Fractal structure of isothermal lines and loops on the cosmic microwave background

Naoki Kobayashi, Yoshihiro Yamazaki, Hiroto Kuninaka, Makoto Katori, Mitsugu Matsushita, Satoki Matsushita, Lung Yih Chiang

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    The statistics of isothermal lines and loops of the cosmic microwave background (CMB) radiation on the sky map is studied and the fractal structure is confirmed in the radiation temperature fluctuation. We estimate the fractal exponents, such as the fractal dimension De of the entire pattern of isothermal lines, the fractal dimension Dc of a single isothermal line, the exponent ε in Korčak's law for the size distribution of isothermal loops, the two kind of Hurst exponents, He for the profile of the CMB radiation temperature, and Hc for a single isothermal line. We also perform fractal analysis of two artificial sky maps simulated by a standard model in physical cosmology, the WMAP best-fit A cold dark matter (ACDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the ACDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by He = 0.23 < 1=2.

    Original languageEnglish
    Article number074003
    JournalJournal of the Physical Society of Japan
    Volume80
    Issue number7
    DOIs
    Publication statusPublished - 2011 Jul

    Fingerprint

    fractals
    cosmic microwave background radiation
    microwaves
    exponents
    sky
    dark matter
    cosmology
    temperature
    statistics
    radiation
    estimates
    profiles
    simulation

    Keywords

    • Cosmic microwave background radiation
    • Fractal analysis
    • Hurst exponent
    • Isothermal lines and loops
    • Self-affinity

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Kobayashi, N., Yamazaki, Y., Kuninaka, H., Katori, M., Matsushita, M., Matsushita, S., & Chiang, L. Y. (2011). Fractal structure of isothermal lines and loops on the cosmic microwave background. Journal of the Physical Society of Japan, 80(7), [074003]. https://doi.org/10.1143/JPSJ.80.074003

    Fractal structure of isothermal lines and loops on the cosmic microwave background. / Kobayashi, Naoki; Yamazaki, Yoshihiro; Kuninaka, Hiroto; Katori, Makoto; Matsushita, Mitsugu; Matsushita, Satoki; Chiang, Lung Yih.

    In: Journal of the Physical Society of Japan, Vol. 80, No. 7, 074003, 07.2011.

    Research output: Contribution to journalArticle

    Kobayashi, N, Yamazaki, Y, Kuninaka, H, Katori, M, Matsushita, M, Matsushita, S & Chiang, LY 2011, 'Fractal structure of isothermal lines and loops on the cosmic microwave background', Journal of the Physical Society of Japan, vol. 80, no. 7, 074003. https://doi.org/10.1143/JPSJ.80.074003
    Kobayashi, Naoki ; Yamazaki, Yoshihiro ; Kuninaka, Hiroto ; Katori, Makoto ; Matsushita, Mitsugu ; Matsushita, Satoki ; Chiang, Lung Yih. / Fractal structure of isothermal lines and loops on the cosmic microwave background. In: Journal of the Physical Society of Japan. 2011 ; Vol. 80, No. 7.
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