The analysis of the hydrogen broad Balmer line ratios: possible implications to the physical properties of the BLR of AGN

We analyze the ratios of the broad hydrogen Balmer emission lines (from H\alpha to H\epsilon) in the context of estimating the physical conditions in the broad line region (BLR) of active galactic nuclei (AGN). The Balmer emission lines are obtained in three ways: i) using photoionization models obtained by a spectral synthesis code CLOUDY; ii) calculated using the recombination theory for hydrogenic ions; iii) measured from the sample of observed spectra taken from the Sloan Digital Sky Survey database. We investigate the Balmer line ratios in the frame of the so called Boltzmann-plot (BP), analyzing 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 is in that way different from the Balmer decrement. We found that for a certain range of thermodynamic parameters, there are objects that follow the BP. These AGN may have a BLR consisting of mostly high density plasma.