Numerical studies of (in)stabilities of shocks in perturbed advective flows around black holes

Abstract: Using two-dimensional hydrodynamic simulations, we investigate the stability of shocked accretion flows around black holes under non-axisymmetric perturbations. By systematically exploring the parameter space of specific energy and angular momentum that permits shock formation in advective accretion flows, we demonstrate that quasi-periodic oscillations (QPOs) naturally emerge in perturbed systems. Our spectral analysis reveals characteristic QPO frequencies spanning 0.44-146.57 Hz, effectively bridging the observed low-frequency (LFQPOs) and high-frequency QPOs (HFQPOs) in black hole X-ray binaries. The quality factors of these oscillations range from 1.66 to 203.58, with multiple Lorentzian components indicating distinct oscillation modes. Through wavelet analysis and cross-validation with recent observations (e.g., Swift J1727.8-1613 and GX 339-4), we establish that shock instabilities driven by acoustic wave interactions between the non-axisymmetric perturbation and the shock location can quantitatively explain the temporal features observed in accreting black hole systems. Furthermore, we characterize the adiabatic index dependence of shock morphology, showing that increasing the adiabatic index from 4/3 to 1.4 changes shock positions outward while maintaining oscillation coherence.