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Context. Dense and cold molecular cores and filaments are surrounded by an envelope of translucent gas. Some of the low-Jemission lines of CO and HCO+isotopologues are more sensitive to the conditions either in the translucent environment or in the dense and cold one because their intensities result from a complex interplay of radiative transfer and chemical properties of these heterogeneous lines of sight (LoSs). Aims. We extend our previous single-zone modeling with a more realistic approach that introduces multiple layers to take account of possibly varying conditions along the LoS. We used the IRAM-30m data from the ORION-B large program toward the Horsehead nebula in order to demonstrate our method’s capability and effectiveness. Methods. We propose a cloud model composed of three homogeneous slabs of gas along each LoS, representing an outer envelope and a more shielded inner layer. We used the non-LTE radiative transfer code RADEX to model the line profiles from the kinetic temperature (Tkin), the volume density (nH2), kinematics, and chemical properties of the different layers. We then used a fast and robust maximum likelihood estimator to simultaneously fit the observed lines of the CO and HCO+isotopologues. To limit the variance on the estimates, we propose a simple chemical model by constraining the column densities. Results. A single-layer model cannot reproduce the spectral line asymmetries that result from a combination of different radial velocities and absorption effects among layers. A minimal heterogeneous model (three layers only) is sufficient for the Horsehead application, as it provides good fits of the seven fitted lines over a large part of the studied field of view. The decomposition of the intensity into three layers allowed us to discuss the distribution of the estimated physical or chemical properties along the LoS. About 80% of the12CO integrated intensity comes from the outer envelope, while ~55% of the integrated intensity of the (1 − 0) and (2 − 1) lines of C18O comes from the inner layer. For the lines of the13CO and the HCO+isotopologues, integrated intensities are more equally distributed over the cloud layers. The estimated column density ratioN(13CO)/N(C18O) in the envelope increases with decreasing visual extinction, and it reaches 25 in the pillar outskirts. While the inferredTkinof the envelope varies from 25 to 40 K, that of the inner layer drops to ~15 K in the western dense core. The estimatednH2in the inner layer is ~3 × 104cm−3toward the filament, and it increases by a factor of ten toward dense cores. Conclusions. Our proposed method correctly retrieves the physical and chemical properties of the Horsehead nebula. It also offers promising prospects for less supervised model fits of wider-field datasets.more » « lessFree, publicly-accessible full text available December 1, 2025
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Context.Observations of ionic, atomic, or molecular lines are performed to improve our understanding of the interstellar medium (ISM). However, the potential of a line to constrain the physical conditions of the ISM is difficult to assess quantitatively, because of the complexity of the ISM physics. The situation is even more complex when trying to assess which combinations of lines are the most useful. Therefore, observation campaigns usually try to observe as many lines as possible for as much time as possible. Aims.We have searched for a quantitative statistical criterion to evaluate the full constraining power of a (combination of) tracer(s) with respect to physical conditions. Our goal with such a criterion is twofold. First, we want to improve our understanding of the statistical relationships between ISM tracers and physical conditions. Secondly, by exploiting this criterion, we aim to propose a method that helps observers to make their observation proposals; for example, by choosing to observe the lines with the highest constraining power given limited resources and time. Methods.We propose an approach based on information theory, in particular the concepts of conditional differential entropy and mutual information. The best (combination of) tracer(s) is obtained by comparing the mutual information between a physical parameter and different sets of lines. The presented analysis is independent of the choice of the estimation algorithm (e.g., neural network orχ2minimization). We applied this method to simulations of radio molecular lines emitted by a photodissociation region similar to the Horsehead Nebula. In this simulated data, we considered the noise properties of a state-of-the-art single dish telescope such as the IRAM 30m telescope. We searched for the best lines to constrain the visual extinction,AVtot, or the ultraviolet illumination field,G0. We ran this search for different gas regimes, namely translucent gas, filamentary gas, and dense cores. Results.The most informative lines change with the physical regime (e.g., cloud extinction). However, the determination of the optimal (combination of) line(s) to constrain a physical parameter such as the visual extinction depends not only on the radiative transfer of the lines and chemistry of the associated species, but also on the achieved mean signal-to-noise ratio. The short integration time of the CO isotopologueJ= 1 − 0 lines already yields much information on the total column density for a large range of (AVtot,G0) space. The best set of lines to constrain the visual extinction does not necessarily combine the most informative individual lines. Precise constraints on the radiation field are more difficult to achieve with molecular lines. They require spectral lines emitted at the cloud surface (e.g., [CII] and [CI] lines). Conclusions.This approach allows one to better explore the knowledge provided by ISM codes, and to guide future observation campaigns.more » « lessFree, publicly-accessible full text available November 1, 2025
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Abstract Dissociative recombination of N$$_2$$ H$$^+$$ is explored in a two-step theoretical study. In a first step, a diatomic (1D) rough model with a frozen NN bond and frozen angles is adopted, in the framework of the multichannel quantum defect theory (MQDT). The importance of the indirect mechanism and of the bending mode is revealed, in spite of the disagreement between our cross section and the experimental one. In the second step, we use our recently elaborated 3D approach based on the normal mode approximation combined with R-matrix theory and MQDT. This approach results in satisfactory agreement with storage-ring measurements, significantly better at very low energy than the former calculations.more » « less
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Context.One of the main problems in astrochemistry is determining the amount of sulfur in volatiles and refractories in the interstellar medium. The detection of the main sulfur reservoirs (icy H2S and atomic gas) has been challenging, and estimates are based on the reliability of models to account for the abundances of species containing less than 1% of the total sulfur. The high sensitivity of theJames WebbSpace Telescope provides an unprecedented opportunity to estimate the sulfur abundance through the observation of the [SI] 25.249 µm line. Aims.Our aim is to determine the amount of sulfur in the ionized and warm molecular phases toward the Orion Bar as a template to investigate sulfur depletion in the transition between the ionized gas and the molecular cloud in HII regions. Methods.We used the [S III] 18.7 µm, [S IV] 10.5 µm, and [S l] 25.249 µm lines to estimate the amount of sulfur in the ionized and molecular gas along the Orion Bar. For the theoretical part, we used an upgraded version of the Meudon photodissociation region (PDR) code to model the observations. New inelastic collision rates of neutral atomic sulfur with ortho-and para- molecular hydrogen were calculated to predict the line intensities. Results.The [S III] 18.7 µm and [S IV] 10.5 µm lines are detected over the imaged region with a shallow increase (by a factor of 4) toward the HII region. This suggests that their emissions are partially coming from the Orion Veil. We estimate a moderate sulfur depletion, by a factor of ~2, in the ionized gas. The corrugated interface between the molecular and atomic phases gives rise to several edge-on dissociation fronts we refer to as DF1, DF2, and DF3. The [S l] 25.249 µm line is only detected toward DF2 and DF3, the dissociation fronts located farthest from the HII region. This is the first ever detection of the [S l] 25.249 µm line in a PDR. The detailed modeling of DF3 using the Meudon PDR code shows that the emission of the [S l] 25.249 µm line is coming from warm (>40 K) molecular gas located atAV~1–5 mag from the ionization front. Moreover, the intensity of the [S l] 25.249 µm line is only accounted for if we assume the presence of undepleted sulfur. Conclusions.Our data show that sulfur remains undepleted along the ionic, atomic, and molecular gas in the Orion Bar. This is consistent with recent findings that suggest that sulfur depletion is low in massive star-forming regions because of the interaction of the UV photons coming from the newly formed stars with the interstellar matter.more » « less
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