Parsec-scale cosmic-ray ionisation rate in Orion

Context.Small amounts of atomic hydrogen, detected as absorption dips in the 21 cm line spectrum, are a well-known characteristic of dark clouds. The abundance of hydrogen atoms measured in the densest regions of molecular clouds can only be explained by the dissociation of H2by cosmic rays.Aims.We wish to assess the role of Galactic cosmic rays in the formation of atomic hydrogen, for which we use recent developments in the characterisation of the low-energy spectra of cosmic rays and advances in the modelling of their propagation in molecular clouds.Methods.We modelled the attenuation of the interstellar cosmic rays that enter a cloud and computed the dissociation rate of molecular hydrogen that is due to collisions with cosmic-ray protons and electrons as well as fast hydrogen atoms. We compared our results with the available observations.Results.The cosmic-ray dissociation rate is entirely determined by secondary electrons produced in primary ionisation collisions. These secondary particles constitute the only source of atomic hydrogen at column densities above ~1021cm−2. We also find that the dissociation rate decreases with column density, while the ratio between the dissociation and ionisation rates varies between about 0.6 and 0.7. From comparison with observations, we conclude that a relatively flat spectrum of interstellar cosmic-ray protons, such as suggested by the most recent Voyager 1 data, can only provide a lower bound for the observed atomic hydrogen fraction. An enhanced spectrum of low-energy protons is needed to explain most of the observations.Conclusions.Our findings show that a careful description of molecular hydrogen dissociation by cosmic rays can explain the abundance of atomic hydrogen in dark clouds. An accurate characterisation of this process at high densities is crucial for understanding the chemical evolution of star-forming regions.

We extend the analytic theory presented by Sternberg et al. and Bialy & Sternberg for the production of atomic hydrogen (H i) via far-ultraviolet (FUV) photodissociation at the boundaries of dense interstellar molecular (H2) clouds to also include the effects of penetrating (low-energy) cosmic rays (CRs) for the growth of the total H i column densities. We compute the steady-state abundances of the H i and H2 in one-dimensional gas slabs in which the FUV photodissociation rates are reduced by depth-dependent H2 self-shielding and dust absorption and the CR ionization rates are either constant or reduced by transport effects. The solutions for the H i and H2 density profiles and the integrated H i columns depend primarily on the ratios I UV/Rn and ζ/Rn, where I UV is the intensity of the photodissociating FUV field, ζ is the H2 CR ionization rate, n is the hydrogen gas density, and R is the dust surface H2 formation rate coefficient. We present computations for a wide range of FUV field strengths, CR ionization rates, and dust-to-gas ratios. We develop analytic expressions for the growth of the H i column densities. For Galactic giant molecular clouds (GMCs) with multiphased (warm/cold) H i envelopes, the interior CR zones will dominate the production of the H i only if s−1, where M GMC is the GMC mass, and including attenuation of the CR fluxes. For most Galactic GMCs and conditions, FUV photodissociation dominates over CR ionization for the production of the H i column densities. Furthermore, the CRs do not affect the H i-to-H2 transition points.

Cosmic rays (CRs) are the primary driver of ionization in star-forming molecular clouds (MCs). Despite their potential impacts on gas dynamics and chemistry, no simulations of star cluster formation following the creation of individual stars have included explicit cosmic-ray transport (CRT) to date. We conduct the first numerical simulations following the collapse of a 2000M ⊙ MC and the subsequent star formation including CRT using the STAR FORmation in Gaseous Environments framework implemented in the GIZMO code. We show that when CRT is streaming-dominated, the CR energy in the cloud is strongly attenuated due to energy losses from the streaming instability. Consequently, in a Milky Way–like environment the median CR ionization rate in the cloud is low (ζ ≲ 2 × 10−19 s−1) during the main star-forming epoch of the calculation and the impact of CRs on the star formation in the cloud is limited. However, in high-CR environments, the CR distribution in the cloud is elevated (ζ ≲ 6 × 10−18), and the relatively higher CR pressure outside the cloud causes slightly earlier cloud collapse and increases the star formation efficiency by 50% to ∼13%. The initial mass function is similar in all cases except with possible variations in a high-CR environment. Further studies are needed to explain the range of ionization rates observed in MCs and explore star formation in extreme CR environments.

Context. The abundance of deuterated molecules in a star-forming region is sensitive to the environment in which they are formed. Deuteration fractions, in other words the ratio of a species containing D to its hydrogenated counterpart, therefore provide a powerful tool for studying the physical and chemical evolution of a star-forming system. While local low-mass star-forming regions show very high deuteration ratios, much lower fractions are observed towards Orion and the Galactic centre. Astration of deuterium has been suggested as a possible cause for low deuteration in the Galactic centre.Aims. We derive methanol deuteration fractions at a number of locations towards the high-mass star-forming region NGC 6334I, located at a mean distance of 1.3 kpc, and discuss how these can shed light on the conditions prevailing during its formation.Methods. We use high sensitivity, high spatial and spectral resolution observations obtained with the Atacama Large Millimeter/ submillimeter Array to study transitions of the less abundant, optically thin, methanol-isotopologues:13CH3OH, CH318OH, CH2DOH and CH3OD, detected towards NGC 6334I. Assuming local thermodynamic equilibrium (LTE) and excitation temperatures of ~120–330 K, we derive column densities for each of the species and use these to infer CH2DOH/CH3OH and CH3OD/CH3OH fractions.Results. We derive column densities in a range of (0.8–8.3) × 1017cm−2for13CH3OH, (0.13–3.4) × 1017cm−2for CH318OH, (0.03–1.63) × 1017cm−2for CH2DOH and (0.15–5.5) × 1017cm−2for CH3OD in a ~1″ beam. Interestingly, the column densities of CH3OD are consistently higher than those of CH2DOH throughout the region by factors of 2–15. We calculate the CH2DOH to CH3OH and CH3OD to CH3OH ratios for each of the sampled locations in NGC 6334I. These values range from 0.03% to 0.34% for CH2DOH and from 0.27% to 1.07% for CH3OD if we use the13C isotope of methanol as a standard; using the18O-methanol as a standard, decreases the ratios by factors of between two and three.Conclusions. All regions studied in this work show CH2DOH/CH3OH as well as CH2DOH/CH3OD values that are considerably lower than those derived towards low-mass star-forming regions and slightly lower than those derived for the high-mass star-forming regions in Orion and the Galactic centre. The low ratios indicate a grain surface temperature during formation ~30 K, for which the efficiency of the formation of deuterated species is significantly reduced. Therefore, astration of deuterium in the Galactic centre cannot be the explanation for its low deuteration ratio but rather the high temperatures characterising the region.

Context. The Rosette molecular cloud complex is a well-known Galactic star-forming region with a morphology pointing towards triggered star formation. The distribution of its young stellar population and the gas properties point to the possibility that star formation is globally triggered in the region. Aims. We focus on the characterisation of the most massive pre- and protostellar cores distributed throughout the molecular cloud in order to understand the star formation processes in the region. Methods. We observed a sample of 33 dense cores, identified in Herschel continuum maps, with the Effelsberg 100-m telescope. Using NH3 (1,1) and (2,2) measurements, we characterise the dense core population, computing rotational and gas kinetic temperatures and NH3 column density with multiple methods. We also estimated the gas pressure ratio and virial parameters to examine the stability of the cores. Using results from Berschel data, we examined possible correlations between gas and dust parameters. Results. Ammonia emission is detected towards 31 out of the 33 selected targets. We estimate kinetic temperatures to be between 12 and 20 K, and column densities within the 1014−2 × 1015 cm−2 range in the selected targets. Our virial analysis suggests that most sources are likely to be gravitationally bound, while the line widths are dominated by non-thermal motions. Our results are compatible with large-scale dust temperature maps suggesting that the temperature decreases and column density increases with distance from NGC 2244 except for the densest protoclusters. We also identify a small spatial shift between the ammonia and dust peaks in the regions most exposed to irradiation from the nearby NGC 2244 stellar cluster. However, we find no trends in terms of core evolution with spatial location, in the prestellar to protostellar core abundance ratio, or the virial parameter. Conclusions. Star formation is more likely based on the primordial structure of the cloud in spite of the impact of irradiation from the nearby cluster, NGC 2244. The physical parameters from the NH3 measurements suggest gas properties in between those of low- and high-mass star-forming regions, suggesting that the Rosette molecular cloud could host ongoing intermediate-mass star formation, and is unlikely to form high-mass stars.

Stars form from molecular gas under complex conditions influenced by multiple competing physical mechanisms, such as gravity, turbulence, and magnetic fields. However, accurately identifying the fraction of gas actively involved in star formation remains challenging. Using dust continuum observations from the Herschel Space Observatory, we derived column density maps and their associated probability distribution functions (N-PDFs). Assuming that the power-law component in the N-PDFs corresponds to gravitationally bound (and thus star-forming) gas, we analyzed a diverse sample of molecular clouds spanning a wide range of mass and turbulence conditions. This sample included 21 molecular clouds from the solar neighborhood (d < 500 pc) and 16 high-mass star-forming molecular clouds. For these two groups, we employed the counts of young stellar objects (YSOs) and mid to far-infrared luminosities as proxies for star formation rates (SFRs), respectively. Both groups revealed a tight linear correlation between the mass of the gravitationally bound gas and the SFR, suggesting a universally constant star formation efficiency in the gravitationally bound gas phase. The star-forming gas mass derived from threshold column densities (Nthreshold) varies from cloud to cloud and is widely distributed over the range of ~1–17×1021 cm−2 based on N-PDF analysis. However, in solar neighborhood clouds it is in rough consistency with the traditional approach using AV≥ 8 mag. In contrast, in highly turbulent regions (e.g., the Galactic Central Molecular Zone) where the classical approach fails, the gravitationally bound gas mass and SFR still follow the same correlation as other high-mass star-forming regions in the Milky Way. Our findings also strongly support the interpretation that gas in the power-law component of the N-PDF is undergoing self-gravitational collapse to form stars.

A review is given of low-energy cosmic rays (1 MeV-10 GeV), which play an important role in the physics and chemistry of interstellar medium of our Galaxy. According to the generally accepted theory of star formation, cosmic rays penetrate into molecular clouds and ionize the dense gaseous medium of star formation centers besides due to a process of ambipolar diffusion they establish a star formation time scale of about 100-1000 thousand years. The source of cosmic rays in the Galaxy are supernovae remnants where diffusion acceleration at the shock front accelerates particles up to energies of 1015 eV. Being the main source of ionization in the inner regions of molecular clouds, cosmic rays play a fundamental role in the global chemistry of clouds, triggering the entire chain of ion-molecular reactions that make it possible to obtain basic molecules. The review also noted the importance of cosmic rays in atmospheric chemistry: playing a significant role in the formation of nitric oxide, especially with an increase in the flux, they cause a decrease in the concentration of ozone in the atmosphere with all climatic consequences.

In this work, we investigate how deuterium fractionation correlates with CO depletion factor in the Barnard 5 filament in the low-mass star formation region of the Perseus molecular cloud. Reactions of deuteration start in the gas phase, and CO concentration in the gas affects the rate of these reactions. The lines N2H+(1-0), N2D+(1-0), H13CO+(1-0), DCO+(2- 1), and C18O(2-1) were observed with the IRAM-30m telescope. The column densities were calculated from the observation maps. The maps of the deuterium fraction N2D+/N2H+ , DCO+/HCO+ , and CO depletion factor were plotted to analyse their distribution in the filament. Based on the distributions of the deuterium fraction and CO depletion factor, we conclude that the deuterium fraction increases with CO depletion in nitrogen-bearing species by more than a factor of 2. The deuterium fraction of DCO+/HCO+ increases by a factor of 2 along the direction from the protostar to the cold dense core.

Pillars and globules are present in many high-mass star-forming regions, such as the Eagle nebula (M16) and the Rosette molecular cloud, and understanding their origin will help characterize triggered star formation. The formation mechanisms of these structures are still being debated. Recent numerical simulations have shown how pillars can arise from the collapse of the shell in on itself and how globules can be formed from the interplay of the turbulent molecular cloud and the ionization from massive stars. The goal here is to test this scenario through recent observations of two massive star-forming regions, M16 and Rosette. The column density structure of the interface between molecular clouds and H ii regions was characterized using column density maps obtained from far-infrared imaging of the Herschel HOBYS key programme. Then, the DisPerSe algorithm was used on these maps to detect the compressed layers around the ionized gas and pillars in different evolutionary states. Finally, their velocity structure was investigated using CO data, and all observational signatures were tested against some distinct diagnostics established from simulations. The column density profiles have revealed the importance of compression at the edge of the ionized gas. The velocity properties of the structures, i.e. pillars and globules, are very close to what we predict from the numerical simulations. We have identified a good candidate of a nascent pillar in the Rosette molecular cloud that presents the velocity pattern of the shell collapsing on itself, induced by a high local curvature. Globules have a bulk velocity dispersion that indicates the importance of the initial turbulence in their formation, as proposed from numerical simulations. Altogether, this study re-enforces the picture of pillar formation by shell collapse and globule formation by the ionization of highly turbulent clouds.

Context. The cosmic-ray ionization rate (ζ2) is one of the key parameters in star formation, since it regulates the chemical and dynamical evolution of molecular clouds by ionizing molecules and determining the coupling between the magnetic field and gas. Aims. However, measurements of ζ2 in dense clouds (e.g., nH ≥ 104 cm−3) are difficult and sensitive to the model assumptions. The aim is to find a convenient analytic approach that can be used in high-mass star-forming regions (HMSFRs), especially for warm gas environments such as hot molecular cores (HMCs). Methods. We propose a new analytic approach to calculate ζ2 through HCO+, N2H+, and CO measurements. By comparing our method with various astrochemical models and with observations found in the literature, we identify the parameter space for which the analytic approach is applicable. Results. Our method gives a good approximation, to within 50%, of ζ2 in dense and warm gas (e.g., nH ≥ 104 cm−3, T = 50, 100 K) for AV ≥ 4 mag and t ≥ 2 × 104 yr at Solar metallicity. The analytic approach gives better results for higher densities. However, it starts to underestimate ζ2 at low metallicity (Z = 0.1 Z⊙) when the value is too high (ζ2 ≥ 3 × 10−15 s−1). By applying our method to the OMC-2 FIR4 envelope and the L1157-B1 shock region, we find ζ2 values of (1.0 ± 0.3) × 10−14 s−1 and (2.2 ± 0.4) × 10−16 s−1, consistent with those previously reported. Conclusions. We calculate ζ2 toward a total of 82 samples in HMSFRs, finding that the average value of ζ2 toward all HMC samples (ζ2 = (7.4±5.0)×10−16 s−1) is more than an order of magnitude higher than the theoretical prediction of cosmic-ray attenuation models, favoring the scenario that locally accelerated cosmic rays in embedded protostars should be responsible for the observed high ζ2.

For decades, the detection of phosphorus-bearing molecules in the interstellar medium was restricted to high-mass star-forming regions (e.g., SgrB2 and Orion KL) and the circumstellar envelopes of evolved stars. However, recent higher-sensitivity observations have revealed that molecules such as PN and PO are present not only toward cold massive cores and low-mass star-forming regions with PO/PN ratios ≥1 but also toward the giant molecular clouds in the Galactic center known to be exposed to highly energetic phenomena such as intense UV radiation fields, shock waves, and cosmic rays. In this paper, we carry out a comprehensive study of the chemistry of phosphorus-bearing molecules across different astrophysical environments that cover a range of physical conditions (cold molecular dark clouds, warm clouds, and hot cores/hot corinos) and are exposed to different physical processes and energetic phenomena (proto-stellar heating, shock waves, intense UV radiation, and cosmic rays). We show how the measured PO/PN ratio (either ≥1, as in, e.g., hot molecular cores, or ≤1, as in UV strongly illuminated environments) can provide constraints on the physical conditions and energetic processing of the source. We propose that the reaction P + OH → PO + H, not included in previous works, could be an efficient gas-phase PO formation route in shocks. Our modeling provides a template with which to study the detectability of P-bearing species not only in regions in our own Galaxy but also in extragalactic sources.

Context. Observations of the emission of the carbon cycle species (C, C+, CO) are commonly used to diagnose gas properties in the interstellar medium, but they are significantly sensitive to the cosmic-ray ionization rate. The carbon-cycle chemistry is known to be quite sensitive to the cosmic-ray ionization rate, ζ, controlled by the flux of low-energy cosmic rays which get attenuated through molecular clouds. However, astrochemical models commonly assume a constant cosmic-ray ionization rate in the clouds. Aims. We investigate the effect of cosmic-ray attenuation on the emission of carbon cycle species from molecular clouds, in particular the [CII] 158 μm, [CI] 609 μm, and CO (J = 1–0) 115.27 GHz lines. Methods. We used a post-processed chemical model of diffuse and dense simulated molecular clouds and quantified the variation in both column densities and velocity-integrated line emission of the carbon cycle with different cosmic-ray ionization rate models. Results. We find that the abundances and column densities of carbon cycle species are significantly impacted by the chosen cosmic-ray ionization rate model: no single constant ionization rate can reproduce the abundances modeled with an attenuated cosmic-ray model. Further, we show that constant ionization rate models fail to simultaneously reproduce the integrated emission of the lines we consider, and their deviations from a physically derived cosmic-ray attenuation model is too complex to be simply corrected. We demonstrate that the two clouds we modeled exhibit a similar average AV,eff – nH relationship, resulting in an average relation between the cosmic-ray ionization rate and density ζ(nH). Conclusions. We conclude by providing a number of implementation recommendations for cosmic rays in astrochemical models, but emphasize the necessity for column-dependent cosmic-ray ionization rate prescriptions.

The effects of cosmic ray (CR) diffusion and finite Larmor radius (FLR) corrections have been studied on the linear gravitational instability of thermally conducting plasmas typically in the H ii regions of molecular clouds. The hydrodynamic fluid–fluid approach is considered for interacting CRs with gravitating, magnetized, and thermally conducting gas in molecular clouds. The magnetohydrodynamic fluid model is formulated considering CR pressure gradients, CR diffusion, and radiative and FLR effects in terms of particle Larmor radius. The dispersion relation of the gravitational instability is analytically derived using the normal mode analysis, and the effects of CRs and FLR corrections have been discussed in longitudinal and transverse modes. It is observed that in the absence of CRs, the FLR effects (magnetic viscosity) reduce the growth rate for wavenumber smaller than a critical value, and above it gets increased. However, the growth rate is strongly suppressed in the presence of combined CRs and FLR effects. The individual behaviour of FLR effects is observed to destabilize the growth rate of the gravitational instability in the presence of CR effects. The CR pressure decreases the growth rates of the gravitational and thermal instabilities, whereas parallel CR diffusion enhances the growth rate of the gravitational instability. The Jeans length of the gravitating gas cloud gets increased due to an increase in the CR-to-gas pressure ratio. It is found that the gravitational collapse of the system is supported by high-energy (above knee) CR particles with the Larmor radii comparable to the cloud size. The present results have been applied to understand the role of CRs and FLR corrections on the gravitational collapse in the H ii regions of molecular clouds.

For many years feedback processes generated by OB-stars in molecular clouds, including expanding ionization fronts, stellar winds, or UV-radiation, have been proposed to trigger subsequent star formation. However, hydrodynamic models including radiation and gravity show that UV-illumination has little or no impact on the global dynamical evolution of the cloud. The Rosette molecular cloud, irradiated by the NGC2244 cluster, is a template region for triggered star-formation, and we investigated its spatial and density structure by applying a curvelet analysis, a filament-tracing algorithm (DisPerSE), and probability density functions (PDFs) on Herschel column density maps, obtained within the HOBYS key program. The analysis reveals not only the filamentary structure of the cloud but also that all known infrared clusters except one lie at junctions of filaments, as predicted by turbulence simulations. The PDFs of sub-regions in the cloud show systematic differences. The two UV-exposed regions have a double-peaked PDF we interprete as caused by shock compression. The deviations of the PDF from the log-normal shape typically associated with low- and high-mass star-forming regions at Av~3-4m and 8-10m, respectively, are found here within the very same cloud. This shows that there is no fundamental difference in the density structure of low- and high-mass star-forming regions. We conclude that star-formation in Rosette - and probably in high-mass star-forming clouds in general - is not globally triggered by the impact of UV-radiation. Moreover, star formation takes place in filaments that arose from the primordial turbulent structure built up during the formation of the cloud. Clusters form at filament mergers, but star formation can be locally induced in the direct interaction zone between an expanding HII--region and the molecular cloud.

Context. Low-energy cosmic rays (<1 TeV) play a fundamental role in the chemical and dynamical evolution of molecular clouds, as they control the ionisation, dissociation, and excitation of H2. Their characterisation is therefore important both for the interpretation of observations and for the development of theoretical models. However, the methods used so far for estimating the cosmic-ray ionisation rate in molecular clouds have several limitations due to uncertainties in the adopted chemical networks. Aims. We refine and extend a previously proposed method to estimate the cosmic-ray ionisation rate in molecular clouds by observing rovibrational transitions of H2 at near-infrared wavelengths, which are mainly excited by secondary cosmic-ray electrons. Methods. Combining models of interstellar cosmic-ray propagation and attenuation in molecular clouds with the rigorous calculation of the expected secondary electron spectrum and updated electron-H2 excitation cross sections, we derive the intensity of the four H2 rovibrational transitions observable in cold dense gas: (1−0)O(2), (1−0)Q(2), (1−0)S(0), and (1−0)O(4). Results. The proposed method allows the estimation of the cosmic-ray ionisation rate for a given observed line intensity and H2 column density. We are also able to deduce the shape of the low-energy cosmic-ray proton spectrum impinging upon the molecular cloud. In addition, we present a look-up plot and a web-based application that can be used to constrain the low-energy spectral slope of the interstellar cosmic-ray proton spectrum. We finally comment on the capability of the James Webb Space Telescope to detect these near-infrared H2 lines, which will make it possible to derive, for the first time, spatial variation in the cosmic-ray ionisation rate in dense gas. Besides the implications for the interpretation of the chemical-dynamic evolution of a molecular cloud, it will finally be possible to test competing models of cosmic-ray propagation and attenuation in the interstellar medium, as well as compare cosmic-ray spectra in different Galactic regions.