A unified polar cap/striped wind model for pulsed radio and gamma-ray emission in pulsars

Because of the recent discovery by Fermi of about 50 new gamma-ray pulsars, it has become possible to look for the statistical properties of their pulsed high-energy emission, especially their light curves and phase-resolved spectra. These pulsars emit, by definition, mostly gamma-ray photons, but some of them are also detected in the radio band. For those seen in these two extreme energies, the relation between the time lag of the radio/gamma-ray pulses and the gamma-ray peak separation, when both high-energy pulses are seen, helps to constrain the magnetospheric emission mechanisms and location. This idea is analysed in detail in this paper, assuming a polar cap model for the radio pulses and a striped wind geometry for the pulsed high-energy counterpart. Combining the time-dependent emissivity in the wind, supposed to be inverse Compton radiation, with a simple polar cap emission model along and around the magnetic axis, we compute the radio and gamma-ray light curves, summarizing the results in several phase plots. We study the phase lag as well as the gamma-ray peak separation dependence on the pulsar inclination angle and on the viewing angle. Using the gamma-ray pulsar catalogue, compiled from the Fermi data, we are able to predict the radio lag/peak separation relation and to compare it with available observations taken from this catalogue. This simple geometric model, combining polar cap and striped wind radiation, is satisfactory for explaining the observed radio/gamma-ray correlation. This supports the idea of distinct emission locations for the radio and gamma-ray radiation. Nevertheless, time retardation effects, such as curved space-time and magnetic field lines winding up close to the neutron star, can lead to a discrepancy between our predicted time lag and a more realistic relation as deduced from the gamma-ray catalogue. Moreover, as there is no accurate polar cap description available so far, large uncertainties remain on the altitude and geometry of the radio emission.