  We estimate the effects on the decay constants of charmonium and on heavy
meson masses due to the charm quark in the sea. Our goal is to understand
whether for these quantities $N_f=2+1$ lattice QCD simulations provide results
that can be compared with experiments or whether $N_f=2+1+1$ QCD including the
charm quark in the sea needs to be simulated. We consider two theories, $N_f=0$
QCD and QCD with $N_f=2$ charm quarks in the sea. The charm sea effects (due to
two charm quarks) are estimated comparing the results obtained in these two
theories, after matching them and taking the continuum limit. The absence of
light quarks allows us to simulate the $N_f=2$ theory at lattice spacings down
to $0.023$ fm that are crucial for reliable continuum extrapolations. We find
that sea charm quark effects are below $1\%$ for the decay constants of
charmonium. Our results show that decoupling of charm works well up to energies
of about $500$ MeV. We also compute the derivatives of the decay constants and
meson masses with respect to the charm mass. For these quantities we again do
not see a significant dynamical charm quark effect, albeit with a lower
precision. For mesons made of a charm quark and a heavy antiquark, whose mass
is twice that of the charm quark, sea effects are only about $0.1\%$ in the
ratio of vector to pseudoscalar masses.
