5 Discussion

Our analysis of the blue hook stars in $\omega$ Cen shows that these stars do indeed reach effective temperatures of more than 35 000 K (cf. Fig. 4 and Table 1), well beyond the hot end of the canonical EHB. In addition, most of them show at least solar helium abundances with the helium abundance increasing with effective temperature (cf. Fig. 4), in contrast to canonical EHB stars such as those studied in NGC 6752 by Moehler et al. (2000). We now discuss both of these results in more detail.

The coolest star in our sample (BC8117) at $T_{\rm eff} \approx 30~000$ K lies near the hot end of the canonical EHB and shows the same low helium abundance as the EHB stars in NGC 6752 (see Fig. 4). Most likely, BC 8117 is the descendant of an early hot flasher. All of the other stars in our sample have temperatures $\ga$35 000 K and, except for the low gravity star D10763, lie in the general vicinity of the track for a late hot flasher in Fig. 4. Although limited, our data suggest that the blue hook stars may be separated from the canonical EHB stars by a temperature gap from $\approx$31 000 K to $\approx$35 000 K. As discussed in Sect. 2, such a temperature gap is predicted by the flash-mixing scenario.

Figure 5: HB evolutionary tracks for 4 canonical stars near the hot end of the EHB and 4 late hot flashers from Brown et al. (2001). Each track is represented by a series of points separated by a time interval of $5 \times 10^6$ yr. The solid line is the canonical ZAHB. Note the temperature gap between the canonical and flash-mixed tracks.

The HB track for the early hot flasher in Fig. 4 passes through the temperature gap, thus raising the possibility that canonical EHB stars might populate this gap during their post-ZAHB evolution. To examine this possibility more closely, we plot in Fig. 5 the HB evolutionary tracks from Brown et al. (2001) for 4 canonical stars near the hot end of the EHB and 4 late hot flashers. The latter tracks span the range in RGB mass loss over which flash mixing occurs. Each track is represented by a series of points separated by a time interval of $5 \times 10^6$yr in order to illustrate where the evolution is slowest. Figure 5 shows that canonical EHB stars spend almost their entire HB lifetime at temperatures close to their ZAHB temperatures. While these stars evolve into the temperature gap near the end of the HB phase, they do so at a time when their evolution is very rapid. Thus one would not expect to find many evolved EHB stars within the temperature gap or along the part of the terminal-age HB (TAHB) that extends into the temperature gap in Fig. 4. We conclude that the flash-mixed stars should remain well separated in temperature from the canonical EHB stars also when HB evolution is taken into account.

Contrary to our original expectations, the atmospheres of the blue hook stars still show some hydrogen. This result may be understood in light of the recent calculations of Schlattl & Weiss (2002, priv. comm.), who found that a small amount of hydrogen survives the flash mixing. The observed atmospheric hydrogen abundance of the blue hook stars is, however, substantially greater than the predicted envelope hydrogen abundance ( $X \approx 10^{-4}$) in the models of Schlattl & Weiss after flash mixing. This apparent discrepancy could be readily explained by the outward diffusion of hydrogen into the atmospheres of the blue hook stars and the gravitational settling of helium. Such diffusive processes are believed to be responsible for the low helium abundances of the sdB stars and are estimated to operate on a time scale much shorter than the HB lifetime. The range in the hydrogen abundances of the blue hook stars might indicate that varying amounts of hydrogen survive flash mixing or that the efficiency of diffusion differs from star to star. In any case the high helium abundances observed in some of the blue hook stars would be difficult to understand if their atmospheres were not enriched in helium during the helium flash. The increase in the mean atmospheric helium abundance with increasing effective temperature is also consistent with flash mixing.

The presence of a hydrogen-rich surface layer would shift the evolutionary track for the late hot flasher in Fig. 4 towards cooler temperatures. This evolutionary track, taken from the blue hook sequences of Brown et al. (2001), has a helium/carbon-rich envelope with no hydrogen. In order to estimate the size of this temperature shift, we computed a series of ZAHB models in which hydrogen-rich layers with masses of 10^-7, 10^-6, 10^-5 and 10^-4 $M_{\odot }$ were added to the ZAHB model from the late hot flasher in Fig. 4. A hydrogen layer of 10^-4 $M_{\odot }$ corresponds to the case in which $\approx$10 percent of the envelope hydrogen survives flash mixing and in which all of this hydrogen then diffuses to the surface. This should be a firm upper limit to the mass of any hydrogen layer, given the results of Schlattl & Weiss (2002, priv. comm.) and the fact that any hydrogen present in the deeper layers of the envelope would not have sufficient time to diffuse to the surface during the HB phase. As expected, the ZAHB location of the late hot flasher in Fig. 4 shifts redward as the mass of the hydrogen layer increases and we see that the addition of a hydrogen layer of <10^-4 $M_{\odot }$ would actually improve the agreement between the predicted and observed temperatures of the blue hook stars while at the same time preserving the temperature gap between these stars and the canonical EHB stars.

A most intriguing puzzle is posed by D10763, which is the most helium-rich star in our sample: While it is among the faintest stars visually, its low surface gravity suggests a very high luminosity, which would put it to a distance of about 50 kpc for a mass of 0.5  $M_{\odot }$. Its heliocentric radial velocity of $+170\pm40$ km s^-1, however, suggests that it is a member of $\omega$ Cen. The spectrum also shows no evidence for features from a cool star (e.g., stronger Ca II K line or G band), which might influence the parameter determination from the Balmer lines. We have currently no explanation for this object.