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

Abstract

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 r 0 ∼ 60 r g , and predicts a period variation δ P/ P ∼ 0.23 due to the motion of the instability region.