Electron temperatures and densities of planetary nebulae determined from the nebular hydrogen recombination spectrum and temperature and density variations

A method is presented to derive electron temperatures and densities of planetary nebulae (PNe) simultaneously, using the observed hydrogen recombination spectrum, which includes continuum and line emission. By matching theoretical spectra to observed spectra around the Balmer jump at about 3646A, we determine electron temperatures and densities for 48 Galactic PNe. The electron temperatures based on this method are found to be systematically lower than those derived from [O III] 4959/4363 and [O III] (88\mu+52\mu)/4959 ratios. And the electron densities based on this method are found to be systematically higher than those derived from forbidden line ratios. These results suggest that temperature and density fluctuations are generally present within nebulae. In addition, He/H abundances of PNe are found to be positively correlated with the difference between T_e([O III]) and T_e(Bal), suggesting that He/H abundances might have been overestimated generally because of the possible existence of H-deficient knots.