Abstract
We present a linear analysis of the magnetorotational instability (MRI) in differentially rotating disks and derive the most general instability criterion to date. Our analysis improves on earlier work on this topic in that it simultaneously accounts for arbitrary geometry and the full effects of magnetic diffusion. We allow the magnetic field to have arbitrary orientation and for linear modes to propagate at an angle to the rotation axis. We also include in our analysis all three forms of magnetic diffusion: ohmic dissipation, ambipolar diffusion, and Hall currents. Previous analyses have included either arbitrary geometry or ambipolar diffusion, but never both. The simultaneous inclusion of these effects allows us to identify a new unstable mode in which ambipolar diffusion and differential rotation can couple and amplify the magnetic field. We provide a physical explanation of this mode. Our linear analysis is aimed at determining which parts of protoplanetary disks may be unstable to the MRI. Accordingly, we outline the conditions that are likely to obtain in protoplanetary disks and make estimates of the coupling between the gas and the magnetic field. We derive a linear stability criterion that can be applied to protoplanetary disks.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 509-525 |
| Number of pages | 17 |
| Journal | Astrophysical Journal |
| Volume | 608 |
| Issue number | 1 I |
| DOIs | |
| State | Published - Jun 10 2004 |
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Keywords
- Accretion, accretion disks
- MHD
- Planetary systems: protoplanetary disks
ASJC Scopus subject areas
- Space and Planetary Science
Cite this
Linear analysis of the magnetorotational instability, including ambipolar diffusion, with application to protoplanetary disks. / Desch, Steven.
In: Astrophysical Journal, Vol. 608, No. 1 I, 10.06.2004, p. 509-525.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Linear analysis of the magnetorotational instability, including ambipolar diffusion, with application to protoplanetary disks
AU - Desch, Steven
PY - 2004/6/10
Y1 - 2004/6/10
N2 - We present a linear analysis of the magnetorotational instability (MRI) in differentially rotating disks and derive the most general instability criterion to date. Our analysis improves on earlier work on this topic in that it simultaneously accounts for arbitrary geometry and the full effects of magnetic diffusion. We allow the magnetic field to have arbitrary orientation and for linear modes to propagate at an angle to the rotation axis. We also include in our analysis all three forms of magnetic diffusion: ohmic dissipation, ambipolar diffusion, and Hall currents. Previous analyses have included either arbitrary geometry or ambipolar diffusion, but never both. The simultaneous inclusion of these effects allows us to identify a new unstable mode in which ambipolar diffusion and differential rotation can couple and amplify the magnetic field. We provide a physical explanation of this mode. Our linear analysis is aimed at determining which parts of protoplanetary disks may be unstable to the MRI. Accordingly, we outline the conditions that are likely to obtain in protoplanetary disks and make estimates of the coupling between the gas and the magnetic field. We derive a linear stability criterion that can be applied to protoplanetary disks.
AB - We present a linear analysis of the magnetorotational instability (MRI) in differentially rotating disks and derive the most general instability criterion to date. Our analysis improves on earlier work on this topic in that it simultaneously accounts for arbitrary geometry and the full effects of magnetic diffusion. We allow the magnetic field to have arbitrary orientation and for linear modes to propagate at an angle to the rotation axis. We also include in our analysis all three forms of magnetic diffusion: ohmic dissipation, ambipolar diffusion, and Hall currents. Previous analyses have included either arbitrary geometry or ambipolar diffusion, but never both. The simultaneous inclusion of these effects allows us to identify a new unstable mode in which ambipolar diffusion and differential rotation can couple and amplify the magnetic field. We provide a physical explanation of this mode. Our linear analysis is aimed at determining which parts of protoplanetary disks may be unstable to the MRI. Accordingly, we outline the conditions that are likely to obtain in protoplanetary disks and make estimates of the coupling between the gas and the magnetic field. We derive a linear stability criterion that can be applied to protoplanetary disks.
KW - Accretion, accretion disks
KW - MHD
KW - Planetary systems: protoplanetary disks
UR - http://www.scopus.com/inward/record.url?scp=3142755005&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3142755005&partnerID=8YFLogxK
U2 - 10.1086/392527
DO - 10.1086/392527
M3 - Article
AN - SCOPUS:3142755005
VL - 608
SP - 509
EP - 525
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 1 I
ER -