Dark Matter
Dark Matter — Galactic Rotation & Halo Profile · Astrophysics
Pin down the dark-matter halo from how galaxies rotate — distinguish particle dark matter from modified gravity.
📋 The problem
Galaxies rotate as if far more mass is present than we see. Either dark matter exists, or gravity is modified. Fitting halo profiles (NFW) to rotation curves — and recovering halo parameters across many galaxies — discriminates the hypotheses.
🧗 Why it's a grand challenge
Baryonic uncertainties, beam smearing, and degeneracies between halo profiles and modified-gravity laws make inference ambiguous; conclusions must hold across diverse galaxies.
🧮 Governing model
v(r) = √(G·M(r)/r); ρ_NFW(r) = ρ_s / [(r/r_s)(1+r/r_s)²]Circular velocity v(r)=√(G·M(r)/r) with an NFW halo ρ(r)=ρ_s/[(r/r_s)(1+r/r_s)²]; infer halo parameters from rotation curves.
Current best: SPARC rotation-curve NFW/MOND fits
🧭 Possible approaches
- Bayesian / simulation-based inference of halo parameters from rotation curves
- Joint baryon+halo modeling to break degeneracies
- Population-level tests of NFW vs MOND
🎯 Build the benchmark
Recover the dark-matter halo profile from HI/Hα rotation curves (reduced χ² ≲ 1.2; M200 within ~0.1 dex).
Metric: rotcurve_chi2 — reduced χ² of rotation-curve fit (lower better)
Datasets to start from: SPARC galaxy rotation-curve database, THINGS HI velocity fields
🤖 Build an AI agent to solve it
An agent that fits halos across a galaxy catalog and quantifies the evidence for dark matter vs modified gravity.
Once a benchmark exists, an AI4Science agent can iterate solutions against it — every verified solution earns PWM.
This is a frontier framing page — an open problem, not yet benchmarked or verified, unlike PWM's mature computational-imaging benchmarks.