Fractal dimension and thermodynamic fluctuation properties of IDV light curves

TL;DR

This paper investigates the fractal and thermodynamic fluctuation properties of IDV light curves of BL Lac objects across optical, radio, and X-ray bands, revealing differences in predictability and spectral characteristics.

Contribution

It introduces a method to analyze fractal dimensions and thermodynamic fluctuations of IDV light curves, providing new insights into their spectral and predictability properties.

Findings

Optical and X-ray IDV light curves exhibit Brownian noise characteristics.

Radio band IDV light curves have higher predictability indices.

Fractal dimension correlates strongly with spectral index.

Abstract

Fractals are a basic tool to phenomenologically describe natural objects having a high degree of temporal or spatial variability. From a physical point of view the fractal properties of natural systems can also be interpreted by using the standard formalism of thermodynamical fluctuations. In the present paper we introduce and analyze the fractal dimension of the Intra - Day- Variability (IDV) light-curves of the BL Lac objects, in the optical, radio and X-ray bands, respectively. A general description of the fluctuation spectrum of these systems based on general thermodynamical principles is also proposed. Based on the general fractal properties of a given physical system, we also introduce the predictability index for the IDV light curves. We have explicitly determined the fractal dimension for the R-band observations of five blazars, as well as for the radio band observations of the compact extragalactic radio source J 1128+5925, and of several X-ray sources. Our results show that the fractal dimension of the optical and X-ray observations indicates an almost pure "Brownian noise" (random walk) spectrum, with a very low predictability index, while in the radio band the predictability index is much higher. We have also studied the spectral properties of the IDV light curves, and we have shown that their spectral index is very closely correlated with the corresponding fractal dimension.