{
  "id": "1502.05628",
  "version": "v1",
  "published": "2015-02-19T17:08:18.000Z",
  "updated": "2015-02-19T17:08:18.000Z",
  "title": "Overshooting by differential heating",
  "authors": [
    "R. Andrássy",
    "H. C. Spruit"
  ],
  "comment": "16 pages, 9 figures, accepted for publication in A&A",
  "categories": [
    "astro-ph.SR",
    "physics.flu-dyn"
  ],
  "abstract": "On the long nuclear time scale of stellar main-sequence evolution, even weak mixing processes can become relevant for redistributing chemical species in a star. We investigate a process of \"differential heating,\" which occurs when a temperature fluctuation propagates by radiative diffusion from the boundary of a convection zone into the adjacent radiative zone. The resulting perturbation of the hydrostatic equilibrium causes a flow that extends some distance from the convection zone. We study a simplified differential-heating problem with a static temperature fluctuation imposed on a solid boundary. The astrophysically relevant limit of a high Reynolds number and a low P\\'eclet number (high thermal diffusivity) turns out to be interestingly non-intuitive. We derive a set of scaling relations for the stationary differential heating flow. A numerical method adapted to a high dynamic range in flow amplitude needed to detect weak flows is presented. Our two-dimensional simulations show that the flow reaches a stationary state and confirm the analytic scaling relations. These imply that the flow speed drops abruptly to a negligible value at a finite height above the source of heating. We approximate the mixing rate due to the differential heating flow in a star by a height-dependent diffusion coefficient and show that this mixing extends about $4\\%$ of the pressure scale height above the convective core of a $10\\,M_\\odot$ zero-age main sequence star.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-19T17:08:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convection zone",
      "long nuclear time scale",
      "zero-age main sequence star",
      "stellar main-sequence evolution",
      "pressure scale height"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}