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, not as a substitute for them.

Problem Set 1
Stellar Kinematics & Mass Estimation
M–σ relation, Keplerian fast-mover velocities, and the anisotropy degeneracy. Applies the Häberle (2024) detection and Baumgardt (2017) N-body limit to concrete velocity calculations.
40 marks · ~3–4 hr velocity-dispersion anisotropy-degeneracy-explorer
Problem Set 2
Pulsar Timing & TRAPUM Constraints
Line-of-sight acceleration limits from period derivatives, point-mass vs. Plummer mass model comparison, and SKA observation design to reach the Häberle mass scale.
40 marks · ~3–4 hr pulsar-accel-mapper
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
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

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.