Probing the role of polycyclic aromatic hydrocarbons in the
  photoelectric heating within photodissociation regions
  We observationally investigate the relation between the photoelectric heating
efficiency in PDRs and the charge of PAHs, which are considered to play a key
role in photoelectric heating. Using PACS onboard Herschel, we observed six
PDRs spanning a wide range of FUV radiation fields (G_0=100-10^5). To measure
the photoelectric heating efficiency, we obtained the intensities of the main
cooling lines, i.e., the [OI]63um, 145um, and [CII]158um, as well as the FIR
continuum intensity. We used Spitzer/IRS spectroscopic mapping observations to
investigate the MIR PAH features in the same regions. We decomposed the MIR PAH
emission into that of neutral (PAH^0) and positively ionized (PAH^+) species to
derive the fraction of the positively charged PAHs, and compare it to the
photoelectric heating efficiency. The heating efficiency traced by
([OI]63um+[OI]145um+[CII]158um) / TIR, ranges between 0.1% and 0.9% in
different sources, and the fraction of PAH^+ relative to (PAH^0 + PAH^+) spans
from 0(+11)% to 87(+/-10)%. All positions with a high PAH^+ fraction show a low
heating efficiency, and all positions with a high heating efficiency have a low
PAH^+ fraction, supporting the scenario in which a positive grain charge
results in a decreased heating efficiency. Theoretical estimates of the
photoelectric heating efficiency show a stronger dependence on the charging
parameter gamma=G_0 T^{1/2}/n_e than the observed efficiency reported in this
study, and the discrepancy is significant at low gamma. The photoelectric
heating efficiency on PAHs, traced by ([OI]63um+[OI]145um+[CII]158um) /
(PAH+[OI]63um+[OI]145um+[CII]158um), shows a much better match between the
observations and the theoretical estimates. The good agreement of the
photoelectric heating efficiency on PAHs with a theoretical model indicates the
dominant contribution of PAHs to the photoelectric heating. (abridged for
arXiv)
