Planet-disk Interactions Research Articles

Constraining the mass of the planet(s) sculpting a disk cavity

The large cavities observed in the dust and gas distributions of transition disks may be explained by planet-disk interactions. At ~145 pc, 2MASS J16042165-2130284 (J1604) is a 5-12 Myr old transitional disk with different gap sizes in the mm- and $\mu$m-sized dust distributions (outer edges at ~79 and at ~63 au, respectively). Its $^{12}$CO emission shows a ~30 au cavity. This radial structure suggests that giant planets are sculpting this disk. We aim to constrain the masses and locations of plausible giant planets around J1604. We observed J1604 with the Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) at the Very Large Telescope (VLT), in IRDIFS\_EXT, pupil-stabilized mode, obtaining YJH- band images with the integral field spectrograph (IFS) and K1K2-band images with the Infra-Red Dual-beam Imager and Spectrograph (IRDIS). The dataset was processed exploiting the angular differential imaging (ADI) technique with high-contrast algorithms. Our observations reach a contrast of $\Delta K, YH$ ~12 mag from 0.15" to 0.80" (~22 to 115 au), but no planet candidate is detected. The disk is directly imaged in scattered light at all bands from Y to K, and it shows a red color. This indicates that the dust particles in the disk surface are mainly $\gtrsim0.3\,\mu$m-sized grains. We confirm the sharp dip/decrement in scattered light in agreement with polarized light observations. Comparing our images with a radiative transfer model we argue that the southern side of the disk is most likely the nearest. This work represents the deepest search yet for companions around J1604. We reach a mass sensitivity of $\gtrsim 2-3M_{Jup}$ from ~22 to ~115 au according to a hot start scenario. We propose that a brown dwarf orbiting inside of ~15 au and additional Jovian planets at larger radii could account for the observed properties of J1604 while explaining our lack of detection.

Formation and composition of planets around very low mass stars

The recent detection of planets around very low mass stars raises the question of the formation, composition and potential habitability of these objects. We use planetary system formation models to infer the properties, in particular their radius distribution and water content, of planets that may form around stars ten times less massive than the Sun. Our planetary system formation and composition models take into account the structure and evolution of the protoplanetary disk, the planetary mass growth by accretion of solids and gas, as well as planet-planet, planet-star and planet-disk interactions. We show that planets can form at small orbital period in orbit about low mass stars. We show that the radius of the planets is peaked at about 1 rearth and that they are, in general, volatile rich especially if proto-planetary discs orbiting this type of stars are long-lived. Close-in planets orbiting low-mass stars similar in terms of mass and radius to the ones recently detected can be formed within the framework of the core accretion paradigm as modeled here. The properties of protoplanetary disks, and their correlation with the stellar type, are key to understand their composition.

Cavity and other radial substructures in the disk around HD 97048

Context: Gaps, cavities and rings in circumstellar disks are signposts of disk evolution and planet-disk interactions. We follow the recent suggestion that Herbig Ae/Be disks with a flared disk harbour a cavity, and investigate the disk around HD~97048. Aims: We aim to resolve the 34$\pm$ 4 au central cavity predicted by Maaskant et al. (2013) and to investigate the structure of the disk. Methods: We image the disk around HD~97048 using ALMA at 0.85~mm and 2.94~mm, and ATCA (multiple frequencies) observations. Our observations also include the 12CO J=1-0, 12CO J=3-2 and HCO+ J=4-3 emission lines. Results: A central cavity in the disk around HD~97048 is resolved with a 40-46 au radius. Additional radial structure present in the surface brightness profile can be accounted for either by an opacity gap at ~90 au or by an extra emitting ring at ~150 au. The continuum emission tracing the dust in the disk is detected out to 355 au. The 12CO J=3-2 disk is detected 2.4 times farther out. The 12CO emission can be traced down to $\approx$ 10 au scales. Non-Keplerian kinematics are detected inside the cavity via the HCO+ J=4-3 velocity map. The mm spectral index measured from ATCA observations suggests that grain growth has occurred in the HD~97048 disk. Finally, we resolve a highly inclined disk out to 150 au around the nearby 0.5~$M_{\odot}$ binary ISO-ChaI 126. Conclusions: The data presented here reveal a cavity in the disk of HD 97048, and prominent radial structure in the surface brightness. The cavity size varies for different continuum frequencies and gas tracers. The gas inside the cavity follows non-Keplerian kinematics seen in HCO+ emission. The variable cavity size along with the kinematical signature suggests the presence of a substellar companion or massive planet inside the cavity.

Can dead zones create structures like a transition disk?

[Abridged] Regions of low ionisation where the activity of the magneto-rotational instability is suppressed, the so-called dead zones, have been suggested to explain gaps and asymmetries of transition disks. We investigate the gas and dust evolution simultaneously assuming simplified prescriptions for a dead zone and a magnetohydrodynamic (MHD) wind acting on the disk. We explore whether the resulting gas and dust distribution can create signatures similar to those observed in transition disks. For the dust evolution, we included the transport, growth, and fragmentation of dust particles. To compare with observations, we produced synthetic images in scattered optical light and in thermal emission at mm wavelengths. In all models with a dead zone, a bump in the gas surface density is produced that is able to efficiently trap large particles ($\gtrsim 1$ mm) at the outer edge of the dead zone. The gas bump reaches an amplitude of a factor of $\sim5$, which can be enhanced by the presence of an MHD wind that removes mass from the inner disk. While our 1D simulations suggest that such a structure can be present only for $\sim$1 Myr, the structure may be maintained for a longer time when more realistic 2D/3D simulations are performed. In the synthetic images, gap-like low-emission regions are seen at scattered light and in thermal emission at mm wavelengths, as previously predicted in the case of planet-disk interaction. As a conclusion, main signatures of transition disks can be reproduced by assuming a dead zone in the disk, such as gap-like structure in scattered light and millimetre continuum emission, and a lower gas surface density within the dead zone. Previous studies showed that the Rossby wave instability can also develop at the edge of such dead zones, forming vortices and also creating asymmetries.

The SHARDDS survey: First resolved image of the HD 114082 debris disk in the Lower Centaurus Crux with SPHERE

We present the first resolved image of the debris disk around the 16+/-8 Myr old star, HD 114082. The observation was made in the H-band using the SPHERE instrument. The star is at a distance of 92+/-6 pc in the Lower Centaurus Crux association. Using a Markov Chain Monte Carlo analysis, we determined that the debris is likely in the form of a dust ring with an inner edge of 27.7+2.8/-3.5 au, position angle -74+0.5/-1.5 deg, and an inclination with respect to the line of sight of 6.7+3.8/-0.4 deg. The disk imaged in scattered light has a surface density declining with radius like ~r^(-4), steeper than expected for grain blowout by radiation pressure. We find only marginal evidence (2 sigma) of eccentricity, and rule out planets more massive than 1.0 Mjup orbiting within 1 au of the ring's inner edge, since such a planet would have disrupted the disk. The disk has roughly the same fractional disk luminosity (Ldisk/L*=3.3x10^(-3)) as HR4796A and Beta Pictoris, however it was not detected by previous instrument facilities most likely because of its small angular size (radius~0.4"), low albedo (~0.2) and low scattering efficiency far from the star due to high scattering anisotropy. With the arrival of extreme adaptive optics systems like SPHERE and GPI, the morphology of smaller, fainter and more distant debris disks are being revealed, providing clues to planet-disk interactions in young protoplanetary systems.

Shadows cast on the transition disk of HD 135344B

The protoplanetary disk around the F-type star HD 135344B (SAO 206462) is in a transition stage and shows many intriguing structures both in scattered light and thermal (sub-)millimeter emission which are possibly related to planet formation processes. We study the morphology and surface brightness of the disk in scattered light to gain insight into the innermost disk regions, the formation of protoplanets, planet-disk interactions traced in the surface and midplane layers, and the dust grain properties of the disk surface. We have carried out high-contrast polarimetric differential imaging (PDI) observations with VLT/SPHERE and obtained polarized scattered light images with ZIMPOL in R- and I-band and with IRDIS in Y- and J-band. The scattered light images reveal with unprecedented angular resolution and sensitivity the spiral arms as well as the 25 au cavity of the disk. Multiple shadow features are discovered on the outer disk with one shadow only being present during the second observation epoch. A positive surface brightness gradient is observed in the stellar irradiation corrected images in southwest direction possibly due to an azimuthally asymmetric perturbation of the temperature and/or surface density by the passing spiral arms. The disk integrated polarized flux, normalized to the stellar flux, shows a positive trend towards longer wavelengths which we attribute to large aggregate dust grains in the disk surface. Part of the the non-azimuthal polarization signal in the Uphi image of the J-band observation could be the result of multiple scattering in the disk. The detected shadow features and their possible variability have the potential to provide insight into the structure of and processes occurring in the innermost disk regions.

Multiple rings in the transition disk and companion candidates around RX J1615.3-3255

We search for signs of ongoing planet-disk interaction and study the distribution of small grains at the surface of the transition disk around RXJ1615.3-3255 (RX J1615). We observed RXJ1615 with VLT/SPHERE. We image the disk for the first time in scattered light and detect two arcs, two rings, a gap and an inner disk with marginal evidence for an inner cavity. The shapes of the arcs suggest that they probably are segments of full rings. Ellipse fitting for the two rings and inner disk yield a disk inclination i = 47 \pm 2 degrees and find semi-major axes of 1.50 \pm 0.01" (278 au), 1.06 \pm 0.01" (196 au) and 0.30 \pm 0.01" (56 au), respectively. We determine the scattering surface height above the midplane, based on the projected ring center offsets. Nine point sources are detected between 2.1" and 8.0" separation and considered as companion candidates. With NACO data we recover four of the nine point sources, which we determine not to be co-moving, and therefore unbound to the system. We present the first detection of the transition disk of RXJ1615 in scattered light. The height of the rings indicate limited flaring of the disk surface, which enables partial self-shadowing in the disk. The outermost arc either traces the bottom of the disk or it is another ring with semi-major axis > 2.35" (435 au). We explore both scenarios, extrapolating the complete shape of the feature, which will allow to distinguish between the two in future observations. The most interesting scenario, where the arc traces the bottom of the outer ring, requires the disk truncated at r ~ 360 au. The closest companion candidate, if indeed orbiting the disk at 540 au, would then be the most likely cause for such truncation. This companion candidate, as well as the remaining four, require follow up observations to determine if they are bound to the system.

The frequency of binary star interlopers amongst transitional discs

Using Non-Redundant Mask interferometry (NRM), we searched for binary companions to objects previously classified as Transitional Disks (TD). These objects are thought to be an evolutionary stage between an optically thick disk and optically thin disk. We investigate the presence of a stellar companion as a possible mechanism of material depletion in the inner region of these disks, which would rule out an ongoing planetary formation process in distances comparable to the binary separation. For our detection limits, we implement a new method of completeness correction using a combination of randomly sampled binary orbits and Bayesian inference. The selected sample of 24 TDs belong to the nearby and young star forming regions: Ophiuchus ($\sim$ 130 pc), Taurus-Auriga ($\sim$ 140 pc) and IC348 ( $\sim$ 220 pc). These regions are suitable to resolve faint stellar companions with moderate to high confidence levels at distances as low as 2 au from the central star. With a total of 31 objects, including 11 known TDs and circumbinary disks from the literature, we have found that a fraction of 0.38 $\pm$ 0.09 of the SEDs of these objects are likely due to the tidal interaction between a close binary and its disk, while the remaining SEDs are likely the result of other internal processes such as photoevaporation, grain growth, planet disk interactions. In addition, we detected four companions orbiting outside the area of the truncation radii and we propose that the IR excesses of these systems are due to a disk orbiting a secondary companion

Investigating dust trapping in transition disks with millimeter-wave polarization

Spatially resolved polarized (sub-)mm emission has been observed for example in the protoplanetary disk around HL Tau. Magnetically aligned grains are commonly interpreted as the source of polarization. However, self-scattering by large dust grains with a high enough albedo is another polarization mechanism, becoming a compelling method independent of the spectral index to constrain the dust grain size in protoplanetary disks. We study the dust polarization at mm wavelength in the dust trapping scenario proposed for transition disks, when a giant planet opens a gap in the disk. We investigate the characteristic polarization patterns and their dependence on disk inclination, dust size evolution, planet position, and observing wavelength. We combine two-dimensional hydrodynamical simulations of planet-disk interactions with self-consistent dust growth models. These size-dependent dust density distributions are used for follow-up three-dimensional radiative transfer calculations to predict the polarization degree at ALMA bands due to scattered thermal emission. We find that the polarization pattern of a disk with a planetary gap after 1 Myr of dust evolution shows a distinctive three ring structure. Two narrow inner rings are located at the planet gap edges. For increasing observing wavelengths all three rings slightly change their position, where the innermost and outermost rings move inward. This distance is detectable comparing the results at ALMA bands 3, 6 and 7. Within the highest polarized intensity regions the polarization vectors are oriented in the azimuthal direction. For an inclined disk there is an interplay between polarization originating from a flux gradient and inclination-induced quadrupole polarization. For intermediate inclined transition disks the polarization degree is as high as ~ 2% at band 3, which is well above the detection limit of future ALMA observations.

IN SITU AND EX SITU FORMATION MODELS OF KEPLER 11 PLANETS

ABSTRACT We present formation simulations of the six Kepler 11 planets. Models assume either in situ or ex situ assembly, the latter with migration, and are evolved to the estimated age of the system, . Models combine detailed calculations of both the gaseous envelope and the condensed core structures, including accretion of gas and solids, of the disk’s viscous and thermal evolution, including photo-evaporation and disk-planet interactions, and of the planet’s evaporative mass loss after disk dispersal. Planet–planet interactions are neglected. Both sets of simulations successfully reproduce measured radii, masses, and orbital distances of the planets, except for the radius of Kepler 11b, which loses its entire gaseous envelope shortly after formation. Gaseous (H+He) envelopes account for % of the planet masses, and between and % of the planet radii. In situ models predict a very massive inner disk, whose solid surface density ( ) varies from over 104 to at stellocentric distances . Initial gas densities would be in excess of if solids formed locally. Given the high disk temperatures ( ), planetary interiors can only be composed of metals and highly refractory materials. Sequestration of hydrogen by the core and subsequent outgassing is required to account for the observed radius of Kepler 11b. Ex situ models predict a relatively low-mass disk, whose initial varies from to at and whose initial gas density ranges from to . All planetary interiors are expected to be rich in H2O, as core assembly mostly occurs exterior to the ice condensation front. Kepler 11b is expected to have a steam atmosphere, and H2O is likely mixed with H+He in the envelopes of the other planets. Results indicate that Kepler 11g may not be more massive than Kepler 11e.

CONSTRAINING THE MOVEMENT OF THE SPIRAL FEATURES AND THE LOCATIONS OF PLANETARY BODIES WITHIN THE AB AUR SYSTEM

ABSTRACT We present a new analysis of multi-epoch, H-band, scattered light images of the AB Aur system. We use a Monte Carlo radiative transfer code to simultaneously model the system’s spectral energy distribution (SED) and H-band polarized intensity (PI) imagery. We find that a disk-dominated model, as opposed to one that is envelope-dominated, can plausibly reproduce AB Aur’s SED and near-IR imagery. This is consistent with previous modeling attempts presented in the literature and supports the idea that at least a subset of AB Aur’s spirals originate within the disk. In light of this, we also analyzed the movement of spiral structures in multi-epoch H-band total light and PI imagery of the disk. We detect no significant rotation or change in spatial location of the spiral structures in these data, which span a 5.8-year baseline. If such structures are caused by disk–planet interactions, the lack of observed rotation constrains the location of the orbit of planetary perturbers to be >47 au.

On the orbital evolution of a pair of giant planets in mean motion resonance

Pairs of extrasolar giant planets in a mean motion commensurability are common with 2:1 resonance occurring most frequently. Disc-planet interaction provides a mechanism for their origin. However, the time scale on which this could operate in particular cases is unclear. We perform 2D and 3D numerical simulations of pairs of giant planets in a protoplanetary disc as they form and maintain a mean motion commensurability. We consider systems with current parameters similar to those of HD 155358, 24 Sextantis and HD 60532, and disc models of varying mass, decreasing mass corresponding to increasing age. For the lowest mass discs, systems with planets in the Jovian mass range migrate inwards maintaining a 2:1 commensurability. Systems with the inner planet currently at around 1 au from the central star could have originated at a few au and migrated inwards on a time scale comparable to protoplanetary disc lifetimes. Systems of larger mass planets such as HD 60532 attain 3:1 resonance as observed. For a given mass accretion rate, results are insensitive to the disc model for the range of viscosity prescriptions adopted, there being good agreement between 2D and 3D simulations. However, in a higher mass disc a pair of Jovian mass planets passes through 2:1 resonance before attaining a temporary phase lasting a few thousand orbits in an unstable 5:3 resonance prior to undergoing a scattering. Thus finding systems in this commensurability is unlikely.

Azimuthal asymmetries in the debris disk around HD 61005

Debris disks offer valuable insights into the latest stages of circumstellar disk evolution, and can possibly help us to trace the outcomes of planetary formation processes. In the age range 10 to 100\,Myr, most of the gas is expected to have been removed from the system, giant planets (if any) must have already been formed, and the formation of terrestrial planets may be on-going. Pluto-sized planetesimals, and their debris released in a collisional cascade, are under their mutual gravitational influence, which may result into non-axisymmetric structures in the debris disk. High angular resolution observations are required to investigate these effects and constrain the dynamical evolution of debris disks. Furthermore, multi-wavelength observations can provide information about the dust dynamics by probing different grain sizes. Here we present new VLT/SPHERE and ALMA observations of the debris disk around the 40\,Myr-old solar-type star HD\,61005. We resolve the disk at unprecedented resolution both in the near-infrared (in scattered and polarized light) and at millimeter wavelengths. Thanks to the new observations, we propose a solution for both the radial and azimuthal distribution of the dust grains in the debris disk. We find that the disk has a moderate eccentricity ($e \sim 0.1$) and that the dust density is two times larger at the pericenter compared to the apocenter. With no giant planets detected in our observations, we investigate alternative explanations besides planet-disk interactions to interpret the inferred disk morphology. We postulate that the morphology of the disk could be the consequence of a massive collision between $\sim$\,1000\,km-sized bodies at $\sim$\,61\,au. If this interpretation holds, it would put stringent constraints on the formation of massive planetesimals at large distances from the star.

A hot Jupiter orbiting a 2-million-year-old solar-mass T Tauri star.

Hot Jupiters are giant Jupiter-like exoplanets that orbit their host stars 100 times more closely than Jupiter orbits the Sun. These planets presumably form in the outer part of the primordial disk from which both the central star and surrounding planets are born, then migrate inwards and yet avoid falling into their host star. It is, however, unclear whether this occurs early in the lives of hot Jupiters, when they are still embedded within protoplanetary disks, or later, once multiple planets are formed and interact. Although numerous hot Jupiters have been detected around mature Sun-like stars, their existence has not yet been firmly demonstrated for young stars, whose magnetic activity is so intense that it overshadows the radial velocity signal that close-in giant planets can induce. Here we report that the radial velocities of the young star V830 Tau exhibit a sine wave of period 4.93 days and semi-amplitude 75 metres per second, detected with a false-alarm probability of less than 0.03 per cent, after filtering out the magnetic activity plaguing the spectra. We find that this signal is unrelated to the 2.741-day rotation period of V830 Tau and we attribute it to the presence of a planet of mass 0.77 times that of Jupiter, orbiting at a distance of 0.057 astronomical units from the host star. Our result demonstrates that hot Jupiters can migrate inwards in less than two million years, probably as a result of planet–disk interactions.

Formation, Orbital and Internal Evolutions of Young Planetary Systems

The growing body of observational data on extrasolar planets and protoplanetary disks has stimulated intense research on planet formation and evolution in the past few years. The extremely diverse, sometimes unexpected physical and orbital characteristics of exoplanets lead to frequent updates on the mainstream scenarios for planet formation and evolution, but also to the exploration of alternative avenues. The aim of this review is to bring together classical pictures and new ideas on the formation, orbital and internal evolutions of planets, highlighting the key role of the protoplanetary disk in the various parts of the theory. We begin by briefly reviewing the conventional mechanism of core accretion by the growth of planetesimals, and discuss a relatively recent model of core growth through the accretion of pebbles. We review the basic physics of planet-disk interactions, recent progress in this area, and discuss their role in observed planetary systems. We address the most important effects of planets internal evolution, like cooling and contraction, the mass-luminosity relation, and the bulk composition expressed in the mass-radius and mass-mean density relations.

Gaps, rings, and non-axisymmetric structures in protoplanetary disks: Emission from large grains

Dust grains with sizes around (sub)mm are expected to couple only weakly to the gas motion in regions beyond 10 au of circumstellar disks. In this work, we investigate the influence of the spatial distribution of such grains on the (sub)mm appearance of magnetized protoplanetary disks. We perform non-ideal global 3D magneto-hydrodynamic stratified disk simulations including particles of different sizes (50 micron to 1 cm), using a Lagrangian particle solver. We calculate the spatial dust temperature distribution, including the dynamically coupled submicron-sized dust grains, and derive ideal continuum re-emission maps of the disk through radiative transfer simulations. Finally, we investigate the feasibility to observe specific structures in the thermal re-emission maps with the Atacama Large Millimeter/submillimeter Array (ALMA). The pressure bump close to the outer edge of the dead-zone leads to particle trapping in ring structures. More specifically, vortices in the disk concentrate the dust and create an inhomogeneous distribution of the solid material in the azimuthal direction. The large-scale disk perturbations are preserved in the (sub)mm re-emission maps. The observable structures are very similar to those expected to result from planet-disk interaction. The larger dust particles increase the brightness contrast between gap and ring structures. We find that rings, gaps and the dust accumulation in the vortex could be traced with ALMA down to a scale of a few astronomical units in circumstellar disks located in nearby star-forming regions. Finally, we present a brief comparison of these structures with those recently found with ALMA in the young circumstellar disks of HL Tau and Oph IRS 48.

Self-organisation in protoplanetary discs

Context. Recent observations have revealed organised structures in protoplanetary discs, such as axisymmetric rings or horseshoe concentrations, evocative of large-scale vortices. These structures are often interpreted as the result of planet-disc interactions. However, these discs are also known to be unstable to the magneto-rotational instability (MRI) which is believed to be one of the dominant angular momentum transport mechanism in these objects. It is therefore natural to ask whether the MRI itself could produce these structures without invoking planets.

THE VLA VIEW OF THE HL TAU DISK: DISK MASS, GRAIN EVOLUTION, AND EARLY PLANET FORMATION

ABSTRACT 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 (1–3) × 10−3 M ⊙, 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.

The SPHERE view of the planet-forming disk around HD 100546

We image with unprecedented spatial resolution and sensitivity disk features that could be potential signs of planet-disk interaction. Two companion candidates have been claimed in the disk around the young Herbig Ae/Be star HD100546. Thus, this object serves as an excellent target for our investigation of the natal environment of giant planets. We exploit the power of extreme adaptive optics operating in conjunction with the new high-contrast imager SPHERE to image HD100546 in scattered light. We obtain the first polarized light observations of this source in the visible (with resolution as fine as 2 AU) and new H and K band total intensity images that we analyze with the Pynpoint package. The disk shows a complex azimuthal morphology, where multiple scattering of photons most likely plays an important role. High brightness contrasts and arm-like structures are ubiquitous in the disk. A double-wing structure (partly due to ADI processing) resembles a morphology newly observed in inclined disks. Given the cavity size in the visible (11 AU), the CO emission associated to the planet candidate 'c' might arise from within the circumstellar disk. We find an extended emission in the K band at the expected location of 'b'. The surrounding large-scale region is the brightest in scattered light. There is no sign of any disk gap associated to 'b'.

Growth of eccentric modes in disc–planet interactions

We formulate a set of linear equations that describe the behaviour of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure and self-gravity, and is exchanged with the planet via secular interactions. Excitation and damping of eccentricity can occur through Lindblad and corotation resonances, as well as viscosity. We compute normal modes of the coupled disc-planet system in the case of short-period giant planets orbiting inside an inner cavity, possibly carved by the stellar magnetosphere. Three-dimensional effects allow for a mode to be trapped in the inner parts of the disc. This mode can easily grow within the disc's lifetime. An eccentric mode dominated by the planet can also grow, although less rapidly. We compute the structure and growth rates of these modes and their dependence on the assumed properties of the disc.