A computer program for fast non-LTE analysis of interstellar line spectra
TL;DR: In this paper, the authors 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.
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;
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TL;DR: In this paper, the authors discuss both the observation and chemistry of complex molecules in assorted interstellar regions in the Milky Way and discuss both their spectra and chemistry, and conclude that complex molecules are excellent probes of the physical conditions and history of the sources where they reside.
Abstract: Of the over 150 different molecular species detected in the interstellar and circumstellar media, approximately 50 contain 6 or more atoms. These molecules, labeled complex by astronomers if not by chemists, all contain the element carbon and so can be called organic. In the interstellar medium, complex molecules are detected in the denser sources only. Although, with one exception, complex molecules have only been detected in the gas phase, there is strong evidence that they can be formed in ice mantles on interstellar grains. The nature of the gaseous complex species depends dramatically on the source where they are found: in cold, dense regions they tend to be unsaturated (hydrogen-poor) and exotic, whereas in young stellar objects, they tend to be quite saturated (hydrogen-rich) and terrestrial in nature. Based on both their spectra and chemistry, complex molecules are excellent probes of the physical conditions and history of the sources where they reside. Because they are detected in young stellar objects, complex molecules are expected to be common ingredients for new planetary systems. In this review, we discuss both the observation and chemistry of complex molecules in assorted interstellar regions in the Milky Way.
1,470 citations
TL;DR: In the last decade, observations of the cool interstellar medium (ISM) in distant galaxies via molecular and atomic fine structure line (FSL) emission have gone from a curious look into a few extreme, rare objects to a mainstream tool for studying galaxy formation out to the highest redshifts as mentioned in this paper.
Abstract: Over the past decade, observations of the cool interstellar medium (ISM) in distant galaxies via molecular and atomic fine structure line (FSL) emission have gone from a curious look into a few extreme, rare objects to a mainstream tool for studying galaxy formation out to the highest redshifts. Molecular gas has been observed in close to 200 galaxies at z > 1, including numerous AGN host-galaxies out to z ∼ 7, highly star-forming submillimeter galaxies, and increasing samples of main-sequence color-selected star-forming galaxies at z ∼ 1.5 to 2.5. Studies have moved well beyond simple detections to dynamical imaging at kiloparsec-scale resolution and multiline, multispecies studies that determine the physical conditions in the ISM in early galaxies. Observations of the cool gas are the required complement to studies of the stellar density and star-formation history of the Universe as they reveal the phase of the ISM that immediately precedes star formation in galaxies. Current observations suggest that t...
1,041 citations
Additional excerpts
...3 (see also Figures in van der Tak et al. 2007)....
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Cornell University1, California Institute of Technology2, Jet Propulsion Laboratory3, Imperial College London4, Spanish National Research Council5, University of La Laguna6, University of Edinburgh7, UK Astronomy Technology Centre8, University of Colorado Boulder9, University of California, Irvine10, University of Sussex11, University of Pennsylvania12, European Space Agency13, Goddard Space Flight Center14, Paris Diderot University15, University of Paris-Sud16, Aix-Marseille University17, University of Cambridge18, Virginia Tech19, University of Padua20, Institut d'Astrophysique de Paris21, Harvard University22, University of British Columbia23, University of Minnesota24, Japan Aerospace Exploration Agency25, University College London26, Johns Hopkins University27
TL;DR: Despite the overall downturn in cosmic star formation towards the highest redshifts, it seems that environments mature enough to form the most massive, intense starbursts existed at least as early as 880 million years after the Big Bang.
Abstract: Massive present-day early-type (elliptical and lenticular) galaxies probably gained the bulk of their stellar mass and heavy elements through intense, dust-enshrouded starbursts--that is, increased rates of star formation--in the most massive dark-matter haloes at early epochs. However, it remains unknown how soon after the Big Bang massive starburst progenitors exist. The measured redshift (z) distribution of dusty, massive starbursts has long been suspected to be biased low in z owing to selection effects, as confirmed by recent findings of systems with redshifts as high as ~5 (refs 2-4). Here we report the identification of a massive starburst galaxy at z = 6.34 through a submillimetre colour-selection technique. We unambiguously determined the redshift from a suite of molecular and atomic fine-structure cooling lines. These measurements reveal a hundred billion solar masses of highly excited, chemically evolved interstellar medium in this galaxy, which constitutes at least 40 per cent of the baryonic mass. A `maximum starburst' converts the gas into stars at a rate more than 2,000 times that of the Milky Way, a rate among the highest observed at any epoch. Despite the overall downturn in cosmic star formation towards the highest redshifts, it seems that environments mature enough to form the most massive, intense starbursts existed at least as early as 880 million years after the Big Bang.
631 citations
TL;DR: In this article, the authors enumerate the major surveys of CO emission along the Galactic plane and summarize the various approaches that leverage these data to determine the large-scale distribution of molecular gas: its radial and vertical distributions, its concentration into clouds, and its relationship to spiral structure.
Abstract: In the past twenty years, the reconnaissance of 12 CO and 13 CO emission in the Milky Way by single-dish millimeter-wave telescopes has expanded our view and understanding of interstellar molecular gas. We enumerate the major surveys of CO emission along the Galactic plane and summarize the various approaches that leverage these data to determine the large-scale distribution of molecular gas: its radial and vertical distributions, its concentration into clouds, and its relationship to spiral structure. The integrated properties of molecular clouds are compiled from catalogs derived from the CO surveys using uniform assumptions regarding the Galactic rotation curve, solar radius, and the CO-to-H2 conversion factor. We discuss the radial variations of cloud surface brightness, the distributions of cloud mass and size, and scaling relations between velocity dispersion, cloud size, and surface density that affirm that the larger clouds are gravitationally bound. Measures of density structure and gas kinematics within nearby, well-resolved clouds are examined and attributed to the effects of magnetohydrodynamic turbulence. We review the arguments for short, intermediate, and long molecular lifetimes based on the observational record. The review concludes with questions that shall require further observational attention.
459 citations
Cites methods from "A computer program for fast non-LTE..."
...Using the RADEX code (van der Tak et al. 2007) with N CO/δv ∼ 1017 cm−2 (km s−1)−1, the VHRG gas requires temperatures in excess of 40 K and densities greater than 104–5 cm−3....
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TL;DR: In this paper, the optically thin critical densities and the effective excitation densities to produce a 1 K km/s (or 0.818 Jy cm/s ) spectral line are tabulated for 12 commonly observed dense gas molecular tracers.
Abstract: The optically thin critical densities and the effective excitation densities to produce a 1 K km/s (or 0.818 Jy km/s ) spectral line are tabulated for 12 commonly observed dense gas molecular tracers. The dependence of the critical density and effective excitation density on physical assumptions (i.e., gas kinetic temperature and molecular column density) is analyzed. Critical densities for commonly observed dense gas transitions in molecular clouds (i.e., HCN 1–0, HCO+ 1–0, N2H+ 1–0) are typically 1-2 orders of magnitude larger than effective excitation densities because the standard definitions of critical density do not account for radiative trapping and 1 K km/s lines are typically produced when radiative rates out of the upper energy level of the transition are faster than collisional depopulation. The use of effective excitation density has a distinct advantage over the use of critical density in characterizing the differences in density traced by species such as NH3, HCO+, N2H+, and HCN, as well as their isotopologues; but, the effective excitation density has the disadvantage that it is undefined for transitions when Eu/kTk, for low molecular column densities, and for heavy molecules with complex spectra (i.e., CH3CHO).
415 citations
References
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Book•
01 Jan 1979
TL;DR: Inverse square law for a uniformly bright sphere as discussed by the authors is used to define specific intensity and its moments, which is defined as the specific intensity or brightness of a sphere in terms of specific intensity.
Abstract: Chapter 1 Fundamentals of Radiative Transfer 1.1 The Electromagnetic Spectrum Elementary Properties of Radiation 1.2 Radiative Flux Macroscopic Description of the Propagation of Radiation Flux from an Isotropic Source-The Inverse Square Law 1.3 The Specific Intensity and Its Moments Definition of Specific Intensity or Brightness Net Flux and Momentum Flux Radiative Energy Density Radiation Pressure in an Enclosure Containing an Isotropic Radiation Field Constancy of Specific Intensity Along Rays in Free Space Proof of the Inverse Square Law for a Uniformly Bright Sphere 1.4 Radiative Transfer Emission Absorption The Radiative Transfer Equation Optical Depth and Source Function Mean Free Path Radiation Force 1.5 Thermal Radiation Blackbody Radiation Kirchhoff's Law for Thermal Emission Thermodynamics of Blackbody Radiation The Planck Spectrum Properties of the Planck Law Characteristic Temperatures Related to Planck Spectrum 1.6 The Einstein Coefficients Definition of Coefficients Relations between Einstein Coefficients Absorption and Emission Coefficients in Terms of Einstein Coefficients 1.7 Scattering Effects Random Walks Pure Scattering Combined Scattering and Absorption 1.8 Radiative Diffusion The Rosseland Approximation The Eddington Approximation Two-Stream Approximation Problems References Chapter 2 Basic Theory of Radiation Fields 2.1 Review of Maxwell's Equations 2.2 Plane Electromagnetic Waves 2.3 The Radiation Spectrum 2.4 Polarization and Stokes Parameters 62 Monochromatic Waves Quasi-monochromatic Waves 2.5 Electromagnetic Potentials 2.6 Applicability of Transfer Theory and the Geometrical Optics Limit Problems References Chapter 3 Radiation from Moving Charges 3.1 Retarded Potentials of Single Moving Charges: The Lienard-Wiechart Potentials 3.2 The Velocity and Radiation Fields 3.3 Radiation from Nonrelativistic Systems of Particles Larmor's Formula The Dipole Approximation The General Multipole Expansion 3.4 Thomson Scattering (Electron Scattering) 3.5 Radiation Reaction 3.6 Radiation from Harmonically Bound Particles Undriven Harmonically Bound Particles Driven Harmonically Bound Particles Problems Reference Chapter 4 Relativistic Covariance and Kinematics 4.1 Review of Lorentz Transformations 4.2 Four-Vectors 4.3 Tensor Analysis 4.4 Covariance of Electromagnetic Phenomena 4.5 A Physical Understanding of Field Transformations 129 4.6 Fields of a Uniformly Moving Charge 4.7 Relativistic Mechanics and the Lorentz Four-Force 4.8 Emission from Relativistic Particles Total Emission Angular Distribution of Emitted and Received Power 4.9 Invariant Phase Volumes and Specific Intensity Problems References Chapter 5 Bremsstrahlung 5.1 Emission from Single-Speed Electrons 5.2 Thermal Bremsstrahlung Emission 5.3 Thermal Bremsstrahlung (Free-Free) Absorption 5.4 Relativistic Bremsstrahlung Problems References Chapter 6 Synchrotron Radiation 6.1 Total Emitted Power 6.2 Spectrum of Synchrotron Radiation: A Qualitative Discussion 6.3 Spectral Index for Power-Law Electron Distribution 6.4 Spectrum and Polarization of Synchrotron Radiation: A Detailed Discussion 6.5 Polarization of Synchrotron Radiation 6.6 Transition from Cyclotron to Synchrotron Emission 6.7 Distinction between Received and Emitted Power 6.8 Synchrotron Self-Absorption 6.9 The Impossibility of a Synchrotron Maser in Vacuum Problems References Chapter 7 Compton Scattering 7.1 Cross Section and Energy Transfer for the Fundamental Process Scattering from Electrons at Rest Scattering from Electrons in Motion: Energy Transfer 7.2 Inverse Compton Power for Single Scattering 7.3 Inverse Compton Spectra for Single Scattering 7.4 Energy Transfer for Repeated Scatterings in a Finite, Thermal Medium: The Compton Y Parameter 7.5 Inverse Compton Spectra and Power for Repeated Scatterings by Relativistic Electrons of Small Optical Depth 7.6 Repeated Scatterings by Nonrelativistic Electrons: The Kompaneets Equation 7.7 Spectral Regimes for Repeated Scattering by Nonrelativistic Electrons Modified Blackbody Spectra y"1 Wien Spectra y"1 Unsaturated Comptonization with Soft Photon Input Problems References Chapter 8 Plasma Effects 8.1 Dispersion in Cold, Isotropic Plasma The Plasma Frequency Group and Phase Velocity and the Index of Refraction 8.2 Propagation Along a Magnetic Field Faraday Rotation 8.3 Plasma Effects in High-Energy Emission Processes Cherenkov Radiation Razin Effect Problems References Chapter 9 Atomic Structure 9.1 A Review of the Schrodinger Equation 9.2 One Electron in a Central Field Wave Functions Spin 9.3 Many-Electron Systems Statistics: The Pauli Principle Hartree-Fock Approximation: Configurations The Electrostatic Interaction LS Coupling and Terms 9.4 Perturbations, Level Splittings, and Term Diagrams Equivalent and Nonequivalent Electrons and Their Spectroscopic Terms Parity Spin-Orbit Coupling Zeeman Effect Role of the Nucleus Hyperfine Structure 9.5 Thermal Distribution of Energy Levels and Ionization Thermal Equilibrium: Boltzmann Population of Levels The Saha Equation Problems References Chapter 10 Radiative Transitions 10.1 Semi-Classical Theory of Radiative Transitions The Electromagnetic Hamiltonian The Transition Probability 10.2 The Dipole Approximation 10.3 Einstein Coefficients and Oscillator Strengths 10.4 Selection Rules 10.5 Transition Rates Bound-Bound Transitions for Hydrogen Bound-Free Transitions (Continuous Absorption) for Hydrogen Radiative Recombination - Milne Relations The Role of Coupling Schemes in the Determination of f Values 10.6 Line Broadening Mechanisms Doppler Broadening Natural Broadening Collisional Broadening Combined Doppler and Lorentz Profiles Problems References Chapter 11 Molecular Structure 11.1 The Born-Oppenheimer Approximation: An Order of Magnitude Estimate of Energy Levels 11.2 Electronic Binding of Nuclei The H2+ Ion The H2 Molecule 11.3 Pure Rotation Spectra Energy Levels Selection Rules and Emission Frequencies 11.4 Rotation-Vibration Spectra Energy Levels and the Morse Potential Selection Rules and Emission Frequencies 11.5 Electronic-Rotational-Vibrational Spectra Energy Levels Selection Rules and Emission Frequencies Problems References Solutions Index
3,243 citations
TL;DR: In this paper, 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.
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.
1,542 citations
"A computer program for fast non-LTE..." refers methods in this paper
...The input format for spectroscopic and collisional data is that of the LAMDA database (Schöier et al. 2005)2 where an online calculator for molecular line intensities3, based on our program, can also be found4....
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...Throughout this section, molecular data have been taken from the LAMDA database (Schöier et al. 2005)....
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TL;DR: In this article, the transitions of a number of astrophysically interesting species are summarized, including energy levels, statistical weights, Einstein A-coefficients and collisional rate coefficients.
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.
1,407 citations
TL;DR: In this article, the chemical composition of the various regions in the core of the Orion molecular cloud (OMC-1) was investigated based on results from the Caltech Owens Valley Radio Observatory (OVRO) spectral line survey (Sutton et al., Blake et al.).
Abstract: We present here an investigation of the chemical composition of the various regions in the core of the
Orion molecular cloud (OMC-1) based on results from the Caltech Owens Valley Radio Observatory (OVRO) millimeter-wave spectral line survey (Sutton et al.; Blake et al.). This survey covered a 55 GHz interval in the
1.3 mm (230 GHz) atmospheric window and contained emission from over 800 resolved spectral features. Of the 29 identified species 14 have a sufficient number of detected transitions to be investigated with an LTE "rotation diagram" technique, in which large numbers of lines are used to estimate both the rotational excitation
and the overall abundance. The rotational temperatures and column densities resulting from these fits have then been used to model the emission from those remaining species which either have too few lines or which are too weak to be so analyzed. When different kinematic sources of emission are blended to produce a single feature, Gaussian fits have been used to derive the individual contributions to the total line profile. The uniformly calibrated data in the unique and extensive Caltech spectral line survey lead to accurate estimates of the chemical and physical parameters of the Orion molecular cloud, and place significant constraints on models of interstellar chemistry.
A global analysis of the observed abundances shows that the markedly different chemical compositions of
the kinematically and spatially distinct Orion subsources may be interpreted in the framework of an evolving,
initially quiescent, gas-phase chemistry influenced by the process of massive star formation. The chemical composition
of the extended Orion cloud complex is similar to that found in a number of other objects, but the central regions of OMC-1 have had their chemistry selectively altered by the radiation and high-velocity outflow from the young stars embedded deep within the interior of the molecular cloud. Specifically, the extended ridge clouds are inferred to have a low (subsolar) gas-phase oxygen content from the prevalence of reactive carbon-rich species like CN, CCH, and C_3H_2 also found in more truly quiescent objects such as TMC-1. The similar abundances of these and other simple species in clouds like OMC-1, Sgr B2, and TMC-1 lend support to gas-phase ion-molecule models of interstellar chemistry, but grain processes may also play a significant role in maintaining the overall chemical balance in such regions through selective depletion mechanisms and grain mantle processing. In contrast, the chemical compositions of the more turbulent plateau and hot core components of OMC-1 are dominated by high-temperature, shock-induced gas and grain surface neutral-neutral reaction processes. The high silicon/sulfur oxide and water content of the plateau gas is best modeled by fast shock disruption of smaller grain cores to release the more refractory elements followed by a predominantly neutral chemistry in the cooling postshock regions, while a more passive release of grain mantle products driven toward kinetic equilibrium most naturally explains the prominence of fully hydrogenated
N-containing species like HCN, NH_3 , CH_3CN, and C_2H_5CN in the hot core. The clumpy nature of the outflow is illustrated by the high-velocity emission observed from easily decomposed molecules such as H_2CO. Areas immediately adjacent to the shocked core in which the cooler, ion-rich gas of the surrounding molecular cloud is mixed with water/oxygen rich gas from the plateau source are proposed to give rise to the enhanced abundances of complex internal rotors such as CH_30H, HCOOCH_3 , and CH_30CH_3 whose line widths are similar to carbon-rich species such as CN and CCH found in the extended ridge, but whose rotational temperatures are somewhat higher and whose spatial extents are much more compact.
897 citations
"A computer program for fast non-LTE..." refers methods in this paper
...If many lines have been observed, a popular method is the ‘rotation diagram’, also called ‘Boltzmann plot’ or ‘population diagram’ (e.g., Blake et al. 1987; Helmich et al. 1994; Goldsmith & Langer 1999)....
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TL;DR: In this paper, the authors developed the use of the population diagram method to analyze molecular emission in order to derive physical properties of interstellar clouds, focusing particular attention on how the optical depth affects the derived total column density and the temperature.
Abstract: We develop the use of the population diagram method to analyze molecular emission in order to derive physical properties of interstellar clouds. We focus particular attention on how the optical depth affects the derived total column density and the temperature. We derive an optical depth correction factor that can be evaluated based on observations and that incorporates the effect of saturation on derived upper level populations. We present analytic results for linear molecules in local thermodynamic equilibrium (LTE). We investigate numerically how subthermal excitation influences the population diagram technique, studying how the determination of kinetic temperature is affected when the local density is insufficient to achieve LTE. We present results for HC3N and CH3OH, representative of linear and nonlinear molecules, respectively. In some cases, alternative interpretations to the standard optically thin and thermalized picture yield significantly different results for column density and kinetic temperature, and we discuss this behavior. The population diagram method can be a very powerful tool for determining physical conditions in dense clouds if proper recognition is given to effects of saturation and subthermal excitation. We argue that the population diagram technique is, in fact, superior to fitting intensities of different transitions directly, and we indicate how it can be effectively employed.
742 citations
"A computer program for fast non-LTE..." refers methods in this paper
...If many lines have been observed, a popular method is the ‘rotation diagram’, also called ‘Boltzmann plot’ or ‘population diagram’ (e.g., Blake et al. 1987; Helmich et al. 1994; Goldsmith & Langer 1999)....
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