Temporal 1/f^\alpha Fluctuations from Fractal Magnetic Fields in Black Hole Accretion Flow

Rapid fluctuation with a frequency dependence of $1\mathrm{/}{f}^{\alpha }$ (with $\alpha \simeq 1 - 2$) is characteristic of radiation from black-hole objects. Its origin remains poorly understood. We examine the three-dimensional magnetohydrodynamical (MHD) simulation data, finding that a magnetized accretion disk exhibits both $1\mathrm{/}{f}^{\alpha }$ fluctuation (with $\alpha \simeq 2$) and a fractal magnetic structure (with the fractal dimension of $D\sim 1.9$). The fractal field configuration leads reconnection events with a variety of released energy and of duration, thereby producing $1\mathrm{/}{f}^{\alpha }$ fluctuations.