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The required density profile $\rho_{DM}(r)$ of the dark matter halo is often modeled using the Navarro-Frenk-White (NFW) profile-profile/), although local field perturbations suggest a $\rho \propto r^{-2}$ dependence at the very edge of the observable boundary, possibly related to gravitational drag from intergalactic filaments [2].
The relationship between the maximum rotational velocity, $v_{max}$, and the total visible luminosity, $L$, known as the Tully-Fisher relation (or Baryonic Tully-Fisher relation for spirals)…