Oscillations of the black hole photon ring as a probe of ultralight dilaton fields

Advancements of very long baseline interferometry (VLBI) have facilitated unprecedented probing of superradiant phenomena in the vicinities of supermassive black holes (SMBHs), establishing an ideal laboratory to detect ultralight bosons beyond the Standard Model. In this study, we delve into how ultralight dilaton clouds, formed via SMBH superradiance, impact the black hole photon rings. Our focus is on the dilaton-electromagnetic coupling term of the form $f(\phi)F_{\mu\nu}F^{\mu\nu}$. By integrating geometric optics with plasma refractive effects in accretion environments, we demonstrate that the dilaton cloud dynamically alters the plasma frequency. Through systematic ray-tracing simulations covering a range of photon frequencies and dilaton coupling strengths, we reveal a photon ring oscillation that follows the period of that of the dilaton field. As the dilaton mass increases, this oscillation becomes suppressed due to the washout effect of the dilaton-induced correction term over the light path integration. We further evaluated the observability of such dilaton-induced photon ring oscillations with current radio interferometric capabilities. Our estimates indicate that this effect could potentially constrain the dilaton-photon coupling to $g_{\phi\gamma}\lesssim 10^{-11}\text{GeV}^{-1}$ for dilaton masses $\mu \lesssim 10^{-18}\,\mathrm{eV}$.