition of one or more components with different densities does affect the line ratios. To this aim we compute the emission line ratios produced by photoionized single-slab clouds for a wide range of hydrogen densities (n_H = 10^9.5−10¹³ cm⁻³), ionization parameters (U = 10⁻⁴− 10^−0.5) and column densities (N_H = 10²³−10²⁵ cm⁻²). Two or more populations of clouds are then combined and the resulting emission line spectrum is compared with a sample of mean observed line ratios. We find that the addition to the standard component of clouds having different densities and located at different positions from the central source introduces many changes in the line ratios, and that these changes are in the direction of a better agreement with the observed emission line ratios.     

On the behaviour of the hydrogen Lyman series in flares

The Lyman spectrum of hydrogen has been computed for a number of flare models, characterized by the column density of hydrogen atoms in the ground state (N ₁), the electron density (n _e) and the electron temperature (T _e). Broadening by the thermal Doppler effect and by Stark effect has been accounted for. The source functions for the individual lines of the series have been derived from non-LTE calculations of the excitation in hydrogen flares. The aim of the investigation is to evaluate the use of the intensities in between two successive Lyman lines for a determination of the value for N ₁, which is a physical parameter of the flare for which only indirect determinations are available. Whilst in principle this method could give reliable results, its practical application meets with difficulties which hardly can be overcome. Therefore, one probably has to base the N ₁ determination on the highest line resolvable in the spectrum.