ALMA observations of the submillimetre hydrogen recombination line from the type 2 active nucleus of NGC 1068

Hydrogen recombination lines at the submillimetre band (submm-RLs) can serve as probes of ionized gas without dust extinction. One therefore expects to probe the broad line region (BLR) of an obscured (type 2) active galactic nucleus (AGN) with those lines. However, admitting the large uncertainty in the continuum level, here we report on the non-detection of both broad and narrow H26$\alpha$ emission line (rest frequency = 353.62 GHz) towards the prototypical type 2 AGN of NGC 1068 with the Atacama Large Millimeter/submillimeter Array (ALMA). We also investigate the nature of BLR clouds that can emit submm-RLs with model calculations. As a result, we suggest that clouds with an electron density ($N_e$) of $\sim$ 10$^9$ cm$^{-3}$ can mainly contribute to broad submm-RLs in terms of the line flux. On the other hand, line flux from other density clouds would be insignificant considering their too large or too small line optical depths. However, even for the case of $N_e \sim 10^9$ cm$^{-3}$ clouds, we also suggest that the expected line flux is extremely low, which is impractical to detect even with ALMA.