Rossby wave instability and high-frequency quasi-periodic oscillations in accretion discs orbiting around black holes

Context. The rather elusive high-frequency quasi-periodic oscillations (HFQPOs) observed in the X-ray light curve of black holes have been seen in a wide range of frequencies, even within one source. Also notable is the detection of "pairs" of HFQPOs with a close-to-integer ratio between the frequencies. Aims. The aim of this paper is to investigate some of the possible observables that we could obtain from the Rossby wave instability (RWI) active in the accretion disc surrounding the compact object. Methods. Using the newly developed GR-AMRVAC code able to follow the evolution of the RWI in a full general relativistic framework, we explore how RWI can reproduce observed HFQPO frequency ratios and whether or not it is compatible with observations. In order to model the emission coming from the disc we have linked our general relativistic simulations to the general relativistic ray-tracing GYOTO code and delivered synthetic observables that can be confronted with actual data from binary systems hosting HFQPOs. Results. We demonstrate that some changes in the physical conditions prevailing in the part of the disc where RWI can be triggered lead to various dominant RWI modes whose ratio recovers frequency ratios observed in various X-ray binary systems. In addition we also show that when RWI is triggered near to the last stable orbit of a spinning black hole, the amplitude of the X-ray modulation increases with the spin of the black hole. Revisiting published data on X-ray binary systems, we show that this type of relationship actually exists in five systems where an indirect measurement of the spin of the black hole is available.