Symmetries of microcanonical entropy surfaces

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical entropy in the low energy regime is considered. The general statements are corroborated by investigations of various examples of classical spin systems.Comment: 15 pages, 5 figures include

Pulsar shadow as the origin of double notches in radio pulse profiles

We present the model of eclipsing 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 favourable for the double eclipse events, which we identify with the double notches observed in pulse profiles of nearby pulsars. For pulsars with large dipole inclinations 70 <~ alpha <~ 110 deg the double notches are predicted to occur within a narrow phase range of 20 to 30 deg before the main radio peak. Application of the model to PSR B0950+08 establishes it as a nearly orthogonal rotator (alpha =~ 75 deg, beta =~ -10 deg) 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 interpeted 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 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.Comment: 28 pages, 13 figures, accepted by ApJ, high-quality figures are available from http://www.ncac.torun.pl/~michalf/inward1_figs