Dark matter, the invisible cosmic glue, shapes our universe in ways we're just beginning to understand. Galaxies spin faster than they should, and clusters pack more punch than their visible parts suggest. It's like there's a hidden dance partner, leading the cosmic waltz.

From galactic rotation curves to gravitational lensing, the evidence for dark matter is stacking up. The Bullet Cluster collision and cosmic microwave background observations add more weight to this mysterious matter's existence. It's a cosmic puzzle we're still piecing together.

Galactic Evidence

Rotation Curves and Velocity Dispersion

• Galactic rotation curves demonstrate unexpected velocity distributions in galaxies
• Outer regions of galaxies rotate faster than predicted by visible matter alone
• Velocity dispersion measures random motions of stars within galaxies
• Higher velocity dispersion in galaxy outskirts indicates presence of additional unseen mass
• Observations reveal flat rotation curves extending far beyond visible galactic disks
• Flat rotation curves suggest presence of dark matter halos surrounding galaxies
• Dark matter halos extend well beyond visible galactic boundaries
• Halo mass estimated to be 5-10 times greater than visible galactic mass

Mass-to-Light Ratio and Dark Matter Distribution

• Mass-to-light ratio compares total mass of a galaxy to its luminous output
• Higher mass-to-light ratios indicate presence of non-luminous matter
• Typical spiral galaxies have mass-to-light ratios of 10-20 solar masses per solar luminosity
• Elliptical galaxies often exhibit even higher mass-to-light ratios
• Dark matter halo forms extended, roughly spherical region around galaxies
• Halo density profile typically modeled as Navarro-Frenk-White (NFW) profile
• NFW profile characterized by central cusp and gradual density decrease with radius
• Alternative halo models include isothermal sphere and Einasto profile

Gravitational Lensing

Principles and Applications of Gravitational Lensing

• Gravitational lensing occurs when massive objects bend light from distant sources
• Based on Einstein's theory of general relativity
• Strong lensing produces multiple images or arcs of background objects
• Weak lensing causes subtle distortions in shapes of background galaxies
• Microlensing temporarily amplifies light from background stars
• Gravitational lensing allows mapping of dark matter distribution in clusters and large-scale structures
• Provides independent method to estimate mass of lensing objects
• Lensing effects more pronounced for more massive and compact objects

The Bullet Cluster: A Compelling Case for Dark Matter

• Bullet Cluster formed by collision of two galaxy clusters
• Observed in visible light, X-rays, and through gravitational lensing
• X-ray observations show hot gas separated from visible galaxies due to collision
• Gravitational lensing reveals mass concentration doesn't match visible matter or hot gas
• Lensing indicates most mass located in regions containing galaxies, not hot gas
• Provides strong evidence for existence of dark matter
• Challenges alternative theories of gravity (MOND) that attempt to explain galaxy dynamics without dark matter
• Similar observations made in other colliding clusters (Abell 520, MACS J0025.4-1222)

Large-Scale Structure

Galaxy Cluster Dynamics and Mass Estimates

• Galaxy clusters contain hundreds to thousands of galaxies bound by gravity
• Cluster masses estimated through various methods
• Virial theorem relates kinetic energy of galaxies to cluster's gravitational potential energy
• X-ray observations of hot intracluster gas provide another mass estimate
• Gravitational lensing offers independent measure of cluster mass
• All methods consistently indicate more mass than accounted for by visible matter
• Typical clusters contain 80-85% dark matter by mass
• Velocity dispersion of galaxies within clusters higher than expected from visible mass alone

Cosmic Microwave Background and Structure Formation

• Cosmic microwave background (CMB) radiation provides snapshot of early universe
• CMB temperature fluctuations reflect density variations in early universe
• Amplitude and angular scale of fluctuations sensitive to cosmic matter composition
• Observations of CMB anisotropies consistent with presence of dark matter
• Dark matter played crucial role in structure formation
• Enabled matter to clump together before recombination, overcoming radiation pressure
• Hierarchical structure formation model explains observed large-scale structure
• Simulations incorporating dark matter successfully reproduce observed cosmic web of galaxies, clusters, and filaments