Herschel 158$ \mu$m [CII] Observations of "CO-dark" Gas in the Perseus
  Giant Molecular Cloud
  We present observations of velocity-resolved [CII] 158 $\mu$m emission from
both a dense and a more diffuse photodissociation region (PDR) in the Perseus
giant molecular cloud (GMC) using the Heterodyne Instrument for the
Far-Infrared onboard the Herschel Space Telescope. We detect [CII] emission
from 80\% of the total positions, with a 95\% detection rate from the dense
boundary region. The integrated intensity of the [CII] emission remains
relatively constant across each boundary, despite the observed range in optical
extinction between 1 mag and 10 mag. This flat profile indicates a constant
heating and cooling rate within both regions observed. The integrated intensity
of [CII] emission is reasonably well correlated with the neutral hydrogen (HI)
column density, as well as total gas column density. This, in addition to the
80$'$ (7 pc) extent of the [CII] emission from cloud center, suggests that the
HI envelope plays a dominant role in explaining the [CII] emission emanating
from Perseus. We compare the [CII] and $^{12}$CO integrated intensities with
predictions from a 1-D, two-sided slab PDR model and show that a simple core
$+$ envelope, equilibrium model without an additional "CO-dark" H$_2$ component
can reproduce observations well. Additional observations are needed to
disentangle how much of the [CII] emission is associated with the "CO-dark"
H$_2$ gas, as well as constrain spatial variations of the dust-to-gas ratio
across Perseus.
