The presence of a surface at the inner boundary, such as in a neutron star or a white dwarf, allows the existence of a standing shock
in steady spherical accretion.
The standing shock can become unstable in 2D or 3D; this is called the {\em standing accretion shock instability} (SASI).
Two mechanisms -- advective-acoustic and purely acoustic -- have been proposed to explain SASI. Using axisymmetric hydrodynamic (HD) and magnetohydrodynamic (MHD)
simulations, we find that the advective-acoustic mechanism better matches the observed oscillation timescales in our simulations. The global shock oscillations present
in the accretion flow can explain many observed high frequency ($\gtrsim 100$ Hz) quasi-periodic oscillations (QPOs) in X-ray binaries (XRBs). The presence of a moderately
strong magnetic field adds more features to the shock oscillation
pattern, giving rise to low frequency modulation in the computed light curve. This low frequency modulation
can be responsible for $\sim 100$ Hz QPOs (known as hHz QPOs). We propose that the appearance of hHz QPO determines the separation of twin peak QPOs of higher frequencies.
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