{"paper":{"title":"Resonant Excitation of Disk Oscillations in Deformed Disks VII: Stability Criterion in MHD Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.HE","authors_text":"Shoji Kato","submitted_at":"2013-10-13T07:30:56Z","abstract_excerpt":"In a disk with an oscillatory deformation from an axisymmetric state with frequency $\\omega_{\\rm D}$ and azimuthal wavenumber $m_{\\rm D}$, a set of two normal mode oscillations with frequency and azimuthal wavenumber being ($\\omega_1$, $m_1$) and ($\\omega_2$, $m_2$) resonantly couple through the disk deformation, when the resonant conditions ($\\omega_1+\\omega_2+\\omega_{\\rm D}=0$ and $m_1+m_2+m_{\\rm D}=0$) are satisfied. In the case of hydrodynamical disks, the resonance amplifies the set of the oscillations if $(E_1/\\omega_1)(E_2/\\omega_2)>0$ (Kato 2013b), where $E_1$ and $E_2$ are wave energi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3453","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}