Multifractal processes and self-organized criticality in the large-scale structure of the universe

In the past five to ten years mounting evidence has arisen indicating that the large-scale spatial number density of galaxies may be governed by fractal or multifractal statistics. In this paper we extend this idea by searching for multifractal behaviour in other density fields. Namely, generalized luminosity density fields (which we define here) constructed from information on both the angular position and the apparent luminosity of galaxies. Using data from the Center for Astrophysics' CfA2 catalogue, we perform various multifractal analyses that reveal that over broad angular scales, the fields studied present two important signatures of multifractal behavior: multiscaling and algebraic probability distributions associated with extreme fluctuations and first-order multifractal phase transitions. Since the presence of both of these phenomena is the defining feature of Self-Organized Criticality, we argue that the spatio-luminous distribution of galaxies in the observable universe may be described as a nonclassical self-organized critical phenomenon resulting from multifractal cascades.