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Mario Flock

Publications and source records attributed to Mario Flock.

At least 19 recordsLinked to original sources

A robust super-time-stepping scheme for Ohmic and ambipolar diffusion

Context. Non-ideal magnetohydrodynamics (MHD) is a key tool for modeling magnetic flux transport in astrophysical systems such as molecular clouds, protostellar cores, and protoplanetary disks. Conventional explicit methods for non-ideal MHD diffusion are severely limited by timestep constraints, while substepping approaches can be unstable due to truncation errors near boundaries and strong magnetic-field gradients. Aims. Our main goal is to address these limitations by developing robust super-time-stepping methods for Ohmic and ambipolar diffusion. Methods. We present a super-time-stepping method based on the stability of the Gegenbauer polynomials. The method is designed to enhance robustness in the presence of strongly anisotropic resistivity and to reduce sensitivity to truncation errors near boundaries. We implement the scheme in the PLUTO code and assess its performance through dedicated Ohmic and ambipolar diffusion tests. We also compare this novel numerical scheme against two common astrophysical problems, namely magnetic reconnection and the magnetorotational instability. Results. The novel Runge-Kutta-Gegenbauer scheme retains computational efficiency beyond purely explicit schemes while providing excellent stability compared with other traditional substepping methods. It remains stable in the presence of strongly anisotropic diffusion, enabling accurate magnetic-field evolution in regimes characteristic of protoplanetary disks and collapsing dense cores. Benchmark tests, including magnetic reconnection and magnetorotational-instability setups, confirm the method's accuracy, efficiency, and suitability for large-scale non-ideal MHD simulations.

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MRI-triggered instability at the inner dead zone edge: disc evolution and burst modes tied to magnetic field strengths

The inner edge of the dead zone (DZIE) in protoplanetary discs is prone to episodic instability caused by the activation of the magneto-rotational instability (MRI) in the weakly turbulent regions. We show how different magnetic field configurations set the inner disc structure and regulate the morphologies of instability cycles. We performed 2D and 3D radiation hydrodynamic simulations of the regions around the DZIE of a Class II disc over a thousand-year timescale. We implemented MRI activation criteria based on ambipolar and Ohmic diffusion coupled to magnetic field strength profiles comprising stellar and disc components. The properties and consequences of the episodic accretion events are highly sensitive to the magnetic field strength. We recover previously reported behaviour by considering relatively strongly magnetised discs. A new burst mode is revealed, in which the midplane MRI activity is restricted to small radii in the presence of weak magnetic fields. In this narrow mode, the pressure bump at the DZIE does not remain static even during quiescence. A distinct dichotomy between the wide and narrow modes is established by the hydrodynamic (in)stability of the ionisation front. Both modes are additionally separated into a reflaring and a non-reflaring version. Our setup does not lead to the classical thermal instability by hydrogen ionisation. In quiescence, the MRI active region shows a layered structure that converges towards the midplane near the star. Our 3D model reveals the breaking of density features produced in the narrow mode, leading to vortices at radii smaller than 0.5 AU. Coupling MRI activity directly to different magnetic field strengths, rather than using simple temperature thresholds, enables a variety of burst modes. Each mode exhibits characteristic accretion burst signatures and has different consequences for planet formation and migration conditions.

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Substructures Induced by Dust Drag in Protoplanetary Disks

Dust substructures observed in protoplanetary disks are commonly attributed to embedded planets; however, intrinsic gas-dust interactions can also generate complex morphologies. We performed two-dimensional, axisymmetric simulations of gas and dust that include dust back-reaction and parameterized turbulence to investigate how the streaming instability (SI) and vertical shear instability (VSI) shape dust distributions. With moderate viscosity and sufficiently high metallicity, we identify a characteristic shuttlecock-shaped dust substructure composed of a dense, vertically settled "head" and a vertically extended "tail." This morphology arises from nonlinear SI driven by marginally coupled grains and the associated modification of gas flows. The dust scale height in the tail exceeds predictions based on the simple diffusion-settling balance, indicating strong self-generated turbulence. With lower viscosity, VSI becomes more vigorous, disrupts midplane structures, and increases vertical stirring; nevertheless, for dust grains with Stokes numbers around 0.01, SI can still attain dust-to-gas ratios of up to 20-50, potentially approaching the Hill density for gravitational binding. Our results demonstrate that intrinsic gas-dust interactions can generate prominent dust substructures even in disks with finite viscosity and, under favorable conditions, concentrate dust to levels relevant for planetesimal 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~$\mu$m, 100~$\mu$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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exoALMA XXII: A Two-dimensional Atlas of Deviations from Keplerian Disks

Protoplanetary disks are the birthplaces of planetary systems, and deviations from Keplerian rotation imprinted in disk gas kinematics serve as key tracers of physical processes and the presence of protoplanets within disks. Using the the CO (J=3-2) data from the exoALMA Large Program encompassing 15 disks, we constructed two-dimensional (2D) maps of centroid velocity, line width, and peak intensity, and extracted non-Keplerian deviations by subtracting smooth Keplerian models. This paper provides the first systematic and uniform overview of 2D gas substructures across the entire exoALMA sample. We find that all targets exhibit large-scale deviations from smooth Keplerian disks, displaying a variety of morphologies including spiral-like structures, arc- or ring-like features, and patterns indicative of variations in the emitting surface height. Non-axisymmetric spiral-arm features are detected or suggested in five disks (CQ Tau, MWC 758, HD 135344B, HD 34282, and SY Cha), and are preferentially found in Herbig Ae/Fe systems. In contrast, some other sources (J1852, PDS 66, and V4046 Sgr), despite exhibiting noticeable deviations, appear to be dynamically quieter. This 2D atlas suggests that kinematic substructures are ubiquitous in large ($\gtrsim$ 100 au) protoplanetary disks with ages of a few million years, based on the observations obtained with sufficient sensitivity at moderate-to-high spatial resolution of $\sim$20 au and high velocity resolution of $\sim$0.1 km s$^{-1}$.

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exoALMA XXI: The Morphology and Dynamics of Vertical Flows

Vertical gas flows, such as winds and meridional circulations, are natural outcomes of protoplanetary disk processes and play a critical role in the earliest stages of planet formation. We analyze vertical gas motions in 14 disks as part of the exoALMA Large Program, focusing on the 12CO J=3-2 and 13CO J=3-2 emission lines. Using discminer to model the Keplerian velocity field, we extract line-of-sight velocity residuals and measure the radial and vertical components of the gas motion. Vertical motions are detected in most disks. Two types of patterns emerge: (1) oscillatory up/down flows, likely linked to instabilities, and (2) transitions from downward to upward motions that we interpret as the base of a disk wind. In most cases, the velocity amplitudes are of a few tens of m/s. Two disks, however, MWC758 and CQ Tau, show two spiral velocity features in their residual maps, red- and blue-shifted, which we interpret as vertical velocities reaching up to 350 m/s (0.7 Cs), consistent with gas motion in eccentric disks. Fast upward motions (up to 500 m/s; 1.8 Cs) is also detected in the outer disk of MWC758. Synthetic observations from (magneto)hydrodynamic simulations validate the reliability of our method. Although strong molecular winds appear to be relatively rare in 12CO and 13CO, our study shows that, when traced by deep high spectral resolution line data, protoplanetary disks exhibit ubiquitous vertical flows. However, their overall velocity structure is highly complex, preventing to identify a coherent, dominant physical mechanism driving the vertical motions across all disks, thus requiring further theoretical investigation.

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exoALMA XX: Tomographic Detection of Embedded Planets in Protoplanetary Disks

The exoALMA Large Program has revealed a wealth of substructures in the dust and molecular line emission of several protoplanetary discs, suggesting that planet formation may unfold within highly dynamic environments. Using synthetic observations of planet-disc interactions and disc instabilities, we demonstrate how the origin of these substructures can be investigated through a tomographic study of molecular lines, extending the scope of the analysis beyond line-centroid kinematics alone. Our results indicate that with only a few hours of ALMA integration at moderate angular resolution ($0.15''-0.30''$), it is possible to identify the key signatures driven by planets more massive than 0.1% of the stellar mass. These signatures manifest not only as deviations from Keplerian motion but also as localized line broadening, enabling accurate constraints on the orbital radius and azimuthal location of the planets. We further show that a diagnostic based on line skewness in spectrally resolved observations can help distinguish between planetary and instability-driven signatures, owing to the distinct degrees of velocity coherence associated with each mechanism. Finally, we apply this tomographic analysis to exoALMA CO line data for the discs of HD 135344B and MWC 758. In HD 135344B, we identify strongly localized velocity and line-width perturbations, suggesting the possibility of three massive planets embedded in the disc: one at $R=95$ au, exterior to the continuum substructures, and two within dust gaps at $R=41$ au and $R=73$ au. For MWC 758, the dominance of vertical-velocity spirals over localized signatures is consistent with predictions from models of moderate disc eccentricities or warps, potentially induced by a substellar companion in the inner regions of the system.

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A Comparative Study of the Streaming Instability: Unstratified Models with Marginally Coupled Grains

The streaming instability is a leading mechanism for concentrating solids and initiating planetesimal formation in protoplanetary disks. Although numerous studies have explored its linear growth, nonlinear evolution, and implications for planet formation, the diversity of numerical methods and dust treatments used across the literature has made it difficult to assess which features of the instability are physically robust and which arise from code-dependent choices. We present the first systematic comparison of seven hydrodynamic codes--spanning finite-volume and finite-difference schemes and modeling dust either as Lagrangian particles or as a pressureless fluid--applied to the unstratified streaming instability with a dimensionless stopping time of unity. All codes reproduce the characteristic sequence of exponential growth, filament formation, and turbulent saturation, demonstrating broad agreement in the qualitative behavior of the instability. Quantitatively, however, the dust model remains the dominant source of variation at moderate resolution: particle-based simulations reach higher peak densities and exhibit broader high-density tails than fluid-based models at $512^2$ resolution, although increasing the number of particles brings their initial maximum density evolution into close agreement with that of dust-fluid models. At $1024^2$, these differences diminish substantially, indicating better agreement of the saturated-state statistics across dust treatments. In terms of computational performance, most particle implementations suffer from imbalanced parallelized loads, while execution on a GPU is at least two to three times more energy efficient and scales better at higher resolutions than on CPUs. Given the intrinsic stochasticity of this nonlinear system, only statistical diagnostics remain meaningful across codes.

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The role of detailed gas and dust opacities in shaping the evolution of the inner disc edge subject to episodic accretion

We investigate the effects of different dust and gas opacity descriptions on the structure and evolution of the inner regions of protoplanetary discs. The influence on the episodic instability of the inner rim is hereby of central interest. 2D axisymmetric radiation hydrodynamic models are employed to simulate the evolution of the inner disc over several thousand years. Our simulations greatly expand on previous models by implementing detailed opacity descriptions in terms of their mean and frequency-dependent values, allowing us to also consider binned frequency-dependent irradiation. The adaptive opacity description significantly affects the structure of the inner disc rim, with gas opacities exerting the greatest influence. The resulting effects include shifts in the position of both the dust sublimation front and the dead zone inner edge, a significantly altered temperature in the dust-free region and the manifestation of an equilibrium temperature degeneracy as a sharp temperature transition. The episodic instability due to MRI activation in the dead zone still occurs, but at lower inner disc densities. While the gas opacities set the initial conditions for the instability, the evolution of the outburst itself is mainly governed by the dust opacities. The analysis of criteria for non-axisymmetric instabilities reveals possible breaking of the density peaks produced by the burst. However, due to the periodicity of the instability, the inner edge itself may remain stable throughout quiescent phases according to linear criteria. Although the thermal structure of the inner disc is crucially affected by different opacity descriptions, the mechanism of the periodic instability of the DZIE remains active and is only marginally influenced by gas opacities. The observational consequences of the severely altered temperatures may be significant and require further investigation.

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exoALMA XIX: Confirmation of Non-thermal Line Broadening in the DM Tau Protoplanetary Disk

Turbulence is expected to transport angular momentum and drive mass accretion in protoplanetary disks. One way to directly measure turbulent motion in disks is through molecular line broadening. DM Tau is one of only a few disks with claimed detection of nonthermal line broadening of 0.25cs-0.33cs, where cs is the sound speed. Using the radiative transfer code mcfost within a Bayesian inference framework that evaluates over five million disk models to efficiently sample the parameter space, we fit high-resolution (0.15", 28 m s-1) 12CO J = 3-2 observations of DM Tau from the exoALMA Large Program. This approach enables us to simultaneously constrain the disk structure and kinematics, revealing a significant nonthermal contribution to the line width of ~0.4cs, inconsistent with purely thermal motions. Using the CO-based disk structure as a starting point, we reproduce the CS J = 7-6 emission well, demonstrating that the CS (which is more sensitive to nonthermal motions than CO) agrees with the turbulence inferred from the CO fit. Establishing a well-constrained background disk model further allows us to identify residual structures in the moment maps that deviate from the expected emission, revealing localized perturbations that may trace forming planets. This framework provides a powerful general approach for extracting disk structure and nonthermal broadening directly from molecular line data and can be applied to other disks with high-quality observations.

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Starlight-driven flared-staircase geometry in radiation hydrodynamic models of protoplanetary disks

Protoplanetary disks observed in millimeter continuum and scattered light show a variety of substructures. Various physical processes in the disk could trigger such features -- one of which that has been previously theorized for passive disks is the thermal wave instability -- the flared disk may become unstable as directly illuminated regions puff up and cast shadows behind them. This would manifest as bright and dark rings, and a staircase-like structure in the disk optical surface. We provide a realistic radiation hydrodynamic model to test the limits of the thermal wave instability in irradiated disks. We carry out global axisymmetric 2D hydrostatic and dynamic simulations including radiation transport with frequency-dependent ray-traced irradiation and flux-limited diffusion (FLD). We found that starlight-driven shadows are most prominent in optically thick, slow cooling disks, shown by our models with high surface densities and dust-to-gas ratios of sub-micron grains of 0.01. We recover that thermal waves form and propagate inwards in the hydrostatic limit. In contrast, our hydrodynamic models show bumps and shadows within 30 au that converge to a quasi-steady state on several radiative diffusion timescales -- indicating a long-lived staircase structure. We find that existing thermal pressure bumps could produce and enhance this effect, forming secondary shadowing downstream. Hydrostatic models with self-consistent dust settling instead show a superheated dust irradiation absorption surface with a radially smooth temperature profile without staircases. We conclude that one can recover thermally induced flared-staircase structures in radiation hydrodynamic simulations of irradiated protoplanetary disks using flux-limited diffusion. We highlight the importance of modeling dust dynamics consistently to explain starlight-driven shadows.

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Polarization at millimeter wavelengths caused by drifting grains in protoplanetary disks

During the evolution of protoplanetary disks, dust grains start to grow, form larger particles, settle to the midplane, and rearrange the disk, mainly by the inward radial drift. Because of this, dust pebbles with an irregular shape usually align mechanically and thus cause polarization signatures in their thermal radiation due to dichroic emission or absorption. The goal of this paper is to evaluate the potential to trace the impact of mechanical grain alignment in protoplanetary disks on the observed degree and orientation of linear polarization at millimeter wavelengths. We combined 3D radiation hydrodynamical simulations to determine the density distribution and the velocity field of gas and dust particles, Monte Carlo dust-gas interaction simulations to calculate the mechanical alignment of dust in a gas flow, and, finally, 3D Monte Carlo polarized radiative transfer simulations to obtain synthetic polarimetric observations. We find that large grains, which contribute the most to the net polarization, are potentially mechanically aligned in the protoplanetary disk under the effect of the vertical shear instability (VSI). Thereby, the drift velocity is parallel to the rotational disk axis. Assuming oblate dust grains that are aligned with their short axis parallel to the direction of the drift velocity, the resulting polarization is usually along the major axis of the disk. This is in contrast to typical drift models that propose either a radial or azimuthal drift velocity component. If hydrodynamical instabilities, such as the VSI, dominate the kinematics in protoplanetary disks, the mechanical alignment of dust is a promising mechanism for grain alignment in these systems. In that case, the resulting millimeter polarization allows us to trace the orientation of aligned millimeter-sized grains.

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Dynamical Analysis of the HD 169142 Planet-Forming Disk: Twelve Years of High-Contrast Polarimetry

We present a dynamical analysis of the HD 169142 planet-forming disk based on high-contrast polarimetric imaging over a twelve-year observational period, offering insights into its disk evolution and planet-disk interactions. This study explores the evolution of scattered-light features and their relationship with millimeter continuum emission. Archival visible-to-near-infrared scattered-light observations from NACO, SPHERE, and GPI combined with new observations from SCExAO reveal persistent non-axisymmetric structures in both the inner and outer rings of the disk. Through Keplerian image transformations and phase cross-correlation techniques, we show that the azimuthal brightness variations in the inner ring follow the local Keplerian velocity, suggesting these are intrinsic disk features rather than planet-induced spirals or shadows. The motion of the outer ring is weakly detected, requiring a longer observational baseline for further confirmation. Comparing scattered-light features with ALMA 1.3 mm-continuum data, we find that the scattered light traces the edges of dust structures in the inner ring, indicating complex interactions and a leaky dust trap around the water-ice snowline. These findings highlight the capability of long-term monitoring of circumstellar disks to distinguish planetary influences from Keplerian disk dynamics.

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Multi dust species inner rim in magnetized protoplanetary disks

The inner regions of protoplanetary disks, within ten astronomical units, are where terrestrial planets are born. By developing a new class of multi-dust radiative magnetized inner rim models, we can gain valuable insights into the conditions during planet formation. Our goal is twofold: to study the influence of highly refractory dust species on the inner rim shape and to determine how the magnetic field affects the inner disk structure. The resulting temperature and density structures are analyzed and compared to observations. The comparison focuses on a median SED of Herbig stars and interferometric constraints from the H, K, and N-band of three Herbig-type star-disk systems: HD 100546, HD 163296, and HD 169142. We investigate 1) the influence of a large-scale magnetic field on the inner disk structure and 2) the effect of having the four most important dust species (corundum, iron, forsterite, and enstatite) shaping the rim. We use frequency-dependent irradiation and the effect of accretion heating. With the Optool package, we obtain frequency-dependent opacities for each dust grain family and calculate the corresponding temperature-dependent Planck and Rosseland opacities. Our models with multiple dust species show a smoother and radially more extended inner rim. Strongly magnetized disks show a substantial increase in the emission flux between the L and N-bands. Weakly magnetized disk models with large-scale vertical magnetic fields < 0.3 Gauss at 1 au best fit with NIR interferometric observations. Our model comparison supports the existence of moderate magnetic fields ($\beta$ > $10^4$), which could still drive a magnetic wind in the inner disk. Our results show that multi-dust models, including magnetic fields, still lack NIR emission, especially in the H-band. One potential solution might be a heated gas disk or evaporating objects like planetesimals close to the star.

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Hydrodynamical simulations of the vertical shear instability with dynamic dust and cooling rates in protoplanetary disks

Turbulence in protoplanetary disks affects dust evolution and planetesimal formation. The vertical shear instability (VSI) is one of the candidate turbulence-driving mechanisms in the outer disk region. Since the VSI requires rapid gas cooling, dust grains in disks can influence and potentially control VSI-driven turbulence. However, VSI-driven turbulence has strong vertical motion, causing vertical dust diffusion. As a result, it remains unclear how turbulent structures and dust distributions form. We aim to clarify whether the VSI can achieve a quasi-steady dust profile under cooling rate evolution associated with turbulently diffusing dust. We also elucidate the dependence of the dust size and dust-to-gas mass ratio on the realization and persistence of the equilibrium state. We perform global two-dimensional hydrodynamical simulations of an axisymmetric disk to investigate how the VSI drives turbulence and maintains a balance between dust settling and diffusion. These simulations account for the dynamic interplay between dust distribution, cooling rates, and turbulence. We find that VSI mixing, dust settling, and local cooling reach an equilibrium, forming a thick dust layer with a dimensionless vertical mixing coefficient of approximately 10^{-3}. The ability of the VSI to sustain this state also depends on the dust size and dust-to-gas mass ratio. Larger grains or lower mass ratios weaken turbulence, leading to dust settling. The condition of equilibrium state existence is consistent with the prediction of the semi-analytic model presented by Fukuhara & Okuzumi (2024). Our results indicate that efficient turbulent dust mixing and efficient cooling can occur simultaneously. They also imply that turbulence in VSI-dominated disks has different intensity levels depending on the grain size. This suggests that the efficiency of dust growth can depend on the VSI in protoplanetary disks.

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exoALMA XIV. Gas Surface Densities in the RX J1604.3-2130 A Disk from Pressure-broadened CO Line Wings

The gas surface density is one of the most relevant physical quantities in protoplanetary disks. However, its precise measurement remains highly challenging due to the lack of a direct tracer. In this study, we report the spatially-resolved detection of pressure-broadened line wings in the CO $J=3-2$ line in the RX J1604.3-2130 A transition disk as part of the exoALMA large program. Since pressure-broadened line wings are sensitive to the total gas volume density, we robustly constrain the radial dependence of the gas surface density and midplane pressure in the region located $50-110$ au from the central star, which encompasses the dust ring of the system. The peak radius of the midplane pressure profile matches the dust ring radial location, directly proving radial dust trapping at a gas pressure maximum. The peak gas surface density is $18-44\ {\rm g\ cm^{-2}}$} and decreases at radii interior to and exterior of the dust ring. A comparison of the gas and dust surface densities suggests that the disk turbulence is as low as $\alpha_{\rm turb} \sim 2\times10^{-4}$. Despite dust trapping, the gas-to-dust surface density ratio at the ring peak is { $70-400$}, which implies already-formed protoplanets and/or less efficient dust trapping. The gas surface density drop at radii interior to the ring is consistent with a gas gap induced by a Jupiter-mass planet. The total gas mass within $50 < r < 110$ au is estimated to be $\sim 0.05-0.1\ M_\odot$ ($50-100\ {M_{\rm Jup}}$), suggesting that planetary system formation is possible.

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exoALMA. XVI. Predicting Signatures of Large-scale Turbulence in Protoplanetary Disks

Turbulent gas motions drive planet formation and protoplanetary disk evolution. However, empirical constraints on turbulence are scarce, halting our understanding of its nature. Resolving signatures of the large-scale perturbations driven by disk instabilities may reveal clues on the origin of turbulence in the outer regions of planet-forming disks. We aim to predict the observational signatures of such large-scale flows, as they would appear in high-resolution Atacama Large Millimeter/submillimeter Array observations of CO rotational lines, such as those conducted by the exoALMA Large Program. Post-processing 3D numerical simulations, we explored the observational signatures produced by three candidate (magneto-)hydrodynamical instabilities to operate in the outer regions of protoplanetary disks: the vertical shear instability (VSI), the magneto-rotational instability (MRI), and the gravitational instability (GI). We found that exoALMA-quality observations should capture signatures of the large-scale motions induced by these instabilities. Mainly, flows with ring, arc, and spiral morphologies are apparent in the residuals of synthetic velocity centroid maps. A qualitative comparison between our predictions and the perturbations recovered from exoALMA data suggests the presence of two laminar disks and a scarcity of ring- and arc-like VSI signatures within the sample. Spiral features produced by the MRI or the GI are still plausible in explaining observed disk perturbations. Supporting these scenarios requires further methodically comparing the predicted perturbations and the observed disks' complex dynamic structure.

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exoALMA XI: ALMA Observations and Hydrodynamic Models of LkCa 15: Implications for Planetary Mass Companions in the Dust Continuum Cavity

In the past decade, the Atacama Large Millimeter/submillimeter Array (ALMA) has revealed a plethora of substructures in the disks surrounding young stars. These substructures have several proposed formation mechanisms, with one leading theory being the interaction between the disk and newly formed planets. In this Letter, we present high angular resolution ALMA observations of LkCa~15's disk that reveal a striking difference in dust and CO emission morphology. The dust continuum emission shows a ring-like structure characterized by a dust-depleted inner region of $\sim$40 au in radius. Conversely, the CO emission is radially smoother and shows no sign of gas depletion within the dust cavity. We compare the observations with models for the disk-planet interaction, including radiative transfer calculation in the dust and CO emission. This source is particularly interesting as the presence of massive planets within the dust cavity has been suggested based on previous NIR observations. We find that the level of CO emission observed within the dust cavity is inconsistent with the presence of planets more massive than Jupiter orbiting between 10-40 au. Instead, we argue that the LkCa~15 innermost dust cavity might be created either by a chain of low-mass planets, or by other processes that do not require the presence of planets.

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