Collisional Excitation Rates Research Articles

X-ray observations of Ca19 +, Ca18 + and satellites from Alcator C-Mod tokamak plasmas

X-ray spectra of n = 2 to 1 transitions in hydrogen-like Ca19 +, helium-like Ca18 + and nearby satellites have been obtained from Alcator C-Mod tokamak plasmas using a spatially imaging high resolution x-ray spectrometer system. For Ca19 +, the intensity ratio of Lyα2 (1s 1S1/2–2p 2P1/2) to Lyα1 (1s 1S1/2–2p 2P3/2) was found to be ∼0.531 ± 0.005 over a range of plasma parameters, which is somewhat greater than the ratio of the statistical weights of the upper n = 2 levels, 1/2. This difference is mainly due to interaction with the 2S1/2 fine structure sub-level. Experimental results are compared to calculations from COLRAD, a collisional-radiative modelling code, and good agreement is shown. For Ca18 +, the intensity ratio of the dielectronic satellite k (1s22p 2P1/2–1s2p2 2D3/2) to the resonance line w (1s2 1S0–1s2p 1P1) is sensitive only to the electron temperature. The observed brightness ratio scaling with Te is in good agreement with the calculated ratio of the respective dielectronic recombination to the collisional excitation rates.

C+IN THE INTERSTELLAR MEDIUM: COLLISIONAL EXCITATION BY H2REVISITED

C$^+$ is a critical constituent of many regions of the interstellar medium, as it can be a major reservoir of carbon and, under a wide range of conditions, the dominant gas coolant. Emission from its 158$\mu$m fine structure line is used to trace the structure of photon dominated regions in the Milky Way and is often employed as a measure of the star formation rate in external galaxies. Under most conditions, the emission from the single [CII] line is proportional to the collisional excitation rate coefficient. We here used improved calculations of the deexcitation rate of [CII] by collisions with H$_2$ to calculate more accurate expressions for interstellar C$^+$ fine structure emission, its critical density, and its cooling rate. The collision rates in the new quantum calculation are $\sim$ 25% larger than those previously available, and narrow the difference between rates for excitation by atomic and molecular hydrogen. This results in [CII] excitation being quasi-independent of the molecular fraction and thus dependent only on the total hydrogen particle density. A convenient expression for the cooling rate at temperatures between 20 K and 400 K, assuming an LTE H$_2$ ortho to para ration is $\Lambda ({\rm LTE~OPR}) = \left(11.5 + 4.0\,e^{-100\,\mathrm K/T^{\rm kin}}\right)\;e^{-91.25\,\mathrm K/T^{\rm kin}}\,n ({\rm C}^{+})\,n({\rm H}_2)\times 10^{-24}\;{\rm ergs}~{\rm cm}^{-3}~{\rm s}^{-1}$. The present work should allow more accurate and convenient analysis of the [\CII] line emission and its cooling.

BASECOL2012: A collisional database repository and web service within the Virtual Atomic and Molecular Data Centre (VAMDC)

The BASECOL2012 database is a repository of collisional data and a web service within the Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu). It contains rate coefficients for the collisional excitation of rotational, ro-vibrational, vibrational, fine, and hyperfine levels of molecules by atoms, molecules, and electrons, as well as fine-structure excitation of some atoms that are relevant to interstellar and circumstellar astrophysical applications. Submissions of new published collisional rate coefficients sets are welcome, and they will be critically evaluated before inclusion in the database. In addition, BASECOL2012 provides spectroscopic data queried dynamically from various spectroscopic databases using the VAMDC technology. These spectroscopic data are conveniently matched to the in-house collisional excitation rate coefficients using the SPECTCOL sofware package (http:// vamdc.eu/software), and the combined sets of data can be downloaded from the BASECOL2012 website. As a partner of the VAMDC, BASECOL2012 is accessible from the general VAMDC portal (http://portal.vamdc.eu) and from user tools such as SPECTCOL.

Rotational excitation of SO2by collision with H2: a collaborative work

The SO2 molecule is detected in a large variety of objects, notably cold dark clouds and star-forming regions. An accurate modeling of the observations requires a very good knowledge of the collisional excitation rates with H2 due to competition between collisional and radiative processes that excite and quench the different rotational levels of the molecule. The results of our recent collisional calculations are summarized. Pierre was associated to all steps of this collaborative work that was a key project in the Molecular Universe European FP6 network.

Atomic data for the X-ray lines of Fe viii and Fe ix

The distorted wave extension of the autostructure code has been used to calculate energy levels, radiative transition probabilities and collisional excitation rates of Fe viii and Fe ix up to n = 6 for Fe ix and n = 7 for Fe viii. We have compared some of the data with previous calculations, finding overall agreement for radiative transition rates, but interesting differences for some collisional data. We have merged our data for the higher energy levels with published R-matrix collisional excitation rates for the lower ones to calculate spectral line intensities and compare them with observations. In particular, we have focused on the transitions from high energy levels of Fe viii & Fe ix which are present in the 93–95 A region. A few new identifications are tentatively provided. We find that Fe ix 5f–3d and Fe viii 7f–3d transitions only comprise a small fraction of the observed lines in the 93–95 A region for quiet Sun conditions, and thus their contribution to the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) 94 A band is expected to be small.

Fe IX CALCULATIONS FOR THE SOLAR DYNAMICS OBSERVATORY

New calculations of the energy levels, radiative transition rates and collisional excitation rates of \ion{Fe}{ix} have been carried out using the Flexible Atomic Code, paying close attention to experimentally identified levels and extending existing calculations to higher energy levels. For lower levels, R-matrix collisional excitation rates from earlier work have been used. Significant emission is predicted by these calculations in the 5f-3d transitions, which will impact analysis of SDO AIA observations using the 94\AA\ filter.

Collisional excitation of doubly deuterated ammonia ND2H by para-H2

Collisional de-excitation rates of partially deuterated molecules are different from the fully hydrogenated species because of lowering of symmetry. We compute the collisional (de)excitation rates of ND2H by ground state para-H2, extending the previous results for He- lium. We describe the changes in the potential energy surface of NH3- H2 involved by the pres- ence of two deuterium nuclei. Cross sections are calculated within the full close-coupling ap- proach and augmented with coupled-state calculations. Collisional rate coefficients are given between 5 and 35 K, a range of temperatures which is relevant to cold interstellar conditions. We find that the collisional rates of ND2H by H2 are about one order of magnitude higher than those obtained with Helium as perturber. These results are essential to radiative transfer modelling and will allow to interpret the millimeter and submillimeter detections of ND2H with better constraints than previously.

Molecular Collisional Data and BASECOL in the VAMDC context

The paper focuses on collisional excitation rates of molecules by He, H 2 and electrons relevant to the interstellar medium, it discusses currently available data, presents very recent work and outlines new work being carried out in order to provide easy access to these molecular data. In particular outlines of the latest developments in the BASECOL database and of the “Virtual Molecular Data Centre” capabilities are provided.

A five-dimensional potential-energy surface for the rotational excitation of SO2 by H2 at low temperatures

The SO(2) molecule is detected in a large variety of astronomical objects, notably molecular clouds and star-forming regions. An accurate modeling of the observations needs a very good knowledge of the collisional excitation rates with H(2) because of competition between collisional and radiative processes that excite and quench the different rotational levels of SO(2). We report here a five-dimensional, rigid-body, interaction potential for SO(2)-H(2). As a first application, we present rate constants for excitation/de-excitation of the 31 first levels of SO(2) by para-H(2) at low temperatures. Propensity rules are discussed.

A NEW CALCULATION OF Ne IX LINE DIAGNOSTICS

We describe the effect that new atomic calculations, including fully relativistic R-matrix calculations of collisional excitation rates and level-specific dielectronic and radiative recombination rates, have on line ratios from the astrophysically significant ion Ne ix. The new excitation rates systematically change some predicted Ne ix line ratios by 25% at temperatures at or below the temperature of maximum emissivity (4 × 106 K), while the new recombination rates lead to systematic changes at higher temperatures. The new line ratios are shown to agree with observations of Capella and σ2 CrB significantly better than older line ratios, showing that 25%–30% accuracy in atomic rates is inadequate for high-resolution X-ray observations from existing spectrometers.

SIMULTANEOUS OBSERVATIONS OF COMET C/2002 T7 (LINEAR) WITH THE BERKELEY-ILLINOIS-MARYLAND ASSOCIATION AND OWENS VALLEY RADIO OBSERVATORY INTERFEROMETERS: HCN AND CH3OH

We present observations of HCN J = 1-0 and CH_3OH J(K_a, K_c) = 3(1, 3)-4(0, 4) A+ emission from comet C/2002 T7 (LINEAR) obtained simultaneously with the Owens Valley Radio Observatory (OVRO) and Berkeley-Illinois-Maryland Association (BIMA) millimeter interferometers. We combined the data from both arrays to increase the (u, v) sampling and signal to noise of the detected line emission. We also report the detection of CH_3OH J(K_a, K_c) = 8(0, 8)-7(1, 7) A^+ with OVRO data alone. Using a molecular excitation code that includes the effects of collisions with water and electrons, as well as pumping by the Solar infrared photons (for HCN alone), we find a production rate of HCN of 2.9 × 10^(26) s^(–1) and for CH_3OH of 2.2 × 10^(27) s^(–1). Compared to the adopted water production rate of 3 × 10^(29) s^(–1), this corresponds to an HCN/H_2O ratio of 0.1% and a CH_3OH/H_2O ratio of 0.7%. We critically assess the uncertainty of these values due to the noise (~10%), the uncertainties in the adopted comet model (~50%), and the uncertainties in the adopted collisional excitation rates (up to a factor of 2). Pumping by Solar infrared photons is found to be a minor effect for HCN, because our 15 synthesized beam is dominated by the region in the coma where collisions dominate. Since the uncertainties in the derived production rates are at least as large as one-third of the differences found between comets, we conclude that reliable collision rates and an accurate comet model are essential. Because the collisionally dominated region critically depends on the water production rate, using the same approximate method for different comets may introduce biases in the derived production rates. Multiline observations that directly constrain the molecular excitation provide much more reliable production rates.

Molecules as diagnostic tools in the interstellar medium

Analysis of light emission from different regions of the interstellar medium and circumstellar environments provides crucial information about the chemical composition and the physical conditions in these regions. Interpretation of the observed spectra requires the knowledge of collisional excitation rates as well as radiative rates participating to the line formation. In the first part, the paper focuses on collisional excitation rates of molecules relevant to the interstellar medium. It discusses currently available data and outlines new work carried out by the authors. Due to the use of accurate ab initio potential energy surfaces, the new rate coefficients differ significantly from previously published ones. In the second part, it is analysed from two examples how the use of the new rate coefficients could lead to important changes in the interpretation of molecular emission emerging from molecular clouds.

Collisional excitation of monodeuterated ammonia NH2D by helium

Context. Observations of deuterated molecules are useful probes of the physical and chemical conditions in star-forming regions. However their detailed interpretation is hampered by the lack of knowledge of the corresponding collisional rate coefficients. Aims. We extend our previous study of ammonia collisional excitation by helium to monodeuterated ammonia NH2D, which has been found to be abundant in a variety of environments. Methods. We introduce the principal isotopic effects in the collisional equations by calculating the relevant angular dependence of the intermolecular potential energy surface. Results. Cross sections are calculated in the coupled states approximation, and collisional rate coefficients are given from 5 to 100 K, a range of temperatures that is relevant in the interstellar medium. Conclusions. These results allow to include justifiable collisional excitation rate coefficients of NH2D by He in the analysis of the emitted radiation for the first time

Probable detection of H2D$\mathsf{^+}$ in the starless core Barnard 68

Context. The presence of H2D + in dense cloud cores underlies ion-molecule reactions that strongly enhance the deuterium fractionation of many molecular species. Aims. We determine the H2D + abundance in one starless core, Barnard 68, that has a particularly well established physical, chemical, and dynamical structure. Methods. We observed the ortho-H2D + ground-state line 110–111 ,t he N 2H + J = 4–3 line, and the H 13 CO + 4–3 line with the APEX telescope. Results. We report the probable detection of the o-H2D + line at an intensity Tmb = 0.22 ± 0.08 K and exclusively thermal line width, and find only upper limits to the N2H + 4–3 and H 13 CO + 4–3 intensities. Conclusions. Within the uncertainties in the chemical reaction rates and the collisional excitation rates, chemical model calculations and excitation simulations reproduce the observed intensities and that of o-H2D + in particular.

Collisional Excitation Rates in the ISM

The paper focuses on collisional excitation rates of molecules by He and H2 relevant to the interstellar medium. It discusses currently available data, presents very recent work and outlines new work being carried out by various teams.

Transverse glow discharges in supersonic air and methane flows

Transverse glow discharges in supersonic air and methane flows are studied both experimentally and theoretically. The experiments show that a diffuse volume discharge filling the whole cross section of the flow can easily be initiated in air, whereas a diffuse discharge in a methane flow shows a tendency to transition into a constricted mode. The electron transport coefficients (mobility and drift velocity) and the kinetic coefficients (such as collisional excitation rates of the vibrational levels of a methane molecule, as well as dissociation and ionization rates) are calculated by numerically solving the Boltzmann equation for the electron energy distribution function. The calculated coefficients are used to estimate the parameters of the plasma and the electric field in the positive column of a discharge in methane.

Collisional excitation rate coefficients of N2H+ by He

Using a recoupling technique with close-coupling spin-free calculations de-excitation rate coefficients are obtained among hyperfine transitions for He colliding with N 2 H + . A recently determined potential energy surface suitable for scattering calculations is used to investigate rate coefficients for temperatures between 5 and 50 K, and for the seven lowest rotational levels of N 2 H + . Fitting functions are provided for the Maxwellian averaged opacity tensors and for the rotational de-excitation collisional rate coefficients. The fitting functions for the opacity tensors can be used to calculate hyperfine (de)-excitation rate coefficients among elastic and inelastic rotational levels, and among the corresponding magnetic sublevels of the hyperfine structure. Certain dynamical approximations are investigated and found to be invalid.

Electron Collision Rates for Ultraviolet and X‐Ray Lines of S x

Electron collisional excitation strengths and rates for ultraviolet and X-ray lines arising from transitions between the fine-structure levels of the 2s22p3 4So, 2Do, and 2Po terms and from these levels to the levels of the 2s2p4, 2p5, 2s22p23s, 2s22p23p, and 2s22p23d configurations have been calculated using Breit-Pauli R-matrix method. Configuration-interaction wave functions have been used for an accurate representation of target levels. These wave functions give excitation energies and oscillator strengths which are in close agreement with experiment and other accurate calculations. The Rydberg series of resonances converging to the n = 2 and n = 3 excited levels are explicitly included in the scattering calculation. Resonance structures make significant contribution to collision strengths. The effective collision strengths are obtained by integrating total collision strengths over a Maxwellian distribution of electron energies, and these are presented over a wide temperature range suitable for modeling of astrophysical plasmas. Significant differences with earlier results of effective collision strengths are noted.

Gold emissivities for hydrocode applications

The Radiom model [M. Busquet, Phys Fluids B 5, 4191 (1993)] is designed to provide a radiative-hydrodynamic code with non-local thermodynamic equilibrium (non-LTE) data efficiently by using LTE tables. Comparison with benchmark data [M. Klapisch and A. Bar-Shalom, J. Quant. Spectrosc. Radiat. Transf. 58, 687 (1997)] has shown Radiom to be inaccurate far from LTE and for heavy ions. In particular, the emissivity was found to be strongly underestimated. A recent algorithm, Gondor [C. Bowen and P. Kaiser, J. Quant. Spectrosc. Radiat. Transf. 81, 85 (2003)], was introduced to improve the gold non-LTE ionization and corresponding opacity. It relies on fitting the collisional ionization rate to reproduce benchmark data given by the Averroès superconfiguration code [O. Peyrusse, J. Phys. B 33, 4303 (2000)]. Gondor is extended here to gold emissivity calculations, with two simple modifications of the two-level atom line source function used by Radiom: (a) a larger collisional excitation rate and (b) the addition of a Planckian source term, fitted to spectrally integrated Averroès emissivity data. This approach improves the agreement between experiments and hydrodynamic simulations.

Effects of the electron energy distribution function on modeled x-ray spectra

This paper presents the results of a broad investigation into the effects of the electron energy distribution function on the predictions of nonlocal thermodynamic equilibrium collisional-radiative atomic kinetics models. The effects of non-Maxwellian and suprathermal ("hot") electron distributions on collisional rates (including three-body recombination) are studied. It is shown that most collisional rates are fairly insensitive to the functional form and the characteristic (central or average) energy of the electron distribution function as long as the characteristic energy is larger than the threshold energy for the collisional process. Collisional excitation and ionization rates are, however, highly sensitive to the number of hot electrons. This permits the development of robust spectroscopic diagnostics that can be used to characterize the electron density, bulk electron temperature, and hot electron fraction of plasmas with nonequilibrium electron distribution functions. Hot electrons are shown to increase and spread out plasma charge state distributions, amplify the intensities of emission lines fed by direct collisional excitation and radiative cascades, and alter the structure of satellite features in both K - and L -shell spectra. The characteristic energy, functional form, and spatial properties of hot electron distributions in plasmas are open to characterization through their effects on high-energy continuum and line emission and on the polarization of spectral lines.