Thin accretion discs around spherically symmetric configurations with nonlinear scalar fields

We study stable circular orbits (SCO) around static spherically symmetric configuration of General Relativity with a non-linear scalar field (SF). The configurations are described by solutions of the Einstein-SF equations with monomial SF potential $V(\phi)=|\phi|^{2n}$, $n>2$, under the conditions of the asymptotic flatness and behavior of SF $\phi\sim 1/r$ at spatial infinity. We proved that under these conditions the solution exists and is uniquely defined by the configuration mass $M>0$ and scalar "charge" $Q$. The solutions and the space-time geodesics have been investigated numerically in the range $n\le40$, $|Q|\le 60$, $M\le60$. We focus on how nonlinearity of the field affects properties of SCO distributions (SCOD), which in turn affect topological form of the thin accretion disk around the configuration. Maps are presented showing the location of possible SCOD types for different $M,Q,n$. We found many differences from the Fisher-Janis-Newman-Winicour metric (FJNW) dealing with the linear SF, though basic qualitative properties of the configurations have much in common with the FJNW case. For some values of $n$, a topologically new SCOD type was discovered that is not available for the FJNW metric. All images of accretion disks have a dark spot in the center (mimicking an ordinary black hole), either because there is no SCO near the center or because of the strong deflection of photon trajectories near the singularity.