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Molecule formation and infrared emission in fast interstellar shocks. I Physical processes
Abstract
The paper analyzes the structure of fast shocks incident upon interstellar gas of ambient density from 10 to the 7th per cu cm, while focusing on the problems of formation and destruction of molecules and infrared emission in the cooling, neutral post shock gas. It is noted that such fast shocks initially dissociate almost all preexisting molecules. Discussion covers the physical processes which determine the post shock structure between 10 to the 4 and 10 to the 2 K. It is shown that the chemistry of important molecular coolants H2, CO, OH, and H2O, as well as HD and CH, is reduced to a relatively small set of gas phase and grain surface reactions. Also, the chemistry follows the slow conversion of atomic hydrogen into H2, which primarily occurs on grain surfaces. The dependence of this H2 formation rate on grain and gas temperatures is examined and the survival of grains behind fast shocks is discussed. Post shock heating and cooling rates are calculated and an appropriate, analytic, universal cooling function is developed for molecules other than hydrogen which includes opacities from both the dust and the lines.
... The H 2 formation rate as catalysed by dust grains (α Z H 2 ) differs depending on the environment (Wakelam et al. 2017), with the traditional rate 3 × 10 −17 cm 3 s −1 for diffuse clouds (Jura 1974;Gry et al. 2002) being lower than the recently measured rate for dense PDRs, 1.5 × 10 −16 cm 3 s −1 (Habart et al. 2004). In order to encompass all environments, we use the average between these two rates with the functional temperature dependence of Hollenbach & McKee (1979). Gas phase H 2 formation is important for low-to zero-metallicity environments (α GP H 2 ) and we use the rate of McKee & Krumholz (2010), which assumes equilibrium in H − . ...
... When H 2 forms, it releases a small amount of heat depending on the formation mechanism. For formation on dust grains and gas phase formation, we use the formulation by Hollenbach & McKee (1979) and for formation by threebody collisions we use Omukai's (2000) formulation: ...
... where Λ H 2 H i(n→0) and Λ H 2 H 2 (n→0) are the low-density limits of the H 2 collisional cooling coefficients from Hollenbach & McKee (1979) in units of cm 3 erg s −1 . ...
We introduce non-equilibrium molecular hydrogen chemistry into the radiation hydrodynamics code Ramses-RT. This is an adaptive mesh refinement grid code with radiation hydrodynamics that couples the thermal chemistry of hydrogen and helium to moment-based radiative transfer with the Eddington tensor closure model. The H2 physics that we include are formation on dust grains, gas phase formation, formation by three-body collisions, collisional destruction, photodissociation, photoionization, cosmic ray ionization, and self-shielding. In particular, we implement the first model for H2 self-shielding that is tied locally to moment-based radiative transfer by enhancing photodestruction. This self-shielding from Lyman-Werner line overlap is critical to H2 formation and gas cooling. We can now track the non-equilibrium evolution of molecular, atomic, and ionized hydrogen species with their corresponding dissociating and ionizing photon groups. Over a series of tests we show that our model works well compared to specialized photodissociation region codes. We successfully reproduce the transition depth between molecular and atomic hydrogen, molecular cooling of the gas, and a realistic Stromgren sphere embedded in a molecular medium. In this paper we focus on test cases to demonstrate the validity of our model on small scales. Our ultimate goal is to implement this in large-scale galactic simulations.
... We refine earlier estimates of Z crit which did not explicitly distinguish between different O I and C II whose fine-structure lines dominate over all other metal transitions 18 . Cooling due to molecules becomes important only at lower temperatures, and cooling due to dust grains only at higher densities 18 ,7,11 . ...
... In evaluating this threshold condition, we solve the respective rate equations for C II (a two-level system) and O I (a three-level system), including all possible radiative and collisional transitions 18 . We assume that the emission of the fine-structure lines proceeds under optically thin conditions, as appropriate for the low atomic abundances considered here 18 . ...
The first stars in the Universe are predicted to have been much more massive than the Sun. Gravitational condensation accompanied by cooling of the primordial gas due to molecular hydrogen, yields a minimum fragmentation scale of a few hundred solar masses. Numerical simulations indicate that once a gas clump acquires this mass, it undergoes a slow, quasi-hydrostatic contraction without further fragmentation. Here we show that as soon as the primordial gas - left over from the Big Bang - is enriched by supernovae to a carbon or oxygen abundance as small as ~0.01-0.1% of that found in the Sun, cooling by singly-ionized carbon or neutral oxygen can lead to the formation of low-mass stars. This mechanism naturally accommodates the discovery of solar mass stars with unusually low (10^{-5.3} of the solar value) iron abundance but with a high (10^{-1.3} solar) carbon abundance. The minimum stellar mass at early epochs is partially regulated by the temperature of the cosmic microwave background. The derived critical abundances can be used to identify those metal-poor stars in our Milky Way galaxy with elemental patterns imprinted by the first supernovae.
... Experimental investigation demonstrates the catalytic role of carbon, silicate, and water ice at temperatures less than 20K [6][7][8] . In addition, observational evidence indicates that H 2 can be efficiently formed over a wide range of temperatures 9,10 . The LH mechanism operating by physisorption is believed to dominate H 2 formation at low temperatures around 10K 11 . ...
The reason for the abundance of molecular hydrogen (H2) in space remains unresolved. Here we study collision dynamics under spacelike conditions to test H2 formation mechanisms where carbonaceous dust grains may have a catalytic role. Density functional theory molecular dynamics simulates atomic hydrogen capture and H2 formation on the surface of buckminsterfullerene as a carbonaceous cosmic dust model. Maximally localized Wannier functions are applied to examine the electronic bonding during transition states. The fullerene surface is shown to be effective at warm (50K) and low (10K) temperatures in achieving atomic H chemisorption, potentially explaining the observed broad temperature range for efficient H2 formation. We revise the Eley-Rideal mechanism and propose that both it and the Langmuir-Hinshelwood mechanism, induced by thermal hopping, contribute to bursts of H2 formation during energetic events. Additionally, we show how fullerene maintains the abundance of H2 in space by selectively preventing H2 molecules from capture.
... Nonequilibrium chemistry was accounted for by using KROME (Grassi et al. 2014), with a chemical network accounting for nine species (H, H + , H − , H 2 , H + 2 , He, He + , He ++ and free electrons), 46 reactions (see Bovino et al. 2016;Pallottini et al. 2017 for details), and fully coupled with the RAMSES-RT module Decataldo et al. 2019). The formation of H 2 molecules, which mainly happens on the surface of dust grains, is regulated by the gas and dust temperature in the RHD simulation, following the rate given by Hollenbach & McKee (1979) and Sternberg & Dalgarno (1989). In the chemistry module, the dust temperature is assumed to be constant at T d = 30 K. Several gas heating and cooling mechanisms were also included. ...
Context. Molecular clouds (MCs) are the places where stars are formed and their feedback starts to take place, regulating the evolution of galaxies. Therefore, MCs represent the critical scale at which to study how ultraviolet (UV) photons emitted by young stars are reprocessed in the far-infrared (FIR) by interaction with dust grains, thereby determining the multiwavelength continuum emission of galaxies.
Aims. Our goal is to analyze the UV and IR emission of a MC at different stages of its evolution and relate its absorption and emission properties with its morphology and star formation rate. Such a study is fundamental to determining how the properties of MCs shape the emission from entire galaxies.
Methods. We considered a radiation-hydrodynamic simulation of a MC with self-consistent chemistry treatment. The MC has a mass of M MC = 10 ⁵ M ⊙ , is resolved down to a scale of 0.06 pc, and evolves for ≃2.4 Myr after the onset of star formation. We post-processed the simulation via Monte Carlo radiative transfer calculations to compute the detailed UV-to-FIR emission of the MC. Such results were compared with data from physically motivated analytical models, other simulations, and observations.
Results. We find that the simulated MC is globally UV-optically thick, but optically thin channels allow for photon escape (0.1–10%), a feature that is not well captured in analytical models. The dust temperature spans a wide range ( T dust ∼ 20–300 K) depending on the dust-to-stellar geometry, which is reproduced reasonably well by analytical models. However, the complexity of the dust temperature distribution is not captured in the analytical models, as is evidenced by the 10 K (20 K) difference in the mass (luminosity) average temperature. Indeed, the total IR luminosity is the same in all the models, but the IR emission peaks at shorter wavelengths in the analytical ones. Compared to a sample of Galactic clouds and other simulations, our spectral energy distribution (SED) is consistent with mid-IR data, but peaks at shorter wavelengths in the IR. This is due to a lack of cold dust, as a consequence of the high gas – and thus dust – consumption in our simulated MC. The attenuation properties of our MC change significantly with time, evolving from a Milky-Way-like relation to a flatter, featureless one. On the IRX-β plane, the MC position strongly depends on the observing direction and on its evolutionary stage. When the MC starts to disperse, the cloud settles at log(IRX) ∼ 1 and β ∼ −0.5, slightly below most of the local empirical relations.
Conclusions. This work represents an important test for MC simulations and a first step toward the implementation of a physically informed, sub-grid model in large-scale numerical simulations to describe the emission from unresolved MC scales and its impact on the global galaxy SED.
... H 2 detections are extremely challenging because H 2 lacks a permanent dipole moment and because its lowest rotational transition requires temperatures of 510 K at least for excitation (Saslaw & Zipoy 1967;Hollenbach & McKee 1979;Lepp & Shull 1983;Galli & Palla 1998;Roussel et al. 2007;Fukui & Kawamura 2010;Dobbs & Pringle 2013;Krumholz 2014;Togi & Smith 2016). Hence, direct detections of molecular hydrogen (see e.g. ...
The latest ALMA and JWST observations provide new information on the birth and evolution of galaxies in the early Universe at the epoch of reionization. Measurements at redshift of their cold-gas budget are particularly important because this budget is known to be the main fuel for star formation. A powerful tool for probing the physics characterising galaxies at high redshift is the m_2_2$ mass.
... Chemistry is often an important component of the evolution of astrophysical plasmas. The creation of simple molecules via gas-and dust-phase chemical reactions can greatly enhance the efficacy of cooling (Hollenbach & McKee 1979;Omukai et al. 2005). The formation and destruction of simple molecules can be energetically important in some circumstances, such as Population III star formation (Omukai & Nishi 1998;Abel et al. 2002;Glover & Abel 2008;Turk et al. 2009). ...
We present the Grackle chemistry and cooling library for astrophysical simulations and models. Grackle provides a treatment of non-equilibrium primordial chemistry and cooling for H, D, and He species, including H2 formation on dust grains; tabulated primordial and metal cooling; multiple UV background models; and support for radiation transfer and arbitrary heat sources. The library has an easily implementable interface for simulation codes written in C, C++, and Fortran as well as a Python interface with added convenience functions for semi-analytical models. As an open-source project, Grackle provides a community resource for accessing and disseminating astrochemical data and numerical methods. We present the full details of the core functionality, the simulation and Python interfaces, testing infrastructure, performance, and range of applicability. Grackle is a fully open-source project and new contributions are welcome.
... where k B is the Boltzmann constant. The sticking coefficient is given by (Hollenbach & McKee 1979;Omukai et al. 2005) S H = 1 + 0.04 T gas + T d 0.5 + 2 × 10 −3 T gas + 8 × 10 −6 T 2 gas −1 × 1 + exp 7.5 × 10 2 1 75 ...
There are two major theoretical issues for the star formation law (the relation between the surface densities of molecular gas and star formation rate on a galaxy scale): (i) At low metallicity, it is not obvious that star-forming regions are rich in H because the H formation rate depends on the dust abundance; and (ii) whether or not CO really traces H is uncertain, especially at low metallicity. To clarify these issues, we use a hydrodynamic simulation of an isolated disc galaxy with a spatial resolution of a few tens parsecs. The evolution of dust abundance and grain size distribution is treated consistently with the metal enrichment and the physical state of the interstellar medium. We compute the H and CO abundances using a subgrid post-processing model based on the dust abundance and the dissociating radiation field calculated in the simulation. We find that when the metallicity is Z ( Gyr), H is not a good tracer of star formation rate because H-rich regions are limited to dense compact regions. At Z, a tight star formation law is established for both H and CO. At old ( Gyr) ages, we also find that adopting the so-called MRN grain size distribution with an appropriate dust-to-metal ratio over the entire disc gives reasonable estimates for the H and CO abundances. For CO, improving the spatial resolution of the simulation is important while the H abundance is not sensitive to sub-resolution structures at Z.
... Self-shielding of H 2 becomes effective around N H ∼ 2 × 10 20 cm −2 , while column densities in excess of N H ∼ 4 × 10 21 cm −2 are required to form CO [68,69]. The range of column densities in between is populated by the 'CO-dark H 2 ' gas that may account on average for (30 − 40)% of the Milky Way molecular mass [70,71]. ...
We explore the structure and statistics of multiphase, magnetized ISM turbulence in the local Milky Way by means of driven periodic box numerical MHD simulations. Using the higher order-accurate piecewise-parabolic method on a local stencil (PPML), we carry out a small parameter survey varying the mean magnetic field strength and density while fixing the rms velocity to observed values. We quantify numerous characteristics of the transient and steady-state turbulence, including its thermodynamics and phase structure, kinetic and magnetic energy power spectra, structure functions, and distribution functions of density, column density, pressure, and magnetic field strength. The simulations reproduce many observables of the local ISM, including molecular clouds, such as the ratio of turbulent to mean magnetic field at 100 pc scale, the mass and volume fractions of thermally stable HI, the lognormal distribution of column densities, the mass-weighted distribution of thermal pressure, and the linewidth-size relationship for molecular clouds. Our models predict the shape of magnetic field probability density functions (PDFs), which are strongly non-Gaussian, and the relative alignment of magnetic field and density structures. Finally, our models show how the observed low rates of star formation per free-fall time are controlled by the multiphase thermodynamics and large-scale turbulence.
... In the minimum mass solar nebula model (Hayashi et al. 1985), the number density of the nebula gas at 1 AU from the central star is about n ≃ 10 14 cm −3 . The collisional cross section of the hydro-gen molecule is roughly estimated as s ≃ 10 −16 cm 2 (e.g., Hollenbach & McKee 1979). So, we obtain l ≃ 100 cm. ...
Millimeter-sized, spherical silicate grains abundant in chondritic meteorites, which are called as chondrules, are considered to be a strong evidence of the melting event of the dust particles in the protoplanetary disk. One of the most plausible scenarios is that the chondrule precursor dust particles are heated and melt in the high-velocity gas flow (shock-wave heating model). We developed the non-linear, time-dependent, and three-dimensional hydrodynamic simulation code for analyzing the dynamics of molten droplets exposed to the gas flow. We confirmed that our simulation results showed a good agreement in a linear regime with the linear solution analytically derived by Sekiya et al. (2003). We found that the non-linear terms in the hydrodynamical equations neglected by Sekiya et al. (2003) can cause the cavitation by producing negative pressure in the droplets. We discussed that the fragmentation through the cavitation is a new mechanism to determine the upper limit of chondrule sizes. We also succeeded to reproduce the fragmentation of droplets when the gas ram pressure is stronger than the effect of the surface tension. Finally, we compared the deformation of droplets in the shock-wave heating with the measured data of chondrules and suggested the importance of other effects to deform droplets, for example, the rotation of droplets. We believe that our new code is a very powerful tool to investigate the hydrodynamics of molten droplets in the framework of the shock-wave heating model and has many potentials to be applied to various problems.
Molecular clouds (MCs) are the birthplaces of new stars in galaxies. A key component of MCs are photodissociation regions (PDRs), where far-ultraviolet radiation plays a crucial role in determining the gas’s physical and chemical state. Traditional PDR models assume a chemical steady state (CSS), where the rates of H 2 formation and photodissociation are balanced. However, real MCs are dynamic and can be out of CSS. In this study, we demonstrate that combining H 2 emission lines observed in the far-ultraviolet or infrared with column density observations can be used to derive the rates of H 2 formation and photodissociation. We derive analytical formulae that relate these rates to observable quantities, which we validate using synthetic H 2 line emission maps derived from the SILCC-Zoom hydrodynamical simulation. Our method estimates integrated H 2 formation and dissociation rates with an accuracy ≈30% (on top of the uncertainties in the observed H 2 emission maps and column densities). Our simulations, valid for column densities N ≤ 2 × 10 ²² cm ⁻² , cover a wide dynamic range of H 2 formation and photodissociation rates, showing significant deviations from CSS, with 74% of the MC’s mass deviating from CSS by a factor greater than 2. Our analytical formulae can effectively distinguish between regions in and out of CSS. When applied to actual H 2 line observations, our method can assess the chemical states of MCs, providing insights into their evolutionary stages and lifetimes. A NASA Small Explorer mission concept, Eos, will be proposed in 2025 and is specifically designed to conduct the types of observations outlined in this study.
New measurements of the ultraviolet surface brightness of the night sky in 71 fields in the galactic longitude range 65degree< or =l/sub i//sub i/< or =145degree are presented. The data were obtained with the Orbiting Astronomical Observatory (OAO-2) at nine wavelengths between 1500 A and 4200 A and have been corrected for the contributions due to zodiacal light and integrated starlight. The residual brightnesses were analyzed with radiative transfer models for the diffuse galactic light which incorporate a z-dependent source function. The results qualitatively confirm earlier findings for this wavelength region, yielding a wavelength dependent albedo of the interstellar grains of approximately ..cap alpha..=0.7 +- 0.1 longward of lambda3000, ..cap alpha..=0.35 +- 0.05 around the pronounced minimum near lambda2200, and ..cap alpha..=0.6 +- 0.05 at lambda1550. The true absorption nature of the bump in the interstellar extinction curve near lambda2200, as well as the increase of the albedo shortward of lambda2000 are thus reconfirmed. The phase function asymmetry factor is found to lie between g=0.6 and g=0.9 for the entire wavelength range, indicating the interstellar grains are strongly forward scattering. (AIP)
The usual book on the theory of spectral line formation begins with an in-depth dis cussion of radiation transfer, including the elegant methods of obtaining analytical solutions for special cases, and of the physics of line broadening. Neither of those features will be found in this book. It is assumed that the reader is already familiar with the essentials of transport theory and of line broadening and is ready to investi gate some of the particular applications of the theory to the flow of line photons through the outer layers of a star, or other tenuous media. The main thrust of this book is toward the compilation and presentation of a vast quantity of computational material available to the author in the form of computer output. The material presented represents a highly filtered sample of the published work in this subject plus an extensive set of previously unpublished results. To present large quantities of computer output in an intelligible and efficient way is a difficult task, for which I have found no really satisfactory solution. Chapters III and IV, in particular, contain almost exclusively this type of presentation. The reader may find these chapters somewhat tedious because of the level of condensation of the material. I have tried to reach a reasonable balance between over condensation and excessive detail, which in the long run may be irrelevant.
The quantity -r(V(r) calculated by Herman and Skillman, using the Hartree-Fock-Slater approach, is approximated by a series of straight lines. With such a potential the radial Schrödinger equation is exactly solvable with Whittaker functions. The bound-state eigenvalue equation is found and is used to adjust the parameters of the straight lines so that the model eigenvalues and those of Herman and Skillman are in reasonable agreement. With the discrete and continuum orbitals of the model, the photo-ionization cross section for all the shells of the elements helium-xenon are computed.
Infrared transmission and reflectivity measurements from 1 to 25 mu (microns) have been made on several samples of green alpha (hexagonal) SiC. The residual ray bands have been observed for the ordinary and extraordinary rays. The resonance frequencies are 2.380×1013 sec-1 (12.60 mu) and 2.356×1013 sec-1 (12.73 mu), respectively. From the reflectivity the high-frequency dielectric constant is found to be 6.7. A careful analysis shows that the residual ray bands can be fitted within experimental error by the classical dispersion theory within the correct choice of the dispersion parameters. From the parameters the value 10.0 is obtained for the low-frequency dielectric constant. The effective charge is 0.94e. Complete description of the residual ray band for the extraordinary ray required, in addition to the main resonance, a weak resonance at 2.647×1013 sec-1 (11.33 mu). A study on the effects of several different surface treatments shows the reflectivities reported here are an intrinsic property of the crystal. The room-temperature absorption coefficient as a function of wavelength in the range 1 to 10 mu has been determined from transmission measurements. A number of weak lattice bands are observed between 5 and 10 mu.
Improved results on the total photo-ionization cross section of atomic helium are given. The total cross section includes contributions from simultaneous ionization and excitation of He+ and double ionization; the combined effect of these two processes adds about 10% to the normal photo-ionization process where He+ is left in the ground state. A lower abundance (10.92 based on 12.00 for hydrogen) is adopted for helium, based on recent radio determinations. In calculating the opacity due to K-shell photo-ionization of heavy elements, a lower abundance (8.00) is also adopted for neon. Brief mention is made of the effects of irregularities in the density distribution of the interstellar gas on the problems of both x-ray and radio-wave absorption.
The author has calculated contributions to the total photoionization cross section of Fei in which the remaining Fe ii ion is left in a low-lying excited state. The excited states considered are (3d)74P, 4F and (3d)65D4p6D, 6F, 6P, 4F, 4D, and 4P. We used the velocity form for the dipole-matrix elements and calculated the cross sections by means of many-body perturbation theory. Our results are compared with the cross section for photoionization of Fei without excitation which we calculated recently. Near threshold the contributions to the total photoionization cross section involving excited (3d)7 and (3d)65D4p excited states of Fei are approximately 20% of the cross section without excitation.