Core helium burning is the dominant source of energy of extreme horizontal branch stars , as the hydrogen envelope is too small to contribute to the nuclear energy output .
The evolution of each mass in the HR diagram occurs along vertical tracks that , when the core helium is consumed , evolve to higher T _ { eff } and then to the white dwarf stage .
The larger is the mass , the smaller is the T _ { eff } of the models , so that the zero age horizontal branch ( ZAHB ) is “ horizontal ” .
In this paper we show that , if the helium mass fraction ( Y ) of the envelope is larger than Y \sim 0.5 , the shape of the tracks changes completely : the hydrogen burning becomes efficient again also for very small envelope masses , thanks to the higher molecular weight and to the higher temperatures of the hydrogen shell .
The larger is Y , the smaller is the envelope mass that provides strong H–shell burning .
These tracks have a curled shape , are located at a T _ { eff } following the approximate relation T _ { eff } =8090+ 32900 \times Y , and become more luminous for larger envelope masses .
Consequently , the ZAHB of the very high helium models is “ vertical ” in the HR diagram .
Synthetic models based on these tracks nicely reproduce the location and shape of the “ blue hook ” in the globular cluster \omega Cen , best fit by a very high T _ { eff } ( bluer ) sequence with Y=0.80 and a cooler ( redder ) one with Y=0.65 .
Although these precise values of Y may depend on the color–T _ { eff } conversions , we know that the helium content of the progenitors of the blue hook stars can not be larger than Y \sim 0.38–0.40 , if they are descendants of the cluster blue main sequence .
Consequently , this interpretation implies that all these objects must in fact be progeny of the blue main sequence , but they have all suffered further deep mixing , that has largely and uniformly increased their surface helium abundance , during the red giant branch evolution .
A late helium flash can not be the cause of this deep mixing , as the models we propose have hydrogen rich envelopes much more massive than those required for a late flash .
We discuss different models of deep mixing proposed in the literature , and conclude that our interpretation of the blue hook can not be ruled out , but requires a much deeper investigation before it can be accepted .