The pulsar shadow as the origin of double notches in radio pulse profiles

We present a model of the eclipsing of a rotating, spatially extended source of directional emission by a central absorber and apply it to the pulsar magnetosphere. The model assumes the radially extended inward radio emission along the local direction of the magnetic field, and the pulsar as the absorber. The geometry of the magnetic field lines of the rotating dipole is favorable for double-eclipse events, which we identify with the double notches observed in pulse profiles of nearby pulsars. For pulsars with large dipole inclinations 70 degrees less than or similar to alpha less than or similar to 110 degrees, the double notches are predicted to occur within a narrow phase range of 20 degrees - 30 degrees before the main radio peak. Application of the model to PSR B0950+08 establishes it as a nearly orthogonal rotator (alpha similar or equal to 75 degrees, beta similar or equal to - 10 degrees) with many pulse components naturally interpreted in terms of the inward radio emission from a large range of altitudes. The inward components include the intermittently strong, leading component of the main pulse, which would traditionally have been interpreted as a conal emission in the outward direction. The model also identifies the magnetic field lines along which the radially extended inward radio emission occurs in B0950+08. These have a narrow range of the footprint parameter s close to similar to 1.1 (closed field line region, near the last open field lines). We describe directional characteristics of inward emission from the radially extended region and compare them with characteristics of extended outward emission. Our work shows that pulse profiles of at least some pulsars may be a superposition of both inward and outward emission.