Variability in active galactic nuclei is observed in ultraviolet to X-ray emission based light curves. This could be attributed to orbital signatures of the plasma that constitutes the accretion flow on the putative disk or in the developing jet clos
e to the inner region of the central black hole. We discuss some theoretical models which build on this view. These models include general relativistic effects such as light bending, aberration effects, gravitational and Doppler redshifts. The novel aspects relate to the treatment of helical flow in cylindrical and conical geometries in the vicinity of a Schwarzschild black hole that leads to amplitude and frequency modulations of simulated light curves as well as the inclusion of beaming effects in these idealized geometries. We then present a suite of time series analysis techniques applicable to data with varied properties which can extract detailed information from them for their use in theoretical models.
Here we present a systematic study of force-free field equation for simple axisymmetric configurations in spherical geometry. The condition of separability of solutions in radial and angular variables leads to two classes of solutions: linear and non
-linear force-free fields. We have studied these linear solutions Chandrasekhar (1956) and extended the non-linear solutions given in Low & Lou (1990) to the irreducible rational form $n= p/q$, which is allowed for all cases of odd $p$ and to cases of $q>p$ for even $p$. We have further calculated their energies and relative helicities for magnetic field configurations in finite and infinite shell geometries. We demonstrate here a method here to be used to fit observed magnetograms as well as to provide good exact input fields for testing other numerical codes used in reconstruction on the non-linear force-free fields.
We point out that the remarkable linearity of the ultra-steep radio spectra of high redshift radio galaxies reflects a previously reported general trend for powerful radio galaxies, according to which the spectral curvature is lesser for sources havi
ng steeper spectra (measured near rest-frame 1 GHz). We argue based on existing theoretical and observational evidence that it is premature to conclude that the particle acceleration mechanism in sources having straight, ultra-steep radio spectra gives rise to an ultra-steep injection spectrum of the radiating electrons. In empirical support to this we show that the estimated injection spectral indices, available for a representative sample of 35 compact steep spectrum (CSS) radio sources are not correlated with their rest-frame (intrinsic) rotation measures, which are known to be typically large, indicating a dense environment, as is also the case for high-$z$ radio galaxies.
