Dark Matter

Evidence for dark matter

Evidence	What it shows
Galaxy rotation curves	Outer stars rotate same as inner; extra mass needed
Galaxy cluster X-ray temperatures	Hot gas needs more mass than visible to bind
Gravitational lensing	Light from distant galaxies bent by unseen mass
Bullet Cluster	Gas (visible) lags behind matter centers (lensing) — DM not gas
CMB power spectrum	Acoustic peaks require ~27% matter, vs ~5% baryonic
Large-scale structure	Galaxy clustering matches DM N-body simulations
BAO (baryon acoustic oscillations)	Sound waves in early universe constrain DM

Universe composition

Component	Fraction of mass-energy
Dark energy	68%
Dark matter	27%
Baryonic matter	5%
Photons (CMB + starlight)	~0.005%
Neutrinos	~0.1-0.5%

Candidate particles

Candidate	Properties	Searches
WIMP	~10-1000 GeV; weak interactions	XENON, LZ, PandaX (no detection)
Axion	~µeV-meV; very light pseudoscalar	ADMX, HAYSTAC (active searches)
Sterile neutrino	keV-MeV scale	X-ray telescopes
Primordial BH	10⁻¹⁶ to 100 M_sun	Microlensing, gravitational waves
Self-interacting DM	Various; interacts with itself, not with us	Astronomical signatures

JavaScript — dark matter calculations

// Galaxy rotation curve - measure mass enclosed within radius
function enclosedMass(v_orbital, r) {
  // For circular orbit: v² = GM/r → M = v²r/G
  const G = 6.674e-11;
  return v_orbital * v_orbital * r / G;
}

// Milky Way: outer stars at ~220 km/s at r ~50 kpc
const M_milkyway = enclosedMass(2.2e5, 50 * 3.086e19);
console.log(`Milky Way mass within 50 kpc: ${(M_milkyway / 1.989e30).toExponential(2)} solar masses`);
// ~5 × 10¹¹ — much more than visible stars (~10¹¹)
// Difference is dark matter

// Mass-to-light ratio
function massToLight(mass_solar, luminosity_solar) {
  return mass_solar / luminosity_solar;
}

// Visible matter: M/L ~ 1
// Galaxies including DM: M/L ~ 30-100
// Galaxy clusters: M/L ~ 200-300

// Check if rotation curve is "flat"
function isFlatRotation(v_at_r, r_array) {
  // If v constant at large r, suggests dark matter halo
  const min_v = Math.min(...v_at_r);
  const max_v = Math.max(...v_at_r);
  return (max_v - min_v) / max_v < 0.2;  // within 20% — flat
}

// Friedmann equation: density parameter
function densityParameter(H_0, density) {
  const G = 6.674e-11;
  const rho_crit = 3 * H_0 * H_0 / (8 * Math.PI * G);
  return density / rho_crit;
}

// H_0 = 70 km/s/Mpc = 2.27e-18 s⁻¹
const H_0 = 2.27e-18;
const G = 6.674e-11;
const rho_crit = 3 * H_0 * H_0 / (8 * Math.PI * G);
console.log(`Critical density: ${rho_crit.toExponential(2)} kg/m³`);
// ~9.5 × 10⁻²⁷ kg/m³ — very dilute on cosmic scale

// Composition of universe
const cosmology = {
  baryonic: 0.05,
  darkMatter: 0.27,
  darkEnergy: 0.68
};
console.log(`Total: ${Object.values(cosmology).reduce((a,b) => a+b)}`); // 1.0

Where dark matter matters

• Cosmology. Foundational to ΛCDM model — current standard cosmology.
• Galaxy formation. DM halos formed first; baryons fell in, made galaxies.
• Particle physics. Beyond Standard Model — DM candidates extend particle physics.
• Astrophysics. Galaxy dynamics, cluster physics, gravitational lensing.
• Modern observations. JWST, future LSST, Euclid will probe DM via cosmic structure.
• Engineering. Direct detection experiments push detector technology limits (background rejection, pure materials).
• Education. Modern cosmology cannot be taught without dark matter.

Common mistakes

• Confusing dark matter with antimatter. Antimatter — opposite charge particles (well-known). Dark matter — unknown, doesn't interact electromagnetically.
• Confusing dark matter with dark energy. Both "dark." Dark matter — gravitates normally (attracts). Dark energy — accelerates expansion (effectively repulsive). Different physics.
• Treating MOND as a viable alternative. Some galaxy rotations fit better; clusters, CMB, structure formation don't. Scientific consensus favors dark matter.
• Believing dark matter is just unseen normal matter. Constrained by big bang nucleosynthesis to ~5% of universe; dark matter is mostly non-baryonic.
• Thinking dark matter is a "fudge." Hypothesis predicts many observations consistently. Concrete predictions; testable. Just not yet identified at particle level.
• Forgetting dark matter is collisionless. Doesn't dissipate energy; halos remain extended (vs gas which collapses to disks).