Fractal features in accretion discs

TL;DR

This paper explores how fractal geometry influences accretion disc dynamics, revealing modifications in flow behavior, stability, and transonicity, with implications for understanding astrophysical accretion processes.

Contribution

It introduces fractal concepts into accretion disc models, showing their effects on flow topology, transonicity, and stability, and provides analytical solutions for fractal flow equilibrium points.

Findings

Fractal flow admits only saddle and center points.

Fractal properties enable transonic flow behavior.

Fractal accretion rate exhibits scaling behavior.

Abstract

Fractal concepts have been introduced in the accretion disc as a new feature. Due to the fractal nature of the flow, its continuity condition undergoes modifications. The conserved stationary fractal flow admits only saddle points and centre-type points in its phase portrait. Completely analytical solutions of the equilibrium point conditions indicate that the fractal properties enable the flow to behave like an effective continuum of lesser density, and facilitates the generation of transonicity. However, strongly fractal flows inhibit multitransonicity from developing. The mass accretion rate exhibits a fractal scaling behaviour, and the entire fractal accretion disc is stable under linearised dynamic perturbations.