What Is The Potential Impact Of A Modified Navarro-Frenk-White Density Profile On The Predicted Galactic Rotation Curves In The Context Of The Latest Planck Cosmological Parameters, Assuming A Warm Dark Matter Component With A Thermal Relic Mass Of 1 KeV And A Velocity Dispersion Of 10^-6 C?

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The potential impact of a modified Navarro-Frenk-White (NFW) density profile, incorporating a warm dark matter (WDM) component with a thermal relic mass of 1 keV and a velocity dispersion of 10−6c{10^{-6}c}, on galactic rotation curves can be analyzed as follows:

  1. Standard NFW Profile and Rotation Curves:

    • The standard NFW profile predicts a density distribution ρ(r)∝r−1(1+r)−2{\rho(r) \propto r^{-1}(1 + r)^{-2}}, leading to a rotation velocity that rises as v(r)∝r{v(r) \propto \sqrt{r}} near the center.

  2. Modified NFW with Core:

    • A modified NFW profile, influenced by WDM, introduces a core where the density becomes approximately constant at small radii. This results in a mass distribution M(r)∝r3{M(r) \propto r^3} within the core radius, leading to a steeper rise in rotation velocity, v(r)∝r{v(r) \propto r}.

  3. Impact on Rotation Curves:

    • Observations often show a more gradual rise in rotation velocities than predicted by the standard NFW profile, suggesting the presence of a core. The modified NFW with a core aligns better with these observations by reducing the central density and thus the steepness of the velocity rise.

  4. Role of WDM Parameters:

    • The 1 keV WDM mass and 10−6c{10^{-6}c} velocity dispersion indicate a scenario where free-streaming suppresses small-scale structure, naturally leading to cored profiles. However, the low velocity dispersion might suggest a less pronounced core, potentially reducing the impact on rotation curves.

  5. Conclusion:

    • The modified NFW profile with a core, under the given WDM parameters, would predict rotation curves that better match observed data, addressing the cusp-core problem. The specific velocity dispersion might influence the core's size and impact, but overall, the use of WDM parameters supports a more observationally consistent rotation curve shape.