The cut-off radius and the scale length induced by the dark matter halo

In order to include Freman's disk in the sequence of virial equilibrium configurations, which a spheroidal bright component may trace out by contracting itself inside a similar spheroidal dark halo, the transition between its configuration at tidal radius to the disk is taken into account. The link between these two configurations is found under the physical conditions that: i) the angular momentum amount is conserved, ii) the rotational velocity of Freeman's truncated mass distribution is constant. An application to the Galaxy is considered by assuming the mass density distributions, either of the dark halo or of the luminous component at Clausius' virial minimum, are both power laws of different exponents.