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.