{
  "id": "2405.14483",
  "version": "v1",
  "published": "2024-05-23T12:15:08.000Z",
  "updated": "2024-05-23T12:15:08.000Z",
  "title": "On resonance coupling in spiral arms: Patterns for flat rotation curve",
  "authors": [
    "Alexander A. Marchuk"
  ],
  "comment": "Accepted for publication in A&A Letters",
  "categories": [
    "astro-ph.GA"
  ],
  "abstract": "To address questions about the physical nature and origin of spiral arms in galaxies, it is necessary to measure their dynamical properties, such as the angular speed $\\Omega_p$ or the corotation radius. Observations suggest that galaxies may contain several independent spiral patterns simultaneously. It was shown that so-called non-linear resonance coupling plays an important role in such systems. We aim to identify cases of independent spiral patterns for galaxies with a flat rotation curve, and to investigate what relative pattern velocities $\\Omega^{out}_{p}/\\Omega^{in}_{p}$ they could have in principle for all possible cases of coupling between the main resonances. We solve equations for the main resonance positions (1:1, 2:1, 4:1) and estimate the ratio $\\varpi$ of the corotation radii for two subsequent patterns. For six close galaxies with flat rotation curves, we collect the measurements of the corotation radii in the literature, using at least three different methods in each case for credibility, and measure the $\\varpi$ ratio. We find $\\varpi$ ratios for all possible cases for the main resonances. For three cases we get $\\varpi>3$, meaning that it will be difficult to fit two or even more spiral patterns in the disc. These ratios have been used to derive the wind up time for spirals, estimated to be several galactic rotations. We find that three pairs of coupling cases, including vastly acknowledged in galaxies $OLR_{in}=CR_{out} \\& CR_{in}=IUHR_{out}$, have very close $\\varpi$ ratios, hence should be found simultaneously, as observed. We find strongly confirmed apparent resonance coupling for six galaxies, and show that the observed $\\varpi$ is in agreement with theory. In two of them we identify a previously unreported form of simultaneous coupling, namely $OLR_{in}=OUHR_{out} \\& OUHR_{in}=CR_{out}$, which was also predicted from the proximity of $\\varpi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-23T12:15:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flat rotation curve",
      "spiral arms",
      "corotation radius",
      "independent spiral patterns",
      "main resonance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}