2003ApJ...599..140P

Using a well-known method for laboratory plasma diagnostics, the Boltzmann plot, we discuss the physical properties in the broad-line regions (BLRs) of active galactic nuclei (AGNs). We apply the Boltzmann plot method to Balmer lines on a sample of 14 AGNs and find that it may indicate the existence of ``case B'' recombination or partial local thermodynamical equilibrium (PLTE). For the BLR of AGNs, where PLTE exists, we estimated the electron temperature and density of the BLRs. The estimated electron temperatures (T∼13,000-37,000 K) are in good agreement with previous estimates. The estimated electron densities depend on the opacity of the emitting plasma in the BLRs. They range from N_e∼10⁹cm^–3 for optically thick to N_e∼10¹⁴cm^–3 for optically thin emission plasma in the BLRs. The estimated electron temperature has been shown to be velocity-dependent, and it decreases for higher velocities. Although the alternative explanation to PLTE indicated by the Boltzmann plot may be considered (e.g., high intrinsic reddening), the method may give a quick estimate of physical conditions in the BLRs before applying the sophisticated methods.