Constraining ModMax Black Holes with EHT and GRAVITY Observations: Optical Signatures and Accretion Disk Properties

In this work, we study photon propagation and the radiative properties of a thin accretion disk around a ModMax black hole and examine the effects of the charge $Q$ (i.e. $Q^2 = Q^2_e +Q^2_m$ is the total dyonic charge, with $Q_e$ and $Q_m$ denoting the electric and magnetic charges, respectively) and the nonlinearity parameter $v$. We determine the event-horizon, photon-sphere, and shadow radii and find that increasing $Q$ decreases these radii, whereas increasing $v$ shifts them toward their Schwarzschild values. Using the EHT shadow measurements of M87$^\star$ and Sgr~A$^\star$, together with the available mass and distance measurements, we perform an MCMC analysis to constrain the ModMax parameters. The strongest upper limits are found to be $Q<0.391$ and $v<4.153$ at the 95\% credible level. We also investigate a Novikov-Thorne thin accretion disk and generate simulated disk images using backward ray tracing. The observed flux increases with $Q$, while increasing $v$ produces a slight decrease in the disk brightness. These results show how the ModMax parameters affect the black-hole shadow and thin-disk emission and provide observational constraints on $Q$ and $v$.