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Michiel Lambrechts

Publications and source records attributed to Michiel Lambrechts.

At least 19 recordsLinked to original sources

Cooling-regulated gas accretion onto gap-opening planets

Gas accretion onto forming planets controls the final masses of giant planets and provides observable signatures of ongoing formation. How this process depends on the cooling properties of these newly attracted gas remains poorly constrained. We present long-term, three-dimensional global hydrodynamical simulations to quantify gas accretion onto gap-opening planets in the mass range between 1 and 3 Jupiter masses. We systematically vary the cooling time, $β$, from near-isothermal ($β=10^{-2}$ in units of orbital time) to near-adiabatic ($β=10^{2}$), and follow the evolution until a quasi-steady state is reached. Our simulations show that the gas accretion rate decreases monotonically with increasing $β$, as $\dot{M}_{\rm acc}\proptoβ^{-0.18}$, reaching values at $β=10^2$ that are approximately an order of magnitude lower than locally isothermal predictions, largely independent of planet mass. The reduction in accretion is traced to thermodynamic restructuring of the circumplanetary region: inefficient cooling weakens shocks, narrows the accretion bands feeding the circumplanetary disk. Our results imply that thermodynamic effects should be taken into account when interpreting observed accretion rates of young planets, and may introduce systematic uncertainties in commonly used locally isothermal assumptions.

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Volatile depletion in rocky planets as a chemical fingerprint of hybrid accretion

Volatile depletion in rocky planets relative to their host stars is commonplace in both the Solar System and exoplanetary systems, yet the connections between planet formation and composition remain elusive. Here we model devolatilization during pebble accretion in combination with collisional growth from volatile-depleted planetesimals to explore the formation pathways of Earth and Mars. Using Bayesian inference, we find that bulk silicate Earth is best reproduced by ${\gtrsim}$75% contribution from two protoplanets formed via pebble accretion, supplemented by up to $\sim$25% material from planetesimals that are compositionally akin to the asteroid Vesta. Using instead a planetesimal volatile-depletion curve that is not observed among known meteorite parent bodies would allow the planetesimal contribution to reach 40$^{+15}_{-14}$%. In comparison, bulk silicate Mars reflects 27$\pm$5% pebble-accreted material and 73${\pm}$5% Vesta-like planetesimals. We identify volatile depletion as a chemical fingerprint of hybrid accretion, in which both pebble accretion and collisional assembly contribute to terrestrial planet growth. By quantitatively linking formation pathways to volatile budgets, our findings demonstrate how planetary accretion histories can be inferred from elemental signatures, with broad implications for interpreting the chemical diversity of rocky exoplanets.

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Dust transport in envelopes of disk-embedded planets: I. Convectively stable envelopes

Planets embedded in protoplanetary disks accrete solids through their gaseous envelopes. The spatial distribution of these dust particles inside the envelopes of disk-embedded planets is poorly known. We present high-resolution two- and three-dimensional multifluid simulations that follow the dynamics of gas and dust around planets similar in mass to Earth. Our simulations resolve an outer recycling flow and an inner convectively stable envelope that is shielded from the recycling flow. We identify strongly dust-depleted envelopes: the dust-to-gas ratio decreases radially inward and is reduced by more than two to four orders of magnitude in the deep interior ($<0.1\,R_{\rm B}$; Bondi radius) compared to its value at the outer edge of the envelope. Small grains, with a dimensionless stopping time ${\rm St}\lesssim10^{-3}$, remain entrained in the recycling flow and do not enter the envelope, whereas large grains (${\rm St}\gtrsim10^{-2}$) penetrate the envelope but settle rapidly onto the core along the midplane. The resulting dust depletion in convectively-stable envelopes implies a substantial reduction in dust opacity throughout much of the envelope, facilitating cooling and a more rapid transition to runaway gas accretion. These results further suggest that enriching the deep envelope ($<0.1\,R_{\rm B}$) with dust or volatiles requires their delivery through large pebbles that then subsequently disintegrate, or sublimate, from their host grains in the deep envelope interior.

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Dust transport in envelopes of disk-embedded planets: II. Fully convective envelopes

We perform 3D multifluid simulations of gas and dust to quantify how convection reshapes the spatial distribution of dust grains inside the envelopes of disk-embedded planets. Building on the first paper of this series, which explored convectively stable envelopes, we here consider envelopes in which convection is sustained by the accretion luminosity. The dust-to-gas ratio inside the planetary envelope is set primarily by the degree of dynamical isolation from the surrounding disk. When convection extends beyond the Bondi radius, the envelope remains connected to the disk flow and maintains a dust-rich state through continuous material exchange. Conversely, when an inner convective layer is separated from an outer recycling layer, the recycling flow filters incoming solids. The dust distribution inside the convective layer is then controlled by the competition between convective stirring and gravitational settling. This yields two regimes: a settling-dominated regime, in which large grains (typically $s\gtrsim0.1$ cm) fall at the terminal velocity and the envelope becomes dust depleted, and a convection-dominated regime, in which smaller grains are trapped in convective circulation and the envelope retains its dust. The delivery and release of volatile species from accreting solids at the envelope sublimation front, together with the efficiency of convective mixing, determine how this material is distributed between the core and envelope. Our findings imply that super-Earths and mini-Neptunes inside the water snowline have volatile-depleted cores and volatile-rich envelopes, while planets at wider orbits can have a wide diversity of envelope compositions from depleted to enriched. This compositional diversity for planetary envelopes appears to be consistent with the large diversity in observed atmospheric compositions of mini-Neptunes.

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Accretion across scales: streamers, surface-layer transport, and rapid replenishment in young protoplanetary discs

Protoplanetary discs evolve around newly-formed stars through an interplay of infall from surrounding turbulent cloud material, accretion towards the young star, and outflow driven mass-loss. It has been challenging to determine if discs are fed predominantly through infall along the disc midplane, or along the poles, and if accretion occurs in a steady or burst-like fashion. Here, we present a suite of 3D ideal magnetohydrodynamical simulations of protoplanetary disc formation and evolution in a dynamic, large-scale molecular cloud environment using the adaptive mesh refinement framework DISPATCH. We focus on nine stellar systems, where we resolve discs down to a scale of 0.8 au. Across the sample, stellar accretion proceeds at rates of $\sim$10$^{-5}$ M$_\odot$ yr$^{-1}$ over 10$^{5}$ yr, with significant variability. Discs grow to 100 au scales and remain gravitationally stable in time, with disc-to-star mass ratios below 10 %. Transient high-density streamers, with 10 kyr infall times, can drive anisotropic mass delivery at rates comparable to the background accretion flow. Their interaction with discs typically results in a temporary reduction of the disc size by half, and disc mass by 40 %. During later quiescent disc evolution stages ($t\gtrsim$50 kyr), accretion predominantly occurs through the midplane and disc surface layers. This is associated with the development of a toroidal magnetic field morphology, which includes field reversals across both disc surfaces. In this way, the full disc mass reservoir is replenished on 10 kyr-timescales. These findings support that the outer parts of very young discs, when well-ionised and close to the ideal MHD regime, are not yet conducive to planet formation, due to high replenishment rates, strong turbulence, and disruptive streamer infall events.

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A break in planet occurrence near the pebble isolation mass should be observable by the Roman microlensing survey

Microlensing detections are uniquely well-suited to probing the population of planets outside the water iceline, down to planetary masses comparable to the Earth. Here, we perform 1D pebble-accretion population synthesis simulations to explore a sample of iceline planets around stars with masses and metallicities similar to the target population of the Galactic Bulge Time-domain microlensing survey of the Nancy Grace Roman Space Telescope. We find that the planet distribution in the microlensing sensitivity space deviates from a log-uniform distribution in mass and orbital radius. When planetary core growth comes to a halt as planets reach the pebble isolation mass, $M_{\mathrm{iso}}$, the combined effects of planetary migration and runaway gas accretion create an occurrence break. Our simulations highlight that, between 1 and 50 AU, the fraction of stars hosting isolation-mass planets (1 to 5 $M_{\mathrm{iso}}$) is lower by a factor 20 compared to less massive planets (0.2 to 1 $M_{\mathrm{iso}}$). If this break in planetary occurrence rates around the pebble isolation mass is detected in future lensing surveys, it would further validate the core accretion paradigm for giant planet formation.

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Gas dynamics around dust asymmetries in turbulent disks

High-resolution ALMA observations have revealed asymmetric dust crescents in several protoplanetary disks, suggesting efficient dust trapping mechanisms potentially linked to gas vortices. While such features have been associated with vortices--whether induced by massive planets, turbulence , or other disk processes--their origin remains unclear. In this study, we investigate the viability of dust trapping by vortices that are self-sustained in disks dominated by Vertical Shear Instability (VSI) turbulence. We perform 3D hydrodynamic simulations using the PLUTO code with Lagrangian particles of three sizes (1 mm, 500~$μ$m, 100~$μ$m) to analyze the gas-dust dynamics around vortices. Our simulations reveal the formation of multiple vortices, including two characteristic large-scale, long-lived vortices that are able to capture the dust particles. We also find that dust vertical diffusion is reduced within vortices, suggesting that these structures preferentially enhance radial and azimuthal motions. Finally we generate synthetic dust continuum images at different wavelength bands and velocity residuals to compare the observable properties with ALMA observations. No clear spiral features are observed in either the synthetic dust images or the velocity residuals, unlike in vortices triggered by planets. Projection effects at high disk inclinations can obscure dust asymmetries, implying that more disks may host dust crescents than currently reported.

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From planetesimals to planets with N-body simulations in the giant-planet formation region

The cores of wide-orbit giant planets can form via pebble accretion if large planetesimals form in the outer regions of protoplanetary discs at sufficiently early times. Streaming instability simulations support mass distributions consistent with Solar System minor body constraints, but when and where planetesimal formation took place remains uncertain. Here, we report on our N-body simulations of core formation through pebble and planetesimal accretion starting from streaming-instability inspired planetesimal mass distributions. We explore two initial radial planetesimal distributions, a ring-like and a spatially more uniform distribution, between 10 and 50 AU. To address the numerical challenge of simulating realistic planetesimal numbers, corresponding to one to ten Earth masses of planetesimals, we made use of GPU acceleration for the N-body interactions (with GENGA) and a newly developed pebble accretion module. We find that the top of the planetesimal mass distribution provides the seeds for core formation through pebble accretion, leading to the formation of multiple giant planets. This is consistent with previous studies not including N-body interactions. Planetesimal surface densities, crudely corresponding to an initial 10% formation efficiency, imply low mean collision rates (around unity) in the gas disc phase. Our simulations show that giant planet formation depends only weakly on the initial locations where planetesimals form, because of rapid dynamical scattering, and on their total mass budget, due to filtering of the pebble flux between embryos. After disc dissipation, giant planet systems stir the remnant primordial planetesimals, making a scattered disc an inherent outcome of giant planet formation. Giant impacts between planetary cores generally appear to be rare in the first 100 Myr.

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Interior dynamics of envelopes around disk-embedded planets

In the core accretion scenario, forming planets start to acquire gaseous envelopes while accreting solids. Conventional one-dimensional models assume envelopes to be static and isolated. However, recent three-dimensional simulations demonstrate dynamic gas exchange from the envelope to the surrounding disk. This process is controlled by the balance between heating, through the accretion of solids, and cooling, which is regulated by poorly-known opacities. In this work, we systemically investigate a wide range of cooling and heating rates, using three-dimensional hydrodynamical simulations. We identify three distinct cooling regimes. Fast-cooling envelopes ($β\lesssim 1$, with $β$ the cooling time in units of orbital time) are nearly isothermal and have inner radiative layers that are shielded from recycling flows. In contrast, slow cooling envelopes ($β\gtrsim10^3$) become fully convective. In the intermediate regime ($1\lesssimβ\lesssim300$), envelopes are characterized by a three-layer structure, comprising an inner convective, a middle radiative, and an outer recycling layer. The development of this radiative layer traps small dust and vapour released from sublimated species. In contrast, fully convective envelopes efficiently exchange material from inner to outer envelope. Such fully convective envelopes are likely to emerge in the inner parts of protoplanetary disks ($\lesssim$ 1 au) where cooling times are long, implying that inner-disk super-Earths may see their growth stalled and be volatile depleted.

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Formation of cold giant planets around late M dwarfs via core accretion and the fate of inner rocky worlds

Modeling the formation of cold giant planets around M dwarfs is difficult because their disks may not contain enough solids to form massive cores and because forming giants are expected to migrate inward through disk interactions. It is also unclear whether inner rocky planets can survive in systems hosting a cold giant, with implications for the habitability of close-in worlds. We investigated the conditions that allow giant planets to form at 1-3 au around a 0.1 M$_\odot$ star and explored when a close-in rocky planet can survive. We perform N-body simulations in which embryos grow through pebble and gas accretion in a disk with a local turbulent viscosity of $α_t = 10^{-4}$. Planet-disk interactions are included using a prescription that triggers outward migration when the planet-to-star mass ratio ($q$) exceeds 0.002. We find that a cold giant can form even in a disk with an initial pebble mass of 6 M$_\oplus$ if the disk gas mass is 10$\%$ of the stellar mass. This requires a compact 20 au disk with a dense inner region set by $α_g = 10^{-4}$, the assembly of a $\sim$5 M$_\oplus$ core within 1 Myr, and a disk lifetime of 10 Myr. A close-in rocky planet can survive if it reaches the inner cavity before the outer body becomes a giant. Thus, giant planet formation around very low-mass stars does not require high dust masses as previously thought. A combination of planet-planet collisions, efficient pebble accretion, and a long disk lifetime plays a key role in enabling the formation of cold giant planets with masses between those of Saturn and Jupiter.

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Cosmic cascades: How disk substructure regulates the flow of water to inner planetary systems

The influx of icy pebbles to the inner regions of protoplanetary disks constitutes a fundamental ingredient in most planet formation theories. The observational determination of the magnitude of this pebble flux and its dependence on disk substructure (disk gaps as pebble traps) would be a significant step forward. In this work we analyze a sample of 21 T Tauri disks (with ages $\approx 0.5{-}2\mathrm{~Myr}$) using JWST/MIRI spectra homogeneously reduced with the JDISCS pipeline and high-angular-resolution ALMA continuum data. We find that the 1500/6000 K water line flux ratio measured with JWST - a tracer of cold water vapor and pebble drift near the snowline - correlates with the radial location of the innermost dust gap in ALMA continuum observations (ranging from 8.7 to 69 au), confirming predictions from recent models that study connections between the inner and outer disk reservoirs. We develop a population synthesis exploration of pebble drift in gapped disks and find a good match to the observed trend for early and relatively effective gaps, while scenarios where pebble drift happens quickly, gaps are very leaky, or where gaps form late are disfavored on a population level. Inferred snowline pebble mass fluxes (ranging between $10^{-6}$ and $10^{-3}~M_\oplus/\mathrm{yr}$ depending on gap position) are comparable to fluxes used in pebble accretion studies and those proposed for the inner Solar System, while system-to-system variations suggest differences in the emerging planetary system architectures and water budgets.

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Super-Earth formation in systems with cold giants

Around our Sun, terrestrial planets did not grow beyond Earth in mass, while super-Earths are found to orbit approximately every other solar-like star. It remains unclear what divides these super-Earth systems from those that form terrestrial planets, and what role wide-orbit gas giants play in this process. Here, we show that the key uncertainty is the degree of viscous heating in the inner disc, which regulates the pebble accretion efficiency. In this parameter study, we assume pebble sizes limited by fragmentation and radial drift. The initial seed planetesimals for embryo growth are taken from the top of the streaming instability mass distribution. We then evaluate the important role of the pebble scale height and the assumed pebble fragmentation velocity. In systems with maximally efficient viscous heating, where all the accretion heating is deposited in the disc midplane, pebble accretion in the terrestrial region is suppressed. More realistic levels of viscous heating, at higher elevations, allow terrestrial embryo formation at Earth-like orbits. We also find that the role of the water iceline is minor, unless it is paired with extreme volatile loss and a change in the pebble fragmentation velocity. Furthermore, we show that in systems with gas-giant formation, the role of mutual pebble filtering by outer pebble-accreting embryos is limited, unless some mechanism of delaying inner disc growth, such as viscous heating or the presence of an iceline, is simultaneously employed. This latter point appears to be consistent with the fact that no strong suppression is seen in the occurrence rate of super-Earths in systems with known gas giants in wider orbits. We conclude that the diversity in inner-disc systems may largely be driven by complex, and as of yet poorly understood, disc accretion physics inside the water iceline.

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Burned to ashes: How the thermal decomposition of refractory organics in the inner protoplanetary disc impacts the gas-phase C/O ratio

The largest reservoir of carbon in protoplanetary discs is stored in refractory organics, which thermally decompose into the gas-phase at the organics line, well interior to the water iceline. Because this region is so close to the host star, it is often assumed that the released gaseous material is rapidly accreted and plays little role in the evolution of the disc composition. However, laboratory experiments show that the thermal decomposition process is irreversible, breaking macromolecular refractory organics into simpler, volatile carbon-bearing compounds. As a result, unlike the iceline of other volatiles, which traps vapor inwards due to recondensation, the organics line remains permeable, allowing gaseous carbon to diffuse outward without returning to the solid phase. In this paper, we investigate how this process affects the disc composition, particularly the gas-phase C/H and C/O ratios, by incorporating it into a 1D evolution model for gas and solids, and assuming refractory organics dominantly decompose into C$_2$H$_2$. Our results show that this process allows this carbon-rich gas to survive well beyond the organics line (out to $7 \mathrm{~au}$ around a solar-mass star) and for much longer timescales, such that its abundance is increased by an order of magnitude. This has several implications in planet formation, notably by altering how the composition of solids and gas relate, and the fraction of heavy elements available to giant planets. In the framework of our model, refractory organics significantly influence the evolution of the gas-phase C/O ratio, which may help interpreting measurements made with Spitzer and JWST.

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A high-resolution survey of protoplanetary disks in Lupus and the nature of compact disks

Most of the exoplanets discovered in our galaxy to date orbit low-mass stars, which tend to host small disks in their early stages. To better elucidate the link between planet formation and disk substructures, observational biases should be reduced through observations of these small, faint disks at the highest resolution using the Atacama Large Millimeter Array (ALMA). In this work, we present new high-resolution (0.03-0.04") ALMA observations at 1.3 mm of 33 disks located in the Lupus star-forming region. Combining archival data and previously published work, we provide a near-complete high resolution image library of 73 protoplanetary (Class II) disks in Lupus. This enable us to measure dust disk radii down to a limit of 0.6 au and analyze intensity profiles using visibility modeling. We show that 67% of Lupus protoplanetary disks have dust radii smaller than 30 au, with new substructures detected in 11, showing some of the shortest separation gaps. The size-luminosity relation in Lupus aligns well with a drift-dominated dust evolution scenario and, for the most compact disks (< 30 au), we found dust masses ranging from 0.3 to 26.3 Earth masses. Assuming that the detected substructures were dynamical effects of planets, we estimated the planet masses to range from 20 to 2000 Earth masses with separations between 2 to 74 au. Our results indicate that two-thirds of the protoplanetary disks in Lupus are smooth, and compact, with substructures being more prominent in the few larger disks. These compact disks are consistent with drift-dominated evolution, with their masses and optical depths suggesting that they may have already experienced some planet formation, with most of the small solids converted into planetesimals and planets. This makes them prime candidates, for explaining the formation and origin of super-Earths. [Abridged]

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The influence of dust growth on the observational properties of circumplanetary discs

Dust growth is often indirectly inferred observationally in star-forming environments, theoretically predicted to produce mm-sized particles in circumstellar discs, and also presumably witnessed by the predecessors of the terrestrial meteoritic record. For those reasons it is believed that young gas giants under formation in protoplanetary discs with putative circumplanetary discs (CPDs) surrounding them, such as PDS 70c, should be containing mm-sized particles. We model the spectra of a set of CPDs, which we obtained from radiation hydrodynamic simulations at varying Rosseland opacities kappa_R. The kappa_R from the hydrodynamic simulations are matched with consistent opacity sets of ISM-like composition, but grown to larger sizes. Our high kappa_R hydro data nominally corresponds to 10 mum-sized particles, and our low kappa_R-cases correspond to mm-sized particles. We investigate the resulting broad spectral features at first while keeping the overall optical depth in the planetary envelope constant. Dust growth to size distributions dominated by millimeter particles generally results in broad, featureless spectra with black-body like slopes in the far-infrared, while size distributions dominated by small dust develop steeper slopes in the far-infrared and maintain some features stemming from individual minerals. We find that significant dust growth from microns to millimeters can explain the broad features of the PDS 70c data, when upscaling the dust masses from our simulations by x100. Furthermore our results indicate that the spectral range of 30-500 mum is an ideal hunting ground for broadband features arising from the CPD, but that longer wavelengths observed with ALMA can also be used for massive circumplanetary discs

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The evolution of the flux-size relationship in protoplanetary discs by viscous evolution and radial pebble drift

In this paper we study the evolution of radiative fluxes, flux radii and observable dust masses in protoplanetary discs, in order to understand how these depend on the angular momentum budget and on the assumed heat sources. We use a model that includes the formation and viscous evolution of protoplanetary gas discs, together with the growth and radial drift of the dust component. We find that we are best able to match the observed fluxes and radii of class 0/I discs when we assume (i) an initial total angular momentum budget corresponding to a centrifugal radius of 40 au around solar-like stars, and (ii) inefficient viscous heating. Fluxes and radii of class II discs appear consistent with disc models with angular momentum budgets equivalent to centrifugal radii of both 40 au or 10 au for solar like stars, and with models where viscous heating occurs at either full efficiency or at reduced efficiency. During the first 0.5 Myr of their evolution discs are generally optically thick at a wavelength of 1.3 mm. However, after this discs are optically thin at mm-wavelengths, supporting standard means of dust mass estimates. Using a disc population synthesis model, we then show that the evolution of the cumulative evolution of the observable dust masses agrees well with that observed in young star forming clusters of different ages.

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UV-processing of icy pebbles in the outer parts of VSI-turbulent disks

Icy dust particles emerge in star-forming clouds and are subsequently incorporated in protoplanetary disks, where they coagulate into larger pebbles up to mm in size. In the disk midplane, ices are shielded from UV radiation, but moderate levels of disk turbulence can lift small particles to the disk surface, where they can be altered, or destroyed. Nevertheless, studies of comets and meteorites generally find that ices at least partly retained their interstellar medium (ISM) composition before being accreted onto these minor bodies. Here we model this process through hydrodynamical simulations with VSI-driven turbulence in the outer protoplanetary disk. We use the PLUTO code in a 2.5 D global accretion setup and include Lagrangian dust particles of 0.1 and 1 mm sizes. In a post-processing step, we use the RADMC3D code to generate the local UV radiation field to assess the level of ice processing of pebbles. We find that a small fraction ($\sim$17$\%$) of 100 $μ$m size particles are frequently lifted up to $Z/R=0.2$ which can result in the loss of their pristine composition as their residence time in this layer allows for effective CO and water photodissociation. The larger 1 mm size particles remain UV-shielded in the disk midplane throughout the dynamical evolution of the disk. Our results indicate that the assembly of icy bodies via the accretion of drifting mm-size icy pebbles can explain the presence of pristine ice from the ISM, even in VSI-turbulent disks. Nevertheless, particles $\leq$ 100 $μ$m experience efficient UV processing and may mix with unaltered icy pebbles, resulting in a less ISM-like composition in the midplane.

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JWST/MIRI detection of a carbon-rich chemistry in a solar nebula analog

It has been proposed, and confirmed by multiple observations, that disks around low mass stars display a molecule-rich emission and carbon-rich disk chemistry as compared to their hotter, more massive solar counterparts. In this work, we present JWST Disk Infrared Spectral Chemistry Survey (JDISCS) MIRI-MRS observations of the solar-mass star DoAr 33, a low-accretion rate T Tauri star showing an exceptional carbon-rich inner disk. We report detections of H$_2$O, OH, and CO$_2$, as well as the more complex hydrocarbons, C$_2$H$_2$ and C$_4$H$_2$. Through the use of thermochemical models, we explore different spatial distributions of carbon and oxygen across the inner disk and compare the column densities and temperatures obtained from LTE slab model retrievals. We find a best match to the observed column densities with models that have carbon enrichment, and the retrieved emitting temperature and area of C$_2$H$_2$ with models that have C/O $=$ 2$-$4 inside the 500 K carbon-rich dust sublimation line. This suggests that the origin of the carbon-rich chemistry is likely due to the sublimation of carbon rich grains near the soot line. This would be consistent with the presence of dust processing as indicated by the detection of crystalline silicates. We propose that this long-lived hydrocarbon rich chemistry observed around a solar-mass star is a consequence of the unusually low M-star-like accretion rate of the central star, which lengthens the radial mixing timescale of the inner disk allowing the chemistry powered by carbon grain destruction to linger.

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