The analysis of the broad hydrogen Balmer line ratios: Possible implications for the physical properties of the broad line region of AGNs

Aims: We analyze the ratios of the broad hydrogen Balmer emission lines (from Hα to Hɛ) in the context of estimating the physical conditions in the broad line region (BLR) of active galactic nuclei (AGNs). Methods: Our measurements of the ratios of the Balmer emission lines are obtained in three ways: i) using photoionization models obtained with a spectral synthesis code CLOUDY; ii) applying the recombination theory for hydrogenic ions; iii) measuring the lines in observed spectra taken from the Sloan Digital Sky Survey database. We investigate the Balmer line ratios in the framework of the so-called Boltzmann plot (BP), analyzing the physical conditions of the emitting plasma for which we could use the BP method. The BP considers the ratio of Balmer lines normalized to the atomic data of the corresponding line transition, and in that way differs from the Balmer decrement. Results: We find that for a certain range of thermodynamic parameters, there are objects that follow the BP. These AGNs may have a BLR consisting of mostly high density plasma.