4.2 Dark matter halos

Dark matter halos are invisible structures that shape our universe. They're made of mysterious particles we can't see but make up most of the matter around us. These halos act like cosmic scaffolding, providing the gravitational pull for galaxies to form and grow.

Scientists study dark matter halos to understand how galaxies evolve. They use complex models to map halo shapes and densities. Observations of galaxy rotation and gravitational lensing provide evidence for these hidden structures that play a crucial role in cosmic architecture.

Composition of dark matter halos

• Dark matter halos consist of non-baryonic matter that does not interact with electromagnetic radiation, making it invisible to telescopes
• Believed to be composed of weakly interacting massive particles (WIMPs) such as neutralinos or axions, although their exact nature remains unknown
• Dark matter accounts for approximately 85% of the matter in the universe and plays a crucial role in the formation and evolution of galaxies

Role in galaxy formation and evolution

• Dark matter halos provide the gravitational potential wells in which galaxies form and evolve over cosmic time
• Act as the scaffolding for the accumulation of baryonic matter, allowing gas to cool and condense, leading to the formation of stars and galaxies
• Interactions between dark matter halos, such as mergers and tidal interactions, can trigger bursts of star formation and shape the morphology of galaxies

Density profiles of halos

Navarro-Frenk-White (NFW) profile

• Describes the average density distribution of dark matter within halos based on N-body simulations
• Characterized by a steep inner slope ($\rho \propto r^{-1}$) and a more gradually declining outer slope ($\rho \propto r^{-3}$)
• Provides a good fit to the density profiles of halos across a wide range of masses, from dwarf galaxies to galaxy clusters

Einasto profile

• An alternative to the NFW profile that provides a better fit to some simulated halos, particularly at small radii
• Characterized by a smoothly varying slope that becomes shallower towards the center of the halo
• Described by three parameters: the scale radius, the density at the scale radius, and the shape parameter $\alpha$

Burkert profile

• Motivated by observations of dwarf galaxies that suggest a flatter inner density profile compared to the NFW profile
• Features a constant-density core at small radii, transitioning to a $\rho \propto r^{-3}$ decline at larger radii
• May be a result of baryonic feedback processes, such as supernova explosions, that can alter the distribution of dark matter in the central regions of halos

Halo mass function

Press-Schechter formalism

• A statistical approach to predicting the number density of dark matter halos as a function of their mass and redshift
• Based on the idea that halos form from peaks in the initial density field that exceed a critical threshold
• Provides a simple analytical expression for the halo mass function, which has been widely used in cosmological studies

Sheth-Tormen formalism

• An extension of the Press-Schechter formalism that accounts for the ellipsoidal collapse of density perturbations, rather than the spherical collapse assumed in the original model
• Results in a better agreement with the halo mass functions derived from N-body simulations, particularly at the high-mass end
• Incorporates two additional parameters that describe the shape and normalization of the mass function

Substructure within halos

Subhalos and satellite galaxies

• Dark matter halos contain smaller, self-bound structures known as subhalos, which can host satellite galaxies
• Subhalos are remnants of smaller halos that have been accreted by larger halos during the hierarchical formation of structure in the universe
• The abundance and distribution of subhalos within a host halo can provide insights into the assembly history of the halo and the properties of the dark matter particles

Tidal stripping and disruption

• As subhalos orbit within their host halo, they experience tidal forces that can strip away their outer layers of dark matter
• Tidal stripping can lead to the formation of tidal streams and the eventual disruption of subhalos, particularly in the central regions of the host halo
• The survival of subhalos and the properties of their associated satellite galaxies depend on the balance between tidal stripping and the gravitational binding energy of the subhalo

Observational evidence for dark matter halos

Rotation curves of galaxies

• The flat rotation curves of spiral galaxies at large radii provide strong evidence for the presence of dark matter halos
• Unlike the expected Keplerian decline ($v \propto r^{-1/2}$), the rotation velocities of galaxies remain nearly constant far beyond the visible extent of the galactic disk
• This behavior can be explained by the presence of an extended dark matter halo that dominates the gravitational potential at large radii

Gravitational lensing

• The gravitational bending of light by massive objects, such as galaxies and clusters, can reveal the presence of dark matter halos
• Strong lensing, which produces multiple images of background sources, can constrain the total mass distribution within the lens, including the dark matter component
• Weak lensing, which induces small distortions in the shapes of background galaxies, can be used to map the large-scale distribution of dark matter and measure the masses of halos

Velocity dispersion of galaxy clusters

• The motion of galaxies within clusters provides a measure of the gravitational potential well, which is dominated by dark matter
• The velocity dispersion of cluster members, as inferred from spectroscopic observations, can be used to estimate the total mass of the cluster, including its dark matter content
• The high velocity dispersions observed in clusters (typically $\sim 1000$ km/s) require the presence of a deep gravitational potential well, consistent with the existence of massive dark matter halos

Simulations of dark matter halo formation

N-body simulations

• Numerical simulations that follow the gravitational evolution of a large number of dark matter particles in an expanding universe
• Provide detailed predictions for the formation and properties of dark matter halos, including their density profiles, shapes, and substructure
• Have played a crucial role in understanding the hierarchical assembly of halos and the development of the cosmic web

Cosmological hydrodynamical simulations

• Simulations that include both dark matter and baryonic physics, such as gas dynamics, star formation, and feedback processes
• Allow for a more realistic modeling of the interplay between dark matter and baryons in the formation and evolution of galaxies
• Can reproduce a wide range of observed galaxy properties, such as stellar masses, sizes, and morphologies, and provide insights into the impact of baryonic physics on the distribution of dark matter

Interplay between dark matter and baryons

Adiabatic contraction

• The process by which the dissipative cooling and condensation of baryons in the center of a dark matter halo leads to a steepening of the dark matter density profile
• As baryons cool and sink to the center of the halo, they deepen the gravitational potential well, causing the dark matter to respond by becoming more concentrated
• Adiabatic contraction can lead to the formation of a dense central cusp in the dark matter distribution, which may be in tension with observations of some dwarf galaxies

Feedback processes

• The injection of energy and momentum into the interstellar and intergalactic medium by astrophysical sources, such as supernovae, stellar winds, and active galactic nuclei (AGN)
• Feedback can heat and expel gas from galaxies, regulating star formation and preventing the overcooling of baryons in the centers of halos
• The redistribution of baryons by feedback processes can also alter the distribution of dark matter, potentially leading to the formation of cores in the dark matter density profile

Impact on galaxy properties

Morphology and size

• The properties of the dark matter halo, such as its mass and concentration, can influence the morphology and size of the galaxy that forms within it
• Galaxies that reside in more massive and concentrated halos tend to be more spheroidal and compact, while those in less massive and more extended halos are more likely to have disk-like morphologies
• The ratio of the galaxy's stellar mass to its halo mass, known as the stellar-to-halo mass ratio (SHMR), varies with halo mass and plays a key role in determining the efficiency of star formation and the overall structure of the galaxy

Star formation history

• The assembly history of the dark matter halo can shape the star formation history of the galaxy that forms within it
• Halos that experience a higher rate of mergers and accretion events may undergo more frequent bursts of star formation, while those with a more quiescent history may exhibit a more gradual and steady star formation rate
• The availability of cold gas for star formation is regulated by the depth of the gravitational potential well, which is determined by the mass and concentration of the dark matter halo

Chemical enrichment

• The chemical enrichment of galaxies, as traced by the abundance of heavy elements in stars and gas, is influenced by the properties of the dark matter halo
• The efficiency of metal retention within a galaxy depends on the depth of the gravitational potential well, with more massive halos being able to retain a larger fraction of the metals produced by stellar nucleosynthesis
• The distribution of metals within a galaxy may also be affected by the interplay between the dark matter halo and baryonic processes, such as gas inflows, outflows, and mixing

Alternative theories to dark matter halos

Modified Newtonian dynamics (MOND)

• A theory that proposes a modification to Newton's laws of gravity at low accelerations, rather than invoking dark matter to explain the observed dynamics of galaxies
• MOND introduces a characteristic acceleration scale below which the gravitational force law transitions from the standard Newtonian form to a regime where the force is proportional to the square root of the acceleration
• While successful in explaining some observational phenomena, such as the Tully-Fisher relation, MOND faces challenges in accounting for the full range of evidence for dark matter, particularly on the scales of galaxy clusters and the large-scale structure of the universe

Scalar field dark matter (SFDM)

• A class of alternative dark matter models in which the dark matter is composed of ultra-light scalar particles, such as axions or fuzzy dark matter
• In SFDM models, the dark matter behaves as a coherent, wave-like field on galactic scales, leading to distinct predictions for the structure and dynamics of galaxies
• One key feature of SFDM is the formation of solitonic cores in the centers of halos, which can potentially resolve the cusp-core problem and other small-scale discrepancies between observations and the predictions of cold dark matter models
• However, SFDM models also face challenges, such as explaining the observed abundance and properties of dwarf galaxies and the large-scale clustering of galaxies