A dark-matter halo is a gravitationally bound concentration of dark matter that hosts galaxies and larger structures.
The cusp--core problem is the tension between the central cusps of collisionless cold-dark-matter halo profiles and the approximately constant-density cores inferred for many dwarf and low-surface-brightness galaxies.
The spherical-collapse model predicts collapse when a linearly extrapolated smoothed overdensity exceeds the threshold in an Einstein-de Sitter universe.
The peak height of a halo of mass is , where is the variance of the linear density field smoothed on the corresponding mass scale.
The Press-Schechter formalism estimates the halo abundance from the Gaussian probability that a smoothed linear overdensity crosses the spherical-collapse threshold, with a factor of two enforcing total mass conservation.
The Press-Schechter differential abundance is
The peak-background split decomposes density fluctuations into long- and short-wavelength parts. A long overdensity lowers the effective local collapse threshold and thereby changes the abundance of halos.
Linear Lagrangian halo bias is the fractional response of halo abundance to a long-wavelength overdensity in the initial coordinates. For Press-Schechter halos, .
Mapping matter and halos from their initial positions adds the matter displacement contribution, giving . Mass conservation requires the mass-weighted consistency relation .
The halo model represents the matter density as a sum of normalized halo profiles and decomposes its power spectrum into same-halo and distinct-halo contributions.
At linear order in halo correlations,
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A dark matter halo is a theoretical structure that surrounds galaxies and galaxy clusters, comprising a significant portion of their total mass. Dark matter, which does not emit, absorb, or reflect light and is therefore invisible to electromagnetic observations, is inferred to exist based on its gravitational effects on visible matter.