Galaxy Rotation Curves
Close to ready. Still to come: clearer wording about the MOND limit, an honest caption for the galaxy view, and sliders that show when they are locked.
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Predict
Predict
If a galaxy had only visible bulge+disk mass, what should happen to orbital speed from $30$ to $50\,{\rm kpc}$, and what would that imply for $M(<R)$?
Play
Play
- Start with `No dark matter` and trace the outer slope from $30$ to $50\,{\rm kpc}$.
- Switch to `Milky Way-like` and compare $V_{\rm total}$ with $V_{\rm Kep}$ at the same radii.
- Increase halo mass and watch the outer curve flatten while $M_{\rm dark}/M_{\rm vis}$ rises.
- Toggle to mass mode and identify where $M_{\rm dark}$ exceeds $M_{\rm vis}$.
- Turn on MOND and compare it to the dark-halo model at galaxy scales.
- Use the normalized inset to contrast solar-system Keplerian behavior with galaxy behavior.
- Run one mystery challenge round, then copy challenge evidence for debrief.
Explain
Explain
At $R=30\,{\rm kpc}$, why can two models produce similar speeds while implying different physical interpretations, and what additional scale-dependent evidence breaks the tie?
Learning goals
- Interpret galaxy rotation curves as velocity-versus-radius observables inferred from Doppler measurements.
- Compare visible-matter-only Keplerian predictions to flat observed curves and infer missing mass.
- Relate bulge, disk, and halo component models to total curve shape and enclosed-mass growth.
- Use baryon fraction and dark-to-visible ratio readouts to reason about mass budgets at large radius.
Misconceptions targeted
- Galaxies should behave like the solar system, so outer stars must always slow as $R^{-1/2}$.
- A face-on schematic means real observations are made face-on too.
- A good MOND fit to galaxy curves means dark matter is ruled out at all scales.
Model notes
- Mass model uses a Hernquist bulge, exact exponential disk rotation (modified Bessel $I_n$/$K_n$ terms), and NFW halo.
- Velocities add in quadrature: $V_{\rm total}^2=V_{\rm bulge}^2+V_{\rm disk}^2+V_{\rm halo}^2$.
- NFW derived quantities ($R_{\rm vir}$, $c$) use internal cosmology defaults ($H_0=67.4\,{\rm km\,s^{-1}\,Mpc^{-1}}$, $\Omega_m=0.315$).
- MOND is shown as an optional comparison curve via full interpolation, not as a full parameter-fitting workflow.
- The galaxy panel is a face-on schematic; published curves are inclination-corrected intrinsic $V(R)$.
- Readout $\Delta\lambda_{21}$ uses $\Delta\lambda_{21}=\lambda_0 V/c$ with $\lambda_0=21.106\,{\rm cm}$.
About this demo
Explore why spiral-galaxy rotation curves stay nearly flat at large radius and what that implies about dark matter across scales.