Answers to frequently asked questions about the pulsar timing array Hellings and Downs curve

Abstract: We answer frequently asked questions (FAQs) about the Hellings and Downs correlation curve -- the "smoking-gun" signature that pulsar timing arrays (PTAs) have detected gravitational waves (GWs). Many of these questions arise from inadvertently applying intuition about the effects of GWs on LIGO-like detectors to the case of pulsar timing, where not all of it applies. This is because Earth-based detectors, like LIGO and Virgo, have arms that are short (km scale) compared to the wavelengths of the GWs that they detect (approx 100-10,000 km). In contrast, PTAs respond to GWs whose wavelengths (tens of light-years) are much shorter than their arms (a typical PTA pulsar is hundreds to thousands of light-years from Earth). To demonstrate this, we calculate the time delay induced by a passing GW along an Earth-pulsar baseline (a "one-arm, one-way" detector) and compare it in the "short-arm" (LIGO-like) and "long-arm" (PTA) limits. This provides qualitative and quantitative answers to many questions about the Hellings and Downs curve. The resulting FAQ sheet should help in understanding the "evidence for GWs" recently announced by several PTA collaborations.