  We derive two field theory models of interacting dark energy, one in which
dark energy is associated with the quintessence and another in which it is
associated with the tachyon. In both, instead of choosing arbitrarily the
potential of scalar fields, these are specified implicitly by imposing that the
dark energy fields must behave as the new agegraphic dark energy. The resulting
models are compared with the Pantheon supernovae sample, CMB distance
information from Planck 2015 data, baryonic acoustic oscillations (BAO) and
Hubble parameter data. For comparison, the noninteracting case and the $\Lambda
CDM$ model also are considered. By use of the $ AIC $ and $ BIC $ criteria, we
obtain strong evidence in favor of the two interacting models, and the coupling
constants are nonvanishing at more than $3\sigma$ confidence level.
