Optically thin two-temperature accretion flows may be thermally and viscously stable , but acoustically unstable .
Here we propose that the O-mode instability of a cooling-dominated optically thin two-temperature inner disk may explain the 23-day quasi-periodic oscillation ( QPO ) period observed in the TeV and X-ray light curves of Mkn 501 during its 1997 high state .
In our model the relativistic jet electrons Compton upscatter the disk soft X-ray photons to TeV energies , so that the instability-driven X-ray periodicity will lead to a corresponding quasi-periodicity in the TeV light curve and produce correlated variability .
We analyse the dependence of the instability-driven quasi-periodicity on the mass ( M ) of the central black hole , the accretion rate ( { \dot { M } } ) and the viscous parameter ( \alpha ) of the inner disk .
We show that in the case of Mkn 501 the first two parameters are constrained by various observational results , so that for the instability occurring within a two-temperature disk where \alpha = 0.05 - 1.0 , the quasi-period is expected to lie within the range of 8 to 100 days , as indeed the case .
In particular , for the observed 23-day QPO period our model implies a viscosity coefficient \alpha \leq 0.28 , a sub-Eddington accretion rate \dot { M } \simeq 0.02 \dot { M } _ { Edd } and a transition radius to the outer standard disk of r _ { 0 } \sim 60 r _ { g } , and predicts a period variation \delta P / P \sim 0.23 due to the motion of the instability region .