Images of Regular Black Holes with Hedgehog Scalar Hair Embedded in Radiatively Inefficient Accretion Flows

How a black hole's geometric critical scale manifests in an accretion-flow image is governed by photon propagation, plasma radiative processes, and instrumental resolution. In this work, we investigate radiatively inefficient accretion flows (RIAF) surrounding geometrically regular black holes with hedgehog scalar hair. Adopting the mass and distance of $\mathrm{M87}^*$, we generate total-intensity synchrotron images and systematically explore the viewing inclination, disk thickness, and observing frequency. For the fiducial setup at $230\,\mathrm{GHz}$, raising $L/M$ from $0$ to $0.9$ contracts the critical curve diameter by $4.78\%$, shrinks the half-flux radius by $4.07\%$, and lowers the required electron-density scale by $9.15\%$. At $84\,\mathrm{GHz}$, the primary brightness peaks shift farther outside the critical curve due to enhanced synchrotron self-absorption, whereas the sharper emission rings at $230$ and $345\,\mathrm{GHz}$ closely trace the critical curve. Ultimately, we find that although the regular core systematically contracts the emission ring and alters the required plasma density, resolving these deviations from a Schwarzschild black hole demands angular resolution finer than that achievable with current baselines.