MRI in very young galaxies
Interstellar turbulence by the magnetorotational instablity

G. Rüdiger, D. Elstner, L.L. Kitchatinov

Bei Anwesenheit nicht zu starker magnetischer Felder führt ein Rotationsgestz mit nach aussen abnehmender Winkelgeschwindigkeit zur Entstehung von Turbulenz durch die sog. Magnetorotationsinstabilität (MRI). Wir haben in diesem Sinne die Instabilität der galaktischen Rotation in zwei Richtungen untersucht. Einmal wurden mit einer linearen Instabiltätsanalyse die Extremwerte des Magnetfeldes bestimmt, innerhalb derer die Instabilität existiert. Die minimale Magnetfeldstärke für Galaxien ergibt sich zu nur 10^{-25} Gauss, ohne die es keine Turbulenzerzeugung gibt. Andererseits würden alle Felder stärker als 6 muGauss jede Instabilität unterdrücken. Eine voll nichtlineare Rechnung mit dem ZEUSMP Code best&aul;tigt die genannte Obergrenze und führt in Übereinstimmung mit den Beobachtungen auf Turbulenzintenitäten von etwa 5 km/s. Die Instabilität besitzt Wachstumszeiten von nur 100 Mio Jahren, sodass die MRI insbesondere die beobachtete Turbulenz in sehr jungen Galaxien erklären kann.

Magnetorotational instablity (MRI) leads to the formation of turbulence by the interaction of differential rotation and a weak axial magnetic field if the angular velocity decreases outwards. A linear model for the MRI is considered for galaxies with their extremely large magnetic Prandtl number. The resulting minimum field of about 10^{-25} Gauss is even small compared to any seed fields currently discussed. We must therefore expect the formation of turbulence in all galaxies treaded by an large-scale intergalactic magnetic field. The growth times of the MRI are estimated as only about 100 Myr what is short compared to the age even of the younger galaxies. MRI is thus a much-promising candidate as the driver of turbulence in very young galaxies where too few supernova explosions exist in order to maintain any turbulence. In NGC 1058 a turbulence intensity of 6 km/s has been observed by Dickey et al. (1990) in regions without any star formation activity so that supernova explosions cannot be the driver of the turbulence.

The magnetic field modes with quadrupolar symmetry are more easily excited than the dipolar modes. So the basic parity-selection problem of the galactic dynamo theory formulated by Krause & Beck (1998) seems to be solved. It consists on the parodox that any galactic dynamo model only amplifies quadrupolar magnetic seed fields rather than fields with dipolar symmetry. Magnetic fields, however, due to battery effects during the protogalactic collapse always have dipolar geometry excluding them as the seed fields for the galactic dynamo. The maximum magnetic field which is still able to excite the MRI in galaxies followed from the perturbation theory to be about 6 muGauss - in excellent agreement with the amplitude of the observed magnetic fields in galaxies.

Our global 3D nonlinear MHD simulations with the ZEUSMP code for vertically stratified galaxies confirm the basic findings of the linear theory. Due to MRI, toroidal and poloidal components of the magnetic fields are generated. The results are applied to very young galaxies which exhibit observable magnetic fields already after a lifetime of only 100 Myr. The MRI-induced interstellar turbulence is minimal at the midplane and grows with the distance to the midplane. Such a behaviour of the interstellar turbulence is known from the observations and cannot be explained by other mechanisms. The turbulence velocity of the interstellar matter reaches values of about 5 km/s in perfect agreement with the measurements. For stronger magnetic fields the MRI is suppressed but it is not suppressed by mild turbulence initially present in the disk.


Fig.1: The stability diagram for axisymmetric quadrupolar magnetic modes. Note that the minimum of the eigenvalue does not change for growing magnetic Prandtl number. From these results the lower and upper limits for the magnetic field amplitude given in text have been derived.


Fig.2: Vertical dependence of the velocity dispersion in MRI-driven turbulence of the interstellar matter.