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Catherine Walsh

Publications and source records attributed to Catherine Walsh.

At least 127 records · Page 7Linked to original sources

Robustness of N2H+ as tracer of the CO snowline

[Abridged] Snowlines in protoplanetary disks play an important role in planet formation and composition. Since the CO snowline is difficult to observe directly with CO emission, its location has been inferred in several disks from spatially resolved ALMA observations of DCO+ and N2H+. N2H+ is considered to be a good tracer of the CO snowline based on astrochemical considerations predicting an anti-correlation between N2H+ and gas-phase CO. In this work, the robustness of N2H+ as a tracer of the CO snowline is investigated. A simple chemical network is used in combination with the radiative transfer code LIME to model the N2H+ distribution and corresponding emission in the disk around TW Hya. The assumed CO and N2 abundances, corresponding binding energies, cosmic ray ionization rate, and degree of large-grain settling are varied to determine the effects on the N2H+ emission and its relation to the CO snowline. For the adopted physical structure of the TW Hya disk and molecular binding energies for pure ices, the balance between freeze-out and thermal desorption predicts a CO snowline at 19 AU, corresponding to a CO midplane freeze-out temperature of 20 K. A model with a total, i.e. gas plus ice, CO abundance of 3e-6 with respect to H2 fits the position of the emission peak observed by Qi et al. 2013 for the TW Hya disk. However, the relationship between N2H+ and the CO snowline is more complicated than generally assumed: for the investigated parameters, the N2H+ column density peaks at least 5 AU outside the CO snowline. Moreover, the N2H+ emission can peak much further out, as far as ~50 AU beyond the snowline. Hence, chemical modeling, as done here, is necessary to derive a CO snowline location from N2H+ observations.

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Grand challenges in protoplanetary disc modelling

The Protoplanetary Discussions conference --- held in Edinburgh, UK, from 7th --11th March 2016 --- included several open sessions led by participants. This paper reports on the discussions collectively concerned with the multiphysics modelling of protoplanetary discs, including the self-consistent calculation of gas and dust dynamics, radiative transfer and chemistry. After a short introduction to each of these disciplines in isolation, we identify a series of burning questions and grand challenges associated with their continuing development and integration. We then discuss potential pathways towards solving these challenges, grouped by strategical, technical and collaborative developments. This paper is not intended to be a review, but rather to motivate and direct future research and collaboration across typically distinct fields based on \textit{community driven input}, to encourage further progress in our understanding of circumstellar and protoplanetary discs.

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A Gap with a Deficit of Large Grains in the protoplanetary disk around TW Hya

We report $\sim$3 au resolution imaging observations of the protoplanetary disk around TW Hya at 145 and 233 GHz with the Atacama Large Millimeter/Submillimeter Array. Our observations revealed two deep gaps ($\sim$25--50 \%) at 22 and 37~au and shallower gaps (a few \%) at 6, 28, and 44~au, as recently reported by Andrews et al. (2016). The central hole with a radius of $\sim3$~au was also marginally resolved. The most remarkable finding is that the spectral index $α(R)$ between bands 4 and 6 peaks at the 22~au gap. The derived power-law index of the dust opacity $β(R)$ is $\sim1.7$ at the 22~au gap and decreases toward the disk center to $\sim0$. The most prominent gap at 22~au could be caused by the gravitational interaction between the disk and an unseen planet with a mass of $\lesssim$1.5 $M_\mathrm{Neptune}$ although other origins may be possible. The planet-induced gap is supported by the fact that $β(R)$ is enhanced at the 22~au gap, indicating a deficit of $\sim$mm-sized grains within the gap due to dust filtration by a planet.

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A primordial origin for molecular oxygen in comets: A chemical kinetics study of the formation and survival of O$_2$ ice from clouds to disks

Molecular oxygen has been confirmed as the fourth most abundant molecule in cometary material O$_2$/H$_2$O $\sim 4$ %) and is thought to have a primordial nature, i.e., coming from the interstellar cloud from which our solar system was formed. However, interstellar O$_2$ gas is notoriously difficult to detect and has only been observed in one potential precursor of a solar-like system. Here, the chemical and physical origin of O$_2$ in comets is investigated using sophisticated astrochemical models. Three origins are considered: i) in dark clouds, ii) during forming protostellar disks, and iii) during luminosity outbursts in disks. The dark cloud models show that reproduction of the observed abundance of O$_2$ and related species in comet 67P/C-G requires a low H/O ratio facilitated by a high total density ($\geq 10^5$ cm$^{-3}$), and a moderate cosmic ray ionisation rate ($\leq 10^{-16}$ s$^{-1}$) while a temperature of 20 K, slightly higher than the typical temperatures found in dark clouds, also enhances the production of O$_2$. Disk models show that O$_2$ can only be formed in the gas phase in intermediate disk layers, and cannot explain the strong correlation between O$_2$ and H$_2$O in comet 67P/C-G together with the weak correlation between other volatiles and H$_2$O. However, primordial O$_2$ ice can survive transport into the comet-forming regions of disks. Taken together, these models favour a dark cloud (or "primordial") origin for O$_2$ in comets, albeit for dark clouds which are warmer and denser than those usually considered as solar system progenitors.

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Cometary ices in forming protoplanetary disc midplanes

Low-mass protostars are the extrasolar analogues of the natal Solar System. Sophisticated physicochemical models are used to simulate the formation of two protoplanetary discs from the initial prestellar phase, one dominated by viscous spreading and the other by pure infall. The results show that the volatile prestellar fingerprint is modified by the chemistry en route into the disc. This holds relatively independent of initial abundances and chemical parameters: physical conditions are more important. The amount of CO2 increases via the grain-surface reaction of OH with CO, which is enhanced by photodissociation of H2O ice. Complex organic molecules are produced during transport through the envelope at the expense of CH3OH ice. Their abundances can be comparable to that of methanol ice (few % of water ice) at large disc radii (R > 30 AU). Current Class II disc models may be underestimating the complex organic content. Planet population synthesis models may underestimate the amount of CO2 and overestimate CH3OH ices in planetesimals by disregarding chemical processing between the cloud and disc phases. The overall C/O and C/N ratios differ between the gas and solid phases. The two ice ratios show little variation beyond the inner 10 AU and both are nearly solar in the case of pure infall, but both are sub-solar when viscous spreading dominates. Chemistry in the protostellar envelope en route to the protoplanetary disc sets the initial volatile and prebiotically-significant content of icy planetesimals and cometary bodies. Comets are thus potentially reflecting the provenances of the midplane ices in the Solar Nebula.

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Setting the volatile composition of (exo)planet-building material. Does chemical evolution in disk midplanes matter?

[Abridged] Chemical evolution in the protoplanetary disk midplane can modify the composition of ices and gases. We have investigated if and how chemical evolution affects the abundances and distributions of key volatile species in the midplane of a protoplanetary disk in the 0.2-30 AU range. A full chemical network including gas-phase, gas-grain interactions and grain-surface chemistry is used to evolve chemistry in time, for 1 Myr. Great diversity is observed in the relative abundance ratios of the main considered species: H2O, CO, CO2, CH4, O2, NH3 and N2. The choice of ionisation level, the choice of initial abundances, as well as the extent of chemical reaction types included are all factors that affect the chemical evolution. The only exception is the inheritance scenario with a low ionisation level, which results in negligible changes compared with the initial abundances, regardless of whether grain-surface chemistry is included. The chemical processing changes the C/O ratios for gas and ice significantly with radius and with model assumptions. For high ionisation levels, chemical processing becomes significant after a few times $10^{5}$~yrs. It is concluded that chemical evolution in the disk midplane needs to be considered in the determination of the volatile composition of planetesimals.

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First detection of gas-phase methanol in a protoplanetary disk

The first detection of gas-phase methanol in a protoplanetary disk (TW Hya) is presented. In addition to being one of the largest molecules detected in disks to date, methanol is also the first disk organic molecule with an unambiguous ice chemistry origin. The stacked methanol emission, as observed with ALMA, is spectrally resolved and detected across six velocity channels ($>3 σ$), reaching a peak signal-to-noise of $5.5σ$, with the kinematic pattern expected for TW~Hya. Using an appropriate disk model, a fractional abundance of $3\times 10^{-12} - 4 \times 10^{-11}$ (with respect to H$_2$) reproduces the stacked line profile and channel maps, with the favoured abundance dependent upon the assumed vertical location (midplane versus molecular layer). The peak emission is offset from the source position suggesting that the methanol emission has a ring-like morphology: the analysis here suggests it peaks at $\approx 30$~AU reaching a column density $\approx 3-6\times10^{12}$~cm$^{-2}$. In the case of TW Hya, the larger (up to mm-sized) grains, residing in the inner 50~AU, may thus host the bulk of the disk ice reservoir. The successful detection of cold gas-phase methanol in a protoplanetary disk implies that the products of ice chemistry can be explored in disks, opening a window to studying complex organic chemistry during planetary system formation.

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Candidate Water Vapor Lines to Locate the H$_{2}$O Snowline through High-Dispersion Spectroscopic Observations I. The Case of a T Tauri Star

Inside the H$_{2}$O snowline of protoplanetary disks, water evaporates from the dust-grain surface into the gas phase, whereas it is frozen out on to the dust in the cold region beyond the snowline. H$_{2}$O ice enhances the solid material in the cold outer part of a disk, which promotes the formation of gas-giant planet cores. We can regard the H$_{2}$O snowline as the surface that divides the regions between rocky and gaseous giant planet formation. Thus observationally measuring the location of the H$_{2}$O snowline is crucial for understanding the planetesimal and planet formation processes, and the origin of water on Earth. In this paper, we find candidate water lines to locate the H$_{2}$O snowline through future high-dispersion spectroscopic observations. First, we calculate the chemical composition of the disk and investigate the abundance distributions of H$_{2}$O gas and ice, and the position of the H$_{2}$O snowline. We confirm that the abundance of H$_{2}$O gas is high not only in the hot midplane region inside the H$_{2}$O snowline but also in the hot surface layer of the outer disk. Second, we calculate the H$_{2}$O line profiles and identify those H$_{2}$O lines which are promising for locating the H$_{2}$O snowline: the identified lines are those which have small Einstein $A$ coefficients and high upper state energies. The wavelengths of the candidate H$_{2}$O lines range from mid-infrared to sub-millimeter, and they overlap with the regions accessible to ALMA and future mid-infrared high dispersion spectrographs (e.g., TMT/MICHI, SPICA).

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Chemical complexity in protoplanetary disks in the era of ALMA and Rosetta

Comets provide a unique insight into the molecular composition and complexity of the material in the primordial solar nebula. Recent results from the Rosetta mission, currently monitoring comet 67P/Churyumov-Gerasimenko in situ, and ALMA (the Atacama Large Millimeter/submillimeter Array), have demonstrated a tantalising link between the chemical complexity now confirmed in disks (via the detection of gas-phase CH3CN; Oberg et al. 2015) and that confirmed on the surface of 67P (Goesmann et al. 2015), raising questions concerning the chemical origin of such species (cloud or inheritance versus disk synthesis). Results from an astrochemical model of a protoplanetary disk are presented in which complex chemistry is included and in which it is assumed that simple ices only are inherited from the parent molecular cloud. The model results show good agreement with the abundances of several COMs observed on the surface of 67P with Philae/COSAC. Cosmic-ray and X-ray-induced photoprocessing of predominantly simple ices inherited by the protoplanetary disk is sufficient to generate a chemical complexity similar to that observed in comets. This indicates that the icy COMs detected on the surface of 67P may have a disk origin. The results also show that gas-phase CH3CN is abundant in the inner warm disk atmosphere where hot gas-phase chemistry dominates and potentially erases the ice chemical signature. Hence, CH3CN may not be an unambiguous tracer of the complex organic ice reservoir. However, a better understanding of the hot gas-phase chemistry of CH3CN is needed to confirm this preliminary conclusion.

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ALMA Observations of a Gap and a Ring in the Protoplanetary Disk around TW Hya

We report the first detection of a gap and a ring in 336 GHz dust continuum emission from the protoplanetary disk around TW Hya, using the Atacama Large Millimeter/Submillimeter Array (ALMA). The gap and ring are located at around 25 and 41 au from the central star, respectively, and are associated with the CO snow line at ~30 au. The gap has a radial width of less than 15 au and a mass deficit of more than 23%, taking into account that the observations are limited to an angular resolution of ~15 au. In addition, the 13CO and C18O J = 3 - 2 lines show a decrement in CO line emission throughout the disk, down to ~10 au, indicating a freeze-out of gas-phase CO onto grain surfaces and possible subsequent surface reactions to form larger molecules. The observed gap could be caused by gravitational interaction between the disk gas and a planet with a mass less than super-Neptune (2M_{Neptune}), or could be the result of the destruction of large dust aggregates due to the sintering of CO ice.

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The molecular composition of the planet-forming regions of protoplanetary disks across the luminosity regime

(Abridged) Near- to mid-IR observations of protoplanetary disks show that the inner regions (<10AU) are rich in small organic volatiles (e.g., C2H2 and HCN). Trends in the data suggest that disks around cooler stars (~3000K) are potentially more carbon- and molecule-rich than their hotter counterparts. Our aims are to explore the composition of the planet-forming region of disks around stars from M dwarf to Herbig Ae and compare with the observed trends. Models of the disk physical structure are coupled with a gas-grain chemical network to map the abundances in the planet-forming zone. N2 self shielding, X-ray-induced chemistry, and initial abundances, are investigated. The composition in the 'observable' atmosphere is compared with that in the midplane where the planet-building reservoir resides. M dwarf disk atmospheres are relatively more molecule rich than those for T Tauri or Herbig Ae disks. The weak far-UV flux helps retain this complexity which is enhanced by X-ray-induced ion-molecule chemistry. N2 self shielding has only a small effect and does not explain the higher C2H2/HCN ratios observed towards cooler stars. The models underproduce the OH/H2O column density ratios constrained in Herbig Ae disks, despite reproducing the absolute value for OH: H2O self shielding only increases this discrepency. The disk midplane content is sensitive to the initial main elemental reservoirs. The gas in the inner disk is generally more carbon rich than the midplane ices and is most significant for disks around cooler stars. The atmospheric C/O ratio appears larger than it actually is when calculated using observable tracers only because gas-phase O2 is predicted to be a significant oxygen reservoir. The models suggest that the gas in the inner regions of disks around cooler stars is more carbon rich; however, calculations of the molecular emission are necessary to confirm the observed trends.

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Resolving structure of the disk around HD100546 at 7 mm with ATCA

There is much evidence that planet formation is occurring in the disk around the Herbig Be star HD100546. To learn more about the processes occurring in this disk we conducted high resolution imaging at 43/45 GHz with the Australia Telescope Compact Array (ATCA). Multiple array configurations were used, providing a best spatial resolution of $\sim$ 0.15 arcsec, or 15 AU at HD100546's distance of $\sim$ 100 pc. Significant structure is revealed, but its precise form is dependent on the $u-v$ plane sampling used for the image reconstruction. At a resolution of $\leq$ 30 AU we detected an inner gap in the disk with a radius of $\sim$ 25 AU and a position angle approximately along the known disk major axis. With different weighting, and an achieved resolution of $\sim$ 15 AU, emission appears at the centre and the disk takes on the shape of an incomplete ring, much like a horseshoe, again with a gap radius of $\sim$ 25 AU. The position angle of the disk major axis and its inclination from face-on are determined to be $140^{\circ}\pm5^{\circ}$ and $40^{\circ}\pm5^{\circ}$ respectively. The $\sim$ 25 AU gap radius is confirmed by a null in the real part of the binned visibilities at 320$\pm$10 k$λ$, whilst the non-axisymmetric nature is also confirmed through significant structure in the imaginary component. The emission mechanism at the central peak is most likely to be free-free emission from a stellar or disk wind. Overall our data support the picture of at least one, but probably several, giant planets orbiting HD100546 within 25 AU.

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A low-mass protostar's disk-envelope interface: disk-shadowing evidence from ALMA DCO+ observations of VLA1623

Due to instrumental limitations and a lack of disk detections, the structure between the envelope and the rotationally supported disk has been poorly studied. This is now possible with ALMA through observations of CO isotopologs and tracers of freezeout. Class 0 sources are ideal for such studies given their almost intact envelope and young disk. The structure of the disk-envelope interface of the prototypical Class 0 source, VLA1623A which has a confirmed Keplerian disk, is constrained from ALMA observations of DCO+ 3-2 and C18O 2-1. The physical structure of VLA1623 is obtained from the large-scale SED and continuum radiative transfer. An analytic model using a simple network coupled with radial density and temperature profiles is used as input for a 2D line radiative transfer calculation for comparison with the ALMA Cycle 0 12m array and Cycle 2 ACA observations of VLA1623. DCO+ emission shows a clumpy structure bordering VLA1623A's Keplerian disk, suggesting a cold ring-like structure at the disk-envelope interface. The radial position of the observed DCO+ peak is reproduced in our model only if the region's temperature is between 11-16K, lower than expected from models constrained by continuum and SED. Altering the density has little effect on the DCO+ position, but increased density is needed to reproduce the disk traced in C18O. The DCO+ emission around VLA1623A is the product of shadowing of the envelope by the disk. Disk-shadowing causes a drop in the gas temperature outside of the disk on >200AU scales, encouraging deuterated molecule production. This indicates that the physical structure of the disk-envelope interface differs from the rest of the envelope, highlighting the drastic impact that the disk has on the envelope and temperature structure. The results presented here show that DCO+ is an excellent cold temperature tracer.

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The complex chemistry of outflow cavity walls exposed: the case of low-mass protostars

Complex organic molecules are ubiquitous companions of young low-mass protostars. Recent observations suggest that their emission stems, not only from the traditional hot corino, but also from offset positions. In this work, 2D physicochemical modelling of an envelope-cavity system is carried out. Wavelength-dependent radiative transfer calculations are performed and a comprehensive gas-grain chemical network is used to simulate the physical and chemical structure. The morphology of the system delineates three distinct regions: the cavity wall layer with time-dependent and species-variant enhancements; a torus rich in complex organic ices, but not reflected in gas-phase abundances; and the remaining outer envelope abundant in simpler solid and gaseous molecules. Strongly irradiated regions, such as the cavity wall layer, are subject to frequent photodissociation in the solid phase. Subsequent recombination of the photoproducts leads to frequent reactive desorption, causing gas-phase enhancements of several orders of magnitude. This mechanism remains to be quantified with laboratory experiments. Direct photodesorption is found to be relatively inefficient. If radicals are not produced directly in the icy mantle, the formation of complex organics is impeded. For efficiency, a sufficient number of FUV photons needs to penetrate the envelope; and elevated cool dust temperatures need to enable grain-surface radical mobility. As a result, a high stellar luminosity and a sufficiently wide cavity favor chemical complexity. Furthermore within this paradigm, complex organics are demonstrated to have unique lifetimes and be grouped into early (formaldehyde, ketene, methanol, formic acid, methyl formate, acetic acid, glycolaldehyde) and late (acetaldehyde, dimethyl ether, ethanol) species.

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Photodesorption of H2O, HDO, and D2O ice and its impact on fractionation

The HDO/H2O ratio in interstellar gas is often used to draw conclusions on the origin of water in star-forming regions and on Earth. In cold cores and in the outer regions of protoplanetary disks, gas-phase water comes from photodesorption of water ice. We present fitting formulae for implementation in astrochemical models using photodesorption efficiencies for all water ice isotopologues obtained using classical molecular dynamics simulations. We investigate if the gas-phase HDO/H2O ratio reflects that present in the ice or whether fractionation can occur during photodesorption. Probabilities for the top four monolayers are presented for photodesorption of X (X=H,D) atoms, OX radicals, and X2O and HDO molecules following photodissociation of H2O, D2O, and HDO in H2O amorphous ice at temperatures from 10-100 K. Isotope effects are found for all products: (1) H atom photodesorption probabilities from H2O ice are larger than those for D atom photodesorption from D2O ice by a factor of 1.1; the ratio of H and D photodesorbed upon HDO photodissociation is a factor of 2. This process will enrich the ice in deuterium atoms over time; (2) the OD/OH photodesorption ratio upon D2O and H2O photodissociation is on average a factor of 2, but the ratio upon HDO photodissociation is almost constant at unity for all temperatures; (3) D atoms are more effective in kicking out neighbouring water molecules than H atoms. However, the ratio of the photodesorbed HDO and H2O molecules is equal to the HDO/H2O ratio in the ice, therefore, there is no isotope fractionation upon HDO and H2O photodesorption. Nevertheless, the enrichment of the ice in D atoms due to photodesorption can over time lead to an enhanced HDO/H2O ratio in the ice, and, when photodesorbed, also in the gas. The extent to which the ortho/para ratio of H2O can be modified by the photodesorption process is also discussed. (Abridged)

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Methanol Along the Path from Envelope to Protoplanetary Disc

Interstellar methanol is considered to be a parent species of larger, more complex organic molecules. A physicochemical simulation of infalling parcels of matter is performed for a low-mass star-forming system to trace the chemical evolution from cloud to disc. An axisymmetric 2D semi-analytic model generates the time-dependent density and velocity distributions, and full continuum radiative transfer is performed to calculate the dust temperature and the UV radiation field at each position as a function of time. A comprehensive gas-grain chemical network is employed to compute the chemical abundances along infall trajectories. Two physical scenarios are studied, one in which the dominant disc growth mechanism is viscous spreading, and another in which continuous infall of matter prevails. The results show that the infall path influences the abundance of methanol entering each type of disc, ranging from complete loss of methanol to an enhancement by a factor of > 1 relative to the prestellar phase. Critical chemical processes and parameters for the methanol chemistry under different physical conditions are identified. The exact abundance and distribution of methanol is important for the budget of complex organic molecules in discs, which will be incorporated into forming planetary system objects such as protoplanets and comets. These simulations show that the comet-forming zone contains less methanol than in the precollapse phase, which is dominantly of prestellar origin, but also with additional layers built up in the envelope during infall. Such intriguing links will soon be tested by upcoming data from the Rosetta mission.

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ALMA hints at the presence of two companions in the disk around HD 100546

HD 100546 is a well-studied Herbig Be star-disk system that likely hosts a close-in companion with compelling observational evidence for an embedded protoplanet at 68 AU. We present ALMA observations of the HD 100546 disk which resolve the gas and dust structure at (sub)mm wavelengths. The CO emission (at 345.795 GHz) originates from an extensive molecular disk (390+/-20 AU in radius) whereas the continuum emission is more compact (230+/-20 AU in radius) suggesting radial drift of the mm-sized grains. The CO emission is similar in extent to scattered light images indicating well-mixed gas and um-sized grains in the disk atmosphere. Assuming azimuthal symmetry, a single-component power-law model cannot reproduce the continuum visibilities. The visibilities and images are better reproduced by a double-component model: a compact ring with a width of 21 AU centered at 26 AU and an outer ring with a width of 75+/-3 AU centered at 190+/-3 AU. The influence of a companion and protoplanet on the dust evolution is investigated. The companion at 10 AU facilitates the accumulation of mm-sized grains within a compact ring, ~ 20 - 30 AU, by ~ 10 Myr. The injection of a protoplanet at 1 Myr hastens the ring formation (~ 1.2 Myr) and also triggers the development of an outer ring (~ 100 - 200 AU). These observations provide additional evidence for the presence of a close-in companion and hint at dynamical clearing by a protoplanet in the outer disk.

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Photodissociation and chemistry of N$_2$ in the circumstellar envelope of carbon-rich AGB stars

The envelopes of AGB stars are irradiated externally by ultraviolet photons; hence, the chemistry is sensitive to the photodissociation of N$_2$ and CO, which are major reservoirs of nitrogen and carbon, respectively. The photodissociation of N$_2$ has recently been quantified by laboratory and theoretical studies. Improvements have also been made for CO photodissociation. For the first time, we use accurate N$_2$ and CO photodissociation rates and shielding functions in a model of the circumstellar envelope of the carbon-rich AGB star, IRC +10216. We use a state-of-the-art chemical model of an AGB envelope, the latest CO and N$_2$ photodissociation data, and a new method for implementing molecular shielding functions in full spherical geometry with isotropic incident radiation. We compare computed column densities and radial distributions of molecules with observations. The transition of N$_2$ $\to$ N (also, CO $\to$ C $\to$ C$^+$) is shifted towards the outer envelope relative to previous models. This leads to different column densities and radial distributions of N-bearing species, especially those species whose formation/destruction processes largely depend on the availability of atomic or molecular nitrogen, for example, C$_n$N ($n$=1, 3, 5), C$_n$N$^-$ ($n$=1, 3, 5), HC$_n$N ($n$=1, 3, 5, 7, 9), H$_2$CN and CH$_2$CN. The chemistry of many species is directly or indirectly affected by the photodissociation of N$_2$ and CO, especially in the outer shell of AGB stars where photodissociation is important. Thus, it is important to include N$_2$ and CO shielding in astrochemical models of AGB envelopes and other irradiated environments. In general, while differences remain between our model of IRC +10216 and the observed molecular column densities, better agreement is found between the calculated and observed radii of peak abundance.

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