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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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
Issue number7
Publication statusPublished - 2011 Jul


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

ASJC Scopus subject areas

  • General Physics and Astronomy


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