  Here we study the rapid X-ray variability (using XMM-Newton observations) of
three neutron-star low-mass X-ray binaries (1RXS J180408.9-342058, EXO
1745-248, and IGR J18245-2452) during their recently proposed very hard
spectral state (Parikh et al. 2017). All our systems exhibit a strong to very
strong noise component in their power density spectra (rms amplitudes ranging
from 34% to 102%) with very low characteristic frequencies (as low as 0.01 Hz).
These properties are more extreme than what is commonly observed in the
canonical hard state of neutron-star low-mass X-ray binaries observed at X-ray
luminosities similar to those we observe from our sources. This suggests that
indeed the very hard state is a distinct spectral-timing state from the hard
state, although we argue that the variability behaviour of IGR J18245-2452 is
very extreme and possibly this source was in a very unusual state. We also
compare our results with the rapid X-ray variability of the accreting
millisecond X-ray pulsars IGR J00291+5934 and Swift J0911.9-6452 (also using
XMM-Newton data) for which previously similar variability phenomena were
observed. Although their energy spectra (as observed using the Swift X-ray
telescope) were not necessarily as hard (i.e., for Swift J0911.9-6452) as for
our other three sources, we conclude that likely both sources were also in very
similar state during their XMM-Newton observations. This suggest that different
sources that are found in this new state might exhibit different spectral
hardness and one has to study both the spectral as well as rapid variability to
identify this unusual state.
