Design Criteria for the Radial Acceleration Relation in Kinetic Completions of RCD

Key Points

• The central aim is to outline the design criteria that kinetic completions must meet to accurately reproduce the radial acceleration relation with appropriate scaling and slope.
• Derived analytic conditions for kinetic completions of RCD.
• Analyzed asymptotic behavior at large X.
• Examined the relationship to deep-MOND slope and transition sharpness.
• Design criteria yield a radial acceleration relation with scale a_0, slope, and scatter.
• Identify connections between asymptotic behavior and deep-MOND slope.
• Provide a constructive framework for engineering functions beyond existing models.

Abstract