Accretion dynamics and shadow images of dyonic ModMax black hole

Abstract We investigate spherical accretion and shadow formation in the spacetime of a static, spherically symmetric dyonic ModMax black hole, focusing on the impact of the nonlinear electrodynamics parameter $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> and the dyonic charge Q . Using the Hamiltonian dynamical approach, we analyze the transonic behavior of perfect fluids with isothermal and polytropic equations of state, including ultra-stiff, ultra-relativistic, radiation, and sub-relativistic fluids. We identify the sonic points and demonstrate how their location shifts with $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> and Q , leading to qualitatively distinct phase-space structures for different fluid types. The shadow images are constructed within an infalling gas model, showing that increasing $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> enlarges the photon sphere and shadow radius while decreasing the observed edge intensity, whereas increasing Q reduces the shadow size and sharpens its intensity gradient. We further compute the mass accretion rate for ultra-stiff and ultra-relativistic fluids and find that it grows with larger values of $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> , indicating that nonlinear electrodynamics enhances the gravitational pull of the black hole. These results provide a unified description of how ModMax electrodynamics modifies both the accretion dynamics and the observable shadow properties of dyonic black holes.