Pulsar Acceleration Mapper

For a point mass M at the cluster centre, the maximum LOS acceleration at projected distance r⊥ occurs at line-of-sight depth z = r⊥/√2 and equals a_max = (2/3√3) × GM/r⊥² (the coefficient ≈ 0.3849).

The Plummer model softens the singularity by replacing r⊥² with (r⊥² + r_c²), representing an extended dark cluster of scale radius r_c.

The Hybrid model splits M equally between a point IMBH and a Plummer cluster, exploring the transition regime favoured by Bañares-Hernández et al. 2025.

Observed acceleration: a_obs = |ṗ / P| × c, where ṗ is the measured spin-period derivative (including intrinsic spin-down, cluster mean field, and IMBH contribution combined). Negative ṗ indicates the cluster is accelerating the pulsar toward the observer.

Tension flag (a_max / a_obs > 2): the model predicts a maximum acceleration more than twice observed — geometrically improbable unless the IMBH exerts no force along that line of sight, which is unlikely for all pulsars simultaneously.