  The distributions and abundances of molecules in protoplanetary disks are
powerful tracers of the physical and chemical disk structures. The abundance
ratios of HCN and its isomer HNC are known to be sensitive to gas temperature.
Their line ratios might therefore offer a unique opportunity to probe the
properties of the emitting gas. Using the 2D thermochemical code DALI, we ran a
set of disk models accounting for different stellar and disk properties, with
an updated chemical network for the nitrogen chemistry. These modeling results
were then compared with observations, including new ALMA observations of HNC
$J=3-2$ for the TW Hya disk and HNC $J=1-0$ for 29 disks in Lupus. Similar to
CN, HCN and HNC have brighter line emission in models with larger disk flaring
angles and higher UV fluxes. HNC and HCN are predicted to be abundant in the
warm surface layer and outer midplane region, which results in ring-shaped
emission patterns. However, the precise emitting regions and emission
morphology depend on the probed transition, as well as on other parameters such
as C and O abundances. The modeled HNC-to-HCN line intensity ratio increases
from $<0.1$ in the inner disk to up to 0.8 in the outer disk regions, which can
be explained by efficient HNC destruction at high temperatures. Disk-integrated
HNC line fluxes from current scarce observations and its radial distribution in
the TW Hya disk are broadly consistent with our model predictions. The
HNC-to-HCN flux ratio robustly increases with radius (decreasing temperature),
but its use as a chemical thermometer in disks is affected by other factors,
including UV flux and C and O abundances. High-spatial resolution ALMA disk
observations of HNC and HCN that can locate the emitting layers would have the
great potential to constrain both the disk thermal and UV radiation structures,
and also to verify our understanding of the nitrogen chemistry.
