{
  "id": "2401.13738",
  "version": "v1",
  "published": "2024-01-24T19:00:02.000Z",
  "updated": "2024-01-24T19:00:02.000Z",
  "title": "Restoration of the Tully-Fisher Relation by Statistical Rectification",
  "authors": [
    "Hai Fu"
  ],
  "comment": "Resubmitted to ApJ Letters. Python notebook and data files are available at https://github.com/fuhaiastro/TFR_Lucy",
  "categories": [
    "astro-ph.GA",
    "astro-ph.IM"
  ],
  "abstract": "I employ the Lucy rectification algorithm to recover the inclination-corrected distribution of local disk galaxies in the plane of absolute magnitude ($M_i$) and \\HI\\ velocity width ($W_{20}$). By considering the inclination angle as a random variable with a known probability distribution, the novel approach eliminates one major source of uncertainty in studies of the Tully-Fisher relation: inclination angle estimation from axial ratio. Leveraging the statistical strength derived from the entire sample of 28,264 \\HI-selected disk galaxies at $z < 0.06$ from the Arecibo Legacy Fast ALFA (ALFALFA) survey, I show that the restored distribution follows a sharp correlation that is approximately a power law between $-16 > M_i > -22$: $M_i = M_0 - 2.5\\beta \\ [\\log(W_{\\rm 20}/250 {\\rm km/s})]$, with $M_0 = -19.77\\pm0.04$ and $\\beta = 4.39\\pm0.06$. At the brighter end ($M_i < -22$), the slope of the correlation decreases to $\\beta \\approx 3.3$, confirming previous results. Because the method accounts for measurement errors, the intrinsic dispersion of the correlation is directly measured: $\\sigma(\\log W_{20}) \\approx 0.06$\\,dex between $-17 > M_i > -23$, while $\\sigma(M_i)$ decreases from $\\sim$0.8 in slow rotators to $\\sim$0.4 in fast rotators. The statistical rectification method holds significant potential, especially in the studies of intermediate-to-high-redshift samples, where limited spatial resolution hinders precise measurements of inclination angles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-24T19:00:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tully-fisher relation",
      "statistical rectification",
      "inclination angle",
      "rectification method holds significant potential",
      "spatial resolution hinders precise measurements"
    ],
    "tags": [
      "github project"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}