A possible disk mechanism for the 23-day QPO in Mkn 501

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 ( M ˙ ) and the viscous parameter (α) 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 α = 0.05–1.0, the quasi-period is expected to lie within the range of 8–100 days, as indeed the case. In particular, for the observed 23-day QPO period our model implies a viscosity coefficient α ⩽ 0.28, a sub-Eddington accretion rate M ˙ ≃ 0.02 M ˙ Edd and a transition radius to the outer standard disk of r0 ∼ 60rg, and predicts a period variation δP/P ∼ 0.23 due to the motion of the instability region.