Statistical Equilibrium

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 56547 Experts worldwide ranked by ideXlab platform

Trujillo J Bueno - One of the best experts on this subject based on the ideXlab platform.

  • theoretical formulation of doppler redistribution in scattering polarization within the framework of the velocity space density matrix formalism
    Astronomy and Astrophysics, 2013
    Co-Authors: L Belluzzi, Landi E Deglinnocenti, Trujillo J Bueno
    Abstract:

    Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications when adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a twolevel atom with infinitely sharp upper and lower levels, and we derive the corresponding Statistical Equilibrium equations, neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as RI) is derived starting from the Statistical Equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.

  • theoretical formulation of doppler redistribution in scattering polarization within the framework of the velocity space density matrix formalism
    arXiv: Solar and Stellar Astrophysics, 2013
    Co-Authors: L Belluzzi, Landi E Deglinnocenti, Trujillo J Bueno
    Abstract:

    Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding Statistical Equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the Statistical Equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.

L Belluzzi - One of the best experts on this subject based on the ideXlab platform.

  • theoretical formulation of doppler redistribution in scattering polarization within the framework of the velocity space density matrix formalism
    Astronomy and Astrophysics, 2013
    Co-Authors: L Belluzzi, Landi E Deglinnocenti, Trujillo J Bueno
    Abstract:

    Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications when adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a twolevel atom with infinitely sharp upper and lower levels, and we derive the corresponding Statistical Equilibrium equations, neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as RI) is derived starting from the Statistical Equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.

  • theoretical formulation of doppler redistribution in scattering polarization within the framework of the velocity space density matrix formalism
    arXiv: Solar and Stellar Astrophysics, 2013
    Co-Authors: L Belluzzi, Landi E Deglinnocenti, Trujillo J Bueno
    Abstract:

    Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding Statistical Equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the Statistical Equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.

Gang Zhao - One of the best experts on this subject based on the ideXlab platform.

  • Statistical Equilibrium of silicon in the solar atmosphere
    Astronomy and Astrophysics, 2008
    Co-Authors: Jianrong Shi, T Gehren, K Butler, L Mashonkina, Gang Zhao
    Abstract:

    Aims. The Statistical Equilibrium of neutral and ionised silicon in the solar photosphere is investigated. Line formation is discussed and the solar silicon abundance determined. Methods. High-resolution solar spectra were used to determine solar log g f eSi values by comparison with Si line synthesis based on LTE and NLTE level populations. The results will be used in a forthcoming paper for differential abundance analyses of metalpoor stars. A detailed analysis of silicon line spectra leads to setting up realistic model atoms, which are exposed to interactions in plane-parallel solar atmospheric models. The resulting departure coefficients are entered into a line-by-line analysis of the visible and near-infrared solar silicon spectrum. Results. The Statistical Equilibrium of Si i turns out to depend marginally on bound-free interaction processes, both radiative and collisional. Bound-bound interaction processes do not play a significant role either, except for hydrogen collisions, which have to be chosen adequately for fitting the cores of the near-infrared lines. Except for some near-infrared lines, the NLTE influence on the abundances is weak. Conclusions. Taking the deviations from LTE in silicon into account, it is possible to calculate the ionisation Equilibrium from neutral and ionised lines. The solar abundance based on the experimental f -values of Garz corrected for the Becker et al.’s measurement is 7.52 ± 0.05. Combined with an extended line sample with selected NIST f -values, the solar abundance is 7.52 ± 0.06, with a nearly perfect ionisation Equilibrium of Δ log e� (Siii/Sii) = −0.01.

  • Statistical Equilibrium of silicon in the solar atmosphere
    arXiv: Astrophysics, 2008
    Co-Authors: Jianrong Shi, T Gehren, K Butler, L Mashonkina, Gang Zhao
    Abstract:

    The Statistical Equilibrium of neutral and ionised silicon in the solar photosphere is investigated. Line formation is discussed and the solar silicon abundance determined. High-resolution solar spectra were used to determine solar $\log gf\epsilon_{\rm Si}$ values by comparison with Si line synthesis based on LTE and NLTE level populations. The results will be used in a forthcoming paper for differential abundance analyses of metal-poor stars. A detailed analysis of silicon line spectra leads to setting up realistic model atoms, which are exposed to interactions in plane-parallel solar atmospheric models. The resulting departure coefficients are entered into a line-by-line analysis of the visible and near-infrared solar silicon spectrum. The Statistical Equilibrium of \ion{Si}{i} turns out to depend marginally on bound-free interaction processes, both radiative and collisional. Bound-bound interaction processes do not play a significant role either, except for hydrogen collisions, which have to be chosen adequately for fitting the cores of the near-infrared lines. Except for some near-infrared lines, the NLTE influence on the abundances is weak. Taking the deviations from LTE in silicon into account, it is possible to calculate the ionisation Equilibrium from neutral and ionised lines. The solar abundance based on the experimental $f$-values of Garz corrected for the Becker et al.'s measurement is $7.52 \pm 0.05$. Combined with an extended line sample with selected NIST $f$-values, the solar abundance is $7.52 \pm 0.06$, with a nearly perfect ionisation Equilibrium of $\Delta\log\epsilon_\odot(\ion{Si}{ii}/\ion{Si}{i}) = -0.01$.

J H Black - One of the best experts on this subject based on the ideXlab platform.

  • a computer program for fast non lte analysis of interstellar line spectra with diagnostic plots to interpret observed line intensity ratios
    Astronomy and Astrophysics, 2007
    Co-Authors: J H Black, F L Schoier, D J Jansen, Ewine F Van Dishoeck
    Abstract:

    Abstract: The large quantity and high quality of modern radio and infrared line observations require efficient modeling techniques to infer physical and chemical parameters such as temperature, density, and molecular abundances. We present a computer program to calculate the intensities of atomic and molecular lines produced in a uniform medium, based on Statistical Equilibrium calculations involving collisional and radiative processes and including radiation from background sources. Optical depth effects are treated with an escape probability method. The program is available on the World Wide Web at http://www.sron.rug.nl/~vdtak/radex/index.shtml . The program makes use of molecular data files maintained in the Leiden Atomic and Molecular Database (LAMDA), which will continue to be improved and expanded. The performance of the program is compared with more approximate and with more sophisticated methods. An Appendix provides diagnostic plots to estimate physical parameters from line intensity ratios of commonly observed molecules. This program should form an important tool in analyzing observations from current and future radio and infrared telescopes. Note: Accepted by AA 18 A4 pages, 11 figures;

  • a computer program for fast non lte analysis of interstellar line spectra
    arXiv: Astrophysics, 2007
    Co-Authors: Floris Van Der Tak, J H Black, D J Jansen, F L Schoeier, Ewine F Van Dishoeck
    Abstract:

    The large quantity and high quality of modern radio and infrared line observations require efficient modeling techniques to infer physical and chemical parameters such as temperature, density, and molecular abundances. We present a computer program to calculate the intensities of atomic and molecular lines produced in a uniform medium, based on Statistical Equilibrium calculations involving collisional and radiative processes and including radiation from background sources. Optical depth effects are treated with an escape probability method. The program is available on the World Wide Web at this http URL . The program makes use of molecular data files maintained in the Leiden Atomic and Molecular Database (LAMDA), which will continue to be improved and expanded. The performance of the program is compared with more approximate and with more sophisticated methods. An Appendix provides diagnostic plots to estimate physical parameters from line intensity ratios of commonly observed molecules. This program should form an important tool in analyzing observations from current and future radio and infrared telescopes.

  • an atomic and molecular database for analysis of submillimetre line observations
    Astronomy and Astrophysics, 2005
    Co-Authors: F L Schoier, F F S Van Der Tak, E F Van Dishoeck, J H Black
    Abstract:

    Atomic and molecular data for the transitions of a number of astrophysically interesting species are summarized, in- cluding energy levels, Statistical weights, Einstein A-coefficients and collisional rate coefficients. Available collisional data from quantum chemical calculations and experiments are extrapolated to higher energies (up to E/k ∼ 1000 K). These data, which are made publically available through the WWW at http://www.strw.leidenuniv.nl/∼moldata, are essential input for non-LTE line radiative transfer programs. An online version of a computer program for performing Statistical Equilibrium calcu- lations is also made available as part of the database. Comparisons of calculated emission lines using different sets of collisional rate coefficients are presented. This database should form an important tool in analyzing observations from current and future (sub)millimetre and infrared telescopes.

  • an atomic and molecular database for analysis of submillimetre line observations
    arXiv: Astrophysics, 2004
    Co-Authors: F L Schoeier, E F Van Dishoeck, F F S Van Der Tak, J H Black
    Abstract:

    Atomic and molecular data for the transitions of a number of astrophysically interesting species are summarized, including energy levels, Statistical weights, Einstein A-coefficients and collisional rate coefficients. Available collisional data from quantum chemical calculations and experiments are extrapolated to higher energies. These data, which are made publically available through the WWW at this http URL, are essential input for non-LTE line radiative transfer programs. An online version of a computer program for performing Statistical Equilibrium calculations is also made available as part of the database. Comparisons of calculated emission lines using different sets of collisional rate coefficients are presented. This database should form an important tool in analyzing observations from current and future (sub)millimetre and infrared telescopes.

G Ruchti - One of the best experts on this subject based on the ideXlab platform.

  • nlte analysis of sr lines in spectra of late type stars with new r matrix atomic data
    Astronomy and Astrophysics, 2012
    Co-Authors: Maria Bergemann, C J Hansen, M A Bautista, G Ruchti
    Abstract:

    We investigate the Statistical Equilibrium of neutral and singly-ionized strontium in late-type stellar atmospheres. Particular attention is given to the completeness of the model atom, which includes new energy levels, transition probabilities, photoionization and electron-impact excitation cross-sections computed with the R-matrix method. The NLTE model is applied to the analysis of Sr I and Sr II lines in the spectra of the Sun, Procyon, Arcturus, and HD 122563, showing a significant improvement in the ionization balance compared to LTE line formation calculations, which predict abundance discrepancies of up to 0.5 dex. The solar Sr abundance is log � = 2.93 ± 0.04 dex, in agreement with the meteorites. We present the grid of NLTE abundance corrections for Sr I and Sr II lines that covers a wide range of stellar parameters.

  • nlte analysis of sr lines in spectra of late type stars with new r matrix atomic data
    arXiv: Solar and Stellar Astrophysics, 2012
    Co-Authors: Maria Bergemann, C J Hansen, M A Bautista, G Ruchti
    Abstract:

    We investigate Statistical Equilibrium of neutral and singly-ionized strontium in late-type stellar atmospheres. Particular attention is given to the completeness of the model atom, which includes new energy levels, transition probabilities, photoionization and electron-impact excitation cross-sections computed with the R-matrix method. The NLTE model is applied to the analysis of Sr I and Sr II lines in the spectra of the Sun, Procyon, Arcturus, and HD 122563, showing a significant improvement in the ionization balance compared to LTE line formation calculations, which predict abundance discrepancies of up to 0.5 dex. The solar Sr abundance is log A = 2.93 \pm 0.04 dex, in agreement with the meteorites. A grid of NLTE abundance corrections for Sr I and Sr II lines covering a large range of stellar parameters is presented.