Angular Momentum Transport by Magnetohydrodynamic Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability

By Takayoshi Sano, S. Inutsuka, N. J. Turner, James M. Stone. 2003

242 citations recorded by the source corpus.

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard α disk model. From our numerical experiments we find that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength and is unaffected by ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly isothermal calculations, where pressure varies little with time. Over the entire region of parameter space explored, turbulence driven by the MRI has many characteristic ratios such as that of the Maxwell stress to the magnetic pressure. We also find that the amplitudes of the spatial fluctuations in density and the time variability in the stress are characterized by the ratio of magnetic pressure to gas pressure in the nonlinear regime. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of nonsteady magnetic reconnection.

Subfields: Astronomy and Astrophysics

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Citations in the corpus

MHD simulations of the magnetorotational instability in a shearing box with zero net flux II. The effect of transport coefficients (2007, background): “Unfortunately because of the limited computational resources available during the 90’s, these early calculations were restricted to low and moderate resolutions, having at most 64 grid cells per disk scale height (Hawley et al. 1995, 1996; Fleming et al. 2000; Sano et al. 2004).”
SUSTAINED MAGNETOROTATIONAL TURBULENCE IN LOCAL SIMULATIONS OF STRATIFIED DISKS WITH ZERO NET MAGNETIC FLUX (2009, background): “From the first three-dimensional studies (Hawley et al. 1995), it has been known that for unstratified simulations the saturation amplitude depends on parameters such as the net flux and geometry of the magnetic field threading the domain (Sano et al. 2004).”
Magnetically Driven Accretion in the Kerr Metric. III. Unbound Outflows (2004, background): “It may also be related to the generic conclusion of shearing-box studies that a net vertical field enhances the saturation magnetic field strength resulting from the MRI (e.g., Sano et al. 2004).”
MHD simulations of the magnetorotational instability in a shearing box with zero net flux - I. The issue of convergence (2007, background): “These differences may be due to, for example, a variation of the importance of compressibility as has been considered by Sano et al. (2004), or a variation of the effective Prandtl number.”
Accretion disc viscosity: how big is alpha? (2007, background): “Most interesting here is the paper by Sano et al. (2004) who find that the saturation level of the MRI turbulence depends on the gas pressure in the (shearing) box.”
Paleomagnetic Records of Meteorites and Early Planetesimal Differentiation (2010, background): “The inner ionized region of the protoplanetary disk is thought to have been unstable to the magnetorotational instability (Balbus 2003, 2009), which likely generated spatially complex fields of up to ∼100 µT (Sano et al. 2004; Johansen 2009).”
LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW (2012, background): “The dependence of α on net vertical magnetic flux has already been extensively discussed in unstratified shearing-box simulations (Hawley et al. 1995; Sano et al. 2004; Pessah et al. 2007; Longaretti & Lesur 2010).”
Theory of Star Formation (2007, background): “The effective value of α depends on the mean vertical magnetic flux, which presumably evolves over long timescales, and can easily exceed 0.1 (e.g., Hawley, Gammie, & Balbus 1996; Stone et al. 1996; Sano et al. 2004).”
ASSESSING QUANTITATIVE RESULTS IN ACCRETION SIMULATIONS: FROM LOCAL TO GLOBAL (2011, background): “…et al. 1995, 1996; Brandenburg et al. 1995; Stone et al. 1996; Fleming et al. 2000; Miller & Stone 2000; Sano & Inutsuka 2001; Sano & Stone 2002; Sano et al. 2004; Fromang & Papaloizou 2007; Simon et al. 2009) The first shearing box simulations employed comparatively few total zones (e.g.,…”
Simulations of magnetized discs around black holes: Effects of black hole spin, disc thickness and magnetic field geometry (2010, background): “3a), is a clear sign that the flow dynamics are quite 6 Sano et al. (2004) found that having about six grid cells per wavelength of the fastest growing MRI mode during saturation leads to convergent behaviour for the electromagnetic stresses, although their determination of six cells was based upon…”
General relativistic magnetohydrodynamic simulations of magnetically choked accretion flows around black holes (2012, methodology): “We consider both explicit convergence testing and socalled “convergence quality factors” that (e.g.) measure how many grid cells resolve various critical length scales (Sano et al. 2004; Hawley et al. 2011; Shiokawa et al. 2012; Sorathia et al. 2011).”