Evolution of magnetized protoplanetary disks

We investigate the global evolution of a turbulent protoplanetary disk incorporating the effects of Maxwell stress due to a large-scale magnetic field permeating the disk. A magnetic field is produced continuously by an αΩ dynamo and the resultant Maxwell stress assists the viscous stress in p roviding the means for disk evolution. The most striking feature of magnetized disk evolution is the presence of the surface density bulge located in the “magnetic gap”, the region of the disk where the degree of ionization is too low to allow for coupli ng between the magnetic field and the gas. The bulge persists for a time of the order of 105–106 yr. The presence and persistence of the surface density bulge may have important implications for the process of planet formation and the overall characteristics of resultant planetary systems.

Aims. Accretion bursts triggered by the magnetorotational instability (MRI) in the innermost disk regions were studied for protoplanetary gas-dust disks that formed from prestellar cores of a various mass Mcore and mass-to-magnetic flux ratio λ. Methods. Numerical magnetohydrodynamics simulations in the thin-disk limit were employed to study the long-term (~1.0 Myr) evolution of protoplanetary disks with an adaptive turbulent α-parameter, which explicitly depends on the strength of the magnetic field and ionization fraction in the disk. The numerical models also feature the co-evolution of gas and dust, including the back-reaction of dust on gas and dust growth. Results. A dead zone with a low ionization fraction of x≲10−13 and temperature on the order of several hundred Kelvin forms in the inner disk soon after its formation, extending from several to several tens of astronomical units depending on the model. The dead zone features pronounced dust rings that are formed due to the concentration of grown dust particles in the local pressure maxima. Thermal ionization of alkaline metals in the dead zone trigger the MRI and associated accretion burst, which is characterized by a sharp rise, small-scale variability in the active phase, and fast decline once the inner MRI-active region is depleted of matter. The burst occurrence frequency is highest in the initial stages of disk formation and is driven by gravitational instability (GI), but it declines with diminishing disk mass-loading from the infalling envelope. There is a causal link between the initial burst activity and the strength of GI in the disk fueled by mass infall from the envelope. We find that the MRI-driven burst phenomenon occurs for λ = 2–10, but diminishes in models with Mcore ≲ M⊙, suggesting a lower limit on the stellar mass for which the MRI-triggered burst can occur. Conclusions. The MRI-triggered bursts occur for a wide range of mass-to-magnetic flux ratios and initial cloud core masses. The burst occurrence frequency is highest in the initial disk formation stage and reduces as the disk evolves from a gravitationally unstable to a viscous-dominated state. The MRI-triggered bursts are intrinsically connected with the dust rings in the inner disk regions, and both can be a manifestation of the same phenomenon, that is to say the formation of a dead zone.

Context. During the evolution of protoplanetary disks into planetary systems we expect to detect signatures that trace mechanisms such as planet–disk interaction. Protoplanetary disks display a large variety of structures in recently published high-spatial resolution images. However, the three-dimensional morphology of these disks is often difficult to infer from the two-dimensional projected images we observe. Aims. We aim to detect signatures of planet–disk interaction by studying the scattering surface of the protoplanetary disk around HD 34282. Methods. We spatially resolved the disk using the high-contrast imager VLT/SPHERE in polarimetric imaging mode. We retrieved a profile for the height of the scattering surface to create a height-corrected deprojection, which simulates a face-on orientation. Results. The detected disk displays a complex scattering surface. An inner clearing or cavity extending up to r < 0.′′28 (88 au) is surrounded by a bright inclined (i = 56°) ring with a position angle of 119°. The center of this ring is offset from the star along the minor axis with 0.′′07, which can be explained with a disk height of 26 au above the midplane. Outside this ring, beyond its southeastern ansa we detect an azimuthal asymmetry or blob at r ~ 0.′′4. At larger separation, we detect an outer disk structure that can be fitted with an ellipse, which is compatible with a circular ring seen at r = 0.′′62 (=190 au) and a height of 77 au. After applying a height-corrected deprojection we see a circular ring centered on the star at 88 au; what had seemed to be a separate blob and outer ring could now both be part of a single-armed spiral. Conclusions. We present the first scattered-light image of the disk around HD 34282 and resolve a disk with an inner cavity up to r ≈ 90 au and a highly structured scattering surface of an inclined disk at a large height Hscat∕r = 0.′′29 above the midplane at the inner edge of the outer disk. Based on the current data it is not possible to conclude decisively whether Hscat∕r remains constant or whether the surface is flared with at most Hscat ∝ r1.35, although we favor the constant ratio based on our deprojections. The height-corrected deprojection allows for a more detailed interpretation of the observed structures, from which we discern the first detection of a single-armed spiral in a protoplanetary disk.

The evolution of protoplanetary discs and the related process of planet formation is regulated by angular momentum transport and mass-loss processes. Over the past decade, the paradigm of viscosity has been challenged and MHD disc winds appear as a compelling scenario to account for disc accretion. In this work, we aim to construct the equivalent of the widely used analytical description of viscous evolution for the MHD wind case. The transport of angular momentum and mass induced by the wind is parametrized by an α-like parameter and by the magnetic lever arm parameter λ. Extensions of the paradigmatic Lynden-Bell and Pringle similarity solutions to the wind case are presented. We show that wind-driven accretion leads to a steeper decrease in the disc mass and accretion rate than in viscous models due to the absence of disc spreading. If the decline of the magnetic field strength is slower than that of the gas surface density, the disc is dispersed after a finite time. The evolution of the disc in the $\dot{M}_*-M_{D}$ plane is sensitive to the wind and turbulence parameters. A disc population evolving under the action of winds can exhibit a correlation between $\dot{M}_*$ and MD depending on the initial conditions. The simplified framework proposed in this work opens to a new avenue to test the effectiveness of wind-driven accretion from the observed disc demographics and constitutes an important step to include wind-driven accretion in planet population synthesis models.

Context. The final stages of a protoplanetary disk are essential for our understanding of the formation and evolution of planets. Photoevaporation is an important mechanism that contributes to the dispersal of an accretion disk and has significant consequences for the disk’s lifetime. However, the combined effects of photoevaporation and star-disk interaction have not been investigated in previous studies. Aims. A photoevaporative disk evolution model including a detailed formulation of the inner star-disk interaction region will improve the understanding of the final stages of disk evolution. Methods. We combined an implicit disk evolution model with a photoevaporative mass-loss profile. By including the innermost disk regions down to 0.01 AU, we could calculate the star-disk interaction, the stellar spin evolution, and the transition from an accreting disk to the propeller regime self-consistently. Starting from an early Class II star-disk system (with an age of 1 Myr), we calculated the long-term evolution of the system until the disk becomes almost completely dissolved. Results. Photoevaporation has a significant effect on disk structure and evolution. The radial extent of the dead zone decreases, and the number of episodic accretion events (outbursts) is reduced by high stellar X-ray luminosities. Reasonable accretion rates (>10−8 M⊙yr) in combination with photoevaporative gaps are possible for a dead zone that is still massive enough to develop episodic accretion events. Furthermore, the stellar spin evolution during the Class II evolution is less affected by the star-disk interaction in the case of high X-ray luminosities. Conclusions. Our results suggest that the formation of planets, especially habitable planets, in the dead zone is strongly impaired in the case of strong X-ray luminosities. Additionally, the importance of the star-disk interaction during the Class II phase with respect to the stellar spin evolution is reduced.

In our Galaxy, star formation occurs in a variety of environments, with a large fraction of stars formed in clusters hosting massive stars. OB stars have an important feedback on the evolution of protoplanetary disks orbiting around nearby young stars and likely on the process of planet formation occurring in them. The nearby massive association Cyg OB2 is an outstanding laboratory to study this feedback. It is the closest massive association to our Sun and hosts hundreds of massive stars and thousands of low-mass members, both with and without disks. In this paper, we analyze the spatial variation of the disk fraction (i.e., the fraction of cluster members bearing a disk) in Cyg OB2 and study its correlation with the local values of far-ultraviolet (FUV) and extreme-ultraviolet (EUV) radiation fields and the local stellar surface density. We present definitive evidence that disks are more rapidly dissipated in the regions of the association characterized by intense local UV fields and large stellar density. In particular, the FUV radiation dominates disk dissipation timescales in the proximity (i.e., within 0.5 pc) of the O stars. In the rest of the association, EUV photons potentially induce a significant mass loss from the irradiated disks across the entire association, but the efficiency of this process is reduced at increasing distances from the massive stars owing to absorption by the intervening intracluster material. We find that disk dissipation due to close stellar encounters is negligible in Cyg OB2 and likely to have affected 1% or fewer of the stellar population. Disk dissipation is instead dominated by photoevaporation. We also compare our results to what has been found in other young clusters with different massive populations, concluding that massive associations like Cyg OB2 are potentially hostile to protoplanetary disks but that the environments where disks can safely evolve in planetary systems are likely quite common in our Galaxy.

In this article, we proceed to study convection as a possible factor of episodic accretion in protoplanetary disks. Within the model presented in Article~I, the accretion history is analyzed at different rates and areas of matter inflow from the envelope onto the disk. It is shown that the burst-like regime occurs in a wide range of parameters. The long-term evolution of the disk is also modeled, including the decreasing-with-time matter inflow from the envelope. It is demonstrated that the disk becomes convectively unstable and maintains burst-like accretion onto the star for several million years. Meanwhile, the instability expands to an area of several tens of astronomical units and gradually decreases with time. It is also shown that at early stages in the disk evolution, conditions arise for gravitational instability in the outer parts of the disk and for dust evaporation in the convectively unstable inner regions. The general conclusion of the study is that convection can serve as one of the mechanisms of episodic accretion in protostellar disks, but this conclusion needs to be verified using more consistent hydrodynamic models.

Large-scale vertical magnetic fields are believed to play a key role in the evolution of protoplanetary discs. Associated with non-ideal effects, such as ambipolar diffusion, they are known to launch a wind that could drive accretion in the outer part of the disc (R > 1 AU). They also potentially lead to self-organisation of the disc into large-scale axisymmetric structures, similar to the rings recently imaged by sub-millimetre or near-infrared instruments (ALMA and SPHERE). The aim of this paper is to investigate the mechanism behind the formation of these gaseous rings, but also to understand the dust dynamics and its emission in discs threaded by a large-scale magnetic field. To this end, we performed global magneto-hydrodynamics (MHD) axisymmetric simulations with ambipolar diffusion using a modified version of the PLUTO code. We explored different magnetisations with the midplane β parameter ranging from 105 to 103 and included dust grains -treated in the fluid approximation- ranging from 100 μm to 1 cm in size. We first show that the gaseous rings (associated with zonal flows) are tightly linked to the existence of MHD winds. Secondly, we find that millimetre-size dust is highly sedimented, with a typical scale height of 1 AU at R = 100 AU for β = 104, compatible with recent ALMA observations. We also show that these grains concentrate into pressure maxima associated with zonal flows, leading to the formation of dusty rings. Using the radiative transfer code MCFOST, we computed the dust emission and make predictions on the ring-gap contrast and the spectral index that one might observe with interferometers like ALMA.

The evolution of protoplanetary disks in regions with massive OB stars is influenced by externally driven winds that deplete the outer parts of these disks. The winds have previously been studied via forbidden oxygen emission lines, which also arise in isolated disks in low-mass star-forming regions (SFRs) with weak external UV fields in photoevaporative or magnetic (internal) disk winds. It is crucial to determine how to disentangle external winds from internal ones. Here, we report a proxy for unambiguously identifying externally driven winds with a forbidden line of neutral atomic carbon, [C I] 8727 Å. We compare for the first time the spatial location of the emission in the [O I] 5577 Å, [O I] 6300 Å, and [C I] 8727 Å lines traced by VLT/MUSE-NFM with the ALMA Band 7 continuum disk emission in a sample of 12 proplyds in the Orion Nebula Cluster (ONC). We confirm that the [O I] 5577 Å emission is co-spatial with the disk emission, whereas that of [O I] 6300 Å is emitted both on the disk surface and on the ionization front of the proplyds. We show for the first time that the [C I] 8727 Å line is also co-spatial with the disk surface in proplyds, as seen in the MUSE and ALMA data comparison. The peak emission is compatible with the stellar location in all cases, apart from one target with high relative inclination with respect to the ionizing radiation, where the peak emission is located at the disk edge in the direction of the ionizing radiation. To verify whether the [C I] 8727 Å line is detected in regions where external photoevaporation is not expected, we examined VLT/X-Shooter spectra for young stars in low-mass SFRs. Although the [O I] 5577 Å and 6300 Å lines are well detected in all these targets, the total detection rate is ≪10% in the case of the [C I] 8727 Å line. This number increases substantially to a ∼40% detection rate in σ-Orionis, a region with higher UV radiation than in low-mass SFRs, but lower than in the ONC. The spatial location of the [C I] 8727 Å line emission and the lack of its detection in isolated disks in low-mass SFRs strongly suggest that this line is a tell-tale tracer of externally driven photoevaporative winds, which agrees with recent excitation models.

The numerical code PHYVE is a hydrodynamical code that allows to follow the formation and evolution of protoplanetary disks from the collapse of the molecular cloud to the photoevaporation phase. This code is able to model the surface mass density distribution consistently with the disk radial profile (including the disk composition and geometry). We aim at using this code for modeling circumplanetary disks by considering the protoplanetary disk as the source of infalling material, replacing the molecular cloud that was an initial parameter in the protoplanetary disk simulations. We will simulate the circumplanetary disk radial thermal profile and investigate the question of the crucial parameters differing from protoplanetary disks.

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process. As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

Planetary systems are thought to be born in protoplanetary disks. Isotope ratios are a powerful tool for investigating the material origin and evolution from molecular clouds to planetary systems via protoplanetary disks. However, it is challenging to measure the isotope (isotopologue) ratios, especially in protoplanetary disks, because the emission lines of major species are saturated. We developed a new method to overcome these challenges by using optically thin line wings induced by thermal broadening. As a first application of the method, we analyzed two carbon monoxide isotopologue lines, 12CO 3–2 and 13CO 3–2, from archival observations of a protoplanetary disk around TW Hya with the Atacama Large Millimeter/submillimeter Array. The 12CO/13CO ratio was estimated to be 21 ± 5 at disk radii of 70–110 au, which is significantly smaller than the value observed in the local interstellar medium, ∼69. It implies that an isotope exchange reaction occurs in a low-temperature environment with C/O > 1. In contrast, it is suggested that 12CO/13CO is higher than ∼84 in the outer disk (r > 130 au), which can be explained by the difference in the binding energy of the isotopologues on dust grains and the CO gas depletion processes. Our results imply that the gas-phase 12CO/13CO can vary by a factor of >4 even inside a protoplanetary disk and therefore can be used to trace material evolution in disks.

Context. The study of protoplanetary disc evolution and theories of planet formation has predominantly concentrated on solar- (and low-) mass stars since they host the majority of confirmed exoplanets. Nevertheless, the confirmation of numerous planets orbiting stars more massive than the Sun (up to ~3 M⊙) has sparked considerable interest in understanding the mechanisms involved in their formation, and thus in the evolution of their hosting protoplanetary discs. Aims. We aim to improve our knowledge of the evolution of the gaseous component of protoplanetary discs around intermediate-mass stars and to set the stage for future studies of planet formation around them. Methods. We study the long-term evolution of protoplanetary discs affected by viscous accretion and photoevaporation by X-ray and far-ultraviolet (FUV) photons from the central star around stars in the range of 1–3 M⊙, considering the effects of stellar evolution and solving the vertical structure equations of the disc. We explore the effect of different values of the viscosity parameter and the initial mass of the disc. Results. We find that the evolutionary pathway of protoplanetary disc dispersal due to photoevaporation depends on the stellar mass. Our simulations reveal four distinct evolutionary pathways for the gas component not reported before that are a consequence of stellar evolution and that likely have a substantial impact on the dust evolution, and thus on planet formation. As the stellar mass increases from one solar mass to ~1.5–2 M⊙, the evolution of the disc changes from the conventional inside-out clearing, in which X-ray photoevaporation generates inner holes, to a homogeneous disc evolution scenario where both inner and outer discs formed after a gap is opened by photoevaporation vanish over a similar timescale. As the stellar mass continues to increase, reaching ~2–3 M⊙, we identify a distinct pathway that we refer to as revenant disc evolution. In this scenario, the inner and outer discs reconnect after the gap opened. For the largest masses, we observe outside-in disc dispersal, in which the outer disc dissipates first due to a stronger FUV photoevaporation rate. Revenant disc evolution stands out as it is capable of extending the disc lifespan. Otherwise, the disc dispersal timescale decreases with increasing stellar mass except for low-viscosity discs.

Context. The evolution of protoplanetary disks is dominated by the conservation of angular momentum, where the accretion of material onto the central star is fed by the viscous expansion of the outer disk or by disk winds extracting angular momentum without changing the disk size. Studying the time evolution of disk sizes therefore allows us to distinguish between viscous stresses or disk winds as the main mechanism of disk evolution. Observationally, estimates of the size of the gaseous disk are based on the extent of CO submillimeter rotational emission, which is also affected by the changing physical and chemical conditions in the disk during the evolution. Aims. We study how the gas outer radius measured from the extent of the CO emission changes with time in a viscously expanding disk. We also investigate to what degree this observable gas outer radius is a suitable tracer of viscous spreading and whether current observations are consistent with viscous evolution. Methods. For a set of observationally informed initial conditions we calculated the viscously evolved density structure at several disk ages and used the thermochemical code DALI to compute synthetic emission maps, from which we measured gas outer radii in a similar fashion as observations. Results. The gas outer radii (RCO, 90%) measured from our models match the expectations of a viscously spreading disk: RCO, 90% increases with time and, for a given time, RCO, 90% is larger for a disk with a higher viscosity αvisc. However, in the extreme case in which the disk mass is low (Mdisk ≤ 10−4 M⊙) and αvisc is high (≥10−2), RCO, 90% instead decreases with time as a result of CO photodissociation in the outer disk. For most disk ages, RCO, 90% is up to ~12× larger than the characteristic size Rc of the disk, and RCO, 90%/Rc is largest for the most massive disk. As a result of this difference, a simple conversion of RCO, 90% to αvisc overestimates the true αvisc of the disk by up to an order of magnitude. Based on our models, we find that most observed gas outer radii in Lupus can be explained using viscously evolving disks that start out small (Rc(t = 0) ≃ 10 AU) and have a low viscosity (αvisc = 10−4−10−3). Conclusions. Current observations are consistent with viscous evolution, but expanding the sample of observed gas disk sizes to star-forming regions, both younger and older, would better constrain the importance of viscous spreading during disk evolution.

Recent developments in the evolution of protoplanetary discs have suggested that planet formation occurs in regions of the discs with low levels of turbulent viscosity. In such environments, the dynamical corotation torque is thought to play an important role by slowing down the migration of low-mass planets (type I migration). We aim to provide a simple analytical prescription for the dynamical corotation torque for use in 1D global models of planet formation and evolution and assess the importance of the dynamical corotation torque for the migration of low-mass planets in low-viscosity discs. We propose simple prescriptions for calculating in 1D the time evolution of the vortensities of the librating and orbit-crossing flows around a low-mass planet, which both enter the analytical expression for the dynamical corotation torque. One of our prescriptions involves a memory timescale for the librating flow, and 2D hydrodynamical simulations of disc-planet interactions were used to assess the memory timescale and validate our model. The orbital evolution of a low-mass planet is calculated using 1D simulations, where the dynamical corotation torque features our prescriptions for the vortensities of the librating and orbit-crossing flows, and using 2D hydrodynamical simulations of disc-planet interactions, assuming locally isothermal discs. We find very good agreement between the 1D and 2D simulations for a wide parameter space, whether the dynamical corotation torque slows down or accelerates inward migration. We provide maps showing how much the dynamical corotation torque reduces the classical type I migration torque as a function of planet mass and orbital distance. The reduction is about 50% for a 10-Earth-mass planet at 10 au in a young disc with a surface density profile in r^-1/2 and an alpha viscosity of 10^-4. In discs with low turbulent viscosity, the dynamical corotation torque should be taken into account in global models of planet formation and evolution as it can strongly slow down type I migration.