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 3646 Angstrom, we determine electron temperatures and densities for 48 Galactic PNe. The electron temperatures based on this method - hereafter T(e)(Bal) - are found to be systematically lower than those derived from [O III] lambda4959/lambda4363 and [O III] (88 mum + 52 mum)/lambda4959 ratios - hereafter T(e)([O III](na)) and T(e)([O III](fn)). The electron densities based on this method are found to be systematically higher than those derived from [O II] lambda3729/lambda3726, [S II] lambda6731/lambda6716, [Cl III] lambda5537/lambda5517, [ArIV] lambda4740/lambda4711 and [O III] 88 mum/52 mum ratios. These results suggest that temperature and density fluctuations are generally present within nebulae. The comparison of T(e)([O III](na)) and T(e)(Bal) suggests that the fractional mean-square temperature variation (t(2)) has a representative value of 0.031. A majority of temperatures derived from the T(e)([O III](fn)) ratio are found to be higher than those of T(e)([O III](na)), which is attributed to the existence of dense clumps in nebulae - those [O III] infrared fine-structure lines are suppressed by collisional de-excitation in the clumps. By comparing T(e)([O III](fn)), T(e)([O III](na)) and T(e)(Bal) and assuming a simple two-density-component model, we find that the filling factor of dense clumps has a representative value of 7 x 10(-5). The discrepancies between T(e)([O III](na)) and T(e)(Bal) are found to be anticorrelated with electron densities derived from various density indicators; high-density nebulae have the smallest temperature discrepancies. This suggests that temperature discrepancy is related to nebular evolution. In addition, He/H abundances of PNe are found to be positively correlated with the difference between T(e)([O III](na)) and T(e)(Bal), suggesting that He/H abundances might have been overestimated generally because of the possible existence of H-deficient knots. Electron temperatures and densities deduced from spectra around the Paschen jump regions at 8250 Angstrom are also obtained for four PNe: NGC 7027, NGC 6153, M 1-42 and NGC 7009. Electron densities derived from spectra around the Paschen jump regions are in good agreement with the corresponding values derived from spectra around the Balmer jump, whereas temperatures deduced from the spectra around the Paschen jump are found to be lower than the corresponding values derived from spectra around the Balmer jump for all the four cases. The reason remains unclear.