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Published on November 14, 2007

Author: george

Source: authorstream.com

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

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