Blue Loops of Intermediate Mass Stars and CNO Bicycle

The effects of the CNO cycles on the formation of the blue loop are investigated. By using two ways to treat the CNO cycles,it is found that models adopting the CN and NO bicycles develop extensive blue loops while those only considering the CN cycle do not. Taking advantage of this unique opportunity,the properties of the CN and CNO models are compared in order to explore the triggering of the blue loop. The physical conditions in both stellar core and stellar envelope are investigated, and it is found that the abundance discontinuity on the chemical profile is essential factor to cause the stellar luminosity increasing. As soon as the upper edge of the H-burning shell touches the abundance discontinuity, new H-abundant material adds into the shell source and the energy production rate begins to increase. On the other hand, it is also found that the star expands when the effective temperature decreases, or the effective temperature increases when the star contracts. In a convection-dominated envelope, extra heating from its base will leads to more developed connective motion, decrease of the effective temperature, and the star evolves up along the RGB. However in a radiation-dominated envelope, the increase of the luminosity requires the temperature increasing to enlarge the heat conductivity, and the star develops a blue loop. We have defined a parameter η to measure the fraction of convection zone in the total envelope mass, and found the critical value to determine whether a star develops a blue loop is between 0.3 and 0.45. According to the new theory, overshooting from the connective core hinders the formation of the blue loop by displacing the abundance discontinuity farther from the H-burning shell, while the opacity enhancement of the OPAL over the LAOL leads to stronger development of convection in the stellar envelope and makes the blue loop more difficult to occur.