Generalized energy balance method for the determination of central star parameters and optical thickness of a planetary nebula |
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| Authors: | Yu F Malkov V V Golovatyj O V Rokach |
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| Institution: | (1) Crimean Astrophysical Observatory, Nauchny, Crimea, Ukraine;(2) Astronomical Observatory of Lviv University, Lviv, Ukraine |
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| Abstract: | 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. |
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