Time-dependent models of the structure and stability of self-gravitating protoplanetary discs

Angular momentum transport within young massive protoplanetary discs may be dominated by self-gravity at radii where the disc is too weakly ionized to allow the development of the magneto-rotational instability. We use time-dependent one-dimensional disc models, based on a local cooling time calculation of the efficiency of transport, to study the radial structure and stability (against fragmentation) of protoplanetary discs in which self-gravity is the sole transport mechanism. We find that self-gravitating discs rapidly attain a quasi-steady state in which the surface density in the inner disc is high and the strength of turbulence very low (  α∼ 10⁻³  or less inside 5 au). Temperatures high enough to form crystalline silicates may extend out to several astronomical units at early times within these discs. None of our discs spontaneously develop regions that would be unambiguously unstable to fragmentation into substellar objects, though the outer regions (beyond 20 au) of the most massive discs are close enough to the threshold that fragmentation cannot be ruled out. We discuss how the mass accretion rates through such discs may vary with disc mass and with mass of the central star, and note that a determination of the     relation for very young systems may allow a test of the model.     

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.     

Episodic accretion in magnetically layered protoplanetary discs

We study protoplanetary disc evolution assuming that angular momentum transport is driven by gravitational instability at large radii, and magnetohydrodynamic (MHD) turbulence in the hot inner regions. At radii of the order of 1 au such discs develop a magnetically layered structure, with accretion occurring in an ionized surface layer overlying quiescent gas that is too cool to sustain MHD turbulence. We show that layered discs are subject to a limit cycle instability, in which accretion on to the protostar occurs in ∼10⁴-yr bursts with ̇ ∼10⁻⁵ M_⊙ yr⁻¹, separated by quiescent intervals lasting ∼10⁵ yr where ̇ ≈10⁻⁸ M_⊙ yr⁻¹. Such bursts could lead to repeated episodes of strong mass outflow in young stellar objects. The transition to this episodic mode of accretion occurs at an early epoch ( t ≪1 Myr), and the model therefore predicts that many young pre-main-sequence stars should have low rates of accretion through the inner disc. At ages of a few Myr, the discs are up to an order of magnitude more massive than the minimum-mass solar nebula, with most of the mass locked up in the quiescent layer of the disc at r ∼1 au. The predicted rate of low-mass planetary migration is reduced at the outer edge of the layered disc, which could lead to an enhanced probability of giant planet formation at radii of 1–3 au.     

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.     

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.     

The use of genetic algorithms to model protoplanetary discs

The protoplanetary discs of T Tauri and Herbig Ae/Be stars have previously been studied using geometric disc models to fit their spectral energy distribution (SED). The simulations provide a means to reproduce the signatures of various circumstellar structures, which are related to different levels of infrared excess. With the aim of improving our previous model, which assumed a simple flat-disc configuration, we adopt here a reprocessing flared-disc model that assumes hydrostatic, radiative equilibrium. We have developed a method to optimize the parameter estimation based on genetic algorithms (GAs). This paper describes the implementation of the new code, which has been applied to Herbig stars from the Pico dos Dias Survey catalogue, in order to illustrate the quality of the fitting for a variety of SED shapes. The star AB Aur was used as a test of the GA parameter estimation, and demonstrates that the new code reproduces successfully a canonical example of the flared-disc model. The GA method gives a good quality of fit, but the range of input parameters must be chosen with caution, as unrealistic disc parameters can be derived. It is confirmed that the flared-disc model fits the flattened SEDs typical of Herbig stars; however, embedded objects (increasing SED slope) and debris discs (steeply decreasing SED slope) are not well fitted with this configuration. Even considering the limitation of the derived parameters, the automatic process of SED fitting provides an interesting tool for the statistical analysis of the circumstellar luminosity of large samples of young stars.     

The vertical structure of planet-induced gaps in protoplanetary discs

Giant planets embedded in circumstellar discs are expected to open gaps in these discs. We examine the vertical structure of the gap edges. We find that the planet excites spiral arms with significant (Mach number of a half) vertical motion of the gas, and discuss the implications of these motions. In particular, the spiral arms will make the edge appear 'puffed up' relative to the bulk of the disc. Infrared observations (sensitive to dust) would be dominated by the light from the thick inner edge of the disc. Submillimetre observations (sensitive to gas velocities) would appear to be hot in 'turbulent' motions (actually the ordered motion caused by the passage of the spiral arms), but cold in chemistry. Resolved submillimetre maps of circumstellar discs might even be able to detect the spiral arms directly.