A standard model for the visibility of pulsar radio emission is based on the assumption that the emission is confined to a narrow cone about the tangent to a dipolar field line. The widely accepted rotating vector model (RVM) is an approximation in which the line of sight is fixed and the field line is not strictly tangent to it. We refer to an exact treatment (Gangadhara, 2004) as the tangent model. In the tangent model (but not in the RVM) the visible point changes as a function of pulsar rotational phase, ψ, defining a trajectory on a sphere of radius r. We solve for the trajectory and for the angular velocity of the visible point around it. We note the recent claim that this motion is observable using interstellar holography (Pen et al., 2014). We estimate the error introduced by use of the RVM and find that it is significant for pulsars with emission over a wide range of ψ. The RVM tends to underestimate the range of ψ over which emission is visible. We suggest that the geometry alone strongly favors the visible pulsar radio being emitted at a heights more than ten percent of the light-cylinder distance, where our neglect of retardation effects becomes significant.

The 2nd Fermi-LAT pulsar catalog includes 117 γ-ray pulsars, of which roughly one third are millisecond pulsars (MSPs) while the remaining two thirds split evenly into young radio-loud and radio-quiet pulsars. Although this large population will enable future, detailed studies of emission mechanisms and the evolution of the underlying neutron star population, some nearly-universal properties are already clear and unequivocal. We discuss some of these aspects below, including the altitude of the γ-ray emission site, the shape of the γ-ray spectrum, and the implications of the latter for the radiation mechanism.

We study radio emission from pulsar wind nebulae (PWNe) considering the observed spatial structure. We assume spherical symmetry of the PWN, and model the evolution of the magnetic field and the particle energy distribution. We do not consider the synchrotron cooling of particles but consider the adiabatic cooling, because we are mostly interested in the radio emission from PWNe. The model is applied to the Crab Nebula and succeeds to reproduce the observed spatially integrated spectrum in radio with a single power-law injection. In our previous work (a one-zone model), in contrast, the integrated spectrum of the Crab Nebula is reproduced by a broken power-law injection of particles. However, the spatial structure in radio is inconsistent with observations and we need a radial velocity profile which is very different from the model by Kennel & Coroniti. Further studies of the spatial structure of PWNe are important to understand the origin of the radio emission from young PWNe.