Fig. 4.
Photoelectric heating rates as a function of hydrogen number density: (a) graphite and (b) silicate. The solid lines are the W+06 model and the dotted lines are the WD01 model. The assumed grain size distribution is the so-called MRN distribution (Mathis et al., 1977). Other assumed quantities are noted in the panels as the gas temperature T,4 = T/104 K, the radiation intensity JL,-21 = JL/10-21 erg s-1 cm-2 Hz-1 sr-1, the spectral index of the radiation field p, and the dust-to-gas mass ratio D,-4 = D/10-4. The dashed lines are the HI photoionization heating rate and the dot-dashed lines are the HeII photoionization heating rate assuming ionization equilibrium. We also show the redshift at which the number density on the horizontal axis corresponds to the mean density of the Universe.