Turbulence in circumstellar disks

¹ CNRS URA 2464 GIT/SPEC/DRECAM/DSM, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: bdubrulle@cea.fr
² LESIA CNRS UMR 8109, Observatoire de Paris-Meudon, Place Jules Janssen, 92195 Meudon Cedex, France
³ Institut für Theoretische Astrophysik, Tiergartenstraße 15, 69121 Heidelberg, Germany
⁴ LUTh CNRS UMR 8102, Observatoire de Paris-Meudon, Place Jules Janssen, 92195 Meudon Cedex, France
⁵ Université Paris 7 Denis Diderot, 2 Place Jussieu, 75251 Paris Cedex 05, France

Received: 31 January 2003
Accepted: 16 August 2004

Abstract

We investigate the relationship between circumstellar disks and the Taylor-Couette flow. Using the Reynolds similarity principle, this results in a number of parameter-free predictions about stability of the disks, and their turbulent transport properties, provided the disk structure is available. We discuss how the latter can be deduced from interferometric observations of circumstellar material. We use the resulting disk structure to compute the molecular transport coefficients, including the effect of ionization by the central object. The resulting control parameter indicates that the disk is well into the turbulent regime. The analogy is also used to compute the effective accretion rate, as a function of the disk characteristic parameters (orbiting velocity, temperature and density). These values are in very good agreement with experimental, parameter-free predictions derived from the supposed relationship. The turbulent viscosity is also computed and found to correspond to an α-parameter . Predictions regarding fluctuations are also checked: luminosity fluctuations in disks do obey the same universal distribution as energy fluctuations observed in a laboratory turbulent flow. Radial velocity dispersion in the outer part of the disk is predicted to be of the order of 0.1 km s^-1, in agreement with available observations. All these issues provide a proof of the turbulent character of circumstellar disks, as well as a parameter-free theoretical estimate of effective accretion rates.