Hybrid disc geometry for shocked accretion flows: Unveiling QPOs in black hole X-ray binaries
We investigate the efficacy of semi-analytical global accretion solutions in capturing the flow properties observed in two-dimensional numerical simulations of shocked accretion onto black holes. A comparative analysis reveals that no single disc geometry adequately matches the simulation profiles across the entire radial domain. The pre-shock region exhibits closer agreement with the conical disc geometry, while the post-shock region is better described by the vertical equilibrium disc, where enhanced thermal pressure leads to substantial vertical expansion. Motivated by these complementary behaviours, we introduce a hybrid disc geometry in which the pre-shock flow follows the conical solution and the post-shock flow attains vertical equilibrium. This hybrid model satisfactorily reproduces both dynamical and thermodynamical properties of shocked accretion flows with the predicted Mach number and temperature profiles closely matching the simulations and the inferred shock location differing by $\sim10\%$. Within this framework, we delineate the shock parameter space spanned by the energy ($\mathcal{E}$) and angular momentum ($\lambda$) of the flow for weakly and rapidly rotating black holes and investigate the possible origin of Quasi-periodic Oscillations (QPOs) in black hole X-ray binaries (BH-XRBs). We constrain flow parameters that reproduce observed QPO centroid frequencies ($\nu_{\rm QPO}$) demonstrating that oscillations of the shock front provide a self-consistent mechanism for both low and high frequency QPOs. Extending the analysis to ten Galactic BH-XRBs, we demonstrate that the observed $\nu_{\rm QPO}$ are reproduced within physically plausible parameter ranges, which establishes shocked global accretion solutions as a potentially compelling framework for interpreting accretion driven temporal variability.