Abstract. Based on the results of the blue loop formation for models of solar-like metallicity, we have explored the blue loop evolution of metal-poor stars. Three series of models with a wide range of metallicity and the initial helium abundance were calculated. An important parameter, η c , defined as the envelope convection mass divided by the total envelope mass at the bottom of the RGB, was introduced as a criterion to determine the formation of the blue loop. We have found that the low-Z models will develop extensive blue loops when η c is lower than a critical value η crit . The physical explanation for this result could be as follows. Lower Z reduces the envelope opacity and leads to a hotter stellar envelope and a bluer RGB. Thus the model will have a smaller η a at the top and an even smaller η c at the bottom of the RGB. When η c is lower than the critical value η crit , the envelope is radiation-dominated. Under this condition and the constraint of the virial theorem, the response of the star to the increase of the stellar luminosity is to contract to increase the thermal conductivity coefficient in the stellar envelope and to form a blue loop. Compared with the high-Z models, we have confirmed that the development of convection in the stellar envelope is a crucial factor to determine the formation of the blue loop, but the low-Z models reach low η c values in a different way from the high-Z models, in which the modulation of the nuclear reaction rates by higher 14 N abundance in the H-burning shell is responsible for the stars to get small η c values. It has been found that η crit depends not only on the stellar mass, but also on metallicity and the initial helium abundance. Our numerical results show that η crit decreases with Z while slowly increases with Y.

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