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We study the 3.4 − 4.4 μm fundamental rovibrational band of H₃⁺, a key tracer of the ionization of the molecular interstellar medium (ISM), in a sample of 12 local (d < 400 Mpc) (ultra)luminous infrared galaxies ((U)LIRGs) observed with JWST/NIRSpec. TheP,Q, andRbranches of the band are detected in 13 out of 20 analyzed regions within these (U)LIRGs, which increases the number of extragalactic H₃⁺detections by a factor of 6. For the first time in the ISM, the H₃⁺band is observed in emission; we detect this emission in three regions. In the remaining ten regions, the band is seen in absorption. The absorptions are produced toward the 3.4 − 4.4 μm hot dust continuum rather than toward the stellar continuum, indicating that they likely originate in clouds associated with the dust continuum source. The H₃⁺band is undetected in Seyfert-like (U)LIRGs where the mildly obscured X-ray radiation from the active galactic nuclei might limit the abundance of this molecule. For the detections, the H₃⁺abundances,N(H₃⁺)/N_H = (0.5 − 5.5)×10⁻⁷, imply relatively high ionization rates,ζ_H2, of between 3 × 10⁻¹⁶and > 4 × 10⁻¹⁵s⁻¹, which are likely associated with high-energy cosmic rays. In half of the targets, the absorptions are blueshifted by 50–180 km s⁻¹, which is lower than the molecular outflow velocities measured using other tracers such as OH 119 μm or rotational CO lines. This suggests that H₃⁺traces gas close to the outflow-launching sites before it has been fully accelerated. We used nonlocal thermodynamic equilibrium models to investigate the physical conditions of these clouds. In seven out of ten objects, the H₃⁺excitation is consistent with inelastic collisions with H₂in warm translucent molecular clouds (T_kin ∼ 250–500 K andn(H₂) ∼10^2 − 3cm⁻³). In three objects, dominant infrared pumping excitation is required to explain the absorptions from the (3,0) and (2,1) levels of H₃⁺detected for the first time in the ISM. 

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 (T_kin), the volume density (n_H2), 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 inferredT_kinof the envelope varies from 25 to 40 K, that of the inner layer drops to ~15 K in the western dense core. The estimatedn_H2in 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. 

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,A_V^tot, 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 (A_V^tot,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. 

Context.The methyl cation (CH₃⁺) has recently been discovered in the interstellar medium through the detection of 7 μm (1400 cm⁻¹) features toward the d203-506 protoplanetary disk by the JWST. Line-by-line spectroscopic assignments of these features, however, were unsuccessful due to complex intramolecular perturbations preventing a determination of the excitation and abundance of the species in that source. Aims.Comprehensive rovibrational assignments guided by theoretical and experimental laboratory techniques provide insight into the excitation mechanisms and chemistry of CH₃⁺in d203-506. Methods.The rovibrational structure of CH₃⁺was studied theoretically by a combination of coupled-cluster electronic structure theory and (quasi-)variational nuclear motion calculations. Two experimental techniques were used to confirm the rovibrational structure of CH₃⁺:(1) infrared leak-out spectroscopy of the methyl cation, and (2) rotationally resolved photoelectron spectroscopy of the methyl radical (CH₃). In (1), CH₃⁺ions, produced by the electron impact dissociative ionization of methane, were injected into a 22-pole ion trap where they were probed by the pulses of infrared radiation from the FELIX free electron laser. In (2), neutral CH₃, produced by CH₃NO₂pyrolysis in a molecular beam, was probed by pulsed-field ionization zero-kinetic-energy photoelectron spectroscopy. Results.The quantum chemical calculations performed in this study have enabled a comprehensive spectroscopic assignment of thev₂⁺andv₄⁺bands of CH₃⁺detected by the JWST. The resulting spectroscopic constants and derived EinsteinAcoefficients fully reproduce both the infrared and photoelectron spectra and permit the rotational temperature of CH₃⁺(T= 660 ± 80 K) in d203-506 to be derived. A beam-averaged column density of CH₃⁺in this protoplanetary disk is also estimated.