From Detection to Host Galaxy Identification: Precision Continuous Gravitational Wave Localization with a Few Anchor Pulsars

Abstract

Pulsar Timing Arrays (PTAs) are rapidly advancing toward the detection of continuous gravitational waves from individual supermassive binary black holes. While it is well established that coherently utilizing the ``pulsar term" requires astrometric distance uncertainties to be smaller than the gravitational wavelength, achieving this precision across an entire array is observationally prohibitive. Here, we demonstrate that achieving sub-wavelength precision for a few ``anchor" pulsars is sufficient to phase-lock the array and drastically shrink the sky-localization error. Using 20 years of realistically simulated data, we systematically evaluate the localization performance of a 25-pulsar array containing three to six high-precision anchors. We show that while introducing three sub-wavelength anchors can reduce the 90\% credible sky area by a factor of 30 in certain directions, expanding this high-precision subset to six anchor pulsars ensures high-precision localizations across diverse source directions. Evaluating a representative set of sky directions, including local galaxy clusters and the locations of maximum and minimum array sensitivity, this six-anchor configuration yields 90\% credible localization areas ranging from $\sim 0.1$ to $9.2 \text{ deg}^2$ at a signal-to-noise ratio of 20. Furthermore, once this minimal subset crosses the sub-wavelength threshold, further reductions in distance uncertainty yield diminishing returns. This establishes a highly efficient near-term observational strategy: prioritizing intensive parallax campaigns for a small core of stable millisecond pulsars provides a cost-effective pathway to precision multi-messenger astronomy.