arXiv subjects

Hubert Klahr

Publications and source records attributed to Hubert Klahr.

At least 55 records · Page 3Linked to original sources

arXiv2020

Turbulence sets the length scale for planetesimal formation: Local 2D simulations of streaming instability and planetesimal formation

The trans-Neptunian object 2014 MU69, named Arrokoth, is the most recent evidence that planetesimals did not form by successive collisions of smaller objects, but by the direct gravitational collapse of a pebble cloud. But what process sets the physical scales on which this collapse may occur? Star formation has the Jeans mass, that is when gravity is stronger than thermal pressure, helping us to understand the mass of our sun. But what controls mass and size in the case of planetesimal formation? Both asteroids and Kuiper belt objects show a kink in their size distribution at 100 km. Here we derive a gravitational collapse criterion for a pebble cloud to fragment to planetesimals, showing that a critical mass is needed for the clump to overcome turbulent diffusion. We successfully tested the validity of this criterion in direct numerical simulations of planetesimal formation triggered by the streaming instability. Our result can, therefore, explain the sizes for planetesimals found forming in streaming instability simulations in the literature, while not addressing the detailed size distribution. We find that the observed characteristic diameters of $\sim$ 100 km correspond to the critical mass of a pebble cloud set by the strength of turbulent diffusion stemming from streaming instability for a wide region of a solar nebula model from 2 - 60 au, with a tendency to allow for smaller objects at distances beyond and at late times, when the nebula gas gets depleted.

astro-ph.EP↗

arXiv2020

Constraining the parameter space for the Solar Nebula

If we want to understand planetesimal formation, the only data set we have is our own Solar System. It is particularly interesting as it is so far the only planetary system we know of that developed life. Understanding the conditions under which the Solar Nebula evolved is crucial in order to understand the different processes in the disk and the subsequent dynamical interaction between (proto-)planets, once the gas disk is gone. Protoplanetary disks provide a plethora of different parameters to explore. The question is whether this parameter space can be constrained, allowing simulations to reproduce the Solar System. Models and observations of planet formation provide constraints on the initial planetesimal mass in certain regions of the Solar Nebula. By making use of pebble flux-regulated planetesimal formation, we perform a parameter study with nine different disk parameters like the initial disk mass, initial disk size, initial dust-to-gas ratio, turbulence level, and more. We find that the distribution of mass in planetesimals in the disk depends on the planetesimal formation timescale and the pebbles' drift timescale. Multiple disk parameters can influence pebble properties and thus planetesimal formation. However, it is still possible to draw some conclusions on potential parameter ranges. Pebble flux-regulated planetesimal formation seems to be very robust, allowing simulations with a wide range of parameters to meet the initial planetesimal constraints for the Solar Nebula. I.e., it does not require a lot of fine tuning.

astro-ph.EP↗

arXiv2020

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.

astro-ph.EP↗

arXiv2020

The impact of pebble flux regulated planetesimal formation on giant planet formation

Forming gas giant planets by the accretion of 100 km diameter planetesimals, a typical size that results from self-gravity assisted planetesimal formation, is often thought to be inefficient. Many models therefore use small km-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals distributed radially in a minimum mass solar nebula fashion. We wish to investigate the impact of various initial radial density distributions in planetesimals with a dynamical model for the formation of planetesimals on the resulting population of planets. In doing so, we highlight the directive role of the early stages of dust evolution into pebbles and planetesimals in the circumstellar disk on the following planetary formation. We have implemented a two population model for solid evolution and a pebble flux regulated model for planetesimal formation into our global model for planet population synthesis. This framework is used to study the global effect of planetesimal formation on planet formation. As reference, we compare our dynamically formed planetesimal surface densities with ad-hoc set distributions of different radial density slopes of planetesimals. Even though required, it is not solely the total planetesimal disk mass, but the planetesimal surface density slope and subsequently the formation mechanism of planetesimals, that enables planetary growth via planetesimal accretion. Highly condensed regions of only 100 km sized planetesimals in the inner regions of circumstellar disks can lead to gas giant growth. Pebble flux regulated planetesimal formation strongly boosts planet formation, because it is a highly effective mechanism to create a steep planetesimal density profile. We find this to lead to the formation of giant planets inside 1 au by 100 km already by pure planetesimal accretion.

astro-ph.EP↗

arXiv2020

Requirements for gravitational collapse in planetesimal formation --- the impact of scales set by Kelvin-Helmholtz and nonlinear streaming instability

The formation of planetesimals is an unsolved problem in planet formation theory. A prominent scenario for overcoming dust growth barriers in dead zones is the gravitational collapse of locally over-dense regions, shown to robustly produce $\sim$100 km sized objects. Still, the conditions under which planetesimal formation occurs remain unclear. For collapse to proceed, the self-gravity of an overdensity must overcome stellar tidal disruption on large scales and turbulent diffusion on small scales. Here, we relate the scales of streaming and Kelvin-Helmholtz instability, which both regulate particle densities on the scales of gravitational collapse, directly to planetesimal formation. We support our analytic findings by performing 3D hydrodynamical simulations of streaming and Kelvin-Helmholtz instability and planetesimal formation. We find that the vertical extent of the particle mid-plane layer and the radial width of streaming instability filaments are set by the same characteristic length scale, thus governing the strength of turbulent diffusion on the scales of planetesimal formation. We present and successfully test a collapse criterion: $0.1 Q βε^{-1}Z^{-1} \lesssim 1$ and show that even for Solar metallicities, planetesimals can form in dead zones of sufficiently massive disks. For a given gas Toomre-parameter $Q$, pressure gradient $β$, metallicity $Z$ and local particle enhancement $ε$, the collapse criterion also provides a range of unstable scales, instituting a promising path for studying initial planetesimal mass distributions. Streaming instability is not required for planetesimal collapse, but by increasing $ε$, can evolve a system to instability.

astro-ph.EP↗

arXiv2020

Global axisymmetric simulations of photoevaporation and magnetically driven protoplanetary disk winds

Photoevaporation and magnetically driven winds are two independent mechanisms to remove mass from protoplanetary disks. In addition to accretion, the effect of these two principles acting concurrently could be significant and the transition between those two has not been extensively studied and quantified in the literature yet. In order to contribute to the understanding of disk winds, we present the phenomena emerging in the framework of two-dimensional axisymmetric, non-ideal magnetohydrodynamic simulations including EUV-/ X-ray driven photoevaporation. Of particular interest are the examination of the transition region between photoevaporation and magnetically driven wind, the possibility of emerging magneto-centrifugal wind effects, as well as the morphology of the wind itself depending on the strength of the magnetic field. We use the PLUTO code in a 2.5D axisymmetric configuration with additional treatment of EUV-/ X-ray heating and dynamic ohmic diffusion based on a semi-analytical chemical model. We identify the transition between both outflow types to occur for values of the initial plasma beta $β\geq 10^7$, while magnetically driven winds generally outperform photoevaporation for stronger fields. In our simulations we observe irregular and asymmetric outflows for stronger magnetic fields. In the weak field regime the photoevaporation rates are slightly lowered by perturbations of the gas density in the inner regions of the disk. Overall, our results predict a wind with a lever arm smaller than 1.5, consistent with a hot magneto-thermal wind. Stronger accretion flows are present for values of $β< 10^7$.

astro-ph.EP↗

arXiv2019

The DSHARP Rings: Evidence of Ongoing Planetesimal Formation?

Recent high-resolution interferometric observations of protoplanetary disks at (sub-)millimeter wavelengths reveal omnipresent substructures, such as rings, spirals, and asymmetries. A detailed investigation of eight rings detected in five disks by the DSHARP survey came to the conclusion that all rings are just marginally optically thick with optical depths between 0.2 and 0.5 at a wavelength of 1.25 mm. This surprising result could either be coincidental or indicate that the optical depth in all of the rings is regulated by the same process. We investigated if ongoing planetesimal formation could explain the "fine-tuned" optical depths in the DSHARP rings by removing dust and transforming it into "invisible" planetesimals. We performed a one-dimensional simulation of dust evolution in the second dust ring of the protoplanetary disk around HD 163296, including radial transport of gas and dust, dust growth and fragmentation, and planetesimal formation via gravitational collapse of sufficiently dense pebble concentrations. We show that planetesimal formation can naturally explain the observed optical depths if streaming instability regulates the midplane dust-to-gas ratio to unity. Furthermore, our simple monodisperse analytical model supports the hypothesis that planetesimal formation in dust rings should universally limit their optical depth to the observed range.

astro-ph.EP↗

arXiv2019

Linking planetesimal and dust content in protoplanetary disks via a local toy model

If planetesimal formation is an efficient process, as suggested by several models involving gravitational collapse of pebble clouds, then, before long, a significant part of the primordial dust mass should be absorbed in many km sized objects. A good understanding of the total amount of solids in the disk around a young star is crucial for planet formation theory. But as the mass of particles above the mm size cannot be assessed observationally, one must ask how much mass is hidden in bigger objects. We perform 0-d local simulations to study how the planetesimal to dust and pebble ratio is evolving in time and to develop an understanding of the potentially existing mass in planetesimals for a certain amount of dust and pebbles at a given disk age. We perform a parameter study based on a model considering dust growth, planetesimal formation and collisional fragmentation of planetesimals, while neglecting radial transport processes. While at early times, dust is the dominant solid particle species, there is a phase during which planetesimals make up a significant portion of the total mass starting at approximately $10^4 - 10^6$ yr. The time of this phase and the maximal total planetesimal mass strongly depend on the distance to the star $R$, the initial disk mass, and the efficiency of planetesimal formation $ε$. After approximately $10^6$ yr, our model predicts planetesimal collisions to dominate, which resupplies small particles. In our model, planetesimals form fast and everywhere in the disk. For a given $ε$, we were able to relate the dust content and mass of a given disk to its planetesimal content, providing us with some helpful basic intuition about mass distribution of solids and its dependence on underlying physical processes.

astro-ph.EP↗

arXiv2019

The Concentration and Growth of Solids in Fragmenting Circumstellar Disks

Due to the gas rich environments of early circumstellar disks, the gravitational collapse of cool, dense regions of the disk form fragments largely composed of gas. During formation, disk fragments may attain increased metallicities as they interact with the surrounding disk material, whether through particle migration to pressure maxima or through mutual gravitational interaction. In this paper, we investigate the ability of fragments to collect and retain a significant solid component through gas-particle interactions in high-resolution 3D self-gravitating shearing box simulations. The formation of axissymmetric perturbations associated with gravitational instabilities allows particles of intermediate sizes to concentrate through aerodynamic drag forces. By the onset of fragmentation, the mass of local particle concentrations within the fragment are comparable to that of the gas component and the sebsequent gravitational collapse results in the formation of a solid core. We find that these cores can be up to several tens of Earth masses, depending on grain size, before the fragment center reaches temperatures which would sublimate solids. The solid fraction and total mass of the fragment also depend on the metallicity of the young parent protoplanetary disk, with higher initial metallicities resulting in larger fragments and larger solid cores. Additionally, the extended atmospheres of these soon-to-be gas giants or brown dwarfs are occasionally enriched above the initial metallicity, provided no solid core forms in the center and are otherwise lacking in heavier elements when a core does form.

astro-ph.EP↗

arXiv2019

Planetesimal Population Synthesis: Pebble Flux Regulated Planetesimal Formation

We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result --- a radial planetesimal distribution --- can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus they are implemented via free parameters. This enables us to study the influence of the disk properties on the formation of planetesimals, predicting their time dependent formation rates and location of primary pebble accretion. We show that large $α$-values of $0.01$ (strong turbulence) prevent the formation of planetesimals in the inner part of the disk, arguing for lower values of around $0.001$ (moderate turbulence), at which planetesimals form quickly at all places where they are needed for proto-planets. Planetesimals form as soon as dust has grown to pebbles ($\sim\mathrm{mm}$ to $\mathrm{dm}$) and the pebble flux reaches a critical value, which is after a few thousand years at $2-3\,$AU and after a few hundred thousand years at $20-30\,$AU. Planetesimal formation lasts until the pebble supply has decreased below a critical value. The final spatial planetesimal distribution is steeper compared to the initial dust and gas distribution which helps to explain the discrepancy between the minimum mass solar nebula and viscous accretion disks.

astro-ph.EP↗

arXiv2019

Planet formation: The case for large efforts on the computational side

Modern astronomy has finally been able to observe protoplanetary disks in reasonable resolution and detail, unveiling the processes happening during planet formation. These observed processes are understood under the framework of disk-planet interaction, a process studied analytically and modeled numerically for over 40 years. Long a theoreticians' game, the wealth of observational data has been allowing for increasingly stringent tests of the theoretical models. Modeling efforts are crucial to support the interpretation of direct imaging analyses, not just for potential detections but also to put meaningful upper limits on mass accretion rates and other physical quantities in current and future large-scale surveys. This white paper addresses the questions of what efforts on the computational side are required in the next decade to advance our theoretical understanding, explain the observational data, and guide new observations. We identified the nature of accretion, ab initio planet formation, early evolution, and circumplanetary disks as major fields of interest in computational planet formation. We recommend that modelers relax the approximations of alpha-viscosity and isothermal equations of state, on the grounds that these models use flawed assumptions, even if they give good visual qualitative agreement with observations. We similarly recommend that population synthesis move away from 1D hydrodynamics. The computational resources to reach these goals should be developed during the next decade, through improvements in algorithms and the hardware for hybrid CPU/GPU clusters. Coupled with high angular resolution and great line sensitivity in ground based interferometers, ELTs and JWST, these advances in computational efforts should allow for large strides in the field in the next decade.

astro-ph.EP↗

arXiv2019

Dense Particle Clouds in Laboratory Experiments in Context of Drafting and Streaming Instability

The streaming instability, as an example of instabilities driven by particle feedback on a gas flow, has been proven to have a major role in controlling the formation of planetesimals. Here, we present experiments to approach this situation in the laboratory for particles in the Knudsen flow regime. In these experiments, we observe a particle cloud trapped for about 30 s in a rotating system under Earth's gravity. For average dust-to-gas ratios up to 0.08, particles behave like individual test particles. Their sedimentation speed is identical to that of a single free-falling particle, even in locally denser regions. However, for higher dust-to-gas ratios, the motion of particles becomes sensitive to clumping. Particles in locally denser regions now sediment faster. Their sedimentation speed then depends linearly on the overall dust-to-gas ratio. This clearly shows a transition from tracerlike behavior to collective behavior. Beyond these findings, these types of experiments can now be used as a gauge to test the particle feedback models in astrophysical hydrocodes which are currently used for numerical simulations of streaming instabilities.

astro-ph.EP↗

arXiv2019

Mapping the Conditions for Hydrodynamic Instability on Steady State Accretion Models of Protoplanetary Disks

Hydrodynamical instabilities in disks around young stars depend on the thermodynamic stratification of the disk and on the local rate of thermal relaxation. Here, we map the spatial extent of unstable regions for the Vertical Shear Instability (VSI), the Convective OverStability (COS), and the amplification of vortices via the Subcritical Baroclinic Instability (SBI). We use steady state accretion disk models, including stellar irradiation, accretion heating and radiative transfer. We determine the local radial and vertical stratification and thermal relaxation rate in the disk, in dependence of the stellar mass, disk mass and mass accretion rate. We find that passive regions of disks - i.e. the midplane temperature dominated by irradiation - are COS unstable about one pressure scale height above the midplane and VSI unstable at radii $> 10 \, \text{au}$. Vortex amplification via SBI should operate in most parts of active and passive disks. For active parts of disks (midplane temperature determined by accretion power) COS can become active down to the midplane. Same is true for the VSI because of the vertically adiabatic stratification of an internally heated disk. If hydro instabilities or other non-ideal MHD processes are able to create $α$-stresses ($> 10^{-5}$) and released accretion energy leads to internal heating of the disk, hydrodynamical instabilities are likely to operate in significant parts of the planet forming zones in disks around young stars, driving gas accretion and flow structure formation. Thus hydro-instabilities are viable candidates to explain the rings and vortices observed with ALMA and VLT.

astro-ph.EP↗

arXiv2018

Instabilities and Flow Structures in Protoplanetary Disks: Setting the Stage for Planetesimal Formation

This chapter highlights the properties of turbulence and meso-scale flow structures in protoplanetary disks and their role in the planet formation process. Here we focus on the formation of planetesimals from a gravitational collapse of a pebble cloud. Large scale and long lived flow structures - vortices and zonal flows - are a consequence of weak magneto and hydrodynamic instabilities in the pressure and entropy stratified quasi-Keplerian shear flow interacting with the fast rotation of the disk. The vortices and zonal flows on the other hand are particle traps tapping into the radial pebble flux of the disk, leading to locally sufficient accumulations to trigger gravitational collapse, directly converting pebbles to many kilometer sized planetesimals. This collapse is moderated by the streaming instability, which is a back-reaction from the particle accumulations onto the gas flow. Without trapping pebbles and increasing thus the local solid to gas ratio, this back-reaction would ultimately prevent the formation of planetsimals via turbulent diffusion. The formation of long lived flow structures is therefore a necessary condition for an efficient and fast formation of planetesimals.

astro-ph.EP↗

arXiv2018

Pebble trapping backreaction does not destroy vortices

The formation of planets remains one of the most challenging problems of contemporary astrophysics. Starting with micron-sized dust grains, coagulation models predict growth up to centimeter (pebbles), but growth beyond this size is difficult because of fragmentation and drift. Ways to bypass this problem have focused on inhomogeneities in the flow, be that zonal flows, streaming instability, or vortices. Because vortices are in equilibrium between the Coriolis and the pressure force, the pressureless grains will orbit along a vortex streamline experiencing a drag force. This is a very effective mechanism to concentrate pebbles as also seen in numerical simulations and possibly in ALMA observations. Yet, a high pebble load is dangerous for the vortex, and we showed that in two-dimensional simulations the backreaction eventually leads to vortex disruption. We investigate whether the same happens in three dimensions. We perform 3D simulations with pebbles in a local box finding that, although the pebbles disturb the vortex around the midplane, the column does not get destroyed. This result is important because, based on the previous 2D result suggesting complete disruption, the vortex interpretation of ALMA observations has been called into question. We show instead that the vortex behaves like a Taylor column, and the pebbles as obstacles to the flow. Pebble accumulation in the center of the vortices proceeds to roughly the same concentration as in the control run without backreaction.

astro-ph.EP↗

arXiv2018

Vortex Formation and Survival in Protoplanetary Disks subject to Vertical Shear Instability

Several protoplanetary disks observed by ALMA show dust concentrations consistent with particle trapping in giant vortices. The formation and survival of vortices is of major importance for planet formation, because vortices act as particle traps and are therefore preferred locations of planetesimal formation. Recent studies showed that the vertical shear instability (VSI) is capable of generating turbulence and small vortices in protoplanetary disks that have the proper radial and vertical stratification and thermally relax on sufficiently short time scales. But the effect of the azimuthal extend of the disk is often neglected as the disks azimuth is limited to $Δϕ\leq π/2$. We aim to investigate the influence of the azimuthal extent of the disk on the long-term evolution of a protoplanetary disk and the possibility of large vortices forming. To this end, we perform 3-dimensional simulations for up to 1000 local orbits using different values of $Δϕ= π/2 $ to $2π$ for VSI in disks with a prescribed radial density and temperature gradient cooling on short timescales. We find the VSI capable of forming large vortices which can exist at least several hundred orbits in simulations covering a disk with $Δϕ\geq π$. This suggests the VSI to be capable to form vortices or at least to trigger vortex formation via a secondary instability, e.g. Rossby Wave Instability or Kelvin Helmholtz Instability.

astro-ph.EP↗

arXiv2018

Azimuthal and Vertical Streaming Instability at High Dust-to-gas Ratios and on the Scales of Planetesimal Formation

The collapse of dust particle clouds directly to km-sized planetesimals is a promising way to explain the formation of planetesimals, asteroids and comets. In the past, this collapse has been studied in stratified shearing box simulations with super-solar dust-to-gas ratio ε, allowing for streaming instability (SI) and gravitational collapse. This paper studies the non-stratified SI under dust-to-gas ratios from ε=0.1 up to ε=1000 without self-gravity. The study covers domain sizes of L=0.1 H, 0.01 H and 0.001 H, in terms of gas disk scale height H, using the PencilCode. They are performed in radial-azimuthal (2-d) and radial-vertical (2.5-d) extent. The used particles of St=0.01 and 0.1 mark the upper end of the expected dust growth. SI-activity is found up to very high dust-to-gas ratios, providing fluctuations in the local dust-to-gas ratios and turbulent particle diffusion δ. We find an SI-like instability that operates in r-φeven when vertical modes are suppressed. This new azimuthal streaming instability (aSI) shows similar properties and appearance as the SI. Both, SI and aSI, show diffusivity at ε=100 only to be two orders of magnitude lower than at ε=1, suggesting a δ~ ε^{-1} relation that is shallow around ε= 1. The (a)SI ability to concentrate particles is found to be uncorrelated with its strength in particle turbulence. Finally, we performed a resolution study to test our findings of the aSI. This paper stresses out the importance of properly resolving the (a)SI at high dust-to-gas ratios and planetesimal collapse simulations, leading else wise to potentially incomplete results.

astro-ph.EP↗

arXiv2017

The fragmentation criteria in local vertically stratified self-gravitating disk simulations

Massive circumstellar disks are prone to gravitational instabilities, which trigger the formation of spiral arms that can fragment into bound clumps under the right conditions. Two dimensional simulations of self-gravitating disks are useful starting points for studying fragmentation, allowing for high-resolution simulations of thin disks. However, convergence issues can arise in 2D from various sources. One of these sources is the 2D approximation of self-gravity, which exaggerates the effect of self-gravity on small scales when the potential is not smoothed to account for the assumed vertical extent of the disk. This effect is enhanced by increased resolution, resulting in fragmentation at longer cooling timescales $β$. If true, it suggests that the 3D simulations of disk fragmentation may not have the same convergence problem and could be used to examine the nature of fragmentation without smoothing self-gravity on scales similar to the disk scale height. To that end, we have carried out local 3D self-gravitating disk simulations with simple $β$ cooling with fixed background irradiation to determine if 3D is necessary to properly describe disk fragmentation. Above a resolution of $\sim 40$ grid cells per scale height, we find that our simulations converge with respect to the cooling timescale. This result converges in agreement with analytic expectations which place a fragmentation boundary at $β_\mathrm{crit} = 3$.

astro-ph.EP↗