A Square Kilometre Array Pulsar Census
Most of the pulsar science case with the Square Kilometre Array (SKA) depends on long-term precision timing of a large number of pulsars, as well as their astrometric measurements using very long baseline interferometry (VLBI). However, before we can time them, or VLBI them, we must first find them. Here, we describe the considerations and strategies needed when planning an all-sky blind pulsar survey using the SKA. Based on our understanding of the pulsar population, the performance of the now-under-construction SKA elements, and practical constraints such as evading radio frequency interference, we project pulsar survey yields; this is done using two complementary methods for a number of illustrative survey designs, combining SKA-Low and SKA-Mid Bands 1 and 2 in a variety of ways. A composite survey using both SKA-Mid and SKA-Low is optimal, with Mid Band 2 focused in the plane. We find that, given its much higher effective area and survey speed, the best strategy is to use SKA-Low to cover as much sky as possible, ideally also overlapping with the areas covered by Mid. We find that an all-sky blind survey with Phase 1 of the SKA with the AA* array assembly will detect $\sim10,000$ slow pulsars and $\sim 800$ millisecond pulsars (MSPs) if SKA-Mid covers the region within $5°$ of the plane, while higher latitudes will be covered with SKA-Low. For the same survey region the yield with AA4 is $\sim 20\%$ higher, but this increases considerably by broadening the range covered by SKA-Mid Bands 1 and 2. In particular one could expect a yield of $\sim 1300$ MSPs with AA4. The pulsar census will enable us to set new constraints on the uncertain physical properties of the entire neutron star population. This will be crucial for addressing major SKA science questions including the dense-matter equation of state, strong-field gravity tests, and gravitational wave astronomy.