Eccentricity growth of planetesimals in a self-gravitating protoplanetary disc

We investigate the orbital evolution of planetesimals in a self-gravitating circumstellar disc in the size regime (∼1–5000 km) where the planetesimals behave approximately as test particles in the disc's non-axisymmetric potential. We find that the particles respond to the stochastic, regenerative spiral features in the disc by executing large random excursions (up to a factor of 2 in radius in ∼1000 yr), although typical random orbital velocities are of the order of one tenth of the Keplerian speed. The limited time frame and small number of planetesimals modelled do not permit us to discern any net direction of planetesimal migration. Our main conclusion is that the high eccentricities (∼0.1) induced by interaction with spiral features in the disc is likely to be highly unfavourable to the collisional growth of planetesimals in this size range while the disc is in the self-gravitating regime. Thus if , as recently argued by Rice et al., the production of planetesimals gets under way when the disc is in the self-gravitating regime (either at smaller planetesimal size scales, where gas drag is important, or via gravitational fragmentation of the solid component), the planetesimals thus produced would not be able to grow collisionally until the disc ceases to be self-gravitating. It is unclear, however, given the large amplitude excursions undergone by planetesimals in the self-gravitating disc, whether they would be retained in the disc throughout this period, or whether they would instead be lost to the central star.     

Detecting ionized bubbles in redshifted 21-cm maps

Linear transient phenomena induced by flow non-normality in thin self-gravitating astrophysical discs are studied using the shearing sheet approximation. The considered system includes two modes of perturbations: vortex and (spiral density) wave. It is shown that self-gravity considerably alters the vortex mode dynamics; its transient (swing) growth may be several orders of magnitude stronger than in the non-self-gravitating case and two to three times larger than the transient growth of the wave mode. Based on this finding, we comment on the role of vortex mode perturbations in a gravitoturbulent state. We also describe the linear coupling of the perturbation modes, caused by the differential character of disc rotation. The coupling is asymmetric: vortex mode perturbations are able to excite wave mode perturbations, but not vice versa. This asymmetric coupling lends additional significance to the vortex mode as a participant in spiral density waves and shock manifestations in astrophysical discs.     

Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent, and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.     

Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M_⊕) to 1 Jupiter mass (1 M_J) by using the zeus hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses   M _p≳ 0.1 M_J  produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc mid-plane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M_J and is highly efficient, occurring at the local viscous rate. The migration time-scales for planets of mass less than 0.1 M_J, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non-gap) migration for three-dimensional discs. The transition from type I to type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M_J with little migration. Planets with final masses of the order of 10 M_J would undergo large migration, which makes formation and survival difficult.     

On the evolution of giant protoplanets forming in circumbinary discs

We present the results of hydrodynamic simulations of Jovian mass protoplanets that form in circumbinary discs. The simulations follow the orbital evolution of the binary plus protoplanet system acting under their mutual gravitational forces, and forces exerted by the viscous circumbinary disc. The evolution involves the clearing of the inner circumbinary disc initially, so that the binary plus protoplanet system orbits within a low density cavity. Continued interaction between disc and protoplanet causes inward migration of the planet towards the inner binary. Subsequent evolution can take three distinct paths: (i) the protoplanet enters the 4 : 1 mean motion resonance with the binary, but is gravitationally scattered through a close encounter with the secondary star; (ii) the protoplanet enters the 4 : 1 mean motion resonance, the resonance breaks, and the planet remains in a stable orbit just outside the resonance; (iii) when the binary has initial eccentricity   e _bin≥ 0.2  , the disc becomes eccentric, leading to a stalling of the planet migration, and the formation of a stable circumbinary planet.
These results have implications for a number of issues in the study of extrasolar planets. The ejection of protoplanets in close binary systems provides a source of 'free-floating planets', which have been discovered recently. The formation of a large, tidally truncated cavity may provide an observational signature of circumbinary planets during formation. The existence of protoplanets orbiting stably just outside a mean motion resonance (4 : 1) in the simulations indicate that such sites may harbour planets in binary star systems, and these could potentially be observed. Finally, the formation of stable circumbinary planets in eccentric binary systems indicates that circumbinary planets may not be uncommon.     

Radiatively heated, protoplanetary discs with dead zones – I. Dust settling and thermal structure of discs around M stars

The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between two-dimensional self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they include dust settling with multiple grain sizes  ( N = 15)  , the gravitational force of an embedded planet on the disc and the presence of a dead zone (a region with very low levels of turbulence) within it. We show that dust settling drives the temperature of the mid-plane from an   r ^−3/5  distribution (well mixed dust models) towards an   r ^−3/4  . The dead zone, meanwhile, leaves a dusty wall at its outer edge because dust settling in this region is enhanced compared to the active turbulent disc at larger disc radii. The disc heating produced by this irradiated wall provides a positive gradient region of the temperature in the dead zone in front of the wall. This is crucially important for slowing planetary migration because Lindblad torques are inversely proportional to the disc temperature. Furthermore, we show that low turbulence of the dead zone is self-consistently induced by dust settling, resulting in the Kelvin–Helmholtz instability (KHI). We show that the strength of turbulence arising from the KHI in the dead zone is  α= 10⁻⁵  .     

Unstable modes of non-axisymmetric gaseous discs

We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed physical quantities in terms of a complete basis set and a small non-axisymmetry parameter ε. We then derive a linear eigenvalue problem in matrix form, and determine the pattern speed, growth rate and mode shapes of the first three unstable modes. In non-axisymmetric discs, the amplitude and the phase angle of travelling waves are functions of both the radius R and the azimuthal angle φ. This is due to the interaction of different wave components in the response spectrum. We demonstrate that wave interaction in unstable discs, with small initial asymmetries, can develop dense clumps during the phase of exponential growth. Local clumps, which occur on the major spiral arms, can constitute seeds of gas giant planets in accretion discs.     

Do accretion discs regulate the rotation of young stars?

We present a photometric study of I -band variability in the young cluster IC 348. The main purpose of the study was to identify periodic stars. In all, we find 50 periodic stars, of which 32 were previously unknown. For the first time in IC 348, we discover periods in significant numbers of lower-mass stars  ( M < 0.25 M_⊙)  and classical T Tauri stars. This increased sensitivity to periodicities is a result of the enhanced depth and temporal density of our observations, compared with previous studies. The period distribution is at first glance similar to that seen in the Orion nebula cluster (ONC), with the higher-mass stars  ( M > 0.25 M_⊙)  showing a bi-modal period distribution concentrated around periods of 2 and 8 d, and the lower-mass stars showing a uni-modal distribution, heavily biased towards fast rotators. Closer inspection of the period distribution shows that the higher-mass stars show a significant dearth of fast rotators, compared to the ONC, whilst the low-mass stars are rotating significantly faster than those in Orion. We find no correlation between rotation period and K – L colour or Hα equivalent width.
We also present a discussion of our own IC 348 data in the context of previously published period distributions for the ONC, the Orion flanking fields and NGC 2264. We find that the previously claimed correlation between infrared excess and rotation period in the ONC might, in fact, result from a correlation between infrared excess and mass. We also find a marked difference in period distributions between NGC 2264 and IC 348, which presents a serious challenge to the disc-locking paradigm, given the similarity in ages and disc fractions between the two clusters.