Galactic Dark-Matter Halo Profiles

Spherically averaged density profiles are indispensable compressed descriptions of galactic dark-matter halos, but profiles with superficially similar rotation curves need not have the same physical status. The Navarro–Frenk–White (NFW), Moore, and Einasto forms summarize collisionless cosmological simulations; Burkert and pseudo-isothermal laws are economical cored fits to galaxy kinematics; the generalized NFW/Zhao and Dehnen families interpolate between asymptotic slopes; and Hernquist and Jaffe models were devised primarily for stellar systems but provide useful finite-mass analytic potentials. Perfect-fluid dark matter (PFDM), scalar-field halos, and wave-dark-matter solitons instead introduce assumptions about the stressenergy or microscopic dynamics, and therefore cannot be interpreted as merely another choice of fitting function. Here we derive the principal density, mass, circular-speed, and slope relations; compare central and outer asymptotics; explain which fitted parameters carry physical information; and discuss the observational degeneracies that limit cusp–core inference. In a short final part, we address central black holes and emphasize that a galactic density law plus a Newtonian rotation curve does not uniquely determine a relativistic spacetime: the pressure components, equation of state, near-horizon response, and boundary conditions must also satisfy the Einstein equations. Our purpose is astrophysical model selection rather than an exhaustive review of black-hole phenomenology.