1Open Window 2Pulsar Timing 3JWST Accretion 4LISA IMRI Race
Four-stage workflow · observational race to close the IMBH tension

Closing the Constraint Window

Four observational channels compared: which instrument resolves the 6,000–8,200 M☉ tension between Häberle et al. 2024 and Bañares-Hernández et al. 2025 — and when?

🔬 Established astrophysics
No backend · No tracking · State in URL hash · v1.0 · 2026-06-01
01
Häberle et al. 2024 · Bañares-Hernández et al. 2025
The Open Window
Set the lower and upper mass limits to see the tension

The Häberle et al. 2024 proper-motion result establishes a 3σ lower limit of ≥8,200 M☉. Bañares-Hernández et al. 2025 pulsar timing sets a 3σ upper limit of ≤6,000 M☉. These measurements are in tension at the 3σ level — both cannot be simultaneously correct under standard assumptions. Stage 2–4 show what each instrument needs to resolve this.

Inputs
8,200 M☉
6,000 M☉
Stage 1 outputs
Window widthM☉
Tension indicator
Lower bound M_loM☉
Upper bound M_hiM☉
Tension significance
Passes to Stages 2–4: lower bound , upper bound
02
Bañares-Hernández et al. 2025 · MeerKAT / SKA
MeerKAT / SKA Pulsar Timing
More pulsars + longer baseline reduces the mass uncertainty

The Bañares-Hernández et al. 2025 constraint comes from 5 pulsars in OC's core. Adding more pulsars reduces the uncertainty on the gravitational potential. The MeerKAT timing sensitivity on the upper mass limit scales as 1/√N_psr × 1/√baseline. The key insight: to drop the upper limit below 8,200 M☉ requires √(N×B) > 3.66, so at N=5 pulsars a baseline of only ~2.7 years is sufficient — yet the tension persists, highlighting a genuine systematic conflict.

Inputs (M_lo, M_hi from Stage 1)
Constraint bounds from Stage 1
5 pulsars
5 yr
Stage 2 outputs
New upper limit (3σ)M☉
Improvement factor
√(N×B) product
Min baseline needed (at N=5)yr
Min pulsars needed (5 yr)psr
Pulsar timing new upper limit:
03
Chen et al. 2025 · NIRCam / MIRI · Bondi accretion
JWST NIRCam / MIRI Accretion
Accretion luminosity limit → mass limit under Bondi efficiency assumptions

Chen et al. 2025 placed an upper limit on IMBH accretion luminosity from JWST NIRCam/MIRI observations, which translates to a mass limit only under assumptions about the accretion efficiency ε. The constraint weakens for low ε — at ε = 10⁻³ the limit is ~6,000 M☉, consistent with Bañares, but at ε = 10⁻⁵ (radiatively inefficient flow) the limit weakens to ~60,000 M☉, compatible with any proposed mass. The ambient gas density sets the Bondi rate.

Inputs
Constraint bounds from Stage 1
ε = 10⁻³
n = 0.1 cm⁻³
Stage 3 outputs
JWST mass upper limitM☉
Bondi accretion rateM☉/yr
Accretion luminosity limitW
Eddington ratio L/L_Edd (at M_lo)
ε needed to exclude M_lo
JWST upper limit at chosen ε:
04
LISA · IMRI chirp mass · 2030s
LISA Chirp Mass Measurement
IMRI detection gives IMBH mass to sub-percent precision

If a stellar-mass black hole in OC spirals into the IMBH, LISA will measure the chirp mass to ~0.1% accuracy from the inspiral gravitational waveform. This translates to an IMBH mass posterior width that depends on the mass ratio q = m_stellar/M_IMBH and the signal-to-noise ratio. A single IMRI detection definitively closes the constraint window. The expected IMRI rate for a ~10,000 M☉ IMBH in a dense globular cluster is ~10⁻⁸ yr⁻¹ per cluster.

Inputs
M_IMBH (lower bound, Stage 1)
q = 10⁻³
SNR = 100
Stage 4 outputs
IMBH mass uncertainty σ_MM☉
Fractional precision δM/M
N_cycles (approximate)
Window closed? (σ_M vs gap)
Resolves tension?
LISA would measure M_IMBH to — resolves the constraint window definitively
✓ Constraint Window Race — Which Instrument Wins?
Instrument Upper limit / σ_M (M☉) vs. Häberle 8,200 Status
MeerKAT/SKA Pulsar
JWST Accretion
LISA IMRI