{
  "id": "1411.4031",
  "version": "v1",
  "published": "2014-10-24T20:00:05.000Z",
  "updated": "2014-10-24T20:00:05.000Z",
  "title": "Angular Power Spectra with Finite Counts",
  "authors": [
    "Sheldon S. Campbell"
  ],
  "comment": "27 pages, 8 figures",
  "categories": [
    "astro-ph.CO",
    "astro-ph.HE",
    "astro-ph.IM",
    "hep-ph",
    "physics.data-an"
  ],
  "abstract": "Angular anisotropy techniques for cosmic diffuse radiation maps are powerful probes, even for quite small data sets. A popular observable is the angular power spectrum; we present a detailed study applicable to any unbinned source skymap S(n) from which N random, independent events are observed. Its exact variance, which is due to the finite statistics, depends only on S(n) and N; we also derive an unbiased estimator of the variance from the data. First-order effects agree with previous analytic estimates. Importantly, heretofore unidentified higher-order effects are found to contribute to the variance and may cause the uncertainty to be significantly larger than previous analytic estimates---potentially orders of magnitude larger. Neglect of these higher-order terms, when significant, may result in a spurious detection of the power spectrum. On the other hand, this would indicate the presence of higher-order spatial correlations, such as a large bispectrum, providing new clues about the sources. Numerical simulations are shown to support these conclusions. Applying the formalism to an ensemble of Gaussian-distributed skymaps, the noise-dominated part of the power spectrum uncertainty is significantly increased at high multipoles by the new, higher-order effects. This work is important for harmonic analyses of the distributions of diffuse high-energy gamma-rays, neutrinos, and charged cosmic rays, as well as for populations of sparse point sources such as active galactic nuclei.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-24T20:00:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "angular power spectrum",
      "finite counts",
      "quite small data sets",
      "cosmic diffuse radiation maps",
      "higher-order effects"
    ],
    "publication": {
      "doi": "10.1093/mnras/stv135",
      "journal": "Monthly Notices of the Royal Astronomical Society",
      "year": 2015,
      "month": "Apr",
      "volume": 448,
      "number": 3,
      "pages": 2854
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1328066,
      "adsabs": "2015MNRAS.448.2854C"
    }
  }
}