Cosmic Ray Ionization Research Articles

Exploring the Possibility of Identifying Hydride and Hydroxyl Cations of Noble Gas Species in the Crab Nebula Filament

Abstract The first identification of the argonium ion ( ) toward the Crab Nebula supernova remnant was proclaimed by Herschel in the submillimeter and far-infrared domains. Very recently, the discovery of the hydro-helium cation ( ) in the planetary nebula (NGC 7027) by SOFIA has been reported. The elemental abundance of neon is much higher than that of argon. However, the presence of neonium ions ( ) is yet to be confirmed in space. Though the hydroxyl radicals (−OH) are very abundant in both neutral and cationic forms, hydroxyl cations of such noble gases (i.e., ArOH+, NeOH+, and HeOH+) are yet to be identified in space. Here, we employ a spectral synthesis code to examine the chemical evolution of the hydride and hydroxyl cations of the various isotopes of Ar, Ne, and He in the Crab Nebula filament and calculate their line emissivity and intrinsic line surface brightness. We successfully explain the observed surface brightness of two transitions of ArH+ (617 and 1234 GHz), one transition of OH+ (971 GHz), and one transition of H2 (2.12 μm). We also explain the observed surface brightness ratios between various molecular and atomic transitions. We find that our model reproduces the overall observed features when a hydrogen number density of ∼(104–106) cm−3 and a cosmic-ray ionization rate per H2 of ∼(10−11–10−10) s−1 are chosen. We discuss the possibility of detecting some hydride and hydroxyl cations in the Crab and diffuse cloud environment. Some transitions of these molecules are highlighted for future astronomical detection.

Rapid elimination of small dust grains in molecular clouds

We argue that impact velocities between dust grains with sizes of less than ∼0.1 μm in molecular cloud cores are dominated by drift arising from ambipolar diffusion. This effect is due to the size dependence of the dust coupling to the magnetic field and the neutral gas. Assuming perfect sticking in collisions up to ≈50 m s−1, we show that this effect causes rapid depletion of small grains, consistent with starlight extinction and IR and microwave emission measurements, both in the core center (n ∼ 106 cm−3) and envelope (n ∼ 104 cm−3). The upper end of the size distribution does not change significantly if only velocities arising from this effect are considered. We consider the impact of an evolved grain-size distribution on the gas temperature, and argue that if the depletion of small dust grains occurs as expected from our model, then the cosmic ray ionization rate must be well below 10−16 s−1 at a number density of 105 cm−3.

Carbon isotopic fractionation in molecular clouds

Context. Carbon fractionation has been studied from a theoretical point of view with different models of time-dependent chemistry, including both isotope-selective photodissociation and low-temperature isotopic exchange reactions. Aims. Recent chemical models predict that isotopic exchange reactions may lead to a depletion of 13C in nitrile-bearing species, with 12C/13C ratios two times higher than the elemental abundance ratio of 68 in the local interstellar medium. Since the carbon isotopic ratio is commonly used to evaluate the 14N/15N ratios with the double-isotope method, it is important to study carbon fractionation in detail to avoid incorrect assumptions. Methods. In this work, we implemented a gas-grain chemical model with new isotopic exchange reactions and investigated their introduction in the context of dense and cold molecular gas. In particular, we investigated the 12C/13C ratios of HNC, HCN, and CN using a grid of models, with temperatures and densities ranging from 10 to 50 K and 2 × 103 to 2 × 107 cm−3, respectively. Results. We suggest a possible 13C exchange through the 13C + C3 → 12C +13CC2 reaction, which does not result in dilution, but rather in 13C enhancement, for molecules that are formed starting from atomic carbon. This effect is efficient in a range of time between the formation of CO and its freeze-out on grains. Furthermore, the parameter-space exploration shows, on average, that the 12C/13C ratios of nitriles are predicted to be a factor 0.8–1.9 different from the local 12C/13C of 68 for high-mass star-forming regions. This result also affects the 14N/15N ratio: a value of 330 obtained with the double-isotope method is predicted to vary in the range 260–630, up to 1150, depending on the physical conditions. Finally, we studied the 12C/13C ratios of nitriles by varying the cosmic-ray ionisation rate, ζ: the 12C/13C ratios increase with ζ because of secondary photons and cosmic-ray reactions.

CO Depletion in Protoplanetary Disks: A Unified Picture Combining Physical Sequestration and Chemical Processing

Abstract The gas-phase CO abundance (relative to hydrogen) in protoplanetary disks decreases by up to two orders of magnitude from its interstellar medium value of ∼10−4, even after accounting for freeze-out and photodissociation. Previous studies have shown that while local chemical processing of CO and the sequestration of CO ice on solids in the midplane can both contribute, neither of these processes appears capable of consistently reaching the observed depletion factors on the relevant timescale of 1–3 Myr. In this study, we model these processes simultaneously by including a compact chemical network (centered on carbon and oxygen) to 2D (r + z) simulations of the outer (r > 20 au) disk regions that include turbulent diffusion, pebble formation, and pebble dynamics. In general, we find that the CO/H2 abundance is a complex function of time and location. Focusing on CO in the warm molecular layer, we find that only the most complete model (with chemistry and pebble evolution included) can reach depletion factors consistent with observations. In the absence of pressure traps, highly efficient planetesimal formation, or high cosmic-ray ionization rates, this model also predicts a resurgence of CO vapor interior to the CO ice-line. We show the impact of physical and chemical processes on the elemental (C/O) and (C/H) ratios (in the gas and ice phases), discuss the use of CO as a disk mass tracer, and, finally, connect our predicted pebble ice compositions to those of pristine planetesimals as found in the Cold Classical Kuiper Belt and debris disks.

Possible Formation and Destruction of the OD+ Ions in the Interstellar Medium.

The OH+ ion is an important constituent of the interstellar medium (ISM). It can be used as a probe of cosmic ray and X-ray ionization rates in molecular clouds as well as a tracer of oxygen chemistry. The deuterated variant of OH+, the OD+ ion, may also be present in the ISM despite the fact that it has not been detected yet. In this paper, we aim at providing quantitative insight into the OD+ chemistry and at accurately studying the possible formation and destruction processes of OD+ in the ISM. We study the formation and destruction of OD+ through the O+ + HD → OD+ + H and OH+ + D ↔ OD+ + H reactions that can occur in diffuse ISM. Reactive rate constants have been obtained from exact state-to-state quantum wave packet calculations for temperatures ranging from 10 to 1000 K. The new theoretical data are validated through a detailed comparison with available experimental data. The formation of OD+ is found to be less efficient than that of OH+. As a first application, the OD+/OH+ abundance ratio in ISM has been evaluated from a simple astrochemical model, and we found that this ratio can be larger than D/H abundance ratio only at low temperatures. These calculations may help in an astrochemical search of OD+ in cold ISM.

Ionization: a possible explanation for the difference of mean disk sizes in star-forming regions

Context. Surveys of protoplanetary disks in star-forming regions of similar age revealed significant variations in average disk mass in some regions. For instance, disks in the Orion Nebular Cluster (ONC) and Corona Australis (CrA) are on average smaller than disks observed in Lupus, Taurus, Chamaeleon I, or Ophiuchus. Aims. In contrast to previous models that studied the truncation of disks at a late stage of their evolution, we investigate whether disks may already be born with systematically smaller disk sizes in more massive star-forming regions as a consequence of higher ionization rates. Methods. Assuming various cosmic-ray ionization rates, we computed the resistivities for ambipolar diffusion and Ohmic dissipation with a chemical network, and performed 2D nonideal magnetohydrodynamical protostellar collapse simulations. Results. A higher ionization rate leads to stronger magnetic braking, and hence to the formation of smaller disks. Accounting for recent findings that protostars act as forges of cosmic rays and considering only mild attenuation during the collapse phase, we show that a high average cosmic-ray ionization rate in star-forming regions such as the ONC or CrA can explain the detection of smaller disks in these regions. Conclusions. Our results show that on average, a higher ionization rate leads to the formation of smaller disks. Smaller disks in regions of similar age can therefore be the consequence of different levels of ionization, and may not exclusively be caused by disk truncation through external photoevaporation. We strongly encourage observations that allow measuring the cosmic-ray ionization degrees in different star-forming regions to test our hypothesis.

Cosmic Ray Dissociation of Molecular Hydrogen and Dense Cloud Chemistry

Abstract Dissociation of molecular hydrogen by secondary electrons produced by cosmic ray or X-ray ionization plays a crucial role in the chemistry of the densest part of molecular clouds. Here we study the effect of the mean kinetic energy of secondary electrons on this process. We compare predictions using a range of secondary electron energies and predictions of the cross sections with the values in the UMIST database. We find that the predicted column densities change by nearly one dex.

On the Effects of UV Photons/X-Rays on the Chemistry of the Sgr B2 Cloud

Abstract The lines of HOC+, HCO, and CO+ are considered good tracers of photon-dominated regions (PDRs) and X-ray-dominated regions. We study these tracers toward regions of the Sgr B2 cloud selected to be affected by different heating mechanisms. We find the lowest values of the column density ratios of HCO+ versus HOC+, HCO, and CO+ in dense H ii gas, where UV photons dominate the heating and chemistry of the gas. The HOC+, HCO, and CO+ abundances and the above ratios are compared with those of chemical modeling, finding that high-temperature chemistry, a cosmic-ray ionization rate of 10−16 s−1, and timescales >105.0 yr explain well the HOC+ abundances in quiescent Sgr B2 regions, while shocks are also needed to explain the highest HCO abundances derived for these regions. The CO+ is mainly formed in PDRs, since the highest CO+ abundances of ∼(6–10) × 10−10 are found in H ii regions with electron densities >540 cm−3 and CO+ emission is undetected in quiescent gas. Among the ratios, the HCO+/HCO ratio is sensitive to the electron density, as it shows different values in dense and diffuse H ii regions. We compare SiO J = 2–1 emission maps of Sgr B2 with X-ray maps from 2004 and 2012. One known spot shown on the 2012 X-ray map is likely associated with molecular gas at velocities of 15–25 km s−1. We also derive the X-ray ionization rate of ∼10−19 s−1 for Sgr B2 regions pervaded by X-rays in 2004, which is quite low to affect the chemistry of the molecular gas.

Exploring molecular complexity with ALMA (EMoCA): complex isocyanides in Sgr B2(N)

Context.The Exploring Molecule Complexity with ALMA (EMoCA) survey is an imaging spectral line survey using the Atacama Large Millimeter/submillimeter Array (ALMA) to study the hot-core complex Sagittarius B2(N). Recently, EMoCA revealed the presence of three new hot cores in this complex (N3-N5), in addition to providing detailed spectral data on the previously known hot cores in the complex (N1 and N2). The present study focuses on N2, which is a rich and interesting source for the study of complex molecules whose narrow line widths ameliorate the line confusion problem.Aims.We investigate the column densities and excitation temperatures of cyanide and isocyanide species in Sgr B2(N2). We then use state-of-the-art chemical models to interpret these observed quantities. We also investigate the effect of varying the cosmic-ray ionization rate (ζ) on the chemistry of these molecules.Methods.We used the EMoCA survey data to search for isocyanides in Sgr B2(N2) and their corresponding cyanide analogs. We then used the coupled three-phase chemical kinetics code MAGICKAL to simulate their chemistry. Several new species, and over 100 new reactions have been added to the network. In addition, a new single-stage simultaneous collapse/warm-up model has been implemented, thus eliminating the need for the previous two-stage models. A variable, visual extinction-dependentζwas also incorporated into the model and tested.Results.We report the tentative detection of CH3NC and HCCNC in Sgr B2(N2), which represents the first detection of both species in a hot core of Sgr B2. In addition, we calculate new upper limits for C2H5NC, C2H3NC, HNC3, and HC3NH+. Our updated chemical models can reproduce most observed NC:CN ratios reasonably well depending on the physical parameters chosen. The model that performs best has an extinction-dependent cosmic-ray ionization rate that varies from ~2 × 10−15s−1at the edge of the cloud to ~1 × 10−16s−1in the center. Models with higher extinction-dependentζthan this model generally do not agree as well, nor do models with a constantζgreater than the canonical value of 1.3 × 10−17s−1throughout the source. Radiative transfer models are run using results of the best-fit chemical model. Column densities produced by the radiative transfer models are significantly lower than those determined observationally. Inaccuracy in the observationally determined density and temperature profiles is a possible explanation. Excitation temperatures are well reproduced for the true “hot core” molecules, but are more variable for other molecules such as HC3N, for which fewer lines exist in ALMA Band 3.Conclusions.The updated chemical models do a very good job of reproducing the observed abundances ratio of CH3NC:CH3CN towards Sgr B2(N2), while being consistent with upper limits for other isocyanide/cyanide pairs. HCCNC:HC3N is poorly reproduced, however. Our results highlight the need for models withAV-depdendentζ. However, there is still much to be understood about the chemistry of these species, as evidenced by the systematic overproduction of HCCNC. Further study is also needed to understand the complex effect of varyingζon the chemistry of these species. The new single-stage chemical model should be a powerful tool in analyzing hot-core sources in the future.

A new proxy to estimate the cosmic ray ionization rate in dense cores

ABSTRACT Cosmic rays are a global source of ionization, and the ionization fraction represents a fundamental parameter in the interstellar medium. Ions couple to magnetic fields, and affect the chemistry and the dynamics of star-forming regions as well as planetary atmospheres. However, the cosmic ray ionization rate represents one of the bottlenecks for astrochemical models, and its determination is one of the most puzzling problems in astrophysics. While for diffuse clouds reasonable values have been provided from ${\mathrm{ H}_3}^+$ observations, for dense clouds, due to the lack of rotational transitions, this is not possible, and estimates are strongly biased by the employed model. We present here an analytical expression, obtained from first principles, to estimate the cosmic ray ionization rate from observational quantities. The theoretical predictions are validated with high-resolution 3D numerical simulations and applied to the well-known core L1544; we obtained an estimate of ζ2 ∼ 2–3 × 10−17 s−1. Our results and the analytical formulae provided represent the first model-independent robust tool to probe the cosmic ray ionization rate in the densest part of star-forming regions (on spatial scales of R ≤ 0.05 pc). An error analysis is presented to give statistical relevance to our study.

Cold clouds as cosmic-ray detectors

Low energy cosmic-rays (CRs) are responsible for gas heating and ionization of interstellar clouds, which in turn introduces coupling to Galactic magnetic fields. So far the CR ionization rate (CRIR) has been estimated using indirect methods, such as its effect on the abundances of various rare molecular species. Here we show that the CRIR may be constrained from line emission of H2 rovibrational transitions, excited by CRs. We derive the required conditions for CRs to dominate line excitation, and show that CR-excited lines may be detected with the Very Large Telescope (VLT) over 8 hours integration. Our method, if successfully applied to a variety of clouds at different Galactic locations, will provide improved constraints on the spectrum of low energy CRs and their origins.

The CO(3–2)/CO(1–0) Luminosity Line Ratio in Nearby Star-forming Galaxies and Active Galactic Nuclei from xCOLD GASS, BASS, and SLUGS

Abstract We study the luminosity line ratio in a sample of nearby (z < 0.05) galaxies: 25 star-forming galaxies (SFGs) from the xCOLD GASS survey, 36 hard X-ray-selected active galactic nucleus (AGN) host galaxies from the BAT AGN Spectroscopic Survey, and 37 infrared-luminous galaxies from the SCUBA Local Universe Galaxy Survey. We find a trend for r 31 to increase with star formation efficiency (SFE). We model r 31 using the UCL-PDR code and find that the gas density is the main parameter responsible for the variation of r 31, while the interstellar radiation field and cosmic-ray ionization rate play only a minor role. We interpret these results to indicate a relation between SFE and gas density. We do not find a difference in the r 31 value of SFGs and AGN host galaxies, when the galaxies are matched in SSFR (〈r 31〉 = 0.52 ± 0.04 for SFGs and 〈r 31〉 = 0.53 ± 0.06 for AGN hosts). According to the results of the UCL-PDR models, the X-rays can contribute to the enhancement of the CO line ratio, but only for strong X-ray fluxes and for high gas density (n H > 104 cm−3). We find a mild tightening of the Kennicutt–Schmidt relation when we use the molecular gas mass surface density traced by CO(3–2) (Pearson correlation coefficient R = 0.83), instead of the molecular gas mass surface density traced by CO(1–0) (R = 0.78), but the increase in correlation is not statistically significant (p-value = 0.06). This suggests that the CO(3–2) line can be reliably used to study the relation between SFR and molecular gas for normal SFGs at high redshift and to compare it with studies of low-redshift galaxies, as is common practice.

Hall effect in protostellar disc formation and evolution

ABSTRACT The Hall effect is recently shown to be efficient in magnetized dense molecular cores and could lead to a bimodal formation of rotationally supported discs (RSDs) in the first core phase. However, how such Hall dominated systems evolve in the protostellar accretion phase remains unclear. We carry out 2D axisymmetric simulations including Hall effect and ohmic dissipation, with realistic magnetic diffusivities computed from our equilibrium chemical network. We find that Hall effect only becomes efficient when the large population of very small grains (VSGs: ≲100 Å) is removed from the standard Mathis–Rumpl–Nordsieck size distribution. With such an enhanced Hall effect, however, the bimodality of disc formation does not continue into the main accretion phase. The outer part of the initial ∼40 au disc formed in the anti-aligned configuration ($\boldsymbol {\Omega \cdot B}\lt 0$) flattens into a thin rotationally supported Hall current sheet as Hall effect moves the poloidal magnetic field radially inward relative to matter, leaving only the inner ≲10–20 au RSD. In the aligned configuration ($\boldsymbol {\Omega \cdot B}\gt 0$), disc formation is suppressed initially but a counter-rotating disc forms subsequently due to efficient azimuthal Hall drift. The counter-rotating disc first grows to ∼30 au as Hall effect moves the magnetic field radially outward, but only the inner ≲10 au RSD is long lived like in the anti-aligned case. Besides removing VSGs, cosmic ray ionization rate should be below a few 10−16 s−1 for Hall effect to be efficient in disc formation. We conclude that Hall effect produces small ≲10–20 au discs regardless of the polarity of the magnetic field, and that radially outward diffusion of magnetic fields remains crucial for disc formation and growth.

The first steps of interstellar phosphorus chemistry

Context. Phosphorus-bearing species are essential to the formation of life on Earth, however they have barely been detected in the interstellar medium. In particular, towards star-forming regions only PN and PO have been identified so far. Since only a small number of detections of P-bearing molecules are available, their chemical formation pathways are not easy to constrain and are thus highly debatable. An important factor still missing in the chemical models is the initial elemental abundance of phosphorus, that is, the depletion level of P at the start of chemical models of dense clouds. Aims. In order to overcome this problem, we study P-bearing species in diffuse and translucent clouds. In these objects phosphorus is expected to be mainly in the gas phase and therefore the elemental initial abundance needed in our chemical simulations corresponds to the cosmic one and is well constrained. Methods. For the study of P-bearing chemistry we used an advanced chemical model. We updated and significantly extended the P-chemistry network based on chemical databases and previous literature. We performed single-pointing observations with the IRAM 30 m telescope in the 3 mm range towards the line of sight to the strong continuum source B0355+508 aiming for the (2–1) transitions of PN, PO, HCP, and CP. This line of sight incorporates five diffuse and/or translucent clouds. Results. The (2–1) transitions of the PN, PO, HCP, and CP were not detected. We report high signal-to-noise-ratio detections of the (1–0) lines of 13CO, HNC, and CN along with a first detection of C34S towards this line of sight. We have attempted to reproduce the observations of HNC, CN, CS, and CO in every cloud with our model by applying typical physical conditions for diffuse or translucent clouds. We find that towards the densest clouds with vLSR = −10, − 17 km s−1 the best-fit model is given by the parameters (n(H), AV, Tgas) = (300 cm−3, 3 mag, 40 K). Conclusions. According to our best-fit model, the most abundant P-bearing species are HCP and CP (~10−10). The molecules PN, PO, and PH3 also show relatively high predicted abundances of ~10−11. We show that the abundances of these species are sensitive to visual extinction, cosmic-ray ionization rate, and the diffusion-to-desorption energy ratio on dust grains. The production of P-bearing species is favored towards translucent rather than diffuse clouds, where the environment provides a stronger shielding from the interstellar radiation. Based on our improved model, we show that the (1–0) transitions of HCP, CP, PN, and PO are expected to be detectable with estimated intensities of up to ~200 mK.

HD/H2 ratio in the diffuse interstellar medium

ABSTRACT We present a semi-analytical description of the relative hydrogen deuteride (HD)/H2 abundance in the diffuse interstellar medium. We found three asymptotics of the relative HD/H2 abundance for different parts of the medium and their dependence on the physical parameters, namely, number density, intensity of the ultraviolet field, cosmic ray ionization rate, and metallicity. Our calculations are in a good agreement with the full network calculations using Meudon PDR code. We found that in the case of low metallicity and/or higher cosmic ray ionization rate, HD formation rate is significantly enhanced, HD/H2 ratio increases, and the D i/HD transition occurs at lower penetration depth of ultraviolet radiation than the H i/H2 transition. This can explain the observed difference in the HD/H2 abundance between the local and high-redshift measurements.

The Role of C/O in Nitrile Astrochemistry in PDRs and Planet-forming Disks

Abstract Complex nitriles, such as HC3N, and CH3CN, are observed in a wide variety of astrophysical environments, including at relatively high abundances in photon-dominated regions (PDRs) and the ultraviolet exposed atmospheres of planet-forming disks. The latter have been inferred to be oxygen-poor, suggesting that these observations may be explained by organic chemistry in C-rich environments. In this study we first explore if the PDR complex nitrile observations can be explained by gas-phase PDR chemistry alone if the elemental C/O ratio is elevated. In the case of the Horsehead PDR, we find that gas-phase chemistry with C/O ≳ 0.9 can indeed explain the observed nitrile abundances, increasing predicted abundances by several orders of magnitude compared to standard C/O assumptions. We also find that the nitrile abundances are sensitive to the cosmic-ray ionization treatment, and provide constraints on the branching ratios between CH3CN and CH3NC productions. In a fiducial disk model, an elevated C/O ratio increases the CH3CN and HC3N productions by more than an order of magnitude, bringing abundance predictions within an order of magnitude to what has been inferred from observations. The C/O ratio appears to be a key variable in predicting and interpreting complex organic molecule abundances in PDRs across a range of scales.

Chemical Abundances in a Turbulent Medium–H2, OH+, H2O+, ArH+

Abstract Supersonic turbulence results in strong density fluctuations in the interstellar medium (ISM), which have a profound effect on the chemical structure. Particularly useful probes of the diffuse ISM are the ArH+, OH+, H2O+ molecular ions, which are highly sensitive to fluctuations in the density and the H2 abundance. We use isothermal magnetohydrodynamic simulations of various sonic Mach numbers, , and density decorrelation scales, y dec, to model the turbulent density field. We post process the simulations with chemical models and obtain the probability density functions (PDFs) for the H2, ArH+, OH+, and H2O+ abundances. We find that the PDF dispersions increases with increasing and y dec, as the magnitude of the density fluctuations increases, and as they become more coherent. Turbulence also affects the median abundances: when and y dec are high, low-density regions with low H2 abundance become prevalent, resulting in an enhancement of ArH+ compared to OH+ and H2O+. We compare our models with Herschel observations. The large scatter in the observed abundances, as well as the high observed ArH+/OH+ and ArH+/H2O+ ratios are naturally reproduced by our supersonic , large decorrelation scale (y dec = 0.8) model, supporting a scenario of a large-scale turbulence driving. The abundances also depend on the ultraviolet intensity, cosmic-ray ionization rate, and the cloud column density, and the observed scatter may be influenced by fluctuations in these parameters.

Molecular clouds HD/H2 in the early Universe

We present a simplified semi-analytical description of the relative HD/H2 abundance in the cold neutral interstellar medium. With this description we was able to obtain three asymptotics of the relative HD/H2 abundance and its dependence on physical parameters in the medium, namely, the number density of the gas, the intensity of the ultraviolet field, the cosmic ray ionization rate and metallicity. Our calculations in presented simple formalism are in the reasonable agreement with the calculations using the Meudon PDR code. We found that in the case of low metallicity and a higher cosmic ray ionization rate, the relative abundance of HD/H2 is significantly enhanced, which can explain the observed difference between the local and high-z measurements of relative HD/H2 abundance.

Modeling deuterium chemistry in starless cores: full scrambling versus proton hop

We constructed two new models for deuterium and spin-state chemistry for the purpose of modeling the low-temperature environment prevailing in starless and pre-stellar cores. The fundamental difference between the two models is in the treatment of ion-molecule proton-donation reactions of the form XH+ + Y → X + YH+, which are allowed to proceed either via full scrambling or via direct proton hop, that is, disregarding proton exchange. The choice of the reaction mechanism affects both deuterium and spin-state chemistry, and in this work our main interest is on the effect on deuterated ammonia. We applied the new models to the starless core H-MM1, where several deuterated forms of ammonia have been observed. Our investigation slightly favors the proton hop mechanism over full scrambling because the ammonia D/H ratios are better fit by the former model, although neither model can reproduce the observed NH2D ortho-to-para ratio of 3 (the models predict a value of ~2). Extending the proton hop scenario to hydrogen atom abstraction reactions yields a good agreement for the spin-state abundance ratios, but greatly overestimates the deuterium fractions of ammonia. However, one can find a reasonably good agreement with the observations with this model by increasing the cosmic-ray ionization rate over the commonly adopted value of ~ 10−17 s−1. We also find that the deuterium fractions of several other species, such as H2CO, H2O, and CH3, are sensitive to the adopted proton-donation reaction mechanism. Whether the full scrambling or proton hop mechanism dominates may be dependent on the reacting system, and new laboratory and theoretical studies for various reacting systems are needed to constrain chemical models.

Gas and Dust Temperature in Prestellar Cores Revisited: New Limits on Cosmic-Ray Ionization Rate

Abstract We develop a self-consistent model for the equilibrium gas temperature and size-dependent dust temperature in cold, dense, prestellar cores, assuming an arbitrary power-law size distribution of dust grains. Compact analytical expressions applicable to a broad range of physical parameters are derived and compared with predictions of the commonly used standard model. It is suggested that combining the theoretical results with observations should allow us to constrain the degree of dust evolution and the cosmic-ray ionization rate in dense cores, and to help with discriminating between different regimes of cosmic-ray transport in molecular clouds. In particular, assuming a canonical MRN distribution of grain sizes, our theory demonstrates that the gas-temperature measurements in the prestellar core L1544 are consistent with an ionization rate as high as ∼10−16 s−1, an order of magnitude higher than previously thought.