arXiv subjects

Hubert Klahr

Publications and source records attributed to Hubert Klahr.

At least 73 records · Page 4Linked to original sources

arXiv2017

The Planetary Accretion Shock: I. Framework for Radiation-hydrodynamical Simulations and First Results

The key aspect determining the post-formation luminosity of gas giants has long been considered to be the energetics of the accretion shock at the planetary surface. We use 1D radiation-hydrodynamical simulations to study the radiative loss efficiency and to obtain post-shock temperatures and pressures and thus entropies. The efficiency is defined as the fraction of the total incoming energy flux which escapes the system (roughly the Hill sphere), taking into account the energy recycling which occurs ahead of the shock in a radiative precursor. We focus here on a constant equation of state to isolate the shock physics but use constant and tabulated opacities. While robust quantitative results will require a self-consistent treatment including hydrogen dissocation and ionization, the results show the correct qualitative behavior and can be understood semi-analytically. The shock is found to be isothermal and supercritical for a range of conditions relevant to core accretion (CA), with Mach numbers greater than ca. 3. Across the shock, the entropy decreases significantly, by a few entropy units (k_B/baryon). While nearly 100 percent of the incoming kinetic energy is converted to radiation locally, the efficiencies are found to be as low as roughly 40 percent, implying that a meaningful fraction of the total accretion energy is brought into the planet. For realistic parameter combinations in the CA scenario, a non-zero fraction of the luminosity always escapes the system. This luminosity could explain, at least in part, recent observations in the LkCa 15 and HD 100546 systems.

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arXiv2016

The VLA view of the HL Tau Disk - Disk Mass, Grain Evolution, and Early Planet Formation

The first long-baseline ALMA campaign resolved the disk around the young star HL Tau into a number of axisymmetric bright and dark rings. Despite the very young age of HL Tau these structures have been interpreted as signatures for the presence of (proto)planets. The ALMA images triggered numerous theoretical studies based on disk-planet interactions, magnetically driven disk structures, and grain evolution. Of special interest are the inner parts of disks, where terrestrial planets are expected to form. However, the emission from these regions in HL Tau turned out to be optically thick at all ALMA wavelengths, preventing the derivation of surface density profiles and grain size distributions. Here, we present the most sensitive images of HL Tau obtained to date with the Karl G. Jansky Very Large Array at 7.0 mm wavelength with a spatial resolution comparable to the ALMA images. At this long wavelength the dust emission from HL Tau is optically thin, allowing a comprehensive study of the inner disk. We obtain a total disk dust mass of 0.001 - 0.003 Msun, depending on the assumed opacity and disk temperature. Our optically thin data also indicate fast grain growth, fragmentation, and formation of dense clumps in the inner densest parts of the disk. Our results suggest that the HL Tau disk may be actually in a very early stage of planetary formation, with planets not already formed in the gaps but in the process of future formation in the bright rings.

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arXiv2015

The Role of the Cooling Prescription for Disk Fragmentation: Numerical Convergence & Critical Cooling Parameter in Self-Gravitating Disks

Protoplanetary disks fragment due to gravitational instability when there is enough mass for self-gravitation, described by the Toomre parameter, and when heat can be lost at a rate comparable to the local dynamical timescale, described by t_c=beta Omega^-1. Simulations of self-gravitating disks show that the cooling parameter has a rough critical value at beta_crit=3. When below beta_crit, gas overdensities will contract under their own gravity and fragment into bound objects while otherwise maintaining a steady state of gravitoturbulence. However, previous studies of the critical cooling parameter have found dependence on simulation resolution, indicating that the simulation of self-gravitating protoplanetary disks is not so straightforward. In particular, the simplicity of the cooling timescale t_c prevents fragments from being disrupted by pressure support as temperatures rise. We alter the cooling law so that the cooling timescale is dependent on local surface density fluctuations, a means of incorporating optical depth effects into the local cooling of an object. For lower resolution simulations, this results in a lower critical cooling parameter and a disk more stable to gravitational stresses suggesting the formation of large gas giants planets in large, cool disks is generally suppressed by more realistic cooling. At our highest resolution however, the model becomes unstable to fragmentation for cooling timescales up to beta = 10.

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arXiv2015

Particle Trapping and Streaming Instability in Vortices

We analyse the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, i.e. baroclinic vortex growth. Besides the gas drag acting on particles we also allow for back-reaction from dust onto the gas. This becomes important when the local dust-to-gas ratio approaches unity. In our 2D, local, shearing sheet simulations we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, ${\rm St}$. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for ${\rm St}=1$. The increased dust-to-gas ratio triggers the streaming instability, thus counter-intuitively limiting the maximal achievable overdensities. We find that particle trapping inside vortices opens the possibility for gravity-assisted planetesimal formation even for small particles ($\rm{St}=0.01$) and low initial dust-to-gas ratios (1:$10^4$)

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arXiv2014

SPOTS: The Search for Planets Orbiting Two Stars. I. Survey description and first observations

Direct imaging surveys for exoplanets commonly exclude binary stars from their target lists, leaving a large part of the overall planet demography unexplored. To address this gap in our understanding of planet formation and evolution, we have launched the first direct imaging survey dedicated to circumbinary planets: SPOTS, the Search for Planets Orbiting Two Stars. In this paper, we discuss the theoretical context, scientific merit, and technical feasibility of such observations, describe the target sample and observational strategy of our survey, and report on the first results from our pilot survey of 26 targets with the VLT NaCo facility. While we have not found any confirmed substellar companions to date, a number of promising candidate companions remain to be tested for common proper motion in upcoming follow-up observations. We also report on the astrometry of the three resolved binaries in our target sample. This pilot survey constitutes a successful proof of concept for our survey strategy and paves the way for a second stage of exploratory observations with VLT SPHERE.

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arXiv2014

Convective Overstability in radially stratified accretion disks under thermal relaxation

This letter expands the stability criterion for radially stratified, vertically {unstratified} accretion disks incorporating thermal relaxation. We find a linear amplification of epicyclic oscillations in these disks that depends on the effective cooling time, i.e. an overstability. The growth rates of the overstability vanish for both extreme cases, e.g. infinite cooling time and instantaneous cooling, i.e. the adiabatic and fully isothermal cases. However, for thermal relaxation times $τ$ on the order of the orbital frequency, $τΩ\sim 1$, modes grow at a rate proportional to the square of the Brunt-Väisälä frequency. The overstability is based on epicyclic motions, with the thermal relaxation causing gas to heat while radially displaced inwards, and cool while radially displaced outwards. This causes the gas to have a lower density when moving outwards compared to when it moves inwards, so it feels the outwards directed pressure force more strongly on that leg of the journey. We suggest the term ``Convective Overstability" for the phenomenon that has already been numerically studied in the non-linear regime in the context of amplifying vortices in disks, under the name ``Subcritical Baroclinic Instability". The point of the present paper is to make clear that vortex formation in three-dimensional disks is neither subcritical, i.e. does not need a finite perturbation, nor is it baroclinic in the sense of geophysical fluid dynamics, which requires on vertical shear. We find that Convective Overstability is a linear instability that will operate under a wide range of physical conditions for circumstellar disks.

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arXiv2013

Accretion of gas onto gap-opening planets and circumplanetary flow structure in magnetized turbulent disks

We have performed three-dimensional magneto-hydrodynamical simulations of stellar accretion disks, using the PLUTO code, and studied the accretion of gas onto a Jupiter-mass planet and the structure of the circumplanetary gas flow after opening a gap in the disk. We compare our results with simulations of laminar, yet viscous disks with different levels of an $α$-type viscosity. In all cases, we find that the accretion flow across the surface of the Hill sphere of the planet is not spherically or azimuthally symmetric, and is predominantly restricted to the mid-plane region of the disk. Even in the turbulent case, we find no significant vertical flow of mass into the Hill sphere. The outer parts of the circumplanetary disk are shown to rotate significantly below Keplerian speed, independent of viscosity, while the circumplanetary disk density (therefore the angular momentum) increases with viscosity. For a simulation of a magnetized turbulent disk, where the global averaged alpha stress is $α_{MHD}=10^{-3}$, we find the accretion rate onto the planet to be $\dot{M}\approx 2\times10^{-6}M_{J}yr^{-1}$ for a gap surface density of $12 g cm^{-2}$. This is about a third of the accretion rate obtained in a laminar viscous simulation with equivalent $α$ parameter.

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arXiv2013

Gravoturbulent Planetesimal Formation: The Positive Effect of long-lived Zonal Flows

Recent numerical simulations have shown long-lived axisymmetric sub- and super-Keplerian flows in protoplanetary disks. These zonal flows are found in local as well as global simulations of disks unstable to the magnetorotational instability. This paper covers our study of the strength and lifetime of zonal flows and the resulting long-lived gas over- and underdensities as functions of the azimuthal and radial size of the local shearing box. We further investigate dust particle concentrations without feedback on the gas and without self-gravity. Strength and lifetime of zonal flows increase with the radial extent of the simulation box, but decrease with the azimuthal box size. Our simulations support earlier results that zonal flows have a natural radial length scale of 5-7 gas pressure scale heights. This is the first study that combines three-dimensional MHD simulations of zonal flows and dust particles feeling the gas pressure. The pressure bumps trap particles with $\textrm{St} = 1$ very efficiently. We show that $\textrm{St} = 0.1$ particles (of some centimeters in size if at $5\textrm{AU}$ in an MMSN) reach a hundred-fold higher density than initially. This opens the path for particles of $\textrm{St} = 0.1$ and dust-to-gas ratio of 0.01 or for particles of $\textrm{St} \geq 0.5$ and dust-to-gas ratio $10^{-4}$ to still reach densities that potentially trigger the streaming instability and thus gravoturbulent formation of planetesimals.

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arXiv2012

A solution to the radiation pressure problem in the formation of massive stars

We review our recent studies demonstrating that the radiation pressure problem in the formation of massive stars can be circumvented via an anisotropy of the thermal radiation field. Such an anisotropy naturally establishes with the formation of a circumstellar disk. The required angular momentum transport within the disk can be provided by developing gravitational torques. Radiative Rayleigh-Taylor instabilities in the cavity regions - as previously suggested in the literature - are not required and are shown to be not occurring in the context of massive star formation.

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arXiv2011

On the stability of radiation-pressure-dominated cavities

Context: When massive stars exert a radiation pressure onto their environment that is higher than their gravitational attraction, they launch a radiation-pressure-driven outflow. It has been claimed that a radiative Rayleigh-Taylor instability should lead to the collapse of the outflow cavity and foster the growth of massive stars. Aims: We investigate the stability of idealized radiation-pressure-dominated cavities, focusing on its dependence on the radiation transport approach for the stellar radiation feedback. Methods: We compare two different methods for stellar radiation feedback: gray flux-limited diffusion (FLD) and ray-tracing (RT). We also derive simple analytical models to support our findings. Results: Only the FLD cases lead to prominent instability in the cavity shell. The RT cases do not show such instability. The gray FLD method underestimates the opacity at the location of the cavity shell and leads to extended epochs of marginal Eddington equilibrium in the cavity shell, making them prone to the radiative Rayleigh-Taylor instability. In the RT cases, the radiation pressure exceeds gravity by 1-2 orders of magnitude. The radiative Rayleigh-Taylor instability is then consequently suppressed. Conclusions: Treating the stellar irradiation in the gray FLD approximation underestimates the radiative forces acting on the cavity shell. This can lead artificially to situations that are affected by the radiative Rayleigh-Taylor instability. The proper treatment of direct stellar irradiation by massive stars is crucial for the stability of radiation-pressure-dominated cavities.

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arXiv2011

How do Most Planets Form? -- Constraints on Disk Instability from Direct Imaging

Core accretion and disk instability have traditionally been regarded as the two competing possible paths of planet formation. In recent years, evidence have accumulated in favor of core accretion as the dominant mode, at least for close-in planets. However, it might be hypothesized that a significant population of wide planets formed by disk instabilities could exist at large separations, forming an invisible majority. In previous work, we addressed this issue through a direct imaging survey of B2--A0-type stars, and concluded that <30% of such stars form and retain planets and brown dwarfs through disk instability, leaving core accretion as the likely dominant mechanism. In this paper, we extend this analysis to FGKM-type stars by applying a similar analysis to the Gemini Deep Planet Survey (GDPS) sample. The results strengthen the conclusion that substellar companions formed and retained around their parent stars by disk instabilities are rare. Specifically, we find that the frequency of such companions is <8% for FGKM-type stars under our most conservative assumptions, for an outer disk radius of 300 AU, at 99% confidence. Furthermore, we find that the frequency is always <10% at 99% confidence independently of outer disk radius, for any radius from 5 to 500 AU. We also simulate migration at a wide range of rates, and find that the conclusions hold even if the companions move substantially after formation. Hence, core accretion remains the likely dominant formation mechanism for the total planet population, for every type of star from M-type through B-type.

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arXiv2011

High-contrast Imaging Search for Planets and Brown Dwarfs around the Most Massive Stars in the Solar Neighborhood

There has been a long-standing discussion in the literature as to whether core accretion or disk instability is the dominant mode of planet formation. Over the last decade, several lines of evidence have been presented showing that core accretion is most likely the dominant mechanism for the close-in population of planets probed by radial velocity and transits. However, this does not by itself prove that core accretion is the dominant mode for the total planet population, since disk instability might conceivably produce and retain large numbers of planets in the far-out regions of the disk. If this is a relevant scenario, then the outer massive disks of B-stars should be among the best places for massive planets and brown dwarfs to form and reside. In this study, we present high-contrast imaging of 18 nearby massive stars, of which 15 are in the B2--A0 spectral type range and provide excellent sensitivity to wide companions. By comparing our sensitivities to model predictions of disk instability based on physical criteria for fragmentation and cooling, and using Monte-Carlo simulations for orbital distributions, we find that ~85 % of such companions should have been detected in our images on average. Given this high degree of completeness, stringent statistical limits can be set from the null-detection result, even with the limited sample size. We find that <32 % of massive stars form and retain disk instability planets, brown dwarfs and very low-mass stars of <100 Mjup within 300 AU, at 99 % confidence. These results, combined with previous findings in the literature, lead to the conclusion that core accretion is likely the dominant mode of planet formation.

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arXiv2011

3D MHD Simulations of Planet Migration in Turbulent Stratified Disks

We performed 3D MHD simulations of planet migration in stratified disks using the Godunov code PLUTO, where the disk is turbulent due to the magnetorotational instability. We study the migration for planets with different planet-star mass ratios $q=M_{p}/M_{s}$. In agreement with previous studies, for the low-mass planet cases ($q=5\times10^{-6}$ and $10^{-5}$), migration is dominated by random fluctuations in the torque. For a Jupiter-mass planet $(q=M_{p}/M_{s}=10^{-3}$ for $M_{s}=1M_{\odot})$, we find a reduction of the magnetic stress inside the orbit of the planet and around the gap region. After an initial stage where the torque on the planet is positive, it reverses and we recover migration rates similar to those found in disks where the turbulent viscosity is modelled by an $α$ viscosity. For the intermediate-mass planets ($q=5\times10^{-5}, 10^{-4}$ and $2\times10^{-4}$) we find a new and so far unexpected behavior. In some cases they experience sustained and systematic outwards migration for the entire duration of the simulation. For this case, the horseshoe region is resolved and torques coming from the corotation region can remain unsaturated due to the stresses in the disk. These stresses are generated directly by the magnetic field. The magnitude of the horseshoe drag can overcome the negative Lindblad contribution when the local surface density profile is flat or increasing outwards, which we see in certain locations in our simulations due to the presence of a zonal flow. The intermediate-mass planet is migrating radially outwards in locations where there is a positive gradient of a pressure bump (zonal flow).

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arXiv2011

High-resolution simulations of planetesimal formation in turbulent protoplanetary discs

We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $α\approx0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flows and particle concentration in pressure bumps is relatively similar at moderate (256^3) and high (512^3) resolution. In the moderate-resolution simulation we activate particle self-gravity at a time when there is little particle concentration, in contrast with previous simulations where particle self-gravity was activated during a concentration event. We observe that bound clumps form over the next ten orbits, with initial birth masses of a few times the dwarf planet Ceres. At high resolution we activate self-gravity during a particle concentration event, leading to a burst of planetesimal formation, with clump masses ranging from a significant fraction of to several times the mass of Ceres. We present a new domain decomposition algorithm for particle-mesh schemes. Particles are spread evenly among the processors and the local gas velocity field and assigned drag forces are exchanged between a domain-decomposed mesh and discrete blocks of particles. We obtain good load balancing on up to 4096 cores even in simulations where particles sediment to the mid-plane and concentrate in pressure bumps.

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arXiv2011

Three-dimensional simulation of massive star formation in the disk accretion scenario

The most massive stars can form via standard disk accretion - despite of the radiation pressure generated - due to the fact that the massive accretion disk yields a strong anisotropy in the radiation field, releasing most of the radiation pressure perpendicular to the disk accretion flow. Here, we analyze the self-gravity of the forming circumstellar disk as the potential major driver of the angular momentum transport in such massive disks responsible for the high accretion rates needed for the formation of massive stars. For this purpose, we perform self-gravity radiation hydrodynamics simulations of the collapse of massive pre-stellar cores. The formation and evolution of the resulting circumstellar disk is investigated in 1.) axially symmetric simulations using an alpha-shear-viscosity prescription and 2.) a three-dimensional simulation, in which the angular momentum transport is provided self-consistently by developing gravitational torques in the self-gravitating accretion disk. The simulation series of different strength of the alpha-viscosity shows that the accretion history of the forming star is mostly independent of the alpha-viscosity-parameter. The accretion history of the three-dimensional run driven by self-gravity is more time-dependent than the viscous disk evolution in axial symmetry. The mean accretion rate, i.e. the stellar mass growth, is nearly identical to the alpha-viscosity models. We conclude that the development of gravitational torques in self-gravitating disks around forming massive stars provides a self-consistent mechanism to efficiently transport the angular momentum to outer disk radii. Also the formation of the most massive stars can therefore be understood in the standard accretion disk scenario.

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arXiv2011

Radiation pressure feedback in the formation of massive stars

We investigate the radiation pressure feedback in the formation of massive stars in 1, 2, and 3D radiation hydrodynamics simulations of the collapse of massive pre-stellar cores. In contrast to previous research, we consider frequency dependent stellar radiation feedback, resolve the dust sublimation front in the vicinity of the forming star down to 1.27 AU, compute the evolution for several 10^5 yrs covering the whole accretion phase of the forming star, and perform a comprehensive survey of the parameter space. The most fundamental result is that the formation of a massive accretion disk in slowly rotating cores preserves a high anisotropy in the radiation field. The thermal radiation escapes through the optically thin atmosphere, effectively diminishing the radiation pressure feedback onto the accretion flow. Gravitational torques in the self-gravitating disk drive a sufficiently high accretion rate to overcome the residual radiation pressure. Simultaneously, the radiation pressure launches an outflow in the bipolar direction, which grows in angle with time and releases a substantial fraction of the initial core mass from the star-disk system. Summarized, for an initial core mass of 60, 120, 240, and 480 Msol these mechanisms allow the star to grow up to 28.2, 56.5, 92.6, and at least 137.2 Msol respectively.

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arXiv2010

Theory of planet formation

We review the current theoretical understanding how growth from micro-meter sized dust to massive giant planets occurs in disks around young stars. After introducing a number of observational constraints from the solar system, from observed protoplanetary disks, and from the extrasolar planets, we simplify the problem by dividing it into a number of discrete stages which are assumed to occur in a sequential way. In the first stage - the growth from dust to kilometer sized planetesimals - the aerodynamics of the bodies are of central importance. We discuss both a purely coagulative growth mode, as well as a gravoturbulent mode involving a gravitational instability of the dust. In the next stage, planetesimals grow to protoplanets of roughly 1000 km in size. Gravity is now the dominant force. The mass accretion can be strongly non-linear, leading to the detachment of a few big bodies from the remaining planetesimals. In the outer planetary system (outside a few AU), some of these bodies can become so massive that they eventually accrete a large gaseous envelope. This is the stage of giant planet formation, as understood within the core accretion-gas capture paradigm. We also discuss the direct gravitational collapse model where giant planets are thought to form directly via a gravitational fragmentation of the gas disk. In the inner system, protoplanets collide in the last stage - probably after the dispersal of the gaseous disk - in giant impacts until the separations between the remaining terrestrial planets become large enough to allow long term stability. We finish the review with some selected questions.

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arXiv2010

The role of accretion disks in the formation of massive stars

We present radiation hydrodynamics simulations of the collapse of massive pre-stellar cores. We treat frequency dependent radiative feedback from stellar evolution and accretion luminosity at a numerical resolution down to 1.27 AU. In the 2D approximation of axially symmetric simulations, it is possible for the first time to simulate the whole accretion phase of several 10^5 yr for the forming massive star and to perform a comprehensive scan of the parameter space. Our simulation series show evidently the necessity to incorporate the dust sublimation front to preserve the high shielding property of massive accretion disks. Our disk accretion models show a persistent high anisotropy of the corresponding thermal radiation field, yielding to the growth of the highest-mass stars ever formed in multi-dimensional radiation hydrodynamics simulations. Non-axially symmetric effects are not necessary to sustain accretion. The radiation pressure launches a stable bipolar outflow, which grows in angle with time as presumed from observations. For an initial mass of the pre-stellar host core of 60, 120, 240, and 480 Msol the masses of the final stars formed in our simulations add up to 28.2, 56.5, 92.6, and at least 137.2 Msol respectively.

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