  The rare radiative flavour changing top decays $t\to c\gamma$ and $t\to cg$
(and the even rarer $t\to u\gamma$ and $t\to ug$) have been processes of
interest for decades as they offer a key probe for studying top quark
properties. However an explicit analytical study of the branching ratios and
$CP$ asymmetries resulting from these loop level processes has thus far evaded
attention. In this work, we provide the formulation for the $CP$ asymmetry
resulting from the total kinetic contribution of the loop integrals and their
imaginary parts, as well as an updated numerical computation of the predicted
Standard Model (SM) branching fractions. These rare processes are suppressed in
the SM by the Glashow-Iliopoulos-Maiani (GIM) mechanism. However, the results
presented here can easily be exported for use in minimal extensions of the SM
including vector-like quarks or in Two-Higgs-Doublet models where radiative
fermionic decay processes can be enhanced relative to the SM by several orders
of magnitude. Such processes provide an experimentally clean signature for new
fundamental physics and can potentially be tested by current collider
experiments. These topical beyond the SM theories are an elegant means to
provide improved global fits to the latest results emerging from flavour
physics, CKM and precision electroweak measurements.
