2022ApJ...940..110H

We investigate the distributions of the obliquity angle and impact parameters of nulling pulsars of different duty cycles based on the simulation of more than 600,000 samples. We adopt a purely geometric approach for pulsar visibility, in which visible emission is emitted tangentially to the magnetic field line and parallel to the line-of-sight direction. The geometry is incorporated with the model for pulsar magnetospheres of multiple emission states, in which the plasma charge density is dependent on the emission state. We assume that an emission state can only exist between two limiting conditions described by the vacuum and corotation models, respectively. In this model, pulse nulling corresponds to emission switching to a state in which the plasma charge density is zero. The event is detectable only if the switching occurs at source points that lie on a trajectory, whose locus defines the locations of visible emission, within an open-field region. Our results show that detectable nulling is dependent on all three parameters, such that nulling pulsars prefer a small obliquity angle and duty cycle, and tend to have positive impact parameters. We find that the total population of nulling pulsars in our samples is around 23%, of which about 47% possess a duty cycle of 0.1 or smaller. The former implies that there are more nulling pulsars than currently known. Our model predicts that the number of nulling pulsars increases as the obliquity angle decreases, which also implies that the occurrence of nulling in a pulsar should evolve over time.