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 0.44-146.57Hz, effectively bridging the observed low-frequency (LFQPOs) and high-frequency QPOs (HFQPOs) in black hole X-ray binaries. The quality factors ($Q={\mu }_0/2\Delta$) 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 γ-dependence of shock morphology, showing that increasing the adiabatic index from 4/3 to 1.4 changes shock positions outward while maintaining oscillation coherence.