  We evaluate the spin-$3/2 \to$ spin-$1/2$ electromagnetic transitions of the
doubly charmed baryons on 2+1 flavor, $32^3 \times 64$ PACS-CS lattices with a
pion mass of $156(9)$ MeV/c$^2$. A relativistic heavy quark action is employed
to minimize the associated systematic errors on charm-quark observables. We
extract the magnetic dipole, $M1$, and the electric quadrupole, $E2$,
transition form factors. In order to make a reliable estimate of the $M1$ form
factor, we carry out an analysis by including the effect of excited-state
contributions. We find that the $M1$ transition is dominant and light degrees
of freedom ($u/d$- or $s$-quark) play the leading role. $E2$ form factors, on
the other hand, are found to be negligibly small, which in turn, have minimal
effect on the helicity and transition amplitudes. We predict the decay widths
and lifetimes of $\Xi_{cc}^{\ast +,++}$ and $\Omega_{cc}^{\ast +}$ based on our
results. Finite size effects on these ensembles are expected to be around 1\%.
Differences in kinematical and dynamical factors with respect to the
$N\gamma\to\Delta$ transition are discussed and compared to non-lattice
determinations as well keeping possible systematic artifacts in mind. A
comparison to $\Omega_c \gamma \rightarrow \Omega_c^\ast$ transition and a
discussion on systematic errors related to the choice of heavy quark action are
also given. Results we present here are particularly suggestive for
experimental facilities such as LHCb, PANDA, Belle II and BESIII to search for
further states.
