  Chimera states are firstly discovered in nonlocally coupled oscillator
systems. Such a nonlocal coupling arises typically as oscillators are coupled
via an external environment whose characteristic time scale $\tau$ is so small
(i.e., $\tau \rightarrow 0$) that it could be eliminated adiabatically.
Nevertheless, whether the chimera states still exist in the opposite situation
(i.e., $\tau \gg 1$) is unknown. Here, by coupling large populations of
Stuart-Landau oscillators to a diffusive environment, we demonstrate that
spiral wave chimeras do exist in this oscillator-environment coupling system
even when $\tau$ is very large. Various transitions such as from spiral wave
chimeras to spiral waves or unstable spiral wave chimeras as functions of the
system parameters are explored. A physical picture for explaining the formation
of spiral wave chimeras is also provided. The existence of spiral wave chimeras
is further confirmed in ensembles of FitzHugh-Nagumo oscillators with the
similar oscillator-environment coupling mechanism. Our results provide an
affirmative answer to the observation of spiral wave chimeras in populations of
oscillators mediated via a slowly changing environment and give important hints
to generate chimera patterns in both laboratory and realistic chemical or
biological systems.
