  We perform a detailed X-ray study of the filaments surrounding the brightest
cluster galaxies in a sample of nearby galaxy clusters using deep Chandra
observations, namely the Perseus, Centaurus and Virgo clusters, and Abell 1795.
We compare the X-ray properties and spectra of the filaments in all of these
systems, and find that their Chandra X-ray spectra are all broadly consistent
with an absorbed two temperature thermal model, with temperature components at
0.75 and 1.7 keV. We find that it is also possible to model the Chandra ACIS
filament spectra with a charge exchange model provided a thermal component is
also present, and the abundance of oxygen is suppressed relative to the
abundance of Fe. In this model, charge exchange provides the dominant
contribution to the spectrum in the 0.5-1.0 keV band. However, when we study
the high spectral resolution RGS spectrum of the filamentary plume seen in
X-rays in Centaurus, the opposite appears to be the case. The properties of the
filaments in our sample of clusters are also compared to the X-ray tails of
galaxies in the Coma cluster and Abell 3627. In the Perseus cluster, we search
for signs of absorption by a prominent region of molecular gas in the
filamentary structure around NGC 1275. We do find a decrement in the X-ray
spectrum below 2 keV, indicative of absorption. However the spectral shape is
inconsistent with this decrement being caused by simply adding an additional
absorbing component. We find that the spectrum can be well fit (with physically
sensible parameters) with a model that includes both absorption by molecular
gas and X-ray emission from the filament, which partially counteracts the
absorption.
