A pulsar near a central black hole feels a line-of-sight acceleration that drifts its arrival times by Δt ≈ ½(a/c)T². Given the pulsar's distance from cluster centre, the timing precision, and the observation baseline, this tool solves for the minimum IMBH mass detectable.
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Read the description instead →A pulsar at projected distance r from a central mass M_BH feels a line-of-sight acceleration of order a = GM_BH / r² (Newtonian; valid because we're orders of magnitude outside the horizon). That acceleration drifts the apparent pulse-arrival times by Δt ≈ ½ (a/c) T² over an observation baseline T. The IMBH is detectable when Δt exceeds the timing precision σ_t. Solving for the smallest detectable M_BH:
M_min = 2 σ_t c r² / (G T²)
The quadratic in r makes pulsars near the cluster centre disproportionately valuable; the inverse-square in T makes longer baselines the high-leverage investment.
The formula above is the formal sensitivity for an idealised, isolated pulsar with the intrinsic spin-down rate independently known. In practice, a constant line-of-sight acceleration produces a constant ΔP/P shift that is mathematically degenerate with intrinsic pulsar spin-down — the standard timing fit absorbs it, leaving the IMBH signature in higher-order terms (jerk, snap) that are much smaller. Real OC pulsar timing also has to contend with: the cluster's mean gravitational potential (which produces an acceleration of order GM_cluster/r_h² independent of any IMBH), binary orbital motion (for the majority of MSPs), interstellar dispersion variations, and confusion from other accelerating masses.
The practical consequence is that published combined bounds — Bañares et al. 2025's 6,000 M☉ (3σ) and TRAPUM 2026's 10⁵ M☉ (90% CL) — are weaker than per-pulsar formal sensitivities by factors of order 100–1000. The gap on this chart between the purple pulsar dots and the amber published-bound lines IS that systematics penalty. Closing it requires multi-pulsar joint analyses with kinematic priors on the cluster potential, which is what the published papers do.
The teal curve is M_min(r) at your current σ_t and T sliders. The purple dots are real OC pulsars at their own measured σ_t (from the discovery papers) and your T slider value. Where a pulsar's dot lies on the chart is its individual sensitivity; the most sensitive pulsar (lowest-y point) sets the de-facto upper limit at its r. The horizontal amber dashed lines are the published combined upper limits — the tightest ones come from joint analyses that exploit multiple pulsars and cluster-kinematics priors simultaneously.
Conversion from arcsec to physical distance uses an OC distance of 5.43 kpc (Soltis et al. 2021, ApJ 908:L5). 1 arcsec at this distance ≈ 0.0263 pc ≈ 8.13×10¹⁴ m.
The published upper limits also appear in the IMBH Constraint Stacker as horizontal-axis markers, where you can see them in the company of kinematic and JWST constraints. The pulsar list itself comes from tools/data/measurements.js; per-pulsar parameters are illustrative pending a published per-pulsar ephemerides catalog.
The best millisecond pulsars achieve weekly RMS residuals of ~50–100 ns (PSR J1909-3744 at Green Bank Telescope is the gold standard at ~60 ns over 15 years). The four major PTAs — NANOGrav (North America), EPTA (Europe), PPTA (Parkes/Australia), and the MeerKAT-based MPTA — together monitor ~70 pulsars and recently reported (June 2023) evidence for a stochastic gravitational-wave background consistent with supermassive black hole binaries. SKA-Mid (first light ~2028) will push best-pulsar precision to ~10 ns and extend the network to ~200 pulsars.
Omega Centauri hosts ~25 known pulsars as of 2026, almost all discovered by MeerKAT TRAPUM (Chen et al. 2023 reported 13 new ones; subsequent surveys have added ~12 more). Most are millisecond pulsars (P ≈ 2–10 ms). Per-pulsar timing precision varies widely: isolated MSPs with low DM achieve 1–5 μs RMS post-fit residuals; binary MSPs and ones in confused regions are 10× worse. The TRAPUM 2026 IMBH constraint (~10⁵ M☉ at 90% CL) combines ~10 of the best-timed pulsars across a 5-year baseline.
A constant line-of-sight acceleration produces a constant ΔP/P shift that is mathematically indistinguishable from intrinsic pulsar spin-down. Standard pulsar timing software (TEMPO2, PINT) absorbs this into the fitted P-dot, leaving residual signal in higher-order derivatives (jerk, snap) that are much smaller. This is the central reason per-pulsar formal sensitivity (often quoted as M_BH ≲ few M☉) is ~1000× tighter than the published bounds (~10³–10⁵ M☉). Multi-pulsar joint analyses with kinematic priors can recover some of the loss by fitting cluster-potential-induced accelerations across many sightlines simultaneously.