title: Saturation of the turbulent dynamo.
abstract: The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k☆ which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm≫1 and between 2.43% and 0.135% for Pm≪1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.
authors.affiliation: Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg, Germany and Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden.
authors.forename: J
authors.initials: J
authors.lastname: Schober
authors.affiliation: Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Avenida Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Concepción, Chile.
authors.forename: D R G
authors.initials: DR
authors.lastname: Schleicher
authors.affiliation: Research School of Astronomy & Astrophysics, The Australian National University, Canberra, ACT 2611, Australia.
authors.forename: C
authors.initials: C
authors.lastname: Federrath
authors.affiliation: Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany and Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Bovino
authors.affiliation: Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Strasse 2, D-69120 Heidelberg, Germany.
authors.forename: R S
authors.initials: RS
authors.lastname: Klessen