A relativistic orbit model for temporal properties of AGN
  We present a unified model for X-ray quasi-periodic oscillations (QPOs) seen
in Narrow-line Seyfert 1 (NLSy1) galaxies, $\gamma$-ray and optical band QPOs
that are seen in Blazars. The origin of these QPOs is attributed to the plasma
motion in corona or jets of these AGN. In the case of X-ray QPOs, we applied
the general relativistic precession model for the two simultaneous QPOs seen in
NLSy1 1H 0707-945 and deduce orbital parameters, such the radius of the
emission region, and spin parameter $a$ for a circular orbit; we obtained the
Carter's constant $Q$, $a$, and the radius in the case of a spherical orbit
solution. In other cases where only one X-ray QPO is seen, we localized the
orbital parameters for NLSy1 galaxies REJ 1034+396, 2XMM J123103.2+110648, MS
2254.9-3712, Mrk 766, and MCG-06-30-15. By applying the lighthouse model, we
found that a kinematic origin of the jet based $\gamma$-ray and optical QPOs,
in a relativistic MHD framework, is possible. Based on the inbuilt Hamiltonian
formulation with a power-law distribution in the orbital energy of the plasma
consisting of only circular or spherical trajectories, we show that the
resulting Fourier power spectral density (PSD) has a break corresponding to the
energy at ISCO. Further, we derive connection formulae between the slopes in
the PSD and that of the energy distribution. Overall, given the preliminary but
promising results of these relativistic orbit models to match the observed QPO
frequencies and PSD at diverse scales in the inner corona and the jet, it
motivates us to build detailed models, including a transfer function for the
energy spectrum in the corona and relativistic MHD jet models for plasma flow
and its polarization properties.
