Abstract
We consider nonaxisymmetric magnetosonic oscillations of a radially stratified, weakly ionized protoplanetary disk with a vertical magnetic field. The combined effect of the Hall electric field and the density and magnetic field inhomogeneities present in the disk has been previously predicted to lead to an instability of its small azimuthal perturbations. We revise the previous results and take into account the effect of inhomogeneous ionization of the protoplanetary material related to the inhomogeneity of the disk medium. We show that the instability criterion is governed by three parameters: the magnetic field and ionization fraction gradients and the plasma β. We have found that at high values of β typical of protoplanetary disks, the instability does not manifest itself if the gradients are directed oppositely. In the case of codirectional gradients, the interaction of magnetosonic fluctuations with inhomogeneities of a fixed size is resonant in character, giving rise to an instability in a narrow range of wave numbers.
Similar content being viewed by others
References
S. A. Balbus and J. F. Havley, Astrophys. J. 400, 610 (1992).
S. A. Balbus and C. Terquem, Astrophys. J. 552, 235 (2001).
A. Bonano and V. Urpin, Astron. Astrophys. 488, 1 (2008).
B. T. Draine,W. G. Roberge, and A. Dalgarno, Astrophys. J. 264, 485 (1983).
S. Fromang, C. Terquem, and S. A. Balbus, Mon. Not. R. Astron. Soc. 329, 18 (2002).
M. R. Hogerheijde, IAU Symp. 221, 361 (2004).
L. Jin, Astrophys. J. 457, 798 (1996).
A. S. Kingsep, Yu. V. Mokhov, and K. V. Chukbar, Sov. J. Plasma Phys. 10, 495 (1984).
E. Liverts, M. Mond, and A. D. Chernin, Astrophys. J. 666, 1226 (2007).
A. B. Mikhailovskii, J. G. Lominadze, R. M. Galvao, et al., Phys. Plasm. 15, 052103 (2008).
Yu. M. Shtemler, E. Liverts, and M. Mond, Astrophys. J. 665, 1371 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Prudskikh, 2012, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2012, Vol. 38, No. 1, pp. 48–53.
Rights and permissions
About this article
Cite this article
Prudskikh, V.V. Resonant character of the hall instability in protoplanetary disks. Astron. Lett. 38, 45–50 (2012). https://doi.org/10.1134/S1063773712010057
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063773712010057