The Blue Loops

The blue loops described in the HR diagram (Fig. 26.1) by stars in the range of 3-12 M0 allow the stars to spend a fraction of their He-burning lifetime as Cepheids. We can easily understand which effects favor or inhibit the blue loops by using an interesting result by Kippenhahn and Weigert [285]: The blue extension of the loops mainly depends on the potential of the core ®c ~ Mc/Rc. There is a critical value of the potential such that

^crit(M) increases with mass, being typically 0.83, 0.93 and 0.99 for 3, 5 and 7 M0, respectively. Without entering extensive discussions, the consistency of expression (26.11) can be understood in the following way. The core potential grows with the core mass like 0c ~ M^4. This means that any effect which increases the core mass and thus ®c also favors a redward evolution instead of a blue loop. (A red giant of a given mass has a very concentrated core, thus a high core potential, while a blue giant on the loops has a He core inflated by nuclear burning, thus a lower potential.) Thus, one has the following effects [363]:

- Core overshooting: it enlarges the core mass Mc; thus ®c and therefore overshooting reduce the size of the loops or may even suppress it.

- Rotation also reduces the blue loops because of the core extension due to internal mixing.

- Metallicity Z: in general a lower Z reduces the core size (since the opacity is lower, Vrad is also lower). This favors an extension of the blue loops.

- Mass loss by stellar winds, which is rather weak in the luminosity range of Cepheids, reduces the blue loops. The reason is that ®c remains the same, while ^crit(M) becomes smaller since the total mass M is smaller.

- A higher nuclear rate of 12C(a, y)16O increases the blue loops, because it requires a slightly lower T, which reduces the core mass.

- The overshooting below the convective envelopes in some cases may increase the extension of the blue loops, by slightly increasing the critical potential and decreasing the core mass.

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