Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology

Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat $\Lambda$CDM cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an alternative and simple expression for the luminosity distance in a flat $\Lambda$CDM based on hypergeometric functions. Using a timing experiment we compare the computation time for the numerical evaluation of the various exact formulae, as well as for two approximate fitting formulae available in the literature. We find that our novel expression is the most efficient exact expression in the redshift range $z\gtrsim1$. Ideally, it can be combined with the expression based on Carlson's elliptic integrals in the range $z\lesssim1$ for high precision cosmology distance calculations over the entire redshift range. On the other hand, for practical work where relative errors of about 0.1% are acceptable, the analytical approximation proposed by Adachi & Kasai (2012) is a suitable alternative.Comment: 4 pages, 1 figure, accepted for publication in MNRA

SKIRT: hybrid parallelization of radiative transfer simulations

We describe the design, implementation and performance of the new hybrid parallelization scheme in our Monte Carlo radiative transfer code SKIRT, which has been used extensively for modeling the continuum radiation of dusty astrophysical systems including late-type galaxies and dusty tori. The hybrid scheme combines distributed memory parallelization, using the standard Message Passing Interface (MPI) to communicate between processes, and shared memory parallelization, providing multiple execution threads within each process to avoid duplication of data structures. The synchronization between multiple threads is accomplished through atomic operations without high-level locking (also called lock-free programming). This improves the scaling behavior of the code and substantially simplifies the implementation of the hybrid scheme. The result is an extremely flexible solution that adjusts to the number of available nodes, processors and memory, and consequently performs well on a wide variety of computing architectures.Comment: 21 pages, 20 figure

Far-ultraviolet Dust Extinction and Molecular Hydrogen in the Diffuse Milky Way Interstellar Medium

We aim to compare variations in the full-UV dust extinction curve (912-3000 Angstrom), with the HI/H$_2$/total H content along diffuse Milky Way sightlines, to investigate possible connections between ISM conditions and dust properties. We combine an existing sample of 75 UV extinction curves based on IUE and FUSE data, with atomic and molecular column densities measured through UV absorption. The H$_2$ column density data are based on existing Lyman-Werner absorption band models from earlier work on the extinction curves. Literature values for the HI column density were compiled, and improved for 23 stars by fitting a Ly$\alpha$ profile to archived spectra. We discover a strong correlation between the H$_2$ column and the far-UV extinction, and the underlying cause is a linear relationship between H$_2$ and the strength of the far-UV rise feature. This extinction does not scale with HI, and the total H column scales best with $A(V)$ instead. The carrier of the far-UV rise therefore coincides with molecular gas, and further connections are shown by comparing the UV extinction features to the molecular fraction. Variations in the gas-to-extinction ratio $N(\rm{H})/A(V)$ correlate with the UV-to-optical extinction ratio, and we speculate this could be due to coagulation or shattering effects. Based on the H$_2$ temperature, the strongest far-UV rise strengths are found to appear in colder and denser sightlines.Comment: 24 pages, 9 figures, accepted for publication in ApJ; fix missing text in generated pdf due to broken tex comman

PDRs4All VIII. Mid-infrared emission line inventory of the Orion Bar

Context. Mid-infrared emission features are important probes of the properties of ionized gas and hot or warm molecular gas, which are difficult to probe at other wavelengths. The Orion Bar photodissociation region (PDR) is a bright, nearby, and frequently studied target containing large amounts of gas under these conditions. Under the “PDRs4All” Early Release Science Program for JWST, a part of the Orion Bar was observed with MIRI integral field unit (IFU) spectroscopy, and these high-sensitivity IR spectroscopic images of very high angular resolution (0.2′′) provide a rich observational inventory of the mid-infrared (MIR) emission lines, while resolving the H II region, the ionization front, and multiple dissociation fronts. Aims. We list, identify, and measure the most prominent gas emission lines in the Orion Bar using the new MIRI IFU data. An initial analysis summarizes the physical conditions of the gas and demonstrates the potential of these new data and future IFU observations with JWST. Methods. The MIRI IFU mosaic spatially resolves the substructure of the PDR, its footprint cutting perpendicularly across the ionization front and three dissociation fronts. We performed an up-to-date data reduction, and extracted five spectra that represent the ionized, atomic, and molecular gas layers. We identified the observed lines through a comparison with theoretical line lists derived from atomic data and simulated PDR models. The identified species and transitions are summarized in the main table of this work, with measurements of the line intensities and central wavelengths. Results. We identified around 100 lines and report an additional 18 lines that remain unidentified. The majority consists of H I recombination lines arising from the ionized gas layer bordering the PDR. The H I line ratios are well matched by emissivity coefficients from H recombination theory, but deviate by up to 10% because of contamination by He I lines. We report the observed emission lines of various ionization stages of Ne, P, S, Cl, Ar, Fe, and Ni. We show how the Ne III/Ne II, S IV/S III, and Ar III/Ar II ratios trace the conditions in the ionized layer bordering the PDR, while Fe III/Fe II and Ni III/Ni II exhibit a different behavior, as there are significant contributions to Fe II and Ni II from the neutral PDR gas. We observe the pure-rotational H2 lines in the vibrational ground state from 0–0 S(1) to 0–0 S(8), and in the first vibrationally excited state from 1–1 S(5) to 1–1 S(9). We derive H2 excitation diagrams, and for the three observed dissociation fronts, the rotational excitation can be approximated with one thermal (∼700 K) component representative of an average gas temperature, and one nonthermal component (∼2700 K) probing the effect of UV pumping. We compare these results to an existing model of the Orion Bar PDR, and find that the predicted excitation matches the data qualitatively, while adjustments to the parameters of the PDR model are required to reproduce the intensity of the 0–0 S(6) to S(8) lines

PDRs4All II. JWST’s NIR and MIR imaging view of the Orion Nebula

Context. The James Webb Space Telescope (JWST) has captured the most detailed and sharpest infrared (IR) images ever taken of the inner region of the Orion Nebula, the nearest massive star formation region, and a prototypical highly irradiated dense photo-dissociation region (PDR). Aims. We investigate the fundamental interaction of far-ultraviolet (FUV) photons with molecular clouds. The transitions across the ionization front (IF), dissociation front (DF), and the molecular cloud are studied at high-angular resolution. These transitions are relevant to understanding the effects of radiative feedback from massive stars and the dominant physical and chemical processes that lead to the IR emission that JWST will detect in many Galactic and extragalactic environments. Methods. We utilized NIRCam and MIRI to obtain sub-arcsecond images over ∼150′′ and 42′′ in key gas phase lines (e.g., Pa α, Br α, [FeII] 1.64 µm, H2 1–0 S(1) 2.12 µm, 0–0 S(9) 4.69 µm), aromatic and aliphatic infrared bands (aromatic infrared bands at 3.3–3.4 µm, 7.7, and 11.3 µm), dust emission, and scattered light. Their emission are powerful tracers of the IF and DF, FUV radiation field and density distribution. Using NIRSpec observations the fractional contributions of lines, AIBs, and continuum emission to our NIRCam images were estimated. A very good agreement is found for the distribution and intensity of lines and AIBs between the NIRCam and NIRSpec observations. Results. Due to the proximity of the Orion Nebula and the unprecedented angular resolution of JWST, these data reveal that the molecular cloud borders are hyper structured at small angular scales of ∼0.1–1′′ (∼0.0002–0.002 pc or ∼40–400 au at 414 pc). A diverse set of features are observed such as ridges, waves, globules and photoevaporated protoplanetary disks. At the PDR atomic to molecular transition, several bright features are detected that are associated with the highly irradiated surroundings of the dense molecular condensations and embedded young star. Toward the Orion Bar PDR, a highly sculpted interface is detected with sharp edges and density increases near the IF and DF. This was predicted by previous modeling studies, but the fronts were unresolved in most tracers. The spatial distribution of the AIBs reveals that the PDR edge is steep and is followed by an extensive warm atomic layer up to the DF with multiple ridges. A complex, structured, and folded H0/H2 DF surface was traced by the H2 lines. This dataset was used to revisit the commonly adopted 2D PDR structure of the Orion Bar as our observations show that a 3D “terraced” geometry is required to explain the JWST observations. JWST provides us with a complete view of the PDR, all the way from the PDR edge to the substructured dense region, and this allowed us to determine, in detail, where the emission of the atomic and molecular lines, aromatic bands, and dust originate. Conclusions. This study offers an unprecedented dataset to benchmark and transform PDR physico-chemical and dynamical models for the JWST era. A fundamental step forward in our understanding of the interaction of FUV photons with molecular clouds and the role of FUV irradiation along the star formation sequence is provided

PDRs4All: III. JWST\u27s NIR spectroscopic view of the Orion Bar

Context. JWST has taken the sharpest and most sensitive infrared (IR) spectral imaging observations ever of the Orion Bar photodis-sociation region (PDR), which is part of the nearest massive star-forming region the Orion Nebula, and often considered to be the \u27prototypical\u27strongly illuminated PDR. Aims. We investigate the impact of radiative feedback from massive stars on their natal cloud and focus on the transition from the H II region to the atomic PDR -crossing the ionisation front (IF) -, and the subsequent transition to the molecular PDR -crossing the dissociation front (DF). Given the prevalence of PDRs in the interstellar medium and their dominant contribution to IR radiation, understanding the response of the PDR gas to far-ultraviolet (FUV) photons and the associated physical and chemical processes is fundamental to our understanding of star and planet formation and for the interpretation of any unresolved PDR as seen by JWST. Methods. We used high-resolution near-IR integral field spectroscopic data from NIRSpec on JWST to observe the Orion Bar PDR as part of the PDRs4All JWST Early Release Science programme. We constructed a 3″ × 25″ spatio-spectral mosaic covering 0.97-5.27 μm at a spectral resolution R of ~2700 and an angular resolution of 0.075″-0.173″. To study the properties of key regions captured in this mosaic, we extracted five template spectra in apertures centred on the three H2 dissociation fronts, the atomic PDR, and the H II region. This wealth of detailed spatial-spectral information was analysed in terms of variations in the physical conditions-incident UV field, density, and temperature -of the PDR gas. Results. The NIRSpec data reveal a forest of lines including, but not limited to, He I, H I, and C I recombination lines; ionic lines (e.g. Fe III and Fe II); O I and N I fluorescence lines; aromatic infrared bands (AIBs, including aromatic CH, aliphatic CH, and their CD counterparts); pure rotational and ro-vibrational lines from H2; and ro-vibrational lines from HD, CO, and CH+, with most of them having been detected for the first time towards a PDR. Their spatial distribution resolves the H and He ionisation structure in the Huygens region, gives insight into the geometry of the Bar, and confirms the large-scale stratification of PDRs. In addition, we observed numerous smaller-scale structures whose typical size decreases with distance from θ1 Ori C and IR lines from C I, if solely arising from radiative recombination and cascade, reveal very high gas temperatures (a few 1000 K) consistent with the hot irradiated surface of small-scale dense clumps inside the PDR. The morphology of the Bar, in particular that of the H2 lines, reveals multiple prominent filaments that exhibit different characteristics. This leaves the impression of a \u27terraced\u27transition from the predominantly atomic surface region to the CO-rich molecular zone deeper in. We attribute the different characteristics of the H2 filaments to their varying depth into the PDR and, in some cases, not reaching the C+/C/CO transition. These observations thus reveal what local conditions are required to drive the physical and chemical processes needed to explain the different characteristics of the DFs and the photochemical evolution of the AIB carriers. Conclusions. This study showcases the discovery space created by JWST to further our understanding of the impact radiation from young stars has on their natal molecular cloud and proto-planetary disk, which touches on star and planet formation as well as galaxy evolution

PDRs4All: IV. An embarrassment of riches: Aromatic infrared bands in the Orion Bar

Context. Mid-infrared observations of photodissociation regions (PDRs) are dominated by strong emission features called aromatic infrared bands (AIBs). The most prominent AIBs are found at 3.3, 6.2, 7.7, 8.6, and 11.2 µm. The most sensitive, highest-resolution infrared spectral imaging data ever taken of the prototypical PDR, the Orion Bar, have been captured by JWST. These high-quality data allow for an unprecedentedly detailed view of AIBs. Aims. We provide an inventory of the AIBs found in the Orion Bar, along with mid-IR template spectra from five distinct regions in the Bar: the molecular PDR (i.e. the three H2 dissociation fronts), the atomic PDR, and the H II region. Methods. We used JWST NIRSpec IFU and MIRI MRS observations of the Orion Bar from the JWST Early Release Science Program, PDRs4All (ID: 1288). We extracted five template spectra to represent the morphology and environment of the Orion Bar PDR. We investigated and characterised the AIBs in these template spectra. We describe the variations among them here. Results. The superb sensitivity and the spectral and spatial resolution of these JWST observations reveal many details of the AIB emission and enable an improved characterization of their detailed profile shapes and sub-components. The Orion Bar spectra are dominated by the well-known AIBs at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 µm with well-defined profiles. In addition, the spectra display a wealth of weaker features and sub-components. The widths of many AIBs show clear and systematic variations, being narrowest in the atomic PDR template, but showing a clear broadening in the H II region template while the broadest bands are found in the three dissociation front templates. In addition, the relative strengths of AIB (sub-)components vary among the template spectra as well. All AIB profiles are characteristic of class A sources as designated by Peeters (2022, A&A, 390, 1089), except for the 11.2 µm AIB profile deep in the molecular zone, which belongs to class B11.2. Furthermore, the observations show that the sub-components that contribute to the 5.75, 7.7, and 11.2 µm AIBs become much weaker in the PDR surface layers. We attribute this to the presence of small, more labile carriers in the deeper PDR layers that are photolysed away in the harsh radiation field near the surface. The 3.3/11.2 AIB intensity ratio decreases by about 40% between the dissociation fronts and the H II region, indicating a shift in the polycyclic aromatic hydrocarbon (PAH) size distribution to larger PAHs in the PDR surface layers, also likely due to the effects of photochemistry. The observed broadening of the bands in the molecular PDR is consistent with an enhanced importance of smaller PAHs since smaller PAHs attain a higher internal excitation energy at a fixed photon energy. Conclusions. Spectral-imaging observations of the Orion Bar using JWST yield key insights into the photochemical evolution of PAHs, such as the evolution responsible for the shift of 11.2 µm AIB emission from class B11.2 in the molecular PDR to class A11.2 in the PDR surface layers. This photochemical evolution is driven by the increased importance of FUV processing in the PDR surface layers, resulting in a “weeding out” of the weakest links of the PAH family in these layers. For now, these JWST observations are consistent with a model in which the underlying PAH family is composed of a few species: the so-called ‘grandPAHs’

PDRs4All IX. Sulfur elemental abundance in the Orion Bar

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 H$_2$S 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 the James Webb Space Telescope provides an unprecedented opportunity to estimate the sulfur abundance through the observation of the [S I] 25.249 $\mu$m line. We used the [S III] 18.7 $\mu$m, [S IV] 10.5 $\mu$m, and [S l] 25.249 $\mu$m 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. The [S III] 18.7 $\mu$m and [S IV] 10.5 $\mu$m lines are detected over the imaged region with a shallow increase (by a factor of 4) toward the HII region. We estimate a moderate sulfur depletion, by a factor of $\sim$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 $\mu$m line is only detected toward DF2 and DF3, the dissociation fronts located farthest from the HII region. The detailed modeling of DF3 using the Meudon PDR code shows that the emission of the [S l] 25.249 $\mu$m line is coming from warm ($>$ 40 K) molecular gas located at A$_{\rm V}$ $\sim$ 1$-$5 mag from the ionization front. Moreover, the intensity of the [S l] 25.249 $\mu$m line is only accounted for if we assume the presence of undepleted sulfur.Comment: 16 pages, 6 figures. Accepted for publication in Astronomy and Astrophysic

A far-ultraviolet-driven photoevaporation flow observed in a protoplanetary disk

Most low-mass stars form in stellar clusters that also contain massive stars, which are sources of far-ultraviolet (FUV) radiation. Theoretical models predict that this FUV radiation produces photo-dissociation regions (PDRs) on the surfaces of protoplanetary disks around low-mass stars, impacting planet formation within the disks. We report JWST and Atacama Large Millimetere Array observations of a FUV-irradiated protoplanetary disk in the Orion Nebula. Emission lines are detected from the PDR; modelling their kinematics and excitation allows us to constrain the physical conditions within the gas. We quantify the mass-loss rate induced by the FUV irradiation, finding it is sufficient to remove gas from the disk in less than a million years. This is rapid enough to affect giant planet formation in the disk