Harmonic QPOs and Thick Accretion Disk Oscillations in BL Lac Object AO   0235+164
  Periodic outbursts are observed in many AGNs and usually explained with a supermassive black hole binary (SMBHB) scenario. However, multiple periods are observed in some AGNs and cannot be explained with it. Here we analyze the periodicity of the radio light curves of AO 0235+164 at multi-frequencies and report the discovery of six QPOs in integer ratio 1:2:3:4:5:6 of QPO frequencies, of which the second with period $P_2 = (5.46 \pm 0.47) {\rm yr}$ is the strongest. We fit the radio light curves and show that the initial phases of six QPOs have zero or $\pi$ differences relative to each other. We suggest a harmonic relationship of QPOs. The centroid frequency, relative strength, harmonic relationship and relative initial phases of QPOs are independent of radio frequency. The harmonic QPOs are likely due to the quasi-periodic injection of plasma from an oscillating accretion disk into the jet. We estimate the supermassive black hole mass $M_{\rm BH} \simeq (4.72\pm 2.04) \times 10^8 M_\odot$ and the accretion rate $\dot{m}\simeq 0.007$. With the knowledge of accretion disk, it implies that the inner region of accretion disk of AO 0235+164 is a radiatively inefficient accretion flow. The oscillation accretion is due to the p-mode oscillation of the thick disk probably excited by a SMBHB. The theoretical predications of fundamental oscillation frequency and the harmonics are well consistent with the observations. Harmonic QPOs would be absent when the thick disk becomes geometrically thin due to the increase of accretion rate. We discuss the observations of AO 0235+164 basing on the SMBHB-thick disk oscillation scenario. 
F.K. Liu, G. Zhao, Xue-Bing Wu (Peking University)