Magnetorotational instability in Keplerian disks: a nonlocal approach

N.I. Shakura^†^a, b, K.A. Postnov^‡^a, b, D.A. Kolesnikov^§^a, c, G.V. Lipunova^*^a, d
^aLomonosov Moscow State University, Shternberg State Astronomical Institute, Universitetskii prosp. 13, Moscow, 119889, Russian Federation
^bKazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russian Federation
^cTel-Aviv University, Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv, Israel
^dMax-Planck-Institut für Radioastronomie, Auf dem Hügel 69, Bonn, 53121, Germany

We revisit the modal analysis of small perturbations in Keplerian ideal gas flows with a constant vertical magnetic field leading to magnetorotational instability (MRI) using the nonlocal approach. In the general case, MRI modes are described by a Schrödinger-like differential equation with some effective potential, including 'repulsive' (1/r²) and 'attractive' (−1/rr³) terms, and are quantized. In shallow potentials, there are no stationary 'energy levels.' In thin Keplerian accretion discs, the perturbation wavelengths λ =2π /k_z are smaller than the disc semi-thickness h only in 'deep' potential wells. We find that there is a critical magnetic field for the MRI to develop. The instability arises for magnetic fields below this critical value. In thin accretion discs, at low background Alfvén velocity c_A≪ (c_A)_cr, the MRI instability increment ω is suppressed compared to the value obtained in the local perturbation analysis, ω ≈ −√3ic_Ak_z. We also investigate for the first time the case of a radially variable background magnetic field.

Keywords: magnetorotational instability, accretion discs
PACS: 95.30.Qd, 97.10.Gz (all)
DOI: 10.3367/UFNe.2023.09.039554
URL: https://ufn.ru/en/articles/2023/12/f/
Web of Science

001172931200005
Scopus

2-s2.0-85183001473
ADS NASA

2023PhyU...66.1262S
Citation: Shakura N I, Postnov K A, Kolesnikov D A, Lipunova G V "Magnetorotational instability in Keplerian disks: a nonlocal approach" Phys. Usp. 66 1262–1276 (2023)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 16th, December 2022, revised: 21st, September 2023, accepted: 22nd, September 2023

Оригинал: Шакура Н И, Постнов К А, Колесников Д А, Липунова Г В «Магниторотационная неустойчивость в кеплеровских дисках: нелокальный подход» УФН 193 1340–1355 (2023); DOI: 10.3367/UFNr.2023.09.039554

References (35) ↓ Cited by (3) Similar articles (18)

Shakura N I, Sunyaev R A Astron. Astrophys. 24 337 (1973)
Bisnovatyi-Kogan G S, Lovelace R V E New Astron. Rev. 45 663 (2001)
Lipunova G, Malanchev K, Shakura N Accretion Flows In Astrophysics (Astrophysics and Space Science Library) Vol. 454 (Ed. N Shakura) (Cham: Springer, 2018) p. 1
Boneva D V et al Astron. Astrophys. 652 A38 (2021)
Somov B V et al Adv. Space Res. 32 1087 (2003)
Velikhov E P Sov. Phys. JETP 9 995 (1959); Velikhov E P Zh. Eksp. Teor. Fiz. 36 1398 (1959)
Chandrasekhar S Proc. Natl. Acad. Sci. USA 46 253 (1960)
Strutt J W (Lord Rayleigh) Proc. R. Soc. Lond. A 93 148 (1917)
Parker E N Astrophys. J. 145 811 (1966)
Balbus S A, Hawley J F Astrophys. J. 376 214 (1991)
Balbus S A, Hawley J F Rev. Mod. Phys. 70 1 (1998)
Hawley J F, Gammie C F, Balbus S A Astrophys. J. 440 742 (1995)
Sorathia K A et al Astrophys. J. 749 189 (2012)
Hawley J F et al Astrophys. J. 772 102 (2013)
Kato S, Fukue J, Mineshige S Black-Hole Accretion Disks (Kyoto, Japan: Kyoto Univ. Press, 1998)
Shakura N, Postnov K Mon. Not. R. Astron. Soc. 451 3995 (2015)
Zou R et al Phys. Rev. E 101 013201 (2020)
Papaloizou J, Szuszkiewicz E Geophys. Astrophys. Fluid Dyn. 66 223 (1992)
Kumar S, Coleman C S, Kley W Mon. Not. R. Astron. Soc. 266 379 (1994)
Gammie C F, Balbus S A Mon. Not. R. Astron. Soc. 270 138 (1994)
Curry C, Pudritz R E, Sutherland P G Astrophys. J. 434 206 (1994)
Latter H N, Fromang S, Faure J Mon. Not. R. Astron. Soc. 453 3257 (2015)
Knobloch E Mon. Not. R. Astron. Soc. 255 25P (1992)
Dubrulle B, Knobloch E Astron. Astrophys. 274 667 (1993)
Shakura N I, Lipunova G V Mon. Not. R. Astron. Soc. 480 4273 (2018)
Shakura N, Postnov K Mon. Not. R. Astron. Soc. 448 3697 (2015)
Landau L D, Lifshitz E M Quantum Mechanics. Non-Relativistic Theory (Oxford: Butterworth-Heinemann, 1998); Translated from Russian, Landau L D, Lifshitz E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya (Moscow: Nauka, 1989)
Flügge S Practical Quantum Mechanics (Berlin: Springer-Verlag, 1971)
Landau L D, Lifshitz E M Fluid Dynamics (Oxford: Pergamon Press, 1987); Translated from Russian, Landau L D, Lifshitz E M Gidrodinamika (Moscow: Nauka, 1986)
Acheson D J Elementary Fluid Dynamics (Oxford: Clarendon Press, 1990)
Shakura N, Postnov K Accretion Flows In Astrophysics (Astrophysics and Space Science Library) Vol. 454 (Ed. N Shakura) (Cham: Springer, 2018) p. 393
Salmeron R, Königl A, Wardle M Mon. Not. R. Astron. Soc. 375 177 (2007)
Bai X-N, Stone J M Astrophys. J. 769 76 (2013)
Curry C, Pudritz R E Mon. Not. R. Astron. Soc. 281 119 (1996)
Levitan B M, Sargsyan I S Operatory Shturma—Liuvillya I Diraka (Sturm—Liouville And Dirac Operators) (Moscow: Nauka, 1988)