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Mario Flock

Publications and source records attributed to Mario Flock.

At least 73 records · Page 4Linked to original sources

Probing Inner-Edge of Dead Zones in Protoplanetary Disks with ALMA and Next Generation Very Large Array

The discovery of substructures in protoplanetary disks with ALMA has provided us key insights on the formation of planets. However, observational constraints on the formation of rocky planets have been still sparse, especially because of the limited spatial resolution. The inner edge of so-called dead zone is one of the preferential sites of rocky planet formation. We investigate the capabilities of ALMA and ngVLA for observing a dust concentration expected at the inner edge of the dead-zone around a Herbig star. Herbig Ae/Be stars are useful laboratories for exploring the evolution of rocky grains in protoplanetary disks because of their high luminosity which pushes the dead-zone inner edge outward. We find that, thanks to its unprecedented angular resolution and sensitivity, ngVLA can detect the dust concentration at the dead-zone inner edge, with a reasonable integration time of 10 hrs at $λ=3,7$ mm and 1 cm. The dust concentration is expected to be optically thick at the ALMA wavelengths and cannot be spatially resolved due to its limited resolution. On the other hand, the flux density from the inner disk regions ($\sim$3--4 au) observed with current VLA is higher for disks with a dust ring, and hence would be a useful indicator that help us choose potential candidates of disks having a dust concentration at the inner most region. With these observations we can characterize the process of dust concentration in the innermost disk regions, where rocky planets can form.

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TOI-216: Resonant Constraints on Planet Migration

TOI-216 is a pair of close-in planets with orbits deep in the 2:1 mean motion resonance. The inner, Neptune-class planet (TOI-216b) is near 0.12 au (orbital period $P_{\rm b} \simeq 17$ d) and has a substantial orbital eccentricity ($e_{\rm b} \simeq 0.16$), and large libration amplitude ($A_ψ\simeq 60^\circ$) in the resonance. The outer planet (TOI-216c) is a gas giant on a nearly circular orbit. We carry out $N$-body simulations of planet migration in a protoplanetary gas disk to explain the orbital configuration of TOI-216 planets. We find that TOI-216b's migration must have been halted near its current orbital radius to allow for a convergent migration of the two planets into the resonance. For the inferred damping-to-migration timescale ratio $τ_e/τ_a \simeq 0.02$, overstable librations in the resonance lead to a limit cycle with $A_ψ\simeq 80^\circ$ and $e_{\rm b}<0.1$. The system could have remained in this configuration for the greater part of the protoplanetary disk lifetime. If the gas disk was removed from inside out, this would have reduced the libration amplitude to $A_ψ\simeq 60^\circ$ and boosted $e_{\rm b}$ via the resonant interaction with TOI-216c. Our results suggest a relatively fast inner disk removal ($\sim 10^5$ yr). Another means of explaining the large libration amplitude is stochastic stirring from a (turbulent) gas disk. For that to work, overstable librations would need to be suppressed, $τ_e/τ_a \simeq 0.05$, and very strong turbulent stirring (or some other source of large stochastic forcing) would need to overcome the damping effects of gas. Hydrodynamical simulations can be performed to test these models.

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Steady-state accretion in magnetized protoplanetary disks

[abridged] We present a 1+1D global magnetically-driven disk accretion model that captures the essence of the MRI-driven accretion, without resorting to 3D global non-ideal MHD simulations. The gas dynamics is assumed to be solely controlled by the MRI and hydrodynamic instabilities. For given stellar and disk parameters, the Shakura-Sunyaev viscosity parameter $α$ is determined self-consistently under the framework of viscously-driven accretion from detailed considerations of the MRI with non-ideal MHD effects (Ohmic resistivity and ambipolar diffusion), accounting for disk heating by stellar irradiation, non-thermal sources of ionization, and dust effects on the ionization chemistry. Additionally, the magnetic field strength is constrained and adopted to maximize the MRI activity. We demonstrate the use of our framework by investigating steady-state MRI-driven accretion in a fiducial protoplanetary disk model around a solar-type star. We find that the equilibrium solution displays no pressure maximum at the dead zone outer edge, except if a sufficient amount of dust particles have accumulated there before the disk reaches a steady-state accretion regime. Furthermore, the steady-state accretion solution describes a disk that displays a spatially extended long-lived inner disk gas reservoir (the dead zone) accreting a few $10^{-9}\, M_{\odot}.\rm{yr}^{-1}$. By conducting a detailed parameter study, we find that the extend to which the MRI can drive efficient accretion is primarily determined by the total disk gas mass, the representative grain size, the vertically-integrated dust-to-gas mass ratio, and the stellar X-ray luminosity. A self-consistent time-dependent coupling between gas, dust, stellar evolution models and our general framework on million-year timescales is required to fully understand the formation of dead zones and their potential to trap dust particles.

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The Substructures in Disks undergoing Vertical Shear Instability: II. Observational Predictions for the Dust Continuum

High-angular resolution observations at sub-millimeter/millimeter wavelengths of disks surrounding young stars have shown that their morphology is made of azimuthally-symmetric or point-symmetric substructures, in some cases with spiral arms, localized spur- or crescent-shaped features. The majority of theoretical studies with the aim of interpreting the observational results have focused on disk models with planets, under the assumption that the disk substructures are due to the disk-planet interaction. However, so far only in very few cases exoplanets have been detected in these systems. Furthermore, some substructures are expected to appear \textit{before} planets form, as they are necessary to drive the concentration of small solids which can lead to the formation of planetesimals. In this work we present observational predictions from high-resolution 3D radiative hydrodynamical models which follow the evolution of gas and solids in a protoplanetary disk. We focus on substructures in the distribution of millimeter-sized and smaller solid particles produced by the vertical shear instability. We show that their characteristics are compatible with some of the shallow gaps detected in recent observations at sub-mm/mm wavelengths, and present predictions for future observations with better sensitivity and angular resolution with ALMA and a Next Generation Very Large Array.

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Observability of the Vertical Shear Instability in protoplanetary disk CO kinematics

Context. Dynamical and turbulent motions of gas in a protoplanetary disk are crucial for their evolution and affect planet formation. Recent observations suggest weak turbulence in the disk's outer regions. However, the physical mechanism of turbulence in these outer regions remains uncertain. The vertical shear instability (VSI) is a promising mechanism to produce turbulence in disks. Aims. Our aim is to study the observability of the gas velocity structure produced by the VSI via CO kinematics with ALMA. Methods. We perform global 3D hydrodynamical simulations of a VSI-unstable disk. We post-process the simulation results with radiative transfer calculations, and produce synthetic predictions of CO rotational emission lines. Following, we compute the line of sight velocity map, and its deviations from a sub-Keplerian equilibrium solution. We explore the detectability of the VSI by identifying kinematic signatures using realistic simulated observations. Results. Our 3D simulations of the VSI show the steady state dynamics of the gas in great detail. From the velocity structure we infer a turbulent stress value of $α_{rϕ}=1.4 \times 10^{-4}$. On large scales, we observe velocity deviations of 50 m s$^{-1}$ as axisymmetric rings. We find optimal conditions at $i \lesssim 20^{\circ}$ to trace for the kinematic structures of the VSI. We found that current diagnostics to constrain gas turbulence from non-thermal broadening of the line emission are not applicable to anisotropic VSI turbulence. Conclusions. The detection of kinematic signatures produced by the VSI is possible with ALMA. Observations including an extended antenna configuration combined with the highest spectral resolution available are needed for robust detection. The characterization of the large-scale velocity perturbations is required to constrain the turbulence level produced by the VSI from gas observations.

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Thermal Wave Instability as an Origin of Gap and Ring Structures in Protoplanetary Disks

Recent millimeter and infrared observations have shown that gap and ring-like structures are common in both dust thermal emission and scattered-light of protoplanetary disks. We investigate the impact of the so-called Thermal Wave Instability (TWI) on the millimeter and infrared scattered-light images of disks. We perform 1+1D simulations of the TWI and confirm that the TWI operates when the disk is optically thick enough for stellar light, i.e., small-grain-to-gas mass ratio of $\gtrsim0.0001$. The mid-plane temperature varies as the waves propagate and hence gap and ring structures can be seen in both millimeter and infrared emission. The millimeter substructures can be observed even if the disk is fully optically thick since it is induced by the temperature variation, while density-induced substructures would disappear in the optically thick regime. The fractional separation between TWI-induced ring and gap is $Δr/r \sim$ 0.2-0.4 at $\sim$ 10-50 au, which is comparable to those found by ALMA. Due to the temperature variation, snow lines of volatile species move radially and multiple snow lines are observed even for a single species. The wave propagation velocity is as fast as $\sim$ 0.6 ${\rm au~yr^{-1}}$, which can be potentially detected with a multi-epoch observation with a time separation of a few years.

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On moving shadows and pressure bumps in HD 169142

The search for young planets had its first breakthrough with the detection of the accreting planet PDS70b. In this study, we aim to broaden our understanding towards the formation of multi-planet systems such as HR8799 or the Solar System. Our previous study on HD169142, one of the closest Herbig stars, points towards a shadow-casting protoplanetary candidate. Here, we present follow-up observations to test our previously proposed hypothesis. We set our new data into context with previous observations to follow structural changes in the disk over the course of 6 years. We find spatially resolved systematic changes in the position of the previously described surface brightness dip in the inner ring. We further find changes in the brightness structure in azimuthal direction along the ring. And finally, a comparison of our SPHERE data with recent ALMA observations reveals a wavelength dependent radial profile of the bright ring. The time-scale on which the changes in the ring's surface brightness occur suggest that they are caused by a shadow cast by a 1-10Mj planet surrounded by dust, an orbit comparable to those of the giant planets in our own Solar System. Additionally, we find the first indications for temperature-induced instabilities in the ring. And finally, we trace a pressure maxima, for the first time spatially resolved, with a width of 4.5au. The density distribution of the ring at mm wavelengths around the pressure maxima could further indicate effects from snow lines or even the dynamics and feedback of the larger grains.

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Streaming instability in a global patch simulation of protoplanetary disks

In the recent years, sub/mm observations of protoplanetary disks have discovered an incredible diversity of substructures in the dust emission. An important result was the finding that dust grains of mm size are embedded in very thin dusty disks. This implies that the dust mass fraction in the midplane becomes comparable to the gas, increasing the importance of the interaction between the two components there. We address this problem by means of numerical 2.5D simulations in order to study the gas and dust interaction in fully global stratified disks. To this purpose, we employ the recently developed dust grain module in the PLUTO code. Our model focuses on a typical T Tauri disk model, simulating a short patch of the disk at 10 au which includes grains of constant Stokes number of $St=0.01$ and $St=0.1$, corresponding to grains with sizes of 0.9 cm and 0.9 mm, respectively, for the given disk model. By injecting a constant pebble flux at the outer domain, the system reaches a quasi steady state of turbulence and dust concentrations driven by the streaming instability. For our given setup and using resolutions up to 2500 cells per scale height we resolve the streaming instability, leading to local dust clumping and concentrations. Our results show dust density values of around 10-100 times the gas density with a steady state pebble flux between $3.5 \times 10^{-4}$ and $2.5 \times 10^{-3} M_{\rm Earth}/\mathit{year}$ for the models with $\mathit{St}=0.01$ and $\mathit{St}=0.1$. The grain size and pebble flux for model $\mathit{St}=0.01$ compares well with dust evolution models of the first million years of disk evolution. For those grains the scatter opacity dominates the extinction coefficient at mm wavelengths. These types of global dust and gas simulations are a promising tool for studies of the gas and dust evolution at pressure bumps in protoplanetary disks.

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A two-moment radiation hydrodynamics scheme applicable to simulations of planet formation in circumstellar disks

We present a numerical code for radiation hydrodynamics designed as a module for the freely available PLUTO code. We adopt a gray approximation and include radiative transfer following a two-moment approach by imposing the M1 closure to the radiation fields. This closure allows for a description of radiative transport in both the diffusion and free-streaming limits, and is able to describe highly anisotropic radiation transport as can be expected in the vicinity of an accreting planet in a protoplanetary disk. To reduce the computational cost caused by the timescale disparity between radiation and matter fields, we integrate their evolution equations separately in an operator-split way, using substepping to evolve the radiation equations. We further increase the code's efficiency by adopting the reduced speed of light approximation (RSLA). Our integration scheme for the evolution equations of radiation fields relies on implicit-explicit schemes, in which radiation-matter interaction terms are integrated implicitly while fluxes are integrated via Godunov-type solvers. The module is suitable for general astrophysical computations in 1, 2, and 3 dimensions in Cartesian, spherical and cylindrical coordinates, and can be implemented on rotating frames. We demonstrate the algorithm performance on different numerical benchmarks, paying particular attention to the applicability of the RSLA for computations of physical processes in protoplanetary disks. We show 2D simulations of vertical convection in disks and 3D simulations of gas accretion by planetary cores, which are the first of their kind to be solved with a two-moment approach.

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Physical and Chemical Structure of the Disk and Envelope of the Class 0/I Protostar L1527

Sub-millimeter spectral line and continuum emission from the protoplanetary disks and envelopes of protostars are powerful probes of their structure, chemistry, and dynamics. Here we present a benchmark study of our modeling code, RadChemT, that for the first time uses a chemical model to reproduce ALMA C$^{18}$O (2-1) and CARMA $^{12}$CO (1-0) and N$_{2}$H$^{+}$ (1-0) observations of L1527, that allow us to distinguish the disk, the infalling envelope and outflow of this Class 0/I protostar. RadChemT combines dynamics, radiative transfer, gas chemistry and gas-grain reactions to generate models which can be directly compared with observations for individual protostars. Rather than individually fit abundances to a large number of free parameters, we aim to best match the spectral line maps by (i) adopting a physical model based on density structure and luminosity derived primarily from previous work that fit SED and 2D imaging data, updating it to include a narrow jet detected in CARMA and ALMA data near ($\leq 75$au) the protostar, and then (ii) computing the resulting astrochemical abundances for 292 chemical species. Our model reproduces the C$^{18}$O and N$_{2}$H$^{+}$ line strengths within a factor of 3.0; this is encouraging considering the pronounced abundance variation (factor $> 10^3$) between the outflow shell and CO snowline region near the midplane. Further, our modeling confirms suggestions regarding the anti-correlation between N$_{2}$H$^{+}$ and the CO snowline between 400 au to 2,000 au from the central star. Our modeling tools represent a new and powerful capability with which to exploit the richness of spectral line imaging provided by modern submillimeter interferometers.

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The Ophiuchus DIsc Survey Employing ALMA (ODISEA)-III: the evolution of substructures in massive discs at 3-5 au resolution

We present 1.3 mm continuum ALMA long-baseline observations at 3-5 au resolution of 10 of the brightest discs from the Ophiuchus DIsc Survey Employing ALMA (ODISEA) project. We identify a total of 26 narrow rings and gaps distributed in 8 sources and 3 discs with small dust cavities (r $<$10 au). We find that two discs around embedded protostars lack the clear gaps and rings that are ubiquitous in more evolved sources with Class II SEDs. Our sample includes 5 objects with previously known large dust cavities (r $>$20 au). We find that the 1.3 mm radial profiles of these objects are in good agreement with those produced by numerical simulations of dust evolution and planet-disc interactions, which predict the accumulation of mm-sized grains at the edges of planet-induced cavities. Our long-baseline observations resulted in the largest sample of discs observed at $\sim$3-5 au resolution in any given star-forming region (15 objects when combined with Ophiuchus objects in the DSHARP Large Program) and allow for a demographic study of the brightest $\sim5\%$ of the discs in Ophiuchus (i.e. the most likely formation sites of giant planets in the cloud). We use this unique sample to propose an evolutionary sequence and discuss a scenario in which the substructures observed in massive protoplanetary discs are mainly the result of planet formation and dust evolution. If this scenario is correct, the detailed study of disc substructures might provide a window to investigate a population of planets that remains mostly undetectable by other techniques.

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Hydrodynamical simulations of protoplanetary disks including irradiation of stellar photons. I. Resolution study for Vertical Shear Instability (VSI)

In recent years hydrodynamical (HD) models have become important to describe the gas kinematics in protoplanetary disks, especially in combination with models of photoevaporation and/or magnetic-driven winds. We focus on diagnosing the the vertical extent of the VSI at 203 cells per scale height and allude at what resolution per scale height we obtain convergence. Finally, we determine the regions where EUV, FUV and X-Rays are dominant in the disk. We perform global HD simulations using the PLUTO code. We adopt a global isothermal accretion disk setup, 2.5D (2 dimensions, 3 components) which covers a radial domain from 0.5 to 5.0 and an approximately full meridional extension. We determine the 50 cells per scale height to be the lower limit to resolve the VSI. For higher resolutions, greater than 50 cells per scale height, we observe the convergence for the saturation level of the kinetic energy. We are also able to identify the growth of the `body' modes, with higher growth rate for higher resolution. Full energy saturation and a turbulent steady state is reached after 70 local orbits. We determine the location of the EUV-heated region defined by the radial column density to be 10$^{19}$ cm$^{-2}$ located at $H_\mathrm{R}\sim9.7$, and the FUV/X-Rays-heated boundary layer defined by 10$^{22}$ cm$^{-2}$ located at $H_\mathrm{R}\sim6.2$, making it necessary to introduce the need of a hot atmosphere. For the first time, we report the presence of small scale vortices in the r-Z plane, between the characteristic layers of large scale vertical velocity motions. Such vortices could lead to dust concentration, promoting grain growth. Our results highlight the importance to combine photoevaporation processes in the future high-resolution studies of the turbulence and accretion processes in disks.

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A Tale of Two Transition Disks: ALMA long-baseline observations of ISO-Oph 2 reveal two closely packed non-axisymmetric rings and a $\sim$2 au cavity

ISO-Oph 2 is a wide-separation (240 au) binary system where the primary star harbors a massive (M$_{dust}$ $\sim$40 M$_{\oplus}$) ring-like disk with a dust cavity $\sim$50 au in radius and the secondary hosts a much lighter (M$_{dust}$ $\sim$0.8 M$_{\oplus}$) disk. As part of the high-resolution follow-up of the "Ophiuchus Disk Survey Employing ALMA" (ODISEA) project, we present 1.3 mm continuum and $^{12}$CO molecular line observations of the system at 0''02 (3 au) resolution. We resolve the disk around the primary into two non-axisymmetric rings and find that the disk around the secondary is only $\sim$7 au across and also has a dust cavity (r $\sim$2.2 au). Based on the infrared flux ratio of the system and the M0 spectral type of the primary, we estimate the mass of the companion to be close to the brown dwarf limit. Hence, we conclude that the ISO-Oph 2 system contains the largest and smallest cavities, the smallest measured disk size, and the resolved cavity around the lowest mass object (M$_{\star}$ $\sim$0.08 M$_\odot$) in Ophiuchus. From the $^{12}$CO data, we find a bridge of gas connecting both disks. While the morphology of the rings around the primary might be due to an unseen disturber within the cavity, we speculate that the bridge might indicate an alternative scenario in which the secondary has recently flown by the primary star causing the azimuthal asymmetries in its disk. The ISO-Oph 2 system is therefore a remarkable laboratory to study disk evolution, planet formation, and companion-disk interactions.

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High Resolution Parameter Study of the Vertical Shear Instability

Theoretical models of protoplanetary disks have shown the Vertical Shear Instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disk. However, simulations of the VSI have yet to show consistent levels of key disk turbulence parameters like the stress-to-pressure ratio $α$. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disk density gradient $p$ and aspect ratio $h := H/R$. We use full 2$π$ 3D simulations of the disk for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disk aspect ratio with a \review{strong} scaling of $α\propto h^{2.6}$, in contrast to the traditional $α$ model, where viscosity scales as $ν\propto αh^2$ with a constant $α$. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of $χ\approx 10$ and radial widths of approximately 1.5 $H$. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.

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Gas and dust dynamics in starlight-heated protoplanetary disks

Theoretical models of the ionization state in protoplanetary disks suggest the existence of large areas with low ionization and weak coupling between the gas and magnetic fields. In this regime hydrodynamical instabilities may become important. In this work we investigate the gas and dust structure and dynamics for a typical T Tauri system under the influence of the vertical shear instability (VSI). We use global 3D radiation hydrodynamics simulations covering all $360^\circ$ of azimuth with embedded particles of 0.1 and 1mm size, evolved for 400 orbits. Stellar irradiation heating is included with opacities for 0.1- to 10-$μ$m-sized dust. Saturated VSI turbulence produces a stress-to-pressure ratio of $α\simeq 10^{-4}$. The value of $α$ is lowest within 30~au of the star, where thermal relaxation is slower relative to the orbital period and approaches the rate below which VSI is cut off. The rise in $α$ from 20 to 30~au causes a dip in the surface density near 35~au, leading to Rossby wave instability and the generation of a stationary, long-lived vortex spanning about 4~au in radius and 40~au in azimuth. Our results confirm previous findings that mm size grains are strongly vertically mixed by the VSI. The scale height aspect ratio for 1mm grains is determined to be 0.037, much higher than the value $H/r=0.007$ obtained from millimeter-wave observations of the HL~Tau system. The measured aspect ratio is better fit by non-ideal MHD models. In our VSI turbulence model, the mm grains drift radially inwards and many are trapped and concentrated inside the vortex. The turbulence induces a velocity dispersion of $\sim 12$~m/s for the mm grains, indicating that grain-grain collisions could lead to fragmentation.

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Birth of convective low-mass to high-mass second Larson cores

Stars form as an end product of the gravitational collapse of cold, dense gas in magnetized molecular clouds. This multi-scale scenario occurs via the formation of two quasi-hydrostatic cores and involves complex physical processes, which require a robust, self-consistent numerical treatment. The aim of this study is to understand the formation and evolution of the second Larson core and the dependence of its properties on the initial cloud core mass. We used the PLUTO code to perform high resolution, 1D and 2D RHD collapse simulations. We include self-gravity and use a grey FLD approximation for the radiative transfer. Additionally, we use for the gas EOS density- and temperature-dependent thermodynamic quantities to account for the effects such as dissociation, ionisation, and molecular vibrations and rotations. Properties of the second core are investigated using 1D studies spanning a wide range of initial cloud core masses from 0.5 to 100 $M_{\odot}$. Furthermore, we expand to 2D collapse simulations for a few cases of 1, 5, 10, and 20 $M_{\odot}$. We follow the evolution of the second core for $\geq$ 100 years after its formation, for each of these non-rotating cases. Our results indicate a dependence of several second core properties on the initial cloud core mass. For the first time, due to an unprecedented resolution, our 2D non-rotating collapse studies indicate that convection is generated in the outer layers of the second core, which is formed due to the gravitational collapse of a 1 $M_{\odot}$ cloud core. Additionally, we find large-scale oscillations of the second accretion shock front triggered by the standing accretion shock instability, which has not been seen before in early evolutionary stages of stars. We predict that the physics within the second core would not be significantly influenced by the effects of magnetic fields or an initial cloud rotation.

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Planet formation and migration near the silicate sublimation front in protoplanetary disks

The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. A particular puzzle that requires explanation arises from one of the key results of the Kepler mission, namely the increase in the planetary occurrence rate with orbital period up to 10 days for F, G, K and M stars. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. For this analysis we use iterative 2D radiation hydrostatic disk models which include irradiation by the star, and dust sublimation and deposition depending on the local temperature and vapor pressure. We perform a parameter study by varying the magnetized turbulence onset temperature, the accretion stress, the dust mass fraction, and the mass accretion rate. Our models feature a gas-only inner disk, a silicate sublimation front and dust rim starting at around 0.08 au, an ionization transition zone with a corresponding density jump, and a pressure maximum which acts as a pebble trap at around 0.12 au. Migration torque maps show Earth- and super-Earth-mass planets halt in our model disks at orbital periods ranging from 10 to 22 days. Such periods are in good agreement with both the inferred location of the innermost planets in multiplanetary systems, and the break in planet occurrence rates from the Kepler sample at 10 days. In particular, models with small grains depleted produce a trap located at a 10-day orbital period, while models with a higher abundance of small grains present a trap at around a 17-day orbital period. The snow line lies at 1.6 au, near where the occurrence rate of the giant planets peaks. We conclude that the dust sublimation zone is crucial for forming close-in planets, especially when considering tightly packed super-Earth systems.

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The Radial Distribution of Dust Particles in the HL Tau Disk from ALMA and VLA Observations

Understanding planet formation requires to discern how dust grows in protoplanetary disks. An important parameter to measure in disks is the maximum dust grain size present. This is usually estimated through measurements of the dust opacity at different millimeter wavelengths assuming optically thin emission and dust opacity dominated by absorption. However, ALMA observations have shown that these assumptions might not be correct in the case of protoplanetary disks, leading to overestimation of particle sizes and to underestimation of the disk's mass. Here, we present an analysis of high quality ALMA and VLA images of the HL Tau protoplanetary disk, covering a wide range of wavelengths, from 0.8 mm to 1 cm, and with a physical resolution of $\sim$7.35 au. We describe a procedure to analyze a set of millimeter images without any assumption about the optical depth of the emission, and including the effects of absorption and scattering in the dust opacity. This procedure allows us to obtain the dust temperature, the dust surface density and the maximum particle size at each radius. In the HL Tau disk, we found that particles have already grown up to a few millimeters in size. We detect differences in the dust properties between dark and bright rings, with dark rings containing low dust density and small dust particles. Different features in the HL Tau disk seem to have different origins. Planet-disk interactions can explain substructure at the external half of the disk, but the internal rings seem to be associated to the presence of snow lines of several molecules.

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