NGC 6543: Zanstra Temperature of The Cat's Eye

The temperature of central stars of planetary nebulae is an essential parameter for studying the star evolution, in particular through the HR diagram. H photometry of NGC 6543 planetary nebula is obtained in order to determine the Zanstra temperature of its central star. Under the assumptions that the star radiates approximately as a blackbody, and that the nebula is optically thick for the ionizing radiation, the ratio of the integrated narrow band H flux for the star and the nebula provides a temperature estimate. In the present study, the complex structure of the core of the nebula is not resolved and only a lower temperature limit of its central star (T 19000K) is possible to obtain. The errors and the observational limitations are carefully examined.

1. Introduction

NGC 6543 is a large planetary nebula with a strikingly complex, symmetric envelope, and a bright, visible central star. Its favourable position, almost at the north pole of the ecliptic, have made it an obvious candidate for a target to be observed with the 10-inch Great Ohio Telescope (GOT). The present study of this PN involves the Zanstra method (Zanstra, 1931) of determinig the effective temperature of the central star. Providing that the star radiates approximatelly as blackbodies, and that the nebula is optically thick, this method can be applied if two quantities are known: first, the flux of the stellar continuum; secondly, the amount of ionizing photons (lambda > 912 Å), as deduced from the total nebular flux at H. For the nucleus of NGC 6543, the Zanstra method determined temperatures from 39,000 K (Pottasch et al. 1978) to 43,000 K (Castor et al. 1981) while theoretical expectations based on evolutionary calculations (Vanbeveren, 1980) predict a temperature of the order of 90,000 K. Bianchi et al. (1986) fit the observed flux by a Planck function with a temperature 80,000 K, while recent spectophotometry carried out by Hyung et al. (2000) suggests a value of around 50,000 K. Clearly the accuracy of this method depends on how well the model (black body approximation) represents reality. Also, if the nebula is not completely optically thick to the Lyman photons, then only a lower limit for T can be estimated. The purpose of this work is to consider the chalenge of the observational determination of the Zanstra temperature of the Cat's Eye in the context of the theoretical and instrumental dificulties imposed by the method itself and the technical performances of the telescope.

2. Observations

Multiple exposures (2 x 600s and 1 x 300s) totaling 1500s were obtained, yielding a signal-to-noise ratio of 170(90) per pixel, at the center of the nebula (at the outskirts of the nebula, respectively). The CCD pixels were not saturated. Observations were performed at an airmass of about 1.12. Multiple dark frames corresponding to each exposure time were acquired during the observation night. Dawn and twilight sky frames were obtained with 60s exposure each; both sets of flats give a good signal, and they are all used in the reduction procces. A number of 11 'Zero-length' (0.11s) exposures, or 'bias-frames', were obtained the very next day; in order to account for a possible temperature dependence of the intrinsic bias pattern of the CCD, the detector was cooled down at -15°C, the temperature at which all data were observed in the previous night.

The H emission is usually contaminated by the [NII] 6548, 6583 doublet, characterized by a 3:1 line intensity ratio, as given by the corresponding Einstein A coefficients. Our narrow H filter includes only marginaly this emission, corresponding to a transmission coefficient 30%. Specifically for NGC 6543 nebula, the ratio of integrated [NII] and H line fluxes ([NII]/H) is 0.13 for the rings and 0.16 in the core. The effect of contamination is therefore much less than 5%, and is ignored in this paper.

3. Reductions & Data Analysis

Figure 1.a

Figure 1.b

Correction for extinction and absolute flux calibration are not necessary as only flux ratios in the same band-pass are used, and it is assumed that the extinction does not occur in the nebula itself. Special care is taken with the calculation of realistic uncertainties in the flux measurements. An 'error' image, created by combining quadratically the readnoise and the object-frame noise, is used to derive the total uncertainty associated with the stellar and nebular flux.

It is clear from the presented images that the central star is seriously affected by the nebula and it cannnot be measured. The highly symmetric shape of NGC 6543 is preserved, but the complex, peculiar structure consisting of two pairs of bipolar lobes along different axes, which is present in the Balick (1987) H picture, is barely noticeable in the GOT image. Its amorphous look is mostly due to the poor seeing conditions, which do not allow to distinguish features smaller than 5" (or 7 pixels). This factor should be considered if future observations of this type are undertaken.

The radial profile of the nebula (Figure 2., upper left panel) does show some inner structure but nothing resembling the point spread function of a star. Although the star itself cannot be identified and measured, an upper limit of its emitting flux can be estimated by artificially creating/adding a star in the center of the nebula. Consequently, a lower limit of its temperature can be obtained using the Zanstra method. In order to preserve the authenticity of the observed data, one of the two observed stars available in the field is 'pasted' into the spatial origin of the nebula: a rectangular box including (most of) the star is copied into a zero-count image in the place corresponding to the center of the nebula; this image is then added to the object frame. The process is repeated for different 'star' magnitudes. The radial profiles of the artificially created systems consisting of the nebula and the added 'central' star of different brightness are displayed in Figure 2. The cusp that creates at the center with increasing 'star' counts argues for a confident identification of its presence only when a 20 times brighter (in flux) than the original star is added.

Figure 2. Radial profile, or intensity (counts) versus radius (in pixels), for the nebula itself, and the nebula + simulated central star. Different magnitudes of the central star are considered. The middle right pannel illustrates a 2-sigma confidence level for a positive identification of the central star.

4. Method & Results

Among other methods for determining the effective temperature of the central star, the Zanstra method has the advantage that the number of ionizing photons from the star can be counted simply by measuring the nebular flux in a single hydrogen recombination line (e.g. H). With L_f being the luminosity of the star at a particular frequency (H), and the flux from the star approximately represented by the Planck function B(T):

The total number of ionizing photons emitted by the star is

If the absorption of ionizing quanta is considered complete, the total number of ionizations should balance the number of recaptures per unit time (case B recombination), and thus, the luminosity from the entire nebula in a particular emission line (H) can be expressed as:

where _B and ^eff_H are the recombination coefficients, with (e.g. Seaton, 1959).

Therefore, the first equation, rewriten in terms of H fluxes measured from the nebula and the star (with h₀ = 13.6 eV) is:

and the measurements thus determine the temperature T of the ionizing star. The right hand side of this equation is ploted as a function of temperature in Figure 3. Three previously published values of the temperature of the central star and the corresponding flux ratios are indicated. The temperature limit given by the flux ratio corresponding to the case where the artificially added star is 20 times amplified is 19000K (f_star/f_nebula = 0.165 ± 0.01). If the H flux ratio is uncertain by a factor of 2, i.e. the uncertainty interval of identifying an artificial star at the center of the nebula, the temperature is still accurate to within 25%.

Figure 3. Plot of the H flux ratio (star/nebula) as a function of temperature. The calculated flux ratios corresponding to different results of the simulation are recorded. Published values of the temperature of the central star are also indicated. A log-log version of this plot can be found here.

5. Discussion

Despite the problems with determining accurate stellar temperatures, the present data can be definitely used to advance the state of our knowledge of planetary nebulae and the relationship with their nuclei. Similar studies of planetary nebulae, and especially photometry of their central stars should be interesting to perform with this kind of equipment, particularly for objects in which the proximity of the bright inner rims to the central PN nucleus is comparable with the available resolution element.

Acknowledgements

References