We present the revised "Meudon" model of Photon Dominated Region (PDR code), presently available on the web under the Gnu Public Licence at: http://aristote.obspm.fr/MIS. General organisation of the code is described down to a level that should allow most observers to use it as an interpretation tool with minimal help from our part. Two grids of models, one for low excitation diffuse clouds and one for dense highly illuminated clouds, are discussed, and some new results on PDR modelisation highlighted.

We present new analytic theory and radiative transfer computations for the atomic to molecular (HI-to-H 2 ) transitions, and the build-up of atomic-hydrogen (HI) gas columns, in optically thick interstellar clouds, irradiated by far-ultraviolet photodissociating radiation fields. We derive analytic expressions for the total HI column densities for (one-dimensional (1D)) planar slabs, for beamed or isotropic radiation fields, from the weak-to strong-field limits, for gradual or sharp atomic to molecular transitions, and for arbitrary metallicity. Our expressions may be used to evaluate the HI column densities as functions of the radiation field intensity and the H 2 -dust-limited dissociation flux, the hydrogen gas density, and the metallicity-dependent H 2 formation rate-coefficient and far-UV dustgrain absorption cross-section. We make the distinction between "HI-dust" and "H 2 -dust" opacity, and we present computations for the "universal H 2 -dust-limited effective dissociation bandwidth". We validate our analytic formulae with Meudon PDR code computations for the HI-to-H 2 density profiles, and total HI column densities. We show that our general 1D formulae predict HI columns and H 2 mass fractions that are essentially identical to those found in more complicated (and approximate) spherical (shell/core) models. We apply our theory to compute H 2 mass fractions and star-formation thresholds for individual clouds in self-regulated galaxy disks, for a wide range of metallicities. Our formulae for the HI columns and H 2 mass fractions may be incorporated into hydrodynamics simulations for galaxy evolution.

Context. It has been found from ISO, Spitzer, and Herschel observations that molecular hydrogen, H 2 , can form on warm grains. Numerical models of interstellar chemistry have failed to reproduce the observed formation rates of H 2 , which remains a difficulty when interpreting observations of photon-dominated regions (PDRs). Aims. We attempt to include as much experimental and theoretical information as possible to describe H 2 formation in astrophysical environments to solve this problem. Methods. We modified our "Meudon PDR code" to include a detailed treatment of H 2 formation mechanisms including: i) the Langmuir-Hinshelwood mechanism taking into account the contribution of the different sizes of dust grains in the diffusion processes; and ii) the Eley-Rideal mechanism. Results. We are able to form H 2 even in regions where the dust temperature is higher than 25 K. We also show that formation by the Eley-Rideal mechanism can be a significant source of gas heating. We derive line intensities for various astrophysical conditions. Conclusions. Our approach results in a higher H 2 formation rate than for the "standard" 3 × 10 −17 n H n(H) cm 3 s −1 expression.

We report observations of three rotational transitions of molecular oxygen (O 2 ) in emission from the H 2 Peak

Context. The H 2 formation on grains is known to be sensitive to dust temperature, which is also known to fluctuate for small grain sizes due to photon absorption. Aims. We aim at exploring the consequences of simultaneous fluctuations of the dust temperature and the adsorbed H-atom population on the H 2 formation rate under the full range of astrophysically relevant UV intensities and gas conditions. Methods. The master equation approach is generalized to coupled fluctuations in both the grain's temperature and its surface population and solved numerically. The resolution can be simplified in the case of the Eley-Rideal mechanism, allowing a fast computation. For the Langmuir-Hinshelwood mechanism, it remains computationally expensive, and accurate approximations are constructed. Results. We find the Langmuir-Hinshelwood mechanism to become an efficient formation mechanism in unshielded photon dominated region edge conditions when taking those fluctuations into account, despite hot average dust temperatures. It reaches an importance comparable to the Eley-Rideal mechanism. However, we show that a simpler rate equation treatment gives qualitatively correct observable results in full cloud simulations under the most astrophysically relevant conditions. Typical differences are a factor of 2−3 on the intensities of the H 2 v = 0 lines. We also find that rare fluctuations in cloud cores are sufficient to significantly reduce the formation efficiency. Conclusions. Our detailed analysis confirms that the usual approximations used in numerical models are adequate when interpreting observations, but a more sophisticated statistical analysis is required if one is interested in the details of surface processes.

In this paper, we introduce the notion of snapstabilization. A snap-stabilizing algorithm protocol guarantees that, starting from an arbitrary system configuration, the protocol always behaves according to its specification. So, a snap-stabilizing protocol is a self-stabilizing protocol which stabilizes in 0 steps.We propose a snap-stabilizing Propagation of Information with Feedback (PIF) scheme on a rooted tree network. We call this scheme Propagation of information with Feedback and Cleaning (P F C ). We present two algorithms. The first one is a basic P F C scheme which is inherently snapstabilizing. However, it can be delayed Oh 2 steps (where h is the height of the tree) due to some undesirable local states. The second algorithm improves the worst delay of the basic P F C algorithm from Oh 2 to 1 step. The P F C scheme can be used to implement the distributed reset, the distributed infimum computation, and the global synchronizer in O1 waves (or PIF cycles). Moreover, assuming that a (local) checking mechanism exists to detect transient failures or topological changes, the P F C scheme allows processors to (locally) "detect" if the system is stabilized, in O1 waves without using any global metric (such as the diameter or size of the network).Finally, we show that the state requirement for both P F C algorithms matches the exact lower bound of the PIF algorithms on tree networks-3 states per processor, except for the root and leaf processors which use only 2 states. Thus, the proposed algorithms are optimal PIF schemes in terms of the number of states.

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Context.Observations have long demonstrated the molecular diversity of the diffuse interstellar medium (ISM). Only now, with the advent of high-performance computing, does it become possible for numerical simulations of astrophysical fluids to include a treatment of chemistry, to faithfully reproduce the abundances of the many observed species, and especially that of CO, which is used as a proxy for molecular hydrogen. When applying photon-dominated region (PDR) codes to describe the UV-driven chemistry of uniform density cloud models, it is found that the observed abundances of CO are not well reproduced. Aims. Our main purpose is to estimate the effect of assuming uniform density on the line-of-sight in PDR chemistry models, compared to a more realistic distribution for which total gas densities may well vary by several orders of magnitude. A secondary goal of this paper is to estimate the amount of molecular hydrogen that is not properly traced by the CO (J = 1 → 0) line, the so-called "dark molecular gas". Methods. We used results from a magnetohydrodynamical (MHD) simulation as a model for the density structures found in a turbulent diffuse ISM with no star-formation activity. The Meudon PDR code was then applied to several lines of sight through this model, to derive their chemical structures.Results. We found that compared to the uniform density assumption, maximal chemical abundances for H 2 , CO, CH and CN are increased by a factor ∼2-4 when taking into account density fluctuations on the line of sight. The correlations between column densities of CO, CH and CN with respect to those of H 2 are also found to be in better overall agreement with observations. For instance, at N