Graduate Seminar · Compact Objects in Dense Stellar Systems

Problem Sets

Four graduate-level problem sets on the Omega Centauri IMBH evidence record. Each set maps directly to OCS interactive tools with pre-filled parameters and includes click-to-reveal worked solutions.

CC BY 4.0 Solutions: click-to-reveal on each page · ?solutions=1 for print-with-answers Suggested use: 1 set/week, 3–4 hr each
Instructor notes

Each problem set is a self-contained HTML page that prints cleanly to PDF (use browser Print → Save as PDF). Solutions are hidden behind a <details> toggle by default. To generate a version with all solutions open, append ?solutions=1 to any page URL — e.g. omegacentauri.me/pset-1-kinematics.html?solutions=1.

Each page includes pre-filled deeplinks to the relevant OCS interactive tool. Students are expected to use the tool to verify their hand calculations rather than in place of them.

All four sets open with an identical Adopted values box: d = 5.49 kpc, σ0 = 18.2 km/s, Mcl = 4.0 × 106 M☉, rh = 7.0 pc, rc = 3.79 pc, and the Häberle 8,200 M☉ figure stated as a lower bound. Every printed answer reproduces from those givens. Where a competing value circulates in the literature (σ0 = 16.8 km/s from Baumgardt & Hilker 2018, for instance), it is named alongside rather than merged in.

Problem Set 1
Stellar Kinematics & Mass Estimation
The Gültekin M–σ relation and its intrinsic scatter, Keplerian fast-mover velocities, and the anisotropy degeneracy. Applies the Häberle (2024) lower bound and the Baumgardt (2017) N-body upper limit to concrete velocity calculations.
40 marks · ~3–4 hr velocity-dispersion anisotropy-degeneracy-explorer
Open PS 1 → With solutions
Problem Set 2
Pulsar Timing & TRAPUM Constraints
Line-of-sight acceleration limits computed from the published spin-period derivatives of the eight timed OC millisecond pulsars, point-mass vs. Plummer model comparison, and SKA observation design to reach the Häberle mass scale.
40 marks · ~3–4 hr pulsar-accel-mapper
Open PS 2 → With solutions
Problem Set 3
Bayesian Null-Result Analysis
Civiletti (2025) geometric detection model, Bayes factor computation, and prior sensitivity. Contrasts VLA/COSMIC and SKA survey architectures as SETI null-result experiments.
40 marks · ~3–4 hr workflow-null-result
Open PS 3 → With solutions
Problem Set 4
EMRI Gravitational Wave Detectability
ISCO frequency, characteristic strain, LISA sensitivity band placement, spin effects on GW frequency, and EMRI rate estimation for the OC IMBH as a potential LISA source.
40 marks · ~3–4 hr gw-horizon-plotter
Open PS 4 → With solutions

All four problem sets map to OCS tools listed in the tools index. The underlying evidence record is reviewed in the Living IMBH Review. For citation guidance, see the Cite page.