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.

Verdict rule (fixed 2026-09-24, audit P0-11; the previous a_max/a_obs > 2 "tension" mapping was inverted): the mass is excluded for a pulsar when a_max < |a_obs| — the model cannot produce the observed line-of-sight acceleration even at the LOS maximum; a_max above the observation is the compatible case. Comparisons use the intrinsic-Ṗ-corrected a_obs: the measured ṗ is total (intrinsic + cluster + Shklovskii), the intrinsic term is unknown at ~10⁻²⁰ s/s, so a_obs_corr = max(|ṗ| − 10⁻²⁰, 0)/P × c. That unknown caps usable sensitivity at ~10⁻⁹–10⁻¹⁰ m/s² (Paper H pulsar-leg floor).