  Planet-forming disks of gas and dust around young stars contain polycyclic
aromatic hydrocarbons (PAHs). We aim to characterize how the charge state of
PAHs can be used as a probe of flows of gas through protoplanetary gaps. In
this context, our goal is to understand the PAH spectra of four transitional
disks. In addition, we want to explain the observed correlation between PAH
ionization (traced by the 6.2/11.3 feature ratio) and the disk mass (traced by
the 1.3 mm luminosity). We implement a model to calculate the charge state of
PAHs in the radiative transfer code MCMax. The emission spectra and ionization
balance are calculated. A benchmark modeling grid is presented that shows how
PAH ionization and luminosity behave as a function of star and disk properties.
The PAH ionization is most sensitive to ultraviolet (UV) radiation and the
electron density. In optically thick disks, where the UV field is low and the
electron density is high, PAHs are predominantly neutral. Ionized PAHs trace
low-density optically thin disk regions where the UV field is high and the
electron density is low. Such regions are characteristic of gas flows through
the gaps of transitional disks. We demonstrate that fitting the PAH spectra of
four transitional disks requires a contribution of ionized PAHs in gas flows
through the gap. The PAH spectra of transitional disks can be understood as
superpositions of neutral and ionized PAHs. For HD97048, neutral PAHs in the
optically thick disk dominate the spectrum. In the cases of HD169142, HD135344B
and Oph IRS 48, small amounts of ionized PAHs located in the gas flows through
the gap are strong contributors to the total PAH luminosity. The observed trend
between the disk mass and PAH ionization may imply that lower-mass disks have
larger gaps. Ionized PAHs in gas flows through these gaps contribute strongly
to their spectra.
