Growing dust grains in protoplanetary discs - I. Radial drift with toy growth models

In a series of papers, we present a comprehensive analytic study of the global motion of growing dust grains in protoplanetary discs, addressing both the radial drift and the vertical settling of the particles. Here we study how the radial drift of dust particles is affected by grain growth. In a first step, toy models in which grain growth can either be constant, accelerate or decelerate are introduced. The equations of motion are analytically integrable and therefore the grains dynamics is easy to understand. The radial motion of growing grains is governed by the relative efficiency of the growth and migration processes which is expressed by the dimensionless parameter Lambda, as well as the exponents for the gas surface density and temperature profiles, denoted p and q respectively. When Lambda is of order unity, growth and migration are strongly coupled, providing the most efficient radial drift. For the toy models considered, grains pile up when -p+q+1/2<0. Importantly, we show the existence of a second process which can help discs to retain their solid materials. For accelerating growth, grains end up their migration at a finite radius, thus avoiding being accreted onto the central star.Comment: 12 pages, 9 figures. Accepted for publication in MNRAS. v2: typos correcte

Planet gaps in the dust layer of 3D proto-planetary disks: Observability with ALMA

Among the numerous known extrasolar planets, only a handful have been imaged directly so far, at large orbital radii and in rather evolved systems. The Atacama Large Millimeter/submillimeter Array (ALMA) will have the capacity to observe these wide planetary systems at a younger age, thus bringing a better understanding of the planet formation process. Here we explore the ability of ALMA to detect the gaps carved by planets on wide orbits.Comment: 2 pages, 2 figures, to appear in the Proceedings of IAU Symp. 299: Exploring the Formation and Evolution of Planetary Systems (Victoria, Canada

Predicting Dust Distribution in Protoplanetary Discs

We present the results of three-dimensional numerical simulations that include the effects of hydrodynamical forces and gas drag upon an evolving dusty gas disk. We briefly describe a new parallel, two phase numerical code based upon the smoothed particle hydrodynamics (SPH) technique in which the gas and dust phases are represented by two distinct types of particles. We use the code to follow the dynamical evolution of a population of grains in a gaseous protoplanetary disk in order to understand the distribution of grains of different sizes within the disk. Our ``grains'' range from metre to submillimetre in size.Comment: 2 pages, LaTeX with 1 ps figure embedded, using newpasp.sty (supplied). To appear in the proceedings of the XIXth IAP colloquium "Extrasolar Planets: Today and Tomorrow" held in Paris, France, 2003, June 30 -- July 4, ASP Conf. Se

SPH Simulations of Accretion Disks and Narrow Rings

We model a massless viscous disk using Smoothed Particle Hydrodynamics (SPH) and note that it evolves according to the Lynden-Bell \& Pringle theory (1974) until a non-axisymmetric instability develops at the inner edge of the disk. This instability may have the same origin as the instability of initially axisymmetric viscous disks discussed by Lyubarskij et al. (1994). To clarify the evolution we evolved single and double rings of particles. It is actually inconsistent with the SPH scheme to set up a single ring as an initial condition because SPH assumes a smoothed initial state. As would be expected from an SPH simulation, the ring rapidly breaks up into a band. We analyse the stability of the ring and show that the predictions are confirmed by the simulation.Comment: 11 pages, uuencoded compressed postscript with 2 figs, accepted PASA. Also available at http://www.maths.monash.edu.au/~maddison/me/papers.htm

A dynamical test for terrestrial planets in the habitable zone of HD 204313

With improvements in exoplanet detection techniques, the number of multiple planet systems discovered is increasing, while the detection of potentially habitable Earth-mass planets remains complicated and thus requires new search strategies. Dynamical studies of known multiple planet systems are therefore a vital tool in the search for stable and habitable planet candidates. Here, we present a dynamical study of the three-planet system HD 204313 to determine whether it could harbour an Earth-like planet within its habitable zone for a sufficient time to develop life. We found two semi-stable regions in the system, but neither prove stable for long enough for a terrestrial planet to develop life. Our investigations suggest that overlapping weak and high order resonances may be responsible for these semi-stable regions. This study established a framework for a larger project that will study the dynamical stability of the habitable zone of multiple planet systems, providing a list of interesting targets for future habitable low-mass planet searches

3D SPH simulations of grain growth in protoplanetary disks

We present the first results of the treatment of grain growth in our 3D, two-fluid (gas+dust) SPH code describing protoplanetary disks. We implement a scheme able to reproduce the variation of grain sizes caused by a variety of physical processes and test it with the analytical expression of grain growth given by Stepinski & Valageas (1997) in simulations of a typical T Tauri disk around a one solar mass star. The results are in agreement with a turbulent growing process and validate the method. We are now able to simulate the grain growth process in a protoplanetary disk given by a more realistic physical description, currently under development. We discuss the implications of the combined effect of grain growth and dust vertical settling and radial migration on subsequent planetesimal formatio

SPH simulations of grain growth in protoplanetary disks

6 pages, 6 figures, accepted to A&AInternational audienceAims: In order to understand the first stages of planet formation, when tiny grains aggregate to form planetesimals, one needs to simultaneously model grain growth, vertical settling and radial migration of dust in protoplanetary disks. In this study, we implement an analytical prescription for grain growth into a 3D two-phase hydrodynamics code to understand its effects on the dust distribution in disks. Methods: Following the analytic derivation of Stepinski & Valageas (1997), which assumes that grains stick perfectly upon collision, we implement a convenient and fast method of following grain growth in our 3D, two-phase (gas+dust) SPH code. We then follow the evolution of the size and spatial distribution of a dust population in a classical T Tauri star disk. Results: We find that the grains go through various stages of growth due to the complex interplay between gas drag, dust dynamics, and growth. Grains initially grow rapidly as they settle to the mid-plane, then experience a fast radial migration with little growth through the bulk of the disk, and finally pile-up in the inner disk where they grow more efficiently. This results in a bimodal distribution of grain sizes. Using this simple prescription of grain growth, we find that grains reach decimetric sizes in 10^5 years in the inner disk and survive the fast migration phase