What must be true about the density contributed by the dark component in outer galactic regions according to the flat rotation curve?

It must remain relatively constant, contrasting sharply with the light density which plummets.

The observation that orbital velocities remain constant or slightly increase far from the galactic center implies that the enclosed mass continues to increase steadily with radius, even long after the visible stellar disk ends. If velocity ($v$) is constant, then the mass enclosed within that radius ($M(R)$) must be proportional to the radius ($M(R) \propto R$). Since the luminous density drops dramatically near the edge of the disk, the only way for the total enclosed mass to continue increasing linearly with radius is if the mass density ($\rho = dM/dR$) contributed by the unseen component remains stable and relatively constant in these outer regions. This constant density profile contrasts sharply with the sharply declining density profile of visible stars and gas.