Stellar orbit trajectories
Escaped: 0 / 800
Updates the rotation curve and star orbits. Set it to 0 for visible matter only.
Controls halo concentration: a smaller radius packs more dark matter near the center.
Rotation curve
χ² –What the colours mean
- White points are measured speeds of NGC 3198 (SPARC); bars show uncertainty.
- Cyan is the speed expected from visible matter only (stars + gas).
- Purple is the extra speed supplied by the dark matter halo (NFW mode).
- Orange is the combined model (or the MOND prediction in MOND mode). The closer it hugs the white points, the better the fit.
- Residual bars: teal = model is too slow, coral = model is too fast, no bar = perfect match.
- χ² badge: teal good fit, orange fair, red poor.
Why isn't χ² exactly 0?
χ² adds up how far the model is from each measured point, in units of that point's uncertainty. A score of 0 would mean every point matched perfectly, which real data never allows: measurements carry noise, so even a correct model scatters around them by roughly one error bar per point (χ²ᵣ ≈ 1 is a good fit).
Models also simplify reality. NFW assumes a smooth spherical halo, MOND assumes one fixed a0, and both rely on an estimated stellar mass for the visible matter. Their small mismatches add to the score, which is why neither theory reaches 0.
What is a dark matter halo?
An invisible cloud of extra mass around the galaxy whose gravity keeps the outer stars from flying off.
The stars and gas we can see are not heavy enough to hold on to fast-moving stars far from the centre. Measured speeds stay high out to the edge instead of dropping, so astronomers propose a huge, roughly spherical halo of unseen matter that extends well beyond the visible disk.
This simulator uses the standard NFW halo shape. Its total mass (M200) and how tightly it is packed towards the centre (rs) are set by the sliders. More halo mass means faster outer stars.
What is MOND?
Instead of adding invisible mass, MOND slightly changes how gravity behaves where it is extremely weak.
In the outskirts of a galaxy, gravity from the visible matter is very feeble. MOND says that below a tiny threshold acceleration (a0 ≈ 1.2×10⁻¹⁰ m/s²) gravity falls off more gently than Newton predicted, so outer stars keep orbiting quickly and the rotation curve flattens, using only the matter we can see.
v² = ( vbar² + √( vbar⁴ + 4·r·a₀·vbar² ) ) / 2
Both ideas can match this galaxy's curve; they disagree about why. Flip the switch above to compare them.