Astron. Astrophys. 362, L17-L20 (2000)

3. Central star temperature

3.1. Zanstra temperature

The Zanstra temperature requires only a knowledge of the stellar flux density or magnitude and the H flux. The extinction plays only a minor role because these radiation fields are at almost the same wavelength. A value of log H=-11.66 and =1.23 (see Pottasch et al., 2001, hereafter PBF, for a discussion of these quantities). The H Zanstra temperature then becomes T_Z(H)=680 000 K and the helium Zanstra temperature T_Z(HeII)=480 000 K. The difference between these two temperatures occurs in high temperature stars because some photons which doubly ionize helium can ionize hydrogen as well, sometimes twice. It is expected that the actual temperature lies between these values. The models of ST predict this behaviour, and show that probably the true value lies closer to the value given by T_Z=500 000 K. This value is a lower limit.

3.2. Energy balance temperature

The underlying idea of this method (also called the Stoy method) is that the ratio of the sum of the collisionally excited line intensities to the intensity of a hydrogen recombination line reflects the average energy liberated per photoionization, which is a function of the stellar temperature. The method is attractive because it does not require any observation of the central star, but only of the nebular spectrum. In addition there is only a small dependence on the optical thickness of the nebula.

All the collisionally excited lines must be included to obtain the correct temperature. As ST have pointed out, there are three potentially important lines which cannot be measured with present techniques. These are Ly, OV 1215 A, and OVI 1034 A. The intensity of these lines must be estimated.

The ratio of the measured collisional excited line intensities to H is =105 (PBF). This includes the NeV line at 3426 A (Rowlands et al., 1994), which isn't listed by PBF, but is reasonably strong: about 2.9 H. The OV and OVI line intensities can be found by using estimates of the abundances of the appropriate ions from the same reference. The intensities of these lines turns out to be comparatively small, with about unity. The Ly line is important however. It's strength may be estimated as follows. First the amount of neutral hydrogen can be found from

The values of O⁰ and O⁺ may be found in PBF and is

Thus

The ratio of the collisional Lyman to H is given by

where the values of the electron density appearing in both the top and bottom of the equation cancel out, (H) is the effective recombination coefficient and C₁₂ is the collision excitation rate. Values of the collisional excitation rate are listed by Drake (1983) and are a strong function of the electron temperature. This is given by PBF as 16 500  K or slightly higher over much of the nebula. C₁₂ then is cm³s^-1 and (H)= cm³s^-1. The ratio of collisionally excited Ly to H is therefore 28.4. The excitation of the higher Lyman lines should be added to this. Drake gives the collisional excitation rate of Ly as 10% of Ly; we therefore add 10% to the above ratio and ignore the higher Lyman lines. The total ratio of the collisionally excited l s to H is approximately 140.

The predicted has been discussed by Preite-Martinez and Pottasch (1983). The ratio depends not only on the stellar temperature, but also on the model atmosphere used, the abundance of the helium ions (especially doubly ionized helium) and the optical depth in the hydrogen and helium Lyman continua. We shall assume here that the star radiates as a blackbody, which is to be expected for such a hot star. The helium abundances are those appropriate to NGC 6537: He⁺/H=0.062 and He/H=0.087 and are taken from PBF. The electron temperature is the same as above, but is not a critical parameter. Three cases may be distinguished. In Case I the nebula is optically thin to ionizing radiation in H, He⁰ and He⁺. In Case II the nebula is optically thick in He⁺ and thin in the other continua. In Case III the nebula is optically thick for all ionizing continua of H and He. Case I is not realistic for NGC 6537 and we will ignore it and concentrate on the two other cases.

The results are shown in Table 1. The observed value of indicates a temperature of about 370 000 K if Case II is applicable, and about 450 000 K in Case III. This confirms that the temperature of the star is very hot, and considering the possible sources of error, it is consistent with the Zanstra temperature found in the previous section.

Table 1. The ratio for hot blackbodies

3.3. The ionization temperature

As a star becomes hotter it produces more highly charged ionization states. This is the basis for computing an ionization temperature. In fact, this is the only temperature which exists in the literature for NGC 6537. A recent computation of the ionization temperature based on the observed Si⁺⁶ line is 156 000 K (Casassus et al., 2000).

It is not clear how reliable such an estimate of the temperature is. ST(1986) argue quite convincingly that it is not reliable and will only give a lower limit to the temperature. This is based of a series of models made of nebulae with central star temperatures from 40 000 K to 500 000 K. The ratio of the abundance of two highly charged ions (in this case Ne⁺⁵/ Ne⁺⁴) was plotted against the central star temperature. As the stellar temperature increases so does this ratio, at least for temperatures below 150 000 K. Above this temperature the increase of this ratio levels off and may even decrease above 250 000 K. ST say `models for high excitation nebulae seem to have always been built with the lowest effective temperature compatible with the observations'. That this may also be true in the case of Casassus et al, appears from the fact that at a temperature of 156 000 K the emitting star should have m_v=19.5. A star of this magnitude would have easily been seen. Therefore it seems that the ionization temperature does not give a clear indication of the stellar temperature in this case.

© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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