A 5-year high-precision timing program targeting 20+ OC millisecond pulsars to constrain the central mass distribution at ~10⁻⁹ m/s² acceleration sensitivity — delivering Bayesian model discrimination between single IMBH and dark cluster hypotheses before LISA (~2035) · Working draft · April 2026
Relation to companion proposal: The MeerKAT/SKA 3-year PTA proposal is the discovery-phase program; this 5-year program is the precision-phase follow-up with expanded science goals. They can be submitted together as a staged program or independently.
Timing precision (ToA): ~1–3 µs per 1-hr session (bright MSPs)
Acceleration sensitivity: δa_los = c × δṖ/P = c × (δσ_ToA) / (P × T²)
After T = 5 years, σ_ToA = 2 µs:
δa_los ≈ (3×10⁸ m/s × 2×10⁻⁶ s) / (3×10⁻³ s × (5×3.15×10⁷ s)²)
δa_los ≈ 8×10⁻¹² m/s² per bright MSP [corrected: 6×10²/(3×10⁻³×2.48×10¹⁶) = 8×10⁻¹²]
Expected acceleration from 30,000 M☉ IMBH at r = 0.3 pc:
a_los ≈ GM/r² × cos(i) ≈ 4×10⁻⁸ m/s² (mean projection)
Detection significance: 4×10⁻⁸ / 8×10⁻¹² ≈ 5,000σ — highly decisive (conclusion unchanged)
1.2 Model Discrimination Power
Observable
Single IMBH (≥8,200 M☉)
Dark cluster (~2–3×10⁵ M☉)
Radial acceleration profile
Steep gradient, consistent with 1/r²
Shallower, more extended profile
Central acceleration amplitude
High: ~10⁻⁷–10⁻⁶ m/s² for inner MSPs
Lower: ~10⁻⁸–10⁻⁷ m/s²
Higher-order derivatives (jerk)
Detectable after 4+ years for inner MSPs
Detectable but extended spatial distribution
Bayesian evidence ratio
Expected B₁₂ ≫ 10 (decisive) after 5 years
Expected B₁₂ ≫ 10 favoring extended model
1.3 Extended Science: Jerk and Spin Constraints
Jerk measurements (Ṗ̈): Detectable after 4–5 years for the innermost MSPs; directly constrains the radial density gradient and provides independent mass profile
Gravitational wave background: The 18+ OC MSPs also function as a short-baseline PTA for any local GW signal from compact binary systems in the cluster core
Frame-dragging (speculative): For MSPs within ~0.1 pc of a rapidly spinning IMBH (a★ → 1), the Lense-Thirring precession of orbital planes may leave a detectable signature in timing residuals over 5+ years — the only pre-LISA probe of IMBH spin
2. Observation Strategy
Parameter
Value
Cadence
Bi-weekly (26 sessions/year); sessions ~5 hr each (cluster transit)
Pulsars targeted
All 18+ confirmed OC MSPs; priority on <0.5 pc projected separation
Integration per pulsar
1 hr per session (group observations; parallelised with sub-array)
Commensal deep search expected to find 5–10 additional MSPs
SKA-MID transition
Program continues on SKA-MID (~2030+) for 5× timing precision improvement
Total MeerKAT time (5 yr)
~1,300 hours (reduced from raw 1,500 hr via sub-arraying)
3. Work Plan
Year
Milestone
Deliverable
1
MeerKAT time allocation; timing pipeline; initial ephemerides
Year-1 timing baseline
2
First acceleration measurements; preliminary potential map
Conference results
3
Radial acceleration profile; initial IMBH vs dark cluster Bayesian test
Paper #1 (early constraints)
4
Jerk measurements; strong model discrimination
Paper #2 (model comparison)
5
Full Bayesian reconstruction; SKA-MID handoff preparation
Paper #3 (definitive constraints); public dataset
4. Budget
Item
Cost (USD)
PI (0.2 FTE × 5 yr)
400,000
Co-I × 2 (0.15 FTE × 5 yr)
600,000
Postdoc × 2 (1.0 FTE × 5 yr)
950,000
Graduate student (1.0 FTE × 5 yr)
275,000
MeerKAT time + operational costs
250,000
Computing (Bayesian inference, TEMPO2/enterprise)
200,000
Travel + publications + fringe
225,000
Total
~$2.9M (5 yr)
5. References
Bañares-Hernández, A., et al. (2025). New constraints on OC central mass via MSP timing. A&A, 693, A104.
Häberle, M., et al. (2024). Fast-moving stars in ω Cen. Nature, 631, 285.
González Prieto, A., et al. (2025). Growing the IMBH in ω Cen. ApJL, 990, L69.
Chen, W., et al. (2024). MeerKAT + Parkes MSP census; 18 confirmed pulsars.
Prager, B. J., et al. (2017). Using pulsars to probe the potential well of NGC 6752. ApJ, 845, 148.
Freire, P. C. C., et al. (2017). Timing MSPs in globular clusters as IMBH probes. ApJ, 675, 670.
Babak, S., et al. (2017). LISA EMRI science. Phys. Rev. D, 95, 103012.
Working draft · April 2026 · The 5-year program requires sustained MeerKAT access beyond standard TAC allocations; a large program or partnership proposal with SARAO is recommended. ← Return to omegacentauri.me