{
  "id": "2302.04015",
  "version": "v1",
  "published": "2023-02-08T12:06:43.000Z",
  "updated": "2023-02-08T12:06:43.000Z",
  "title": "The appearance of a merging binary black hole very close to a spinning supermassive black hole",
  "authors": [
    "Xiaoyue Zhang",
    "Xian Chen"
  ],
  "categories": [
    "astro-ph.HE",
    "gr-qc"
  ],
  "abstract": "The mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational-wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within $10$ gravitational radii of a Kerr SMBH to determine the redshift and magnification of the GWs emitted by the BBH. We find a positive correlation between redshift and demagnification, which results in a positive correlation between the mass and distance of the BBH in the detector frame. More importantly, we find a higher probability for the signal to appear redshifted and demagnified to a distant observer, rather than blueshifted and magnified. Based on these results, we show that a binary at a cosmological redshift of $z_{\\rm cos}=(10^{-2}-10^{-1})$ and composed of BHs of $(10-20)M_\\odot$ could masquerade as a BBH at a redshift of $z_{\\rm cos}\\sim1$ and containing BHs as large as $(44-110)M_\\odot$. In the case of extreme demagnification, we also find that the same BBH could appear to be at $z_{\\rm cos}>10$ and contain subsolar-mass BHs. Such an effect, if not accounted for, could bias our understanding of the origin of the BHs detected via GWs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-08T12:06:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "merging binary black hole",
      "spinning supermassive black hole",
      "appearance",
      "cosmological redshift",
      "bbh coalesces close"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}