Photon surfaces, shadows and accretion disks in gravity with minimally coupled scalar field

In this article, we conduct a sequential study of possible observable images of black hole simulators described by two recently obtained rotating geometries in Einstein gravity, minimally coupled to a scalar field. One of them, "Kerr-like" (KL), can be seen as a legitimate alternative to the rotating Fisher-Janis-Newman-Winicour (FJNW) solution, and the other (TSL) is a scalar generalization of the Tomimatsu-Sato solution. Unlike the previous version of the rotating FJNW, these solutions do indeed satisfy the system's equations of motion. Our study includes both analytical and numerical calculations of equatorial circular orbits, photon regions, gravitational shadows, and radiation from thin accretion disks for various values of the object's angular momentum and scalar charge. The TSL solution was found to simulate Kerr for all valid parameter values with high accuracy. The maximum difference between the deviations of shadows from a circle for the Kerr and TSL cases does not exceed 1% and fits into the experimental observational data M87*. However, near-extreme objects show two times smaller peak values of the observed outflow luminosity of the accretion disk than for the Kerr black hole. The KL solution cannot be ruled out by the experimental data for small values of the scalar charge either. As the scalar charge increases, the optical properties change dramatically. The shadow can become multiply connected, strongly oblate, and the photon region does not hide the singularity, so it should be classified as a strong singularity.