Scaling Laws for Detecting Continuous Waves from Super Massive Black Hole Binaries with Pular Timing Arrays.

Pulsar Timing Arrays (PTAs) have opened a new window onto the nanohertz gravitational-wave spectrum, with recent evidence for a stochastic background signaling the presence of supermassive black hole binaries (SMBHBs). Beyond the background, individual binaries may be observed as continuous-wave sources, providing direct measurements of binary masses, orbital evolution, and sky locations. In this work, we present analytic and numerical scaling laws that describe how PTA sensitivity to continuous gravitational waves depends on key experimental factors such as the number of pulsars, timing precision, cadence, and data span. These relations clarify how improvements in PTA design and observation strategy translate into enhanced detection prospects for single sources. Our results provide a framework for assessing future PTA capabilities and guiding the search for resolvable SMBHBs in the nanohertz regime.