Intermittent Return‐Current Heating of Real Polar Caps: A Duty‐Cycle Extension for Radio Pulsars

ABSTRACT Radio pulsars often exhibit small, hot polar‐cap regions in thermal x‐rays, and their inferred temperatures can be lower than the upper‐limit values predicted by continuous return‐current heating. In the real polar‐cap framework, particles accelerated in the inner acceleration region return to the stellar surface and deposit energy in a strongly magnetized hot spot. Because pair creation and gap discharges are intrinsically time dependent, we extend this framework by introducing a heating duty cycle , defined as the fraction of a discharge cycle during which return‐current bombardment is active. The cycle‐averaged thermal balance then gives , where is the continuous‐heating temperature. Applying this prescription to a 10‐pulsar sample, we obtain an exploratory phenomenological scaling of with the surface magnetic field and spin parameters. The fitted exponents have large bootstrap uncertainties, reflecting the small and heterogeneous sample, and therefore should not be interpreted as a universal empirical law. The duty‐cycle treatment instead provides an observationally motivated extension of the real polar‐cap model and a framework for assessing how intermittent magnetospheric activity may contribute to the diversity of thermal x‐ray emission from radio pulsars.