How much does the core structure of a three-phase contact line contribute to the line tension near a wetting transition?

We initially simplify a three-phase contact line to a 'primitive' star-shaped structure formed by three planar interfaces meeting at a common line of intersection, and calculate the line tension associated with this primitive picture. Next, we consider the well-known more refined picture of the contact line that includes a 'core structure' consisting of interface deviations away from the planar interface picture. The corresponding contact line properties were calculated earlier, within mean-field theory, using an interface displacement model or a more microscopic density-functional theory. The question we ask is to what extent the thermodynamic line tension of the contact line near a wetting phase transition can be attributed to the core structure. To answer it we compare our result for the line tension contribution associated with the primitive structure to the known line tension of the full structure (within mean-field theory). While our primitive structure calculation provides a surprisingly useful upper bound to the known line tension near a critical wetting transition, the nontrivial core structure of the contact line near first-order wetting is found to be responsible for an important difference between the known line tension and the upper bound provided by the primitive picture calculation. This accounts also for the discrepancy between the line tensions calculated by two different methods in an earlier mean-field density-functional model of a first-order wetting transition.