arXiv subjects

Ryan A. Loomis

Publications and source records attributed to Ryan A. Loomis.

At least 73 records · Page 4Linked to original sources

arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) VIII: CO Gap in AS 209--Gas Depletion or Chemical Processing?

Emission substructures in gas and dust are common in protoplanetary disks. Such substructures can be linked to planet formation or planets themselves. We explore the observed gas substructures in AS 209 using thermochemical modeling with RAC2D and high-spatial resolution data from the Molecules with ALMA at Planet-forming Scales(MAPS) program. The observations of C$^{18}$O J=2-1 emission exhibit a strong depression at 88 au overlapping with the positions of multiple gaps in millimeter dust continuum emission. We find that the observed CO column density is consistent with either gas surface-density perturbations or chemical processing, while C$_2$H column density traces changes in the C/O ratio rather than the H$_2$ gas surface density. However, the presence of a massive planet (> 0.2 M$_{Jup}$) would be required to account for this level of gas depression, which conflicts with constraints set by the dust emission and the pressure profile measured by gas kinematics. Based on our models, we infer that a local decrease of CO abundance is required to explain the observed structure in CO, dominating over a possible gap-carving planet present and its effect on the H$_2$ surface density. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement Series.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) XII: Inferring the C/O and S/H ratios in Protoplanetary Disks with Sulfur Molecules

Sulfur-bearing molecules play an important role in prebiotic chemistry and planet habitability. They are also proposed probes of chemical ages, elemental C/O ratio, and grain chemistry processing. Commonly detected in diverse astrophysical objects, including the Solar System, their distribution and chemistry remain, however, largely unknown in planet-forming disks. We present CS ($2-1$) observations at $\sim0."3$ resolution performed within the ALMA-MAPS Large Program toward the five disks around IM Lup, GM Aur, AS 209, HD 163296, and MWC 480. CS is detected in all five disks, displaying a variety of radial intensity profiles and spatial distributions across the sample, including intriguing apparent azimuthal asymmetries. Transitions of C$_2$S and SO were also serendipitously covered but only upper limits are found. For MWC 480, we present complementary ALMA observations at $\sim0."5$, of CS, $^{13}$CS, C$^{34}$S, H$_2$CS, OCS, and SO$_2$. We find a column density ratio N(H$_{2}$CS)/N(CS)$\sim2/3$, suggesting that a substantial part of the sulfur reservoir in disks is in organic form (i.e., C$_x$H$_y$S$_z$). Using astrochemical disk modeling tuned to MWC 480, we demonstrate that $N$(CS)/$N$(SO) is a promising probe for the elemental C/O ratio. The comparison with the observations provides a super-solar C/O. We also find a depleted gas-phase S/H ratio, suggesting either that part of the sulfur reservoir is locked in solid phase or that it remains in an unidentified gas-phase reservoir. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) I: Program Overview and Highlights

Planets form and obtain their compositions in dust and gas-rich disks around young stars, and the outcome of this process is intimately linked to the disk chemical properties. The distributions of molecules across disks regulate the elemental compositions of planets, including C/N/O/S ratios and metallicity (O/H and C/H), as well as access to water and prebiotically relevant organics. Emission from molecules also encodes information on disk ionization levels, temperature structures, kinematics, and gas surface densities, which are all key ingredients of disk evolution and planet formation models. The Molecules with ALMA at Planet-forming Scales (MAPS) ALMA Large Program was designed to expand our understanding of the chemistry of planet formation by exploring disk chemical structures down to 10 au scales. The MAPS program focuses on five disks - around IM Lup, GM Aur, AS 209, HD 163296, and MWC 480 - in which dust substructures are detected and planet formation appears to be ongoing. We observed these disks in 4 spectral setups, which together cover ~50 lines from over 20 different species. This paper introduces the ApJS MAPS Special Issue by presenting an overview of the program motivation, disk sample, observational details, and calibration strategy. We also highlight key results, including discoveries of links between dust, gas, and chemical sub-structures, large reservoirs of nitriles and other organics in the inner disk regions, and elevated C/O ratios across most disks. We discuss how this collection of results is reshaping our view of the chemistry of planet formation.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS). XV. Tracing protoplanetary disk structure within 20 au

Constraining the distribution of gas and dust in the inner 20 au of protoplanetary disks is difficult. At the same time, this region is thought to be responsible for most planet formation, especially around the water ice line at 3-10 au. Under the assumption that the gas is in a Keplerian disk, we use the exquisite sensitivity of the Molecules with ALMA at Planet-forming Scales (MAPS) ALMA large program to construct radial surface brightness profiles with a ~3 au effective resolution for the CO isotopologue J=2-1 lines using the line velocity profile. IM Lup reveals a central depression in 13CO and C18O that is ascribed to a pileup of ~500 $M_\oplus$ of dust in the inner 20 au, leading to a gas-to-dust ratio of around <10. This pileup is consistent with efficient drift of grains ($\gtrsim$ 100 $M_\oplus$ Myr$^{-1}$) and a local gas-to-dust ratio that suggests that the streaming instability could be active. The CO isotopologue emission in the GM Aur disk is consistent with a small (~15 au), strongly depleted gas cavity within the ~40 au dust cavity. The radial surface brightness profiles for both the AS 209 and HD 163296 disks show a local minimum and maximum in the C18O emission at the location of a known dust ring (~14 au) and gap (~10 au), respectively. This indicates that the dust ring has a low gas-to-dust ratio ($>$ 10) and that the dust gap is gas-rich enough to have optically thick C18O.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS). VII. Sub-stellar O/H and C/H and super-stellar C/O in planet feeding gas

The elemental composition of the gas and dust in a protoplanetary disk influences the compositions of the planets that form in it. We use the Molecules with ALMA at Planet-forming Scales (MAPS) data to constrain the elemental composition of the gas at the locations of potentially forming planets. The elemental abundances are inferred by comparing source-specific gas-grain thermochemical models, with variable C/O ratios and small-grain abundances, from the DALI code with CO and C2H column densities derived from the high-resolution observations of the disks of AS 209, HD 163296, and MWC 480. Elevated C/O ratios (~2.0), even within the CO ice line, are necessary to match the inferred C2H column densities, over most of the pebble disk. Combined with constraints on the CO abundances in these systems, this implies that both the O/H and C/H ratios in the gas are substellar by a factor of 4-10, with the O/H depleted by a factor of 20-50, resulting in the high C/O ratios. This necessitates that even within the CO ice line, most of the volatile carbon and oxygen is still trapped on grains in the midplane. Planets accreting gas in the gaps of the AS 209, HD 163296, and MWC 480 disks will thus acquire very little carbon and oxygen after reaching the pebble isolation mass. In the absence of atmosphere-enriching events, these planets would thus have a strongly substellar O/H and C/H and superstellar C/O atmospheric composition.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) XI: CN and HCN as Tracers of Photochemistry in Disks

UV photochemistry in the surface layers of protoplanetary disks dramatically alters their composition relative to previous stages of star formation. The abundance ratio CN/HCN has long been proposed to trace the UV field in various astrophysical objects, however to date the relationship between CN, HCN, and the UV field in disks remains ambiguous. As part of the ALMA Large Program MAPS (Molecules with ALMA at Planet-forming Scales), we present observations of CN N=1-0 transitions at 0.3'' resolution towards five disk systems. All disks show bright CN emission within $\sim$50-150 au, along with a diffuse emission shelf extending up to 600 au. In all sources we find that the CN/HCN column density ratio increases with disk radius from about unity to 100, likely tracing increased UV penetration that enhances selective HCN photodissociation in the outer disk. Additionally, multiple millimeter dust gaps and rings coincide with peaks and troughs, respectively, in the CN/HCN ratio, implying that some millimeter substructures are accompanied by changes to the UV penetration in more elevated disk layers. That the CN/HCN ratio is generally high (>1) points to a robust photochemistry shaping disk chemical compositions, and also means that CN is the dominant carrier of the prebiotically interesting nitrile group at most disk radii. We also find that the local column densities of CN and HCN are positively correlated despite emitting from vertically stratified disk regions, indicating that different disk layers are chemically linked. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) XIX. Spiral Arms, a Tail, and Diffuse Structures Traced by CO around the GM Aur Disk

The concentric gaps and rings commonly observed in protoplanetary disks in millimeter continuum emission have lent the impression that planet formation generally proceeds within orderly, isolated systems. While deep observations of spatially resolved molecular emission have been comparatively limited, they are increasingly suggesting that some disks interact with their surroundings while planet formation is underway. We present an analysis of complex features identified around GM Aur in $^{12}$CO $J=2-1$ images at a spatial resolution of $\sim40$ au. In addition to a Keplerian disk extending to a radius of $\sim550$ au, the CO emission traces flocculent spiral arms out to radii of $\sim$1200 au, a tail extending $\sim1800$ au southwest of GM Aur, and diffuse structures extending from the north side of the disk up to radii of $\sim1900$ au. The diffuse structures coincide with a "dust ribbon" previously identified in scattered light. The large-scale asymmetric gas features present a striking contrast with the mostly axisymmetric, multi-ringed millimeter continuum tracing the pebble disk. We hypothesize that GM Aur's complex gas structures result from late infall of remnant envelope or cloud material onto the disk. The morphological similarities to the SU Aur and AB Aur systems, which are also located in the L1517 cloud, provide additional support to a scenario in which interactions with the environment are playing a role in regulating the distribution and transport of material in all three of these Class II disk systems. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS). IX. Distribution and Properties of the Large Organic Molecules HC$_3$N, CH$_3$CN, and $c$-C$_3$H$_2$

The precursors to larger, biologically-relevant molecules are detected throughout interstellar space, but determining the presence and properties of these molecules during planet formation requires observations of protoplanetary disks at high angular resolution and sensitivity. Here we present 0.3" observations of HC$_3$N, CH$_3$CN, and $c$-C$_3$H$_2$ in five protoplanetary disks observed as part of the Molecules with ALMA at Planet-forming Scales (MAPS) Large Program. We robustly detect all molecules in four of the disks (GM Aur, AS 209, HD 163296 and MWC 480) with tentative detections of $c$-C$_3$H$_2$ and CH$_3$CN in IM Lup. We observe a range of morphologies -- central peaks, single or double rings -- with no clear correlation in morphology between molecule nor disk. Emission is generally compact and on scales comparable with the millimetre dust continuum. We perform both disk-integrated and radially-resolved rotational diagram analysis to derive column densities and rotational temperatures. The latter reveals 5-10 times more column density in the inner 50-100 au of the disks when compared with the disk-integrated analysis. We demonstrate that CH$_3$CN originates from lower relative heights in the disks when compared with HC$_3$N, in some cases directly tracing the disk midplane. Finally, we find good agreement between the ratio of small to large nitriles in the outer disks and comets. Our results indicate that the protoplanetary disks studied here are host to significant reservoirs of large organic molecules, and that this planet- and comet-building material can be chemically similar to that in our own Solar System. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement Series.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) XVI: Characterizing the impact of the molecular wind on the evolution of the HD 163296 system

During the main phase of evolution of a protoplanetary disk, accretion regulates the inner-disk properties, such as the temperature and mass distribution, and in turn, the physical conditions associated with planet formation. The driving mechanism behind accretion remains uncertain; however, one promising mechanism is the removal of a fraction of angular momentum via a magnetohydrodynamic (MHD) disk wind launched from the inner tens of astronomical units of the disk. This paper utilizes CO isotopologue emission to study the unique molecular outflow originating from the HD 163296 protoplanetary disk obtained with the Atacama Large Millimeter/submillimeter Array. HD~163296 is one of the most well-studied Class II disks and is proposed to host multiple gas-giant planets. We robustly detect the large-scale rotating outflow in the 12CO J=2-1 and the 13CO J=2-1 and J=1-0 transitions. We constrain the kinematics, the excitation temperature of the molecular gas, and the mass-loss rate. The high ratio of the rates of ejection to accretion (5 - 50), together with the rotation signatures of the flow, provides solid evidence for an MHD disk wind. We find that the angular momentum removal by the wind is sufficient to drive accretion through the inner region of the disk; therefore, accretion driven by turbulent viscosity is not required to explain HD~163296's accretion. The low temperature of the molecular wind and its overall kinematics suggest that the MHD disk wind could be perturbed and shocked by the previously observed high-velocity atomic jet. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

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arXiv2021

Molecules with ALMA at Planet-forming Scales (MAPS) VI: Distribution of the small organics HCN, C2H, and H2CO

Small organic molecules, such as C2H, HCN, and H2CO, are tracers of the C, N, and O budget in protoplanetary disks. We present high angular resolution (10-50 au) observations of C2H, HCN, and H2CO lines in five protoplanetary disks from the Molecules with ALMA at Planet-forming Scales (MAPS) ALMA Large Program. We derive column density and excitation temperature profiles for HCN and C2H, and find that the HCN emission arises in a temperate (20-30 K) layer in the disk, while C2H is present in relatively warmer (20-60 K) layers. In the case of HD 163296, we find a decrease in column density for HCN and C2H inside one of the dust gaps near 83 au, where a planet has been proposed to be located. We derive H2CO column density profiles assuming temperatures between 20 and 50 K, and find slightly higher column densities in the colder disks around T Tauri stars than around Herbig Ae stars. The H2CO column densities rise near the location of the CO snowline and/or millimeter dust edge, suggesting an efficient release of H2CO ices in the outer disk. Finally, we find that the inner 50 au of these disks are rich in organic species, with abundances relative to water that are similar to cometary values. Comets could therefore deliver water and key organics to future planets in these disks, similar to what might have happened here on Earth. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

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arXiv2021

Molecules with ALMA at Planet-forming Scales. XX. The Massive Disk Around GM Aurigae

Gas mass remains one of the most difficult protoplanetary disk properties to constrain. With much of the protoplanetary disk too cold for the main gas constituent, H2, to emit, alternative tracers such as dust, CO, or the H2 isotopolog HD are used. However, relying on disk mass measurements from any single tracer requires assumptions about the tracer's abundance relative to \hh\ and the disk temperature structure. Using new Atacama Large Millimeter/submillimeter Array (ALMA) observations from the Molecules with ALMA at Planet-forming Scales (MAPS) ALMA Large Program as well as archival ALMA observations, we construct a disk physical/chemical model of the protoplanetary disk GM Aur. Our model is in good agreement with the spatially resolved CO isotopolog emission from eleven rotational transitions with spatial resolution ranging from 0.15'' to 0.46'' (24-73 au at 159 pc) and the spatially unresolved HD J=1-0 detection from Herschel. Our best-fit model favors a cold protoplanetary disk with a total gas mass of approximately 0.2 solar masses, a factor of 10 reduction in CO gas inside roughly 100 au and a factor of 100 reduction outside of 100 au. Despite its large mass, the disk appears to be on the whole gravitationally stable based on the derived Toomre Q parameter. However, the region between 70 and 100 au, corresponding to one of the millimeter dust rings, is close to being unstable based on the calculated Toomre Q of <1.7. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

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arXiv2021

Discovery of the Pure Polycyclic Aromatic Hydrocarbon Indene ($c$-C$_9$H$_8$) with GOTHAM Observations of TMC-1

Polycyclic Aromatic Hydrocarbons (PAHs) have long been invoked in the study of interstellar and protostellar sources, but the unambiguous identification of any individual PAH has proven elusive until very recently. As a result, the formation mechanisms for this important class of molecules remain poorly constrained. Here we report the first interstellar detection of a pure hydrocarbon PAH, indene (C$_9$H$_8$), as part of the GBT Observations of TMC-1: Hunting for Aromatic Molecules (GOTHAM) survey. This detection provides a new avenue for chemical inquiry, complementing the existing detections of CN-functionalized aromatic molecules. From fitting the GOTHAM observations, indene is found to be the most abundant organic ring detected in TMC-1 to date. And from astrochemical modeling with NAUTILUS, the observed abundance is greater than the model's prediction by several orders of magnitude suggesting that current formation pathways in astrochemical models are incomplete. The detection of indene in relatively high abundance implies related species such as cyanoindene, cyclopentadiene, toluene, and styrene may be detectable in dark clouds.

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arXiv2021

Detection of Two Interstellar Polycyclic Aromatic Hydrocarbons via Spectral Matched Filtering

Ubiquitous unidentified infrared emission bands are seen in many astronomical sources. Although these bands are widely, if not unanimously, attributed to the collective emission from polycyclic aromatic hydrocarbons, no single species from this class has been detected in space. We present the discovery of two -CN functionalized polycyclic aromatic hydrocarbons, 1- and 2-cyanonaphthalene, in the interstellar medium aided by spectral matched filtering. Using radio observations with the Green Bank Telescope, we observe both bi-cyclic ring molecules in the molecular cloud TMC-1. We discuss potential in situ gas-phase formation pathways from smaller organic precursor molecules.

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arXiv2021

The TW Hya Rosetta Stone Project IV: A hydrocarbon rich disk atmosphere

Connecting the composition of planet-forming disks with that of gas giant exoplanet atmospheres, in particular through C/O ratios, is one of the key goals of disk chemistry. Small hydrocarbons like $\rm C_2H$ and $\rm C_3H_2$ have been identified as tracers of C/O, as they form abundantly under high C/O conditions. We present resolved $\rm C_3H_2$ observations from the TW Hya Rosetta Stone Project, a program designed to map the chemistry of common molecules at $15-20$ au resolution in the TW Hya disk. Augmented by archival data, these observations comprise the most extensive multi-line set for disks of both ortho and para spin isomers spanning a wide range of energies, $E_u=29-97$ K. We find the ortho-to-para ratio of $\rm C_3H_2$ is consistent with 3 throughout extent of the emission, and the total abundance of both $\rm C_3H_2$ isomers is $(7.5-10)\times10^{-11}$ per H atom, or $1-10$% of the previously published $\rm C_2H$ abundance in the same source. We find $\rm C_3H_2$ comes from a layer near the surface that extends no deeper than $z/r=0.25$. Our observations are consistent with substantial radial variation in gas-phase C/O in TW Hya, with a sharp increase outside $\sim30$ au. Even if we are not directly tracing the midplane, if planets accrete from the surface via, e.g., meridonial flows, then such a change should be imprinted on forming planets. Perhaps interestingly, the HR 8799 planetary system also shows an increasing gradient in its giant planets' atmospheric C/O ratios. While these stars are quite different, hydrocarbon rings in disks are common, and therefore our results are consistent with the young planets of HR 8799 still bearing the imprint of their parent disk's volatile chemistry.

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arXiv2021

Interstellar Detection of 2-Cyanocyclopentadiene, C$_5$H$_5$CN, a Second Five-Membered Ring Toward TMC-1

Using radio observations with the Green Bank Telescope, evidence has now been found for a second five-membered ring in the dense cloud Taurus Molecular Cloud-1 (TMC-1). Based on additional observations of an ongoing, large-scale, high-sensitivity spectral line survey (GOTHAM) at centimeter wavelengths toward this source, we have used a combination of spectral stacking, Markov chain Monte Carlo (MCMC), and matched filtering techniques to detect 2-cyanocyclopentadiene, a low-lying isomer of 1-cyanocyclopentadiene, which was recently discovered there by the same methods. The new observational data also yields a considerably improved detection significance for the more stable isomer and evidence for several individual transitions between 23 - 32 GHz. Through our MCMC analysis, we derive total column densities of $8.3\times10^{11}$ and $1.9\times10^{11}$ cm$^{-2}$ for 1- and 2-cyanocyclopentadiene respectively, corresponding to a ratio of 4.4(6) favoring the former. The derived abundance ratios point towards a common formation pathway - most likely being cyanation of cyclopentadiene by analogy to benzonitrile.

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arXiv2021

Discovery of Interstellar trans-cyanovinylacetylene (HCCCH=CHCN) and vinylcyanoacetylene (H$_2$C=CHC$_3$N) in GOTHAM Observations of TMC-1

We report the discovery of two unsaturated organic species, trans-(E)-cyanovinylacetylene and vinylcyanoacetylene, using the second data release of the GOTHAM deep survey towards TMC-1 with the 100 m Green Bank Telescope. For both detections, we performed velocity stacking and matched filter analyses using Markov chain Monte Carlo simulations, and for trans-(E)-cyanovinylacetylene, three rotational lines were observed at low signal-to-noise (${\sim}$3$σ$). From this analysis, we derive column densities of $2\times10^{11}$ and $3\times10^{11}$ cm$^{-2}$ for vinylcyanoacetylene and trans-(E)-cyanovinylacetylene, respectively, and an upper limit of $<2\times10^{11}$ cm$^{-2}$ for trans-(Z)-cyanovinylacetylene. Comparisons with G3//B3LYP semi-empirical thermochemical calculations indicate abundances of the [H$_3$C$_5$N}] isomers are not consistent with their thermodynamic stability, and instead their abundances are mainly driven by dynamics. We provide discussion into how these species may be formed in TMC-1, with reference to related species like vinyl cyanide (CH$_2$=CHCN). As part of this discussion, we performed the same analysis for ethyl cyanide (CH$_3$CH$_2$CN), the hydrogenation product of CH$_2$=CHCN. This analysis provides evidence -- at 4.17$σ$ significance -- an upper limit to the column density of $<4\times10^{11}$ cm$^{-2}$; an order of magnitude lower than previous upper limits towards this source.

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arXiv2020

The TW Hya Rosetta Stone Project I: Radial and vertical distributions of DCN and DCO+

Molecular D/H ratios are frequently used to probe the chemical past of Solar System volatiles. Yet it is unclear which parts of the Solar Nebula hosted an active deuterium fractionation chemistry. To address this question, we present 0".2-0".4 ALMA observations of DCO+ and DCN 2-1, 3-2 and 4-3 towards the nearby protoplanetary disk around TW Hya, taken as part of the TW Hya Rosetta Stone project, augmented with archival data. DCO+ is characterized by an excitation temperature of ~40 K across the 70 au radius pebble disk, indicative of emission from a warm, elevated molecular layer. Tentatively, DCN is present at even higher temperatures. Both DCO+ and DCN present substantial emission cavities in the inner disk, while in the outer disk the DCO+ and DCN morphologies diverge: most DCN emission originates from a narrow ring peaking around 30~au, with some additional diffuse DCN emission present at larger radii, while DCO+ is present in a broad structured ring that extends past the pebble disk. Based on parametric disk abundance models, these emission patterns can be explained by a near-constant DCN abundance exterior to the cavity, and an increasing DCO+ abundance with radius. There appears to be an active deuterium fractionation chemistry in multiple disk regions around TW Hya, but not in the cold planetesimal-forming midplane and in the inner disk. More observations are needed to explore whether deuterium fractionation is actually absent in these latter regions, and if its absence is a common feature, or something peculiar to the old TW Hya disk.

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arXiv2020

The TW Hya Rosetta Stone Project II: Spatially resolved emission of formaldehyde hints at low-temperature gas-phase formation

Formaldehyde (H$_2$CO) is an important precursor to organics like methanol (CH$_3$OH). It is important to understand the conditions that produce H$_2$CO and prebiotic molecules during star and planet formation. H$_2$CO possesses both gas-phase and solid-state formation pathways, involving either UV-produced radical precursors or CO ice and cold ($\lesssim 20$ K) dust grains. To understand which pathway dominates, gaseous H$_2$CO's ortho-to-para ratio (OPR) has been used as a probe, with a value of 3 indicating "warm" conditions and $<3$ linked to cold formation in the solid-state. We present spatially resolved ALMA observations of multiple ortho- and para-H$_2$CO transitions in the TW Hya protoplanetary disk to test H$_2$CO formation theories during planet formation. We find disk-averaged rotational temperatures and column densities of $33\pm2$ K, ($1.1\pm0.1)\times10^{12}$ cm$^{-2}$ and $25\pm2$ K, $(4.4\pm0.3)\times10^{11}$ cm$^{-2}$ for ortho- and para-H$_2$CO, respectively, and an OPR of $2.49\pm0.23$. A radially resolved analysis shows that the observed H$_2$CO emits mostly at rotational temperatures of 30-40 K, corresponding to a layer with $z/R\ge0.25$. The OPR is consistent with 3 within 60 au, the extent of the pebble disk, and decreases beyond 60 au to $2.0\pm0.5$. The latter corresponds to a spin temperature of 12 K, well below the rotational temperature. The combination of relatively uniform emitting conditions, a radial gradient in the OPR, and recent laboratory experiments and theory on OPR ratios after sublimation, lead us to speculate that gas-phase formation is responsible for the observed H$_2$CO across the TW Hya disk.

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