Continuum beyond the Lyman limit and effective temperatures of the nuclei of planetary nebulae

Using published data on Hß-,λ4471 Hel- and λ4686 Hell-line fluxes for planetary nebulae the energy distribution in their nuclei is calculated in the wavelength range 100–912 Å by supposing that 1) the spectrum inclination is the same in the regions of continuous absorption of Hl, Hel, and Hell atoms; and 2) discontinuities at 504 Å and 228 Å are present in the nuclei spectra. From 40 investigated nebulae, only for two nuclei the distribution in all three intervals 504–912 Å, 228–504 Å and λ ≦ 228 Å corresponds to one and the same temperature of black-body emission. In 24 cases the emission temperature is the same for the first and the second interval. The energy distribution in the wavelength range shorter than 228 Å corresponds systematically to very high temperatures T_* > 100,000 K. It is concluded that the emission temperature over the surface of nuclei is markedly inhomogeneous and/or the nuclei of planetary nebulae possess a hot corona.     

Generalized energy balance method for the determination of central star parameters and optical thickness of a planetary nebula

A method is proposed allowing a quick self-consistent determination of both the central star parameters (effective temperature, surface gravity, stellar massetc.) and the optical thickness of a planetary nebula (PN). The method is a generalization of the well-known energy balance method. The method has been calibrated and tested using a photoionization model grid computed for this purpose. The internal accuracy of the method is estimated as 0.038dex for the effective temperature of central star and 0.076dex for the surface gravity.The problem of determination of overall energy losses in the nebula required by any kind of energy balance method is considered thoroughly. Approximate expressions are obtained, relating the overall energy losses to the sum of intensities of collisionally excited lines in the optical and ultraviolet spectral ranges and to some other nebular parameters. It is shown that neglecting the energy losses caused by directly unobservable collisional excitation of neutral hydrogen and helium may underestimate the central star temperature by 0.2 or even 0.5dex. Generalized energy balance method is applied to a sample of 41 PN. Central star temperaturesT _GB found by this method show an agreement withHeII Zanstra temperaturesT _z (HeII) whereasT _z (HI) is always less thanT _GB or equal to it within the accuracy of the method. So, we confirm the explanation that the well-known Zanstra discrepancy is caused merely by low optical thickness of many PN in the Lyman continuum of hydrogen. The value ofT _z (HeII) found with modern model atmospheres can be used as good approximation toT _ef for central stars of overwhelming majority of PN whileT _z (HI) is usually close toT _ef for young nebulae only.