Testing Ghasemi-Nodehi-Bambi metric parameters with quasi-periodic oscillations

QPOs are seen as peak features in the X-ray power spectral density of stellar mass black holes and neutron stars, of which frequencies can be measured with high precision. These QPO frequencies are believed to be related to fundamental frequencies of test particles, which are mainly determined by the background metric. We consider the metric introduced in Ghasemi-Nodehi and Bambi (Eur Phys J C 76:290, 2016). The fundamental frequencies in this metric are sensitive to some of the metric parameters but insensitive to other parameters, which means, the differences in fundamental frequencies in this metric and those in the Kerr ones can be significant for small changes of some but not all parameters around the Kerr value. By comparing with the QPO observations of GRO J1655-40, we find that only one parameter of the Ghasemi-Nodehi-Bambi metric can be strongly constrained, but other parameters cannot. We also use nested algorithm to investigate whether better constraints on the Ghasemi-Nodehi-Bambi metric parameters can be obtained from QPO observations of multiple objects by simulations. We find that four parameters can be strongly constrained while other parameters cannot . Our results suggest that QPOs may be important tools for testing the Kerr metric.