Question 1

Why do we expect velocities to decrease with radius beyond the galactic disk?

Accepted Answer

Kepler's third law, derived from Newton's gravity, shows that for a circular orbit around a central mass M, v = sqrt(GM/r). This means velocity falls as 1/sqrt(r) when all mass is contained within the orbit radius. Our solar system follows this: Mercury orbits at ~48 km/s, Neptune at only ~5 km/s. If galaxy mass were concentrated in the visible disk and bulge (as the light distribution suggests), outer stars should show the same Keplerian decline. The flatness of observed rotation curves is a direct indicator that significant mass extends far beyond the visible galaxy.

Question 2

What evidence supports the existence of dark matter besides rotation curves?

Accepted Answer

Multiple independent lines of evidence point to dark matter: gravitational lensing (galaxy clusters bend background light more than their visible mass can explain); the Bullet Cluster (two merging clusters where the gas was slowed by collisions while invisible dark matter passed through, observed separately via lensing); the cosmic microwave background power spectrum (baryon acoustic oscillations require dark matter to seed structure formation); and the large-scale distribution of galaxies (simulations with dark matter match observations; without it they fail). These independent methods converge on the same dark matter fraction.

Question 3

Could modified gravity theories explain flat rotation curves without dark matter?

Accepted Answer

Modified Newtonian Dynamics (MOND), proposed by Mordehai Milgrom in 1983, modifies Newton's second law at very low accelerations to produce flat rotation curves without dark matter. MOND successfully predicts rotation curves of individual galaxies with fewer free parameters than dark matter models. However, MOND cannot explain the Bullet Cluster, the CMB power spectrum, or galaxy cluster dynamics as naturally as particle dark matter.

Question 4

What is the dark matter halo profile and how is it measured?

Accepted Answer

Halo density profiles are inferred by fitting rotation curves and lensing data. The NFW profile from N-body simulations predicts a central cusp (density rising as 1/r toward the center), but some dwarf galaxies show central cores instead — the cusp-core problem, which motivates study of dark matter self-interactions and baryonic feedback.

Question 5

How does dark matter influence galaxy formation?

Accepted Answer

Dark matter halos collapse first from early-universe density fluctuations, providing gravitational wells into which ordinary matter falls to form galaxies. Halo mass and concentration determine galaxy size and rotation speed, reflected in the Tully-Fisher relation between luminosity and maximum rotation velocity.

Question 6

What does the Stellar Mass slider control?

Accepted Answer

Stellar Mass sets the mass of the visible disk and bulge (0.2-5.0 x10^10 solar masses), scaling the Newtonian rotation curve directly. Since Dark Matter Fraction is relative to total mass, raising Stellar Mass while holding that fraction fixed also raises the absolute dark matter mass needed.

Question 7

What happens if I drag Dark Matter Fraction down to 0?

Accepted Answer

At Dark Matter Fraction 0, the observed curve collapses onto the Newtonian curve, reproducing the Keplerian 1/sqrt(r) decline expected from visible matter alone — the mismatch Vera Rubin measured in real galaxies, which is why a non-zero fraction (default 0.85) is needed to match observations.

Question 8

How does the Halo Scale radius r_s change the shape of the rotation curve?

Accepted Answer

r_s is the NFW scale length. A small r_s (near 2 kpc) concentrates dark matter close to the center, flattening the curve quickly at small radii; a large r_s (up to 30 kpc) spreads halo mass over a larger volume, pushing V_max further out with a more gradual rise.

Question 9

What is the difference between V_max and V_flat in the stats bar?

Accepted Answer

V_max is the single highest velocity anywhere on the curve, often near the disk edge where bulge and disk still matter. V_flat is the velocity the curve settles to at large radii once the halo dominates — for a genuinely flat curve, V_max and V_flat converge to nearly the same value.

Question 10

Why does increasing Disk Scale Length change the shape of the inner rotation curve?

Accepted Answer

Disk Scale Length (1-10 kpc) sets how spread out the stellar disk is. A short scale length concentrates the same mass into a smaller region, producing a sharper inner rise; a longer scale length spreads that mass more thinly, so the inner curve rises more gradually, while total stellar mass stays the same.

🌌 Galaxy Rotation Curves — Dark Matter Evidence

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