Abstract:The theory of instability of accretion disks about black holes, neutron stars, or protoplanets is revisited by means of the recent method of the Spectral Web. The cylindrical accretion disk differential equation is shown to be governed by the forward and backward Doppler-shifted continuous Alfvén spectra
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“…These are the points where the magnitude of the Dopplershifted frequency of the mode is equal to its Alfvén frequency and are always centered about the point of corotation, where ω r = Ω(r). In particular, localized MRI and curvature modes in systems with weak magnetic fields (i.e., super-Alfvénic flows) feature structures localized in the inner and outer parts of the system as also obtained by Ogilvie & Pringle (1996) and Goedbloed & Keppens (2022), due to the differing locations of the Alfvén singularities. Inner (MRI) modes are located between the conducting boundary at r 1 and the singularity r out ; outer (curvature) modes are between the singularity r in and the conducting boundary at r 2 (Figures 5(a) and (b)).…”
Section: Global Solutions With a Vertical Magnetic Fieldsupporting
confidence: 53%
“…This can be seen in Figure 6 with m = 10 and k = 80k 1 . The complex eigenvalues are similar to their approximate counterparts in Goedbloed & Keppens (2022). Regardless of the use of a global treatment, these extremely localized instabilities only occupy a narrow region of parameter space, as they are only unstable for very weak magnetic fields (i.e., super-Alfvénic flows).…”
Section: Global Solutions With a Vertical Magnetic Fieldmentioning
confidence: 56%
“…This can be seen in Figure 4(b), where the MRI mode's frequency in the low-B limit converges to Ω 0 , the system's angular velocity at the inner wall, and the ( ) (0.0894Ω 0 in our system), the angular velocity at the outer wall. We also search in the limit of super-Alfvénic flows where ω A = mΩ as studied by Ogilvie & Pringle (1996) and Goedbloed & Keppens (2022). In this region, the high-m, high-k nonaxisymmetric Alfvénic resonance instability is extremely localized due to being confined between two very close-by Alfvénic resonances.…”
Section: Global Solutions With a Vertical Magnetic Fieldmentioning
confidence: 99%
“…Localized nonaxisymmetric MRI mode structures were found to be confined between the Alfvénic resonant points (where the magnitude of the Doppler-shifted wave frequency is equal to the Alfvén frequency; Matsumoto & Tajima 1995). In cylindrical shear flows (Ogilvie & Pringle 1996) and in the compressible limit (Goedbloed & Keppens 2022), it was shown that the forward and backward overlapping of these Alfvén continua results in discrete localized nonaxisymmetric modes at large axial and azimuthal mode numbers. The question arises whether, in a real domain with spatial curvature, global nonaxisymmetric modes with real frequencies can persist.…”
A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.
“…These are the points where the magnitude of the Dopplershifted frequency of the mode is equal to its Alfvén frequency and are always centered about the point of corotation, where ω r = Ω(r). In particular, localized MRI and curvature modes in systems with weak magnetic fields (i.e., super-Alfvénic flows) feature structures localized in the inner and outer parts of the system as also obtained by Ogilvie & Pringle (1996) and Goedbloed & Keppens (2022), due to the differing locations of the Alfvén singularities. Inner (MRI) modes are located between the conducting boundary at r 1 and the singularity r out ; outer (curvature) modes are between the singularity r in and the conducting boundary at r 2 (Figures 5(a) and (b)).…”
Section: Global Solutions With a Vertical Magnetic Fieldsupporting
confidence: 53%
“…This can be seen in Figure 6 with m = 10 and k = 80k 1 . The complex eigenvalues are similar to their approximate counterparts in Goedbloed & Keppens (2022). Regardless of the use of a global treatment, these extremely localized instabilities only occupy a narrow region of parameter space, as they are only unstable for very weak magnetic fields (i.e., super-Alfvénic flows).…”
Section: Global Solutions With a Vertical Magnetic Fieldmentioning
confidence: 56%
“…This can be seen in Figure 4(b), where the MRI mode's frequency in the low-B limit converges to Ω 0 , the system's angular velocity at the inner wall, and the ( ) (0.0894Ω 0 in our system), the angular velocity at the outer wall. We also search in the limit of super-Alfvénic flows where ω A = mΩ as studied by Ogilvie & Pringle (1996) and Goedbloed & Keppens (2022). In this region, the high-m, high-k nonaxisymmetric Alfvénic resonance instability is extremely localized due to being confined between two very close-by Alfvénic resonances.…”
Section: Global Solutions With a Vertical Magnetic Fieldmentioning
confidence: 99%
“…Localized nonaxisymmetric MRI mode structures were found to be confined between the Alfvénic resonant points (where the magnitude of the Doppler-shifted wave frequency is equal to the Alfvén frequency; Matsumoto & Tajima 1995). In cylindrical shear flows (Ogilvie & Pringle 1996) and in the compressible limit (Goedbloed & Keppens 2022), it was shown that the forward and backward overlapping of these Alfvén continua results in discrete localized nonaxisymmetric modes at large axial and azimuthal mode numbers. The question arises whether, in a real domain with spatial curvature, global nonaxisymmetric modes with real frequencies can persist.…”
A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.
“…Shear in the accretion flow converts poloidal field into the toroidal field, while MRI amplifies the poloidal field. Therefore, both poloidal and toroidal fields grow exponentially in a dynamical time (t dyn ≈ 1/Ω ∝ R 3/2 ) and after few dynamical time the system likely enters the non-linear regime under the influence of parasitic instabilities (Goodman & Xu 1994) or due to different super-Alfvénic rotational instabilities (SARIs; Goedbloed & Keppens 2022).…”
Section: Evolution Of the Initial Riaf Runmentioning
Large-scale magnetic fields play a vital role in determining the angular momentum transport and in generating jets/outflows in the accreting systems, yet their origin remains poorly understood. We focus on radiatively inefficient accretion flows (RIAF) around the black holes, and conduct three-dimensional general-relativistic magnetohydrodynamic (GRMHD) simulations using the Athena++ code. We first re-confirm that the dynamo action alone cannot provide sufficient magnetic flux required to produce a strong jet. We next investigate the other possibility, where the large-scale magnetic fields are advected inward from external sources (e.g. the companion star in X-ray binaries, magnetized ambient medium in AGNs). Although the actual configuration of the external fields could be complex and uncertain, they are likely to be closed. As a first study, we treat them as closed field loops of different sizes, shapes and field strengths. Unlike earlier studies of flux transport, where magnetic flux is injected in the initial laminar flow, we injected the magnetic field loops in the quasi-stationary turbulent RIAF in inflow equilibrium and followed their evolution. We found that a substantial fraction (∼ 15% − 40%) of the flux injected at the large radii reaches the black hole with a weak dependence on the loop parameters except when the loops are injected at high latitudes, away from the mid-plane. Relatively high efficiency of flux transport observed in our study hints that a magnetically dominated RIAF, potentially a magnetically-arrested disk, might be formed relatively easily close to the black hole, provided that a source of the large-scale field exists at the larger radii.
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