Effective collision strengths for forbidden transitions among the 3s23p3 fine-structure levels of Cl IIIIII

Effective collision strengths for the 10 astrophysically important fine-structure forbidden transitions among the ⁴S^o, ²D^o and ²P^o levels in the 3s²3p³ configuration of Cl  iii are presented. The calculation employs the multichannel R-matrix method to compute the electron-impact excitation collision strengths in a close-coupling expansion, which incorporates the lowest 23 LS target eigenstates of Cl  iii . These states are formed from the 3s²3p³, 3s3p⁴, 3s²3p²3d and 3s²3p²4s configurations. The Maxwellian-averaged effective collision strengths are presented graphically for all 10 fine-structure transitions over a wide range of electron temperatures appropriate for astrophysical applications [log  T (K)=3.3−log  T (K)=5.9]. Comparisons are made with the earlier seven-state close-coupling calculation of Butler & Zeippen, and in general excellent agreement is found in the low-temperature region where a comparison is possible [log  T (K)=3.3−log  T (K)=4.7]. However, discrepancies of up to 30 per cent are found to occur for the forbidden transitions which involve the ⁴S^o ground state level, particularly for the lowest temperatures considered. At the higher temperatures, the present data are the only reliable results currently available.     

Effective collision strengths for fine-structure forbidden transitions among the 2s22p3 levels of S x

Effective collision strengths for electron-impact excitation of the N-like ion S  x are calculated in the close-coupling approximation using the multichannel R -matrix method. Specific attention is given to the 10 astrophysically important fine-structure forbidden transitions among the ⁴S^o, ²D^o and ²P^o levels in the 2s²2p³ ground configuration. The total (e⁻+ion) wavefunction is expanded in terms of the 11 lowest LS eigenstates of S  x , and each eigenstate is represented by extensive configuration-interaction wavefunctions. The collision strengths obtained are thermally averaged over a Maxwellian distribution of velocities, for all 10 fine-structure transitions, over the range of electron temperatures log  T (K)=4.6–6.7 (the range appropriate for astrophysical applications). The present effective collision strengths are the only results currently available for these fine-structure transition rates.     

Effective collision strengths for fine-structure forbidden transitions among the 3s23p4 levels of Cl ii

The ab initio R -matrix method is used to calculate effective collision strengths for electron-impact excitation of the sulphur-like ion Cl  ii in the close-coupling approximation. All 10 astrophysically important fine-structure forbidden transitions within the 3s²3p⁴     ,     ,     ground configuration levels are considered. The 12 lowest LS target states are included in the calculation. Effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of electron velocities. Results are presented for electron temperatures in the range  log  T (K)=3.3  to  log  T (K)=5.5  , appropriate for astrophysical applications. These are the only effective collision strength data that are currently available.     

3s23p–3s3p2 transitions in S iv

We use both the civ3 and mchf codes to calculate oscillator strengths of allowed and intercombination lines in the  3s²3p–3s3p²  multiplets. Valence, core–valence and some core–core correlation effects are included. The two approaches give results in excellent agreement. Core effects are particularly important for the intercombination lines, though relatively minor for allowed transitions.
We obtain a branching ratio of 1.42 with an estimated accuracy of 0.02 for the     transitions, compared with an experimental value of  1.12±0.1  . The A -values of the     intercombination lines are substantially different from those of previous calculations.     

Electron impact excitation of the ground-state 3P fine-structure levels in atomic oxygen

Fine-structure collision strengths are calculated for transitions between the ground-state levels of atomic oxygen. The R -matrix method is used in which the (2p⁴) ³P, ¹D and ¹S terms are included as well as three pseudo-states chosen to represent the dipole polarizability of the ³P ground state. Very sophisticated configuration–interaction wavefunctions are used for the target states and a recoupling transformation to pair coupling is applied to the inner-region Hamiltonian matrix, with the ³P fine-structure energy levels being adjusted to match the observed splitting prior to diagonalization. Effective collision strengths are obtained by integrating over a Maxwellian distribution and the rate coefficient of the cooling of electron gas is determined. The cooling rates are significantly lower than those currently available, in confirmation of the result deduced from measurements of the Earth's ionosphere electron gas.     

Fe xiii emission lines in active region spectra obtained with the Solar Extreme-Ultraviolet Research Telescope and Spectrograph

Recent fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe  xiii are used to generate emission-line ratios involving 3s²3p²–3s3p³ and 3s²3p²–3s²3p3d transitions in the 170–225 and 235–450 Å wavelength ranges covered by the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS). A comparison of these line ratios with SERTS active region observations from rocket flights in 1989 and 1995 reveals generally very good agreement between theory and experiment. Several new Fe  xiii emission features are identified, at wavelengths of 203.79, 259.94, 288.56 and 290.81 Å. However, major discrepancies between theory and observation remain for several Fe  xiii transitions, as previously found by Landi and others, which cannot be explained by blending. Errors in the adopted atomic data appear to be the most likely explanation, in particular for transitions which have 3s²3p3d ¹D₂ as their upper level. The most useful Fe  xiii electron-density diagnostics in the SERTS spectral regions are assessed, in terms of the line pairs involved being (i) apparently free of atomic physics problems and blends, (ii) close in wavelength to reduce the effects of possible errors in the instrumental intensity calibration, and (iii) very sensitive to changes in N _e over the range  10⁸–10¹¹ cm⁻³  . It is concluded that the ratios which best satisfy these conditions are 200.03/202.04 and 203.17/202.04 for the 170–225 Å wavelength region, and 348.18/320.80, 348.18/368.16, 359.64/348.18 and 359.83/368.16 for 235–450 Å.     

Calculated spectra for HeH+ and its effect on the opacity of cool metal-poor stars

The wavelength and Einstein A coefficient are calculated for all rotation–vibration transitions of  ⁴He¹H⁺, ³He¹H⁺, ⁴He²H⁺  and  ³ He²H⁺  , giving a complete line list and the partition function for  ⁴HeH⁺  and its isotopologues. This opacity is included in the calculation of the total opacity of low-metallicity stars and its effect is analysed for different conditions of temperature, density and hydrogen number fraction. For a low helium number fraction (as in the Sun), it is found that HeH⁺ has a visible but small effect for very low densities  (ρ≤ 10⁻¹⁰ g cm⁻³)  , at temperatures around 3500 K. However, for high helium number fraction, the effect of HeH⁺ becomes important for higher densities  (ρ≤ 10⁻⁶ g cm⁻³)  , its effect being most important for a temperature around 3500 K. Synthetic spectra for a variety of different conditions are presented.     

Extreme ultraviolet transitions of Fe xxi in solar, stellar and laboratory spectra

Recent R -matrix calculations of electron impact excitation rates for transitions among the 2s²2p², 2s2p³ and 2p⁴ levels of Fe  xxi are used to derive theoretical electron density ( N _e) sensitive emission-line ratios involving 2s²2p²–2s2p³ transitions in the ∼98–146Å wavelength range. A comparison of these with observations from the PLT tokamak plasma, for which the electron density has been independently determined, reveals generally very good agreement between theory and experiment, and in some instances removes discrepancies found previously. The observed Fe  xxi ratios for a solar flare, obtained with the OSO–5 satellite, imply electron densities which are consistent, with discrepancies that do not exceed 0.2 dex. In addition, the derived values of N _e are similar to those estimated for the high-temperature regions of other solar flares. The good agreement between theory and observation, in particular for the tokamak spectra, provides experimental support for the accuracy of the present line-ratio calculations, and hence for the atomic data on which they are based.     

Anomalous mixing of the w2Po3/2 and x6Po3/2 levels in Fe ii

The neighbouring lines a ⁶D_5/2– x ⁶P^o_3/2 (1272.617 Å) and a ⁶D_5/2– w ²P^o_3/2 (1272.657 Å) have been observed in the UV spectrum of χ Lupi to be of comparable intensity. The latter, Δ S  = 2, transition would be expected to be very weak. The two upper states should display negligible mixing. We give a detailed, quantitative discussion of how the two upper states are in fact strongly mixed through their mixing with 3d⁶(³D)4p ⁴P^o_3/2, and hence we explain the relative strengths of the two UV lines.     

Inner-shell photoionization of O iii

A 25-state R -matrix calculation is performed to obtain photoionization cross-sections for transitions from the 1s²2s²2p²³P ground state of the O  iii ion. Results are obtained for a range of photon energies, including those at which K-shell photoionization processes take place. We compare our results with those from previous calculations. Excellent agreement is obtained. We also consider resonances owing to transitions of a 1s electron excited into the 2p orbital and compare with a recent calculation.     

State-to-state rotational transition rates of the HCO+ ion by collisions with helium

The rates of rotational transitions for HCO⁺, the most abundant ion in interstellar space, induced by collision with helium are obtained for temperatures ranging from 10 to 80 K. The calculations are based on a new potential energy surface for the He–HCO⁺ interaction and on a scattering matrix whose accuracy was checked by pressure broadening and shift measurements. The rates     decrease for increasing values of j and  Δ j   , with a temperature trend depending on the energy involved in the transitions: if it is small, the rates are almost constant, while an increase with T is found for other cases. Comparison with previous and less accurate results shows an agreement within 50 per cent. Comparison between state-to-state and pressure broadening cross-sections allows us to discuss importance and influence of elastic and inelastic collisions.     

Radiative decay data for highly excited Zr i levels

Radiative lifetimes of 17 excited levels in Zr  i , in the energy interval 29 000–40 974 cm⁻¹, have been investigated using the time-resolved laser-induced fluorescence method. The levels belong to the 4d²5s5p, 4d³5p and 4d5s²5p electronic configurations and were excited in a single-step process from either the ground term, 4d²5s² a ³F, or from the low-lying 4d²5s² a ³P and a ⁵F terms. For three levels, we confirm previous measurements while for 14 of the levels the lifetimes have been measured for the first time. The experimental results are compared to theoretical calculations performed with a multiconfiguration relativistic Hartree–Fock method including core-polarization effects. Theoretical transition probabilities of astrophysical interest, scaled by the experimental lifetimes, for the depopulating channels of the investigated levels are also presented.     

Ultra-high-resolution observations of circumstellar K i and C2 around the post-AGB star HD 56126

We have used the Ultra-High-Resolution Facility (UHRF) at the AAT, operating at a resolution of 0.35 km s⁻¹ (FWHM), to observe K  i and C₂ absorption lines arising in the circumstellar environment of the post-AGB star HD 56126. We find three narrow circumstellar absorption components in K  i , two of which are also present in C₂. We attribute this velocity structure to discrete shells resulting from multiple mass-loss events from the star. The very high spectral resolution has enabled us to resolve the intrinsic linewidths of these narrow lines for the first time, and we obtain velocity dispersions ( b -values) of 0.2–0.3 km s⁻¹ for the K  i components, and 0.54±0.03 km s⁻¹ for the strongest (and best defined) C₂ component. These correspond to rigorous kinetic temperature upper limits of 211 K for K  i and 420 K for C₂, although the b -value ratio implies that these two species do not co-exist spatially. The observed degree of rotational excitation of C₂ implies low kinetic temperatures ( T _k≈10 K) and high densities ( n ≈10⁶ to 10⁷ cm⁻³) within the shell responsible for the main C₂ component. Given this low temperature, the line profiles then imply either mildly supersonic turbulence or an unresolved velocity gradient through the shell.     

Core-polarization effects, oscillator strengths and radiative lifetimes of levels in Pb iii

Transition probabilities and oscillator strengths of 382 lines with astrophysical interest arising from 5d⁹6s²6p, 5d¹⁰6s n l, 5d¹⁰6s², 5d¹⁰6p², 5d¹⁰6p7s and 5d¹⁰6p6d configurations and some levels radiative lifetimes of Pb  iii have been calculated. These values were obtained in intermediate coupling (IC) and using relativistic Hartree–Fock calculations including core-polarization effects. We use for the IC calculations the standard method of least-square fitting from experimental energy levels by means of Cowan computer code. The inclusion in these calculations of the 5d¹⁰6p7s and 5d¹⁰6p6d configurations has facilitated us a complete assignment of the levels of energy in the Pb  iii . Transition probabilities, oscillator strengths and radiative lifetimes obtained are generally in good agreement with the experimental data.     

The cooling function of HD molecule revisited

We report new calculations of the cooling rate of primordial gas by the HD molecule, taking into account its ro-vibrational structure. The HD cooling function is calculated including radiative and collisional transitions for   J ≤ 8  rotational levels, and for the vibrational levels v = 0, 1, 2 and 3. The ro-vibrational level population is calculated from the balance equation assuming steady state. The cooling function is evaluated in the ranges of the kinetic temperatures, T _k, from 10² to  2 × 10⁴ K  and the number densities, n _H, from 1 to  10⁸ cm⁻³  . We find that the inclusion of collisional ro-vibrational transitions increases significantly the HD cooling efficiency, in particular for high densities and temperatures. For   n _H≳ 10⁵  and   T _k∼ 10⁴ K  the cooling function becomes more than an order of magnitude higher than previously reported. We give also the HD cooling rate in the presence of the cosmic microwave radiation field for radiation temperatures of 30, 85 and 276 K (redshifts of 10, 30 and 100). The tabulated cooling functions are available at http://www.cifus.uson.mx/Personal_Pages/anton/DATA/HD_cooling/HD_cool.html . We discuss the relevance to explore the effects of including our results into models and simulations of galaxy formation, especially in the regime when gas cools down from temperatures above ∼3000 K.     

Sextet transitions in Fe ii

We have calculated oscillator strengths for the J – J ' levels of the a  ⁶D– z  ⁶P^o, the a  ⁶D– z  ⁶D^o and the a  ⁶D– z  ⁶F^o multiplets in Fe  ii , using configuration interaction wave functions. The importance of the mixing of the ⁶P^o, ⁶D^o and ⁶F^o states is shown, as is the effect of core polarization of both the 3 p and 3 s orbitals. Good agreement with recent experimental results is obtained.     

On the possibility of observing H2 emission from primordial molecular cloud kernels

We study the prospects for observing H₂ emission during the assembly of primordial molecular cloud kernels. The primordial molecular cloud cores, which resemble those at the present epoch, can emerge around  1+ z ∼20  according to recent numerical simulations. The kernels form inside the cores, and the first stars will appear inside the kernels. A kernel typically contracts to form one of the first generation stars with an accretion rate that is as large as ∼0.01 M_⊙ yr⁻¹. This occurs owing to the primordial abundances, which result in a kernel temperature of order 1000 K, and the collapsing kernel emits H₂ line radiation at a rate ∼10³⁵ erg s⁻¹. Predominantly   J =5-3   ( v =0)  rotational emission of H₂ is expected. At redshift  1+ z ∼20  , the expected flux is ∼0.01 μJy for a single kernel. While an individual object is not observable by any facilities available in the near future, the expected assembly of primordial star clusters on subgalactic scales can result in fluxes at the sub-mJy level. This is marginally observable with ASTRO-F and ALMA. We also examine the rotational   J =2-0   ( v =0)  and vibrational   δv =1  emission lines. The former may possibly be detectable with ALMA.     

H3+ in diffuse interstellar gas

A model is constructed of the material in front of the star Cygnus OB2 no. 12 in which dense cores are embedded in diffuse clumps of gas. The model reproduces the measured abundances of C₂ and CO, and predicts a column density of 910¹⁰ cm² for HCO⁺.     

SN 1988Z: spectro-photometric catalogue and energy estimates★

We present a spectro-photometric catalogue of the evolution of supernova 1988Z, which combines new and published observations in the radio, optical and X-ray bands, with the aim of offering a comprehensive view of the evolution of this object and deriving the total energy radiated since its discovery. The major contribution to the total radiated energy comes at optical to X-ray frequencies, with a total emission of at least 2×10⁵¹ erg (for H₀=50 km s⁻¹ Mpc⁻¹) in 8.5 yr. A model-dependent extrapolation of this value indicates that the total radiated energy may be as high as 10⁵² erg. The high value of the radiated energy supports a scenario in which most of the kinetic energy of the ejecta is thermalized and radiated in a short interaction with a dense circumstellar medium of nearly constant density. In this sense, 1988Z is not a supernova but a young and compact supernova remnant.