arXiv subjects

W. Kley

Publications and source records attributed to W. Kley.

At least 37 records · Page 2Linked to original sources

arXiv2014

Modeling the EUV spectra of optically thick boundary layers of dwarf novae in outburst

Here we compute detailed model spectra of recently published optically thick one-dimensional radial baundary layer (BL) models in cataclysmic variables and compare them with observed soft X-ray/extreme ultraviolet (EUV) spectra of dwarf novae in outburst. Every considered BL model is divided into a number of rings, and for each ring, a structure model along the vertical direction is computed using the stellar-atmosphere method. The ring spectra are then combined into a BL spectrum taking Doppler broadening and limb darkening into account. Two sets of model BL spectra are computed, the first of them consists of BL models with fixed white dwarf (WD) mass (1 M_sun) and various relative WD angular velocities (0.2, 0.4, 0.6 and 0.8 break-up velocities), while the other deals with a fixed relative angular velocity (0.8 break-up velocity) and various WD masses (0.8, 1, and 1.2 M_sun). The model spectra show broad absorption features because of blending of numerous absorption lines, and emission-like features at spectral regions with only a few strong absorption lines. The model spectra are very similar to observed soft X-ray/EUV spectra of SS Cyg and U Gem in outburst. The observed SS Cyg spectrum could be fitted by BL model spectra with WD masses 0.8 - 1 M_sun and relative angular velocities 0.6 - 0.8 break up velocities. These BL models also reproduce the observed ratio of BL luminosity and disk luminosity. The difference between the observed and the BL model spectra is similar to a hot optically thin plasma spectrum and could be associated with the spectrum of outflowing plasma with a mass loss rate compatible with the BL mass accretion rate. The suggested method of computing BL spectra seems very promising and can be applied to other BL models for comparison with EUV spectra of dwarf novae in outburst.

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arXiv2014

The PLATO 2.0 Mission

PLATO 2.0 has recently been selected for ESA's M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 sec readout cadence and 2 with 2.5 sec candence) providing a wide field-of-view (2232 deg2) and a large photometric magnitude range (4-16 mag). It focusses on bright (4-11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2%, 4-10% and 10% for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50% of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0.

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arXiv2013

Influence of viscosity and the adiabatic index on planetary migration

The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state, where the internal dissipation is balanced by radiative transport, and the migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. In this paper we investigate the influence of different viscosity prescriptions (alpha-type and constant) and adiabatic indices on disk structures and how this affects the migration rate of planets embedded in such disks. We perform 3D numerical simulations of accretion disks with embedded planets. We use the explicit/implicit hydrodynamical code NIRVANA that includes full tensor viscosity and radiation transport in the flux-limited diffusion approximation, as well as a proper equation of state for molecular hydrogen. The migration of embedded 20Earthmass planets is studied. Low-viscosity disks have cooler temperatures and the migration rates of embedded planets tend toward the isothermal limit. In these disks, planets migrate inwards even in the fully radiative case. The effect of outward migration can only be sustained if the viscosity in the disk is large. Overall, the differences between the treatments for the equation of state seem to play a more important role in disks with higher viscosity. A change in the adiabatic index and in the viscosity changes the zero-torque radius that separates inward from outward migration. For larger viscosities, temperatures in the disk become higher and the zero-torque radius moves to larger radii, allowing outward migration of a 20 Earth-mass planet to persist over an extended radial range. In combination with large disk masses, this may allow for an extended period of the outward migration of growing protoplanetary cores.

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arXiv2012

Planet-disk interaction and orbital evolution

As planets form and grow within gaseous protoplanetary disks, the mutual gravitational interaction between the disk and planet leads to the exchange of angular momentum, and migration of the planet. We review current understanding of disk-planet interactions, focussing in particular on physical processes that determine the speed and direction of migration. We describe the evolution of low mass planets embedded in protoplanetary disks, and examine the influence of Lindblad and corotation torques as a function of the disk properties. The role of the disk in causing the evolution of eccentricities and inclinations is also discussed. We describe the rapid migration of intermediate mass planets that may occur as a runaway process, and examine the transition to gap formation and slower migration driven by the viscous evolution of the disk for massive planets. The roles and influence of disk self-gravity and magnetohydrodynamic turbulence are discussed in detail, as a function of the planet mass, as is the evolution of multiple planet systems. Finally, we address the question of how well global models of planetary formation that include migration are able to match observations of extrasolar planets.

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arXiv2012

Treating gravity in thin disk simulations

In 2D simulations of thin gaseous disks with embedded planets or self-gravity the gravitational potential needs to be smoothed to avoid singularities in the numerical evaluation of the gravitational potential or force. In order to correctly resemble the realistic case of vertically extended 3D disks the softening prescription used in 2D needs to be adjusted properly. In this paper we analyze the embedded planet and the self-gravity case and provide a method to evaluate the required smoothing in 2D simulations of thin disks. Starting from the averaged hydrodynamic equations and using a vertically isothermal disk model, we calculate the force. We compare our results to the often used Plummer form of the potential which runs as \propto 1/(r^2+ε^2)^{1/2}. For that purpose we compute the required smoothing length εas a function of distance r to the planet or to a disk element within a self-gravitating disk. We find that for larger distances εis determined solely by the vertical disk thickness H. For the planet case we find that outside r\simH a value of ε= 0.7H describes the averaged force very well, while in the self-gravitating disk the value needs to be larger, ε= 1.2H. For smaller distances the smoothing needs to be reduced significantly. Comparing torque densities of 3D and 2D simulations we show that the modification to the vertical density stratification as induced by an embedded planet needs to be taken into account to obtain agreeing results. In disk fragmentation simulations the choice of εcan determine whether a disk will fragment or not. Because a wrong smoothing length can change even the direction of migration, it is very important to include the effect of the planet on the local scale height in 2D planet-disk simulations. We provide an approximate and fast method for this purpose which gives very good agreement to full 3D simulations.

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arXiv2011

Global Structure of Magnetorotationally Turbulent Protoplanetary Discs

The aim of the present paper is to investigate the spatial structure of a protoplanetary disc whose dynamics is governed by magnetorotational turbulence. We perform a series of local 3D chemo-radiative MHD simulations located at different radii of a disc which is twice as massive as the standard minimum mass solar nebula of Hayashi (1981). The ionisation state of the disc is calculated by including collisional ionisation, stellar X-rays, cosmic rays and the decay of radionuclides as ionisation sources, and by solving a simplified chemical network which includes the effect of the absorption of free charges by μm-sized dust grains. In the region where the ionisation is too low to assure good coupling between matter and magnetic fields, a non-turbulent central "dead zone" forms, which ranges approximately from a distance of 2 AU to 4 AU from the central star. The approach taken in the present work allows for the first time to derive the global spatial structure of a protoplanetary disc from a set of physically realistic numerical simulations.

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arXiv2011

Collisions of inhomogeneous pre-planetesimals

In the framework of the coagulation scenario, kilometre-sized planetesimals form by subsequent collisions of pre-planetesimals of sizes from centimetre to hundreds of metres. Pre-planetesimals are fluffy, porous dust aggregates, which are inhomogeneous owing to their collisional history. Planetesimal growth can be prevented by catastrophic disruption in pre-planetesimal collisions above the destruction velocity threshold. We develop an inhomogeneity model based on the density distribution of dust aggregates, which is assumed to be a Gaussian distribution with a well-defined standard deviation. As a second input parameter, we consider the typical size of an inhomogeneous clump. These input parameters are easily accessible by laboratory experiments. For the simulation of the dust aggregates, we utilise a smoothed particle hydrodynamics (SPH) code with extensions for modelling porous solid bodies. The porosity model was previously calibrated for the simulation of silica dust, which commonly serves as an analogue for pre-planetesimal material. The inhomogeneity is imposed as an initial condition on the SPH particle distribution. We carry out collisions of centimetre-sized dust aggregates of intermediate porosity. We vary the standard deviation of the inhomogeneous distribution at fixed typical clump size. The collision outcome is categorised according to the four-population model. We show that inhomogeneous pre-planetesimals are more prone to destruction than homogeneous aggregates. Even slight inhomogeneities can lower the threshold for catastrophic disruption. For a fixed collision velocity, the sizes of the fragments decrease with increasing inhomogeneity. Pre-planetesimals with an active collisional history tend to be weaker. This is a possible obstacle to collisional growth and needs to be taken into account in future studies of the coagulation scenario.

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arXiv2011

On the dynamics and collisional growth of planetesimals in misaligned binary systems

Context. Abridged. Many stars are members of binary systems. During early phases when the stars are surrounded by discs, the binary orbit and disc midplane may be mutually inclined. The discs around T Tauri stars will become mildly warped and undergo solid body precession around the angular momentum vector of the binary system. It is unclear how planetesimals in such a disc will evolve and affect planet formation. Aims. We investigate the dynamics of planetesimals embedded in discs that are perturbed by a binary companion on a circular, inclined orbit. We examine collisional velocities of the planetesimals to determine when they can grow through accretion. We vary the binary inclination, binary separation, D, disc mass, and planetesimal radius. Our standard model has D=60 AU, inclination=45 deg, and a disc mass equivalent to the MMSN. Methods. We use a 3D hydrodynamics code to model the disc. Planetesimals are test particles which experience gas drag, the gravitational force of the disc, the companion star gravity. Planetesimal orbit crossing events are detected and used to estimate collisional velocities. Results. For binary systems with modest inclination (25 deg), disc gravity prevents planetesimal orbits from undergoing strong differential nodal precession (which occurs in absence of the disc), and forces planetesimals to precess with the disc on average. For bodies of different size the orbit planes become modestly mutually inclined, leading to collisional velocities that inhibit growth. For larger inclinations (45 degrees), the Kozai effect operates, leading to destructively large relative velocities. Conclusions. Planet formation via planetesimal accretion is difficult in an inclined binary system with parameters similar to those considered in this paper. For systems in which the Kozai mechanism operates, the prospects for forming planets are very remote.

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arXiv2011

The Planets around the Post-Common Envelope Binary NN Serpentis

We have detected 2 circumbinary planets around the close binary system NN Serpentis using the orbital time delay effect measured via the sharp eclipses of the white dwarf primary. The present pre-cataclysmic binary was formed when the original - 2 M primary expanded into a red giant, causing the secondary star to drop from its original orbit at a separation of about 1.4 A.U. down to its current separation at 0.0043 A.U. A quasi-adiabatic evolution of the circumbinary planets' orbits during the common-envelope phase would have placed them in unstable configurations, suggesting that they may have suffered significant orbital drag effects and were originally in much larger orbits. Alternatively, they may have been created as 2nd-generation planets during the last million years from the substantial amount of material lost during the creation of the binary, making them the youngest planets known. Either solution shows how little we actually understand about planetary formation.

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arXiv2010

Two planets orbiting the recently formed post-common envelope binary NN Serpentis

Planets orbiting post-common envelope binaries provide fundamental information on planet formation and evolution. We searched for such planets in NN Ser ab, an eclipsing short-period binary that shows long-term eclipse time variations. Using published, reanalysed, and new mid-eclipse times of NN Ser ab obtained between 1988 and 2010, we find excellent agreement with the light-travel-time effect by two additional bodies superposed on the linear ephemeris of the binary. Our multi-parameter fits accompanied by N-body simulations yield a best fit for the objects NN Ser (ab)c and d locked in a 2:1 mean motion resonance, with orbital periods P_c=15.5 yrs and P_d=7.7 yrs, masses M_c sin i_c = 6.9 M_Jup and M_d sin i_d = 2.2 M_Jup, and eccentricities e_c=0 and e_d=0.20. A secondary chi**2 minimum corresponds to an alternative solution with a period ratio of 5:2. We estimate that the progenitor binary consisted of an A star with ~2 M_Sun and the present M dwarf secondary at an orbital separation of ~1.5 AU. The survival of two planets through the common-envelope phase that created the present white dwarf requires fine tuning between the gravitational force and the drag force experienced by them in the expanding envelope. The alternative is a second-generation origin in a circumbinary disk created at the end of this phase. In that case, the planets would be extremely young with ages not exceeding the cooling age of the white dwarf of 10**6 yrs.

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arXiv2010

A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion

We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.

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arXiv2010

Vertical Structure and Turbulent Saturation Level in Fully Radiative Protoplanetary Disc Models

We investigate a massive ($\varSigma \sim 10000 g cm^{-2}$ at 1 AU) protoplanetary disc model by means of 3D radiation magnetohydrodynamics simulations. The vertical structure of the disc is determined self-consistently by a balance between turbulent heating caused by the MRI and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: A gas-pressure dominated, optically thick midplane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosphere, the turbulence is supersonic ($M \sim 2$), which is consistent with previous results obtained from the fitting of spectra of YSOs. It is known that the turbulent saturation level in simulations of MRI-induced turbulence does depend on numerical factors such as the numerical resolution and the box size. However, by performing a suite of runs at different resolutions (using up to 64x128x512 grid cells) and with varying box sizes (with up to 16 pressure scaleheights in the vertical direction), we find that both the saturation levels and the heating rates show a clear trend to converge once a sufficient resolution in the vertical direction has been achieved.

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arXiv2009

A torque formula for non-isothermal Type I planetary migration - I. Unsaturated horseshoe drag

We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal effects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs Type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, using three independent numerical methods, and find good agreement.

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arXiv2009

The dynamical role of the circumplanetary disc in planetary migration

Numerical simulations of planets embedded in protoplanetary gaseous discs are a precious tool for studying the planetary migration ; however, some approximations have to be made. Most often, the selfgravity of the gas is neglected. In that case, it is not clear in the literature how the material inside the Roche lobe of the planet should be taken into account. Here, we want to address this issue by studying the influence of various methods so far used by different authors on the migration rate. We performed high-resolution numerical simulations of giant planets embedded in discs. We compared the migration rates with and without gas selfgravity, testing various ways of taking the circum-planetary disc (CPD) into account. Different methods lead to significantly different migration rates. Adding the mass of the CPD to the perturbing mass of the planet accelerates the migration. Excluding a part of the Hill sphere is a very touchy parameter that may lead to an artificial suppression of the type III, runaway migration. In fact, the CPD is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill radius and using a smooth filter. Alternatively, the CPD can be given the acceleration felt by the planet from the rest of the protoplanetary disc. The gas inside the Roche lobe of the planet should be very carefully taken into account in numerical simulations without any selfgravity of the gas. The entire Hill sphere should not be excluded. The method used should be explicitly given. However, no method is equivalent to computing the full selfgravity of the gas.

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arXiv2009

Growth of the MRI in Accretion Discs -- the Influence of Radiation Transport

In this paper we investigate the influence of radiative transport on the growth of the magnetorotational instability (MRI) in accretion discs. The analysis is performed by use of analytical and numerical means. We provide a general dispersion relation together with the corresponding eigenfunctions describing the growth rates of small disturbances on a homogeneous background shear flow. The dispersion relation includes compressibility and radiative effects in the flux-limited diffusion approximation. By introducing an effective speed of sound, all the effects of radiation transport can be subsumed into one single parameter. It can be shown that the growth rates of the vertical modes -- which are the fastest growing ones -- are reduced by radiative transport. For the case of non-vertical modes, the growth rates may instead be enhanced. We quantify the effects of compressibility and radiative diffusion on the growth rates for the gas-pressure dominated case. The analytical discussion is supplemented by numerical simulations, which are also used for a first investigation of the non-linear stage of the MRI in gas-pressure dominated accretion discs with radiation transport included.

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arXiv2008

Planetary Migration in Resonance, the question of the Eccentricities : Les Houches contribution

The formation of resonant planets pairs in exoplanetary systems involves planetary migration inside the protoplanetary disc : an inwards migrating outer planet captures in Mean Motion Resonance an inner planet. During the migration of the resonant pair of planets, the eccentricities are expected to rise excessively, if no damping mechanism is applied on the inner planet. We express the required damping action to match the observations, and we show that the inner disk can play this role. This result applies for instance to the system GJ 876 : we reproduce the observed orbital elements through a fully hydrodynamical simulation of the evolution of the resonant planets.

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arXiv2008

Influence of an inner disc on the orbital evolution of massive planets migrating in resonance

The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary eccentricities if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot occur over large radial distances and has to be terminated sufficiently rapidly through disc dissipation. In this study, we investigate whether the presence of an inner disc might supply an eccentricity damping of the inner planet, and if this effect could explain the observed eccentricities in some systems. To investigate the influence of an inner disc, we first compute hydrodynamic simulations of giant planets orbiting with a given eccentricity around an inner gas disc, and measure the effect of the latter on the planetary orbital parameters. We then perform detailed long term calculations of the GJ 876 system. We also run N-body simulations with artificial forces on the planets mimicking the effects of the inner and outer discs. We find that the influence of the inner disc can not be neglected, and that it might be responsible for the observed eccentricities. In particular, we reproduce quite well the orbital parameters of a few systems engaged in 2:1 mean motion resonances: GJ 876, HD 73526, HD 82943 and HD 128311. Finally, we derive analytically the effect that the inner disc should have on the inner planet to reach a specific orbital configuration with a given damping effect of the outer disc on the outer planet.

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arXiv2007

Stability and Formation of the Resonant System HD 73526

Based on radial velocity measurements it has been found recently that the two giant planets detected around the star HD 73526 are in 2:1 resonance. However, as our numerical integration shows, the derived orbital data for this system result in chaotic behavior of the giant planets, which is uncommon among the resonant extrasolar planetary systems. We intend to present regular (non-chaotic) orbital solutions for the giant planets in the system HD 73526 and offer formation scenarios based on combining planetary migration and sudden perturbative effects such as planet-planet scattering or rapid dispersal of the protoplanetary disk. A comparison with the already studied resonant system HD 128311, exhibiting similar behavior, is also done. The new sets of orbital solutions have been derived by the Systemic Console (www.oklo.org). The stability of these solutions has been investigated by the Relative Lyapunov indicator, while the migration and scattering effects are studied by gravitational N-body simulations applying non-conservative forces as well. Additionally, hydrodynamic simulations of embedded planets in protoplanetary disks are performed to follow the capture into resonance. For the system HD 73526 we demonstrate that the observational radial velocity data are consistent with a coplanar planetary system engaged in a stable 2:1 resonance exhibiting apsidal corotation. We have shown that, similarly to the system HD 128311, the present dynamical state of HD 73526 could be the result of a mixed evolutionary process melting together planetary migration and a perturbative event.

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