We study the relaxation of a compressible plasma to an equilibrium with flow. The constraints of conservation of mass, energy, angular momentum, cross-helicity and relative magnetic helicity are imposed. Equilibria corresponding to the energy extrema while conserving these invariants for parallel flows yield three classes of solutions and one of them with an increasing radial density profile, relevant to solar flux tubes is presented.

We have developed analysis tools to search for quasi periodic oscillations in light curves from active galactic nuclei, using the following time series techniques: Wavelets, periodogram, Lomb–Scargle periodogram, structure function and multi-harmonic analysis of variance.

The analysis tools incorporate different noise models with significant levels for all the techniques that is an improvement over the previous work. By looking for consistently high significance, we make the detection of periodicities more robust. We apply this tool to a previously reported QPO (Espaillat et al. 2008) in the X-ray light curve of 3C 273 with a periodicity of ∼ 3300 s and find that the significance is only 74% in the wavelet and fails to show up above 95% significance in the periodogram and multi-harmonic analysis of variance.

The maximum likelihood estimator is used to determine fit parameters for various parametric models of the Fourier periodogram followed by the selection of the best-fit model amongst competing models using the Akaike information criteria. This analysis, when applied to light curves of active galactic nuclei can be used to infer the presence of quasi-periodicity and break or knee frequencies. The extracted information can be used to place constraints on the mass, spin and other properties of the putative central black hole and the region surrounding it through theoretical models involving disk and jet physics.

Variability in active galactic nuclei is observed in UV 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 close to the inner region of the central black hole. We discuss some theoretical models based 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 for their use in theoretical models.

To investigate the $M_{\bullet}$ − $\sigma$ relation, we consider realistic elliptical galaxy profiles that are taken to follow a single power-law density profile given by $\rho(r) = \rho_0(r/r_0)−\gamma$ or the Nuker intensity profile. We calculate the density using Abel’s formula in the latter case by employing the derived stellar potential; in both cases. We derive the distribution function $f(E)$ of the stars in the presence of the supermassive black hole(SMBH) at the center and hence compute the line-of-sight (LoS) velocity dispersion as a function of radius. For the typical range of values for masses of SMBH, we obtain $M_{\bullet} \propto \sigma^p$ for different profiles. An analytical relation $p = (2\gamma +6)/(2+ \gamma)$ is found which is in reasonable agreement with observations (for $\gamma = 0.75−1.4$,$p = 3.6−5.3$). Assuming that a proportionality relation holds between the black hole mass and bulge mass, $M_{\bullet} = f M_{\rm b}$, and applying this to several galaxies, we find the individual best fit values of $p$ as a function of $f$; also by minimizing $\chi^2$, we find the best fit global $p$ and $f$ . For Nuker profiles, we find that $p = 3.81 \pm 0.004$ and $f = (1.23 \pm 0.09) × 10^{−3}$ which are consistent with the observed ranges.

In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, $z \sim 6–7$. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in-falling gas at $\approx$104 K. We show that even under the existingabundance limits, the primordial black holes of masses $\gtrsim$10−2M$_{\odot}$, can heat the collapsing gas to an extent that the H$_2$ formation is inhibited. The collapsing gas can maintain its temperature at 104 K till the gas reachesa critical density $n_c \approx 10^3$ cm$^{−3}$, at which the roto-vibrational states of H$_2$ approaches local thermodynamicequilibrium and H$_2$ cooling becomes inefficient. In the absence of H$_2$ cooling, the temperature of the collapsing gas stays at $\approx$10$^4$ Keven as it collapses further. We discuss scenarios of subsequent angular momentum removaland the route to find collapse through either a supermassive star or a supermassive disk.

The historical observations of polarized jet emission for Blazars are reviewed and previous models are discussed. Motivated by this, a model for polarization of both steady and transient behavior using a helical magnetic field is presented. The variety of observed correlations and anti-correlations between the electricpolarization angle, the degree of polarization and optical flux can be explained by this model. In addition, the phenomena of quasi-periodic oscillations (QPO) behavior seen in jets in X-ray Binaries (XRBs) is also explained by a model based on helical trajectories of emitting blobs and the resulting time scales and harmonics of the QPO are derived. In both the models, the input parameters are the inclination angle, the Lorentz factor of the jet and pitch angle of the magnetic helix.