{
  "id": "1010.6189",
  "version": "v1",
  "published": "2010-10-29T12:18:46.000Z",
  "updated": "2010-10-29T12:18:46.000Z",
  "title": "Trapped, Two-Armed, Nearly Vertical Oscillations in Disks with Toroidal Magnetic Fields",
  "authors": [
    "Shoji Kato"
  ],
  "comment": "18 pages, 6 figures, accepted PASJ 63, No.1 (2011)",
  "categories": [
    "astro-ph.HE"
  ],
  "abstract": "We have examined trapping of two-armed ($m=2$) nearly vertical oscillations (vertical p-mode) in vertically isothermal ($c_{\\rm s}=$ const.) relativistic disks with toroidal magnetic fields. The magnetic fields are stratified so that the Alfv{\\'e}n speed, $c_{\\rm A}$, is constant in the vertical direction. The ratio of $c_{\\rm A}^2/c_{\\rm s}^2$ in the vertical direction is taken as a parameter examining the effects of magnetic fields on wave trapping. We find that the two-armed nearly vertical oscillations are trapped in the inner region of disks and their frequencies decrease with increase of $c_{\\rm A}^2/c_{\\rm s}^2$. The trapped regions of the fundamental ($n=1$) and the first-overtone ($n=2$) are narrow (less than the length of the Schwarzschild radius, $r_{\\rm g}$) and their frequencies are relatively high (on the order of the angular frequency of disk rotation in the inner region). On contrast to this, the second-overtone ($n=3$) are trapped in a wide region (a few times $r_{\\rm g}$), and their frequencies are low and tend to zero in the limit of $c_{\\rm A}^2/c_{\\rm s}^2=2.0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-29T12:18:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toroidal magnetic fields",
      "vertical oscillations",
      "inner region",
      "vertical direction",
      "relativistic disks"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1093/pasj/63.1.125",
      "journal": "Publications of the Astronomical Society of Japan",
      "year": 2011,
      "month": "Feb",
      "volume": 63,
      "pages": 125
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 874998,
      "adsabs": "2011PASJ...63..125K"
    }
  }
}