{
  "id": "1505.00263",
  "version": "v1",
  "published": "2015-05-01T20:00:25.000Z",
  "updated": "2015-05-01T20:00:25.000Z",
  "title": "How an improved implementation of H$_2$ self-shielding influences the formation of massive stars and black holes",
  "authors": [
    "Tilman Hartwig",
    "Simon C. O. Glover",
    "Ralf S. Klessen",
    "Muhammad A. Latif",
    "Marta Volonteri"
  ],
  "comment": "13 pages, 11 figures, submitted to MNRAS",
  "categories": [
    "astro-ph.GA",
    "astro-ph.CO"
  ],
  "abstract": "The highest redshift quasars at z>6 have mass estimates of about a billion M$_\\odot$. One of the pathways to their formation includes direct collapse of gas, forming a supermassive star ($\\sim 10^5\\,\\mathrm{M}_\\odot$) precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H$_2$) formation is inhibited by a strong external UV flux. Above a certain value of UV flux ($J_{\\rm crit}$), the gas in a halo collapses isothermally at $\\sim10^4$K and provides the conditions for supermassive star formation. However, H$_2$ can self-shield and the effect of photodissociation is reduced. So far, most numerical studies used the local Jeans length to calculate the column densities for self-shielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of $J_{\\rm crit}$. This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H$_2$ against the photodissociating radiation. We estimate $J_{\\rm crit}$ for 4 different haloes and find that our method yields a value of $J_{\\rm crit}$ that is a factor of two smaller than with the Jeans approach ($\\sim\\,2000\\,J_{21}$ vs. $\\sim\\,4000\\,J_{21}$ with $J_{21}=10^{-21}\\,\\mathrm{erg}\\,\\mathrm{s}^{-1}\\,\\mathrm{cm}^{-2}\\,\\mathrm{Hz}^{-1}\\,\\mathrm{sr}^{-1}$). The main reason for this difference is the strong directional dependence of the H$_2$ column density, which cannot be captured with one-dimensional approximations. With this lower value of $J_{\\rm crit}$, the number of haloes exposed to a flux $>J_{\\rm crit}$ is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-01T20:00:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "massive stars",
      "self-shielding influences",
      "column density",
      "direct collapse",
      "implementation"
    ],
    "publication": {
      "doi": "10.1093/mnras/stv1368"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1365982
    }
  }
}