Type 2 quasars are luminous active galactic nuclei (AGN) whose central regions are obscured by large amounts of gas and dust. In this paper, we present a catalog of type 2 quasars from the Sloan Digital Sky Survey (SDSS), selected based on their opti
cal emission lines. The catalog contains 887 objects with redshifts z < 0.83; this is six times larger than the previous version and is by far the largest sample of type 2 quasars in the literature. We derive the [OIII]5008 luminosity function for 10^8.3 Lsun < L[OIII] < 10^10 Lsun (corresponding to intrinsic luminosities up to M[2400A]-28 mag or bolometric luminosities up to 4x10^47 erg/sec). This luminosity function provides strong lower limits to the actual space density of obscured quasars, due to our selection criteria, the details of the spectroscopic target selection, as well as other effects. We derive the equivalent luminosity function for the complete sample of type 1 (unobscured) quasars; then, we determine the ratio of type 2/type 1 quasar number densities. Our best data constrain this ratio to be at least 1.5:1 for 10^8.3 Lsun < L[OIII] < 10^9.5 Lsun at z < 0.3, and at least 1.2:1 for L[OIII]=10^10 Lsun at 0.3 < z < 0.83. Type 2 quasars are at least as abundant as type 1 quasars in the relatively nearby Universe (z < 0.8) for the highest luminosities.
We consider axisymmetric relativistic jets with a toroidal magnetic field and an ultrarelativistic equation of state, with the goal of studying the lateral structure of jets whose pressure is matched to the pressure of the medium through which they p
ropagate. We find all self-similar steady-state solutions of the relativistic MHD equations for this setup. One of the solutions is the case of a parabolic jet being accelerated by the pressure gradient as it propagates through a medium with pressure declining as p(z)propto z^{-2}. As the jet material expands due to internal pressure gradients, it runs into the ambient medium resulting in a pile-up of material along the jet boundary, while the magnetic field acts to produce a magnetic pinch along the axis of the jet. Such jets can be in a lateral pressure equilibrium only if their opening angle theta_j at distance z is smaller than about 1/gamma, where gamma is the characteristic bulk Lorentz-factor at this distance; otherwise, different parts of the jet cannot maintain causal contact. We construct maps of optically thin synchrotron emission from our self-similar models. We suggest that the boundary pile-up may be the reason for the limb-brightening of the sub-parsec jet of M87. We find that if the synchrotron emissivity falls with the distance from the jet axis, the polarization fraction rises toward the edge, as seen in 3C273 and Mkn501. Projection effects and the emissivity pattern of the jet have a strong effect on the observed polarization signal, so the interpretation of the polarization data in terms of the geometry of magnetic fields is rather uncertain. For example, jets with toroidal magnetic fields display the `spine-sheath polarization angle pattern seen in some BL Lac objects.
