Balbus-Hawley Magnetorotational Instability (MRI) : Balbus-Hawley Magnetorotational Instability (MRI) Xiaoan Wu
October 20, 2004
Outline : Outline Mystery of viscosity and possible solutions
How MRI works
Comparison with previous work
Up-to-date developments
Summary
1. Mystery of Viscosity : 1. Mystery of Viscosity
Possible Solutions : Possible Solutions Angular momentum transport
Molecular viscosity (Pringle 1981 says NO!)
Convective turbulence (Lin & Papaloizou 1980, Ryu & Goodman 1992, Stone & Balbus 1996)
Electron viscosity (Paczynski & Jaroszynski 1978)
Tidal effects (Vishniac & Diamond 1989)
Magnetorotational Instability (Balbus & Hawley 1991)
2. Balbus-Hawley’s Solution : 2. Balbus-Hawley’s Solution The tension acts to reduce the angular momentum of m1 and increase that of m2. This further increases the tension and the process “runs away”.
Two fluid elements, in the same orbit, are joined by a field line (Bo). The tension in the line is negligible.
If they are perturbed, the line is stretched and develops tension.
Analogy to a Spring : Koichi Noguchi 2002 Analogy to a Spring
Basic equations : Basic equations
Derivation : Derivation
Dispersion Relation : Dispersion Relation
Q&A : Q&A Critical k?
Why B has to be weak?
Why B can not be too weak?
What if B is not poloidal?
Slide11 : A list of ideal MRI Requirements
Angular velocity decreasing with radius
Subthermal B with a poloidal component
Satisfied in astrophysical discs Fastest growing modes
growth rate
independent of |B|
wavelength proportional to |B|
horizontal displacements This slide is copied from Salmeron’s presentation in Flash Seminars 2003
3. Comparison with previous work : 3. Comparison with previous work Chandrasekhar 1960 first found global instability
Fricki 1969 studied the local instability and derived dispersion relation
Balbus and Hawley’s contributions are :
(1)To show that the instability manifests itself locally under very general conditions
(2) To give a relatively simple derivation
(3) To provide a detailed explanation of the underlying physical cause
(4) To present the limitations of the theory
(5) To point out MRI is the cause of large viscosity in accretion disks.
4. Up-to-date developments : 4. Up-to-date developments Theoretical progresses
Simulations to verify the theory
Experiments
Applications to various astrophysical scenarios
Theoretical progresses : Theoretical progresses Cool environments: not fully ionized, low conductivity, such as protostellar disks
Magnetic diffusion
Ambipolar diffusion
Ohmic dissipation
Hall effect
Desch 2004, ApJ, 608, 509
Simulations : Simulations 66 papers about simulations:
Stone, Hawley, Balbus & Gammie, 1996, ApJ 463, 656
Slide16 : Without MRI With MRI From http://www.astro.virginia.edu/VITA/accdisk.html
Slide17 : From http://www.astro.virginia.edu/VITA/papers/plunge/index.html
Experiments : Experiments Proposal: MRI can be observed in a lab with a rotating apparatus, using metals such as gallium (Ji, Goodman & Kageyama, 2001, MNRAS, L1)
Experiment:
MRI observed in lab:
Sisan et al. 2004, PhRvL, 93
Applications : Applications Accretion disk in Cataclysmic Variables Figure 1. The evolution into quiescence of a disk annulus located at 2 × 1010 cm from a central white dwarf is shown. The solid line represents the disk thermal equilibrium. The middle section, which corresponds to partially ionized gas, is unstable and forces the annulus to a cyclic behavior. The triangles represent the evolution of the annulus. At low state with such a low level of ionization, MHD turbulence dies away. Kristen 2000, Science, 288, 2022
Accretion disks : Accretion disks binary stars
quasars
active galactic nuclei
proto-stellar disks
proto-planetary disks
Other applications : Other applications Magnetized NS Atmosphere
(Kristen 2004MNRAS.352.1381M)
Interstellar turbulence
(Dziourkevitch eta l.., 2004A&A...423L..29D)
MRI on formation GMC
(Kim, Ostriker and Stone, 2003ApJ...599.1157K)
Proto-planetary system
(Matsumura and Pudritz 2003ApJ...598..645M )
Core-collapse Supernova
(Akiyama et al., 2003ApJ...584..954A)
Jet
(Hanasz, Sol and Sauty, C. 2000MNRAS.316..494H )
MRI is critical to human beings
5. Summary : 5. Summary Balbus and Hawley pointed out the significance of MRI which had been discovered by Chandrasekhar and Fricke.
This paper is a masterpiece of art in science.
The instability has a wide variety of applications and favorite for simulation researchers, so that the possibilities for extending its citation rate are almost endless.
Selected References : Selected References Balbus and Hawley 1991, ApJ 376, 214
Desch 2004, ApJ, 608, 509
Ji, Goodman & Kageyama, 2001, MNRAS, L1
Stone, Hawley, Balbus & Gammie 1996, ApJ 463, 656
Kristen 2000, Science, 288, 2022