3. Application to observations
Fig. 1 summarizes the broadband ROSAT observations of X-ray emission from 48 WN and 17 WC stars (data from Pollock et al. 1995). Space does not permit a detailed explanation of this data; however, for multiple observations, the plotted points are averages. Measurements are shown only for stars that (a) are single or single-lined spectroscopic binaries and (b) have detections in contrast to upper limits. Errorbars are large, with only detections not atypical, but within the errors there are no systematic trends between and or .
Using a variance weighted averaging scheme, the ROSAT X-ray luminosity (0.2-2.4 keV) for WN types is erg/s and for WC types is erg/s. Pollock (1987) reported on EINSTEIN IPC broadband measurements (0.2-4.0 keV) of WR stars, with luminosities of erg/s for 16 single and single-lined binaries of low mass function and erg/s for 9 single stars. The EINSTEIN and ROSAT results are marginally consistent.
From Eq. (9), the main contributors to are the emission as characterized by and from the cooling function, and the wind opacity as expressed in and the relative abundances and . Note that for complete ionization in H-poor winds, the factor is insensitive to the wind properties.
For the X-ray emission, the value of is implicitly temperature dependent. For example, if the hot gas were typically of K, then most atoms would be completely ionized, hence the cooling would be from Bremsstrahlung losses and . It is difficult to assess the value of in WC stars relative to WN stars without knowing , but if we assume the ionization and excitation of the gas does not vary much between WN stars and WC stars (i.e., is similar between the two classes), and that is not exceedingly large (i.e., not much greater than K), then we may at least expect that , which will provide an upper limit to the ratio .
To estimate values of , we note that the primary result of O stars evolving to WN stars is to convert 4HHe leaving the metals essentially unchanged, implying . This is not entirely true, since C and O are underabundant but N is enhanced. However, the heavier atoms like S, Si, and Fe are not changed. For WC stars the nucleosynthesis is more complicated; however, the heavier ions of S, Si, and Fe are still not enhanced so that if the X-ray line spectrum is dominated by these metals, then . The influence of lighter ions such as O, Mg, and Ne, which are enhanced by factors of order 200, 10, and 3 in WC stars as compared to WN stars, will tend to increase . For the attentuation of X-rays by the cool wind, the He and metals have comparable influence on the opacity for the WN winds, but for WC winds, the effect of metals is that of He owing to the large C and O abundances.
The quantities needed to evaluate the ratio of to using the proportionality in Eq. (9) are listed in Table 1. We used van der Hucht et al. (1986) as a guide for determining typical WR wind abundances. In the WN case, the wind is assumed to be entirely HeII in the cool wind (although the trace metals are significant for the wind opacity). In the WC case, we assumed a wind with 62% HeII , 25% CIII , and 13% OIII . In both cases the hot gas is taken as completely ionized. With these abundances, we find , as compared to observed ratios of 2.9 from ROSAT and 4.1 from EINSTEIN . The derived upper limit gives the correct trend with , but exceeds the observed values by factors of 4-5. Better knowledge of the hot gas temperature would allow a more accurate assessment of . Lines from Mg and other enhanced metals can contribute significantly to the cooling function, so that a few is not unreasonable and would lower the predicted upper limit to near the observed values. Given the errors in both the data and our approximations, our simple scaling analysis appears capable of explaining the basic features of current X-ray data for single WR stars.
Table 1. Typical WN and WC star parameters.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999