🚀Astrophysics II Unit 11 – Dark Matter: Evidence and Implications

What's Dark Matter Anyway?

• Invisible form of matter that does not interact with electromagnetic radiation (light)
• Accounts for approximately 85% of the matter in the universe
  • Significantly more abundant than ordinary baryonic matter (~5%)
• Does not emit, absorb, or reflect light making it extremely difficult to detect directly
• Presence inferred from its gravitational effects on visible matter, radiation, and the structure of the universe
• Plays a crucial role in the formation and evolution of galaxies and large-scale structures
• Composed of as-yet undiscovered subatomic particles that are distinct from those that make up ordinary matter
• Leading candidates include Weakly Interacting Massive Particles (WIMPs) and axions

Observational Evidence for Dark Matter

• Galactic rotation curves show flat velocity profiles at large radii, inconsistent with visible matter alone
• Gravitational lensing effects around galaxies and clusters indicate more mass than can be accounted for by visible matter
• Bullet Cluster provides strong evidence for dark matter through the separation of gravitational and baryonic components during a galaxy cluster collision
• Cosmic microwave background (CMB) anisotropies and the large-scale structure of the universe require dark matter to explain observed patterns
• Velocity dispersions of galaxies within clusters suggest the presence of additional unseen mass
• Simulations of structure formation in the early universe necessitate dark matter to reproduce observed galaxy distributions
• Discrepancies between the visible mass and dynamical mass of galaxies and clusters point to the existence of dark matter

Galactic Rotation Curves: The Smoking Gun

• Rotation curves plot the orbital velocities of stars and gas as a function of their distance from the galactic center
• Observed rotation curves remain flat at large radii, contrary to expectations based on visible matter distribution
  • Expected Keplerian decline ($v \propto r^{-1/2}$) not observed
• Flat rotation curves imply the presence of a dark matter halo extending well beyond the visible disk of the galaxy
  • Halo mass distribution follows $\rho(r) \propto r^{-2}$ to produce flat rotation curves
• Provides compelling evidence for the existence of dark matter on galactic scales
• Observed in spiral galaxies across a wide range of masses and sizes (Milky Way, Andromeda)
• Alternative theories like Modified Newtonian Dynamics (MOND) attempt to explain rotation curves without dark matter but face challenges on larger scales

Gravitational Lensing and Dark Matter

• Gravitational lensing is the bending of light paths by massive objects, as predicted by general relativity
• Strong lensing occurs when a massive foreground object (lens) creates multiple images or Einstein rings of a background source
  • Allows for the measurement of the total mass within the Einstein radius of the lens
• Weak lensing manifests as small distortions in the shapes of background galaxies due to the gravitational influence of intervening matter
  • Enables the mapping of the mass distribution in galaxies and clusters
• Lensing mass estimates consistently exceed the mass of visible matter, indicating the presence of dark matter
• Bullet Cluster is a prime example of dark matter detection through gravitational lensing
  • Collision of two galaxy clusters shows a separation between the gravitational mass (dark matter) and the baryonic mass (hot gas)
• Cosmic shear measurements from weak lensing surveys provide constraints on the dark matter density and its distribution on large scales

Cosmic Microwave Background and Structure Formation

• Cosmic microwave background (CMB) is the remnant radiation from the early universe, ~380,000 years after the Big Bang
• CMB anisotropies, tiny fluctuations in temperature and polarization, contain information about the matter content and geometry of the universe
• Dark matter plays a crucial role in the growth of primordial density fluctuations that give rise to the observed CMB anisotropies
  • Fluctuations in the dark matter density provide the seeds for structure formation
• CMB power spectrum measurements from experiments like WMAP and Planck are consistent with a universe containing cold dark matter (CDM)
• Dark matter's gravitational influence amplifies density perturbations, leading to the formation of galaxies and large-scale structures
• Baryon acoustic oscillations (BAO) in the CMB and galaxy distribution provide a standard ruler for measuring the expansion history and constraining dark matter properties
• Simulations of structure formation, such as the Millennium Simulation, demonstrate the necessity of dark matter to reproduce the observed cosmic web

Candidate Particles for Dark Matter

• Weakly Interacting Massive Particles (WIMPs) are a leading candidate for cold dark matter
  • Predicted by supersymmetric extensions of the Standard Model
  • Have masses in the GeV to TeV range and interact via the weak force and gravity
  • Thermal relics from the early universe with an annihilation cross-section that naturally produces the observed dark matter density ($\Omega_{\text{DM}} \approx 0.25$)
• Axions are another well-motivated candidate arising from the Peccei-Quinn solution to the strong CP problem in quantum chromodynamics (QCD)
  • Extremely light ($m_a \sim 10^{-5}$ eV) and weakly interacting pseudoscalar particles
  • Can form a coherent Bose-Einstein condensate and behave as cold dark matter
• Sterile neutrinos are hypothetical right-handed neutrinos that interact only via gravity, making them a possible warm dark matter candidate
• Primordial black holes formed in the early universe could contribute to the dark matter density if they have appropriate masses and abundances
• Other exotic candidates include self-interacting dark matter, fuzzy dark matter, and dark sector particles

Detection Methods and Experiments

• Direct detection experiments aim to observe the elastic scattering of dark matter particles off atomic nuclei
  • Detectors use ultra-pure materials (germanium, xenon) and are located deep underground to minimize background noise
  • Examples include XENON, LUX, PandaX, and SuperCDMS
• Indirect detection searches for the products of dark matter annihilation or decay, such as gamma rays, neutrinos, and cosmic rays
  • Observatories like Fermi-LAT, IceCube, and AMS-02 look for signals from dark matter-rich regions (galactic center, dwarf galaxies)
• Collider experiments, such as the Large Hadron Collider (LHC), search for dark matter production in high-energy particle collisions
  • Look for missing transverse energy signatures that could indicate the presence of invisible dark matter particles
• Axion searches employ resonant cavities (haloscopes) and strong magnetic fields to detect the conversion of axions into photons
  • Experiments include ADMX, CAST, and MADMAX
• Gravitational wave observations from black hole mergers can potentially constrain the properties of primordial black hole dark matter
• Future experiments and observatories, such as DARWIN, CTA, and LISA, will continue to search for dark matter signals with increased sensitivity

Implications for Cosmology and the Universe's Fate

• Dark matter plays a crucial role in the formation and evolution of cosmic structures, from individual galaxies to the large-scale structure of the universe
• The nature of dark matter influences the growth of density perturbations and the subsequent formation of galaxies and clusters
  • Cold dark matter (CDM) predicts a hierarchical, "bottom-up" structure formation scenario
  • Warm dark matter (WDM) suppresses structure on small scales, potentially alleviating issues with CDM predictions
• Dark matter's gravitational effects impact the expansion history and geometry of the universe
  • Contributes to the total matter density $\Omega_m$, which affects the universe's curvature and fate
• The interplay between dark matter and dark energy determines the ultimate fate of the universe
  • In the $\Lambda$CDM model, dark energy (in the form of a cosmological constant $\Lambda$) drives accelerated expansion
  • Dark matter's gravitational influence counteracts the expansion, but dark energy eventually dominates, leading to a "Big Freeze" scenario
• The nature of dark matter has implications for the distribution of galaxies and the structure of galactic halos
  • CDM predicts cuspy halo profiles and a large number of low-mass subhalos, which may be in tension with observations
  • Self-interacting dark matter (SIDM) can alleviate these issues by allowing for the formation of cored halos and the suppression of substructure
• Understanding dark matter is crucial for developing a complete picture of the universe's history, from the Big Bang to its ultimate fate
  • Unraveling the nature of dark matter will provide insights into the fundamental laws of physics and the evolution of the cosmos