3. The Pulse Profile

The shape of the pulse profile depends on the anisotropic emission of radiation from the polar caps. It may be modified by Compton scattering or gravitational light bending. For photons whose energy is greater than the cyclotron energy, the scattering cross-section is isotropic so pulse profiles are largely determined by geometry. For photon energies below the cyclotron energy the scattering cross-section in the magnetized accretion column is highly anisotropic. The energy dependence of the pulse profile implies that the spectrum depends on pulse phase. The plasma in the accretion column is so highly magnetized that the cyclotron energy is a significant fraction of the electron rest mass. This makes a quantum treatment of the opacities necessary. The opacity of the accretion column is highly energy and direction dependent. This means that the X-ray spectrum will depend on viewing angle and thus change with pulse phase.

The radiation pressure is important as Cen X-3 radiates at near-Eddington luminosities. This may cause a radiative shock above the surface. The accretion geometry will then be a column and the radiation pattern will be a fan beam as shown in Figure 4.3. If the accreting material is stopped close to the surface the accretion column will be short like a pillbox¹ and the radiation will emerge in a pencil beam as shown in Figure 4.3. Thus luminous X-ray pulsars would be expected to emit a fan beam. However, it is possible that the effects of gravitational light bending will make this appear as a pencil beam (Mészáros and Riffert (1988)).

Figure 8: Formation of a fan beam emission pattern. The infalling material loses its kinetic energy at a shock above the neutron star's surface and forms a tall accretion column. Most of the X-rays are emitted from the sides of the column, causing the observed intensity to be greatest when the line of sight is perpendicular to the magnetic field B. The depth of any CSRF is also expected to be greatest when the intensity is greatest as the scattering cross-section is largest for photons travelling along the magnetic field.

Figure 9: Formation of a pencil beam emission pattern. The infalling material loses its kinetic energy near the neutron star's surface and forms a short accretion column. Most of the X-rays are emitted from the face of the column, causing the observed intensity to be greatest when the line of sight is along the magnetic field B. The depth of any CSRF is also expected to be least when the intensity is greatest as the scattering cross-section is smallest for photons travelling perpendicular to the magnetic field. If enough photons are scattered into a direction perpendicular to the magnetic field the CSRF may appear as an emission line when the line of sight is perpendicular to the magnetic field.

Footnotes

... pillbox¹

A short cylindrical container used for explaining Gauss' law.