A Model of Deep Mixing in Globular Cluster Red Giants

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Abstract
A long-standing problem of large star-to-star variations in the surface abundances of C, N, O, Na, and Al that is observed among red giant stars in globular clusters is discussed in the light of the recent finding by Shetrone that 24Mg is reduced among the Al-enhanced stars. A new scenario of nucleosynthesis and element mixing is proposed, whereby the surface anomalies are explained as the consequence of the inward mixing of hydrogen followed by the outward mixing of nuclear products of hydrogen burning. If hydrogen is carried down into the helium core by some extra mixing mechanism, a hydrogen-burning shell flash is ignited. The flash forces the formation of a convective shell whose outer edge extends into hydrogen-rich layers, bringing in fresh hydrogen to fuel the flash further. During a flash, the temperature at the base of the flash-driven shell can become larger than the temperature in the hydrogen-burning shell during quiescent interflash evolution, and during the decay phase of the flash the nuclear products are dredged up by surface convection, which becomes deeper in mass than during the quiescent phases. The properties of shell flashes induced by the inward mixing of hydrogen are investigated by means of a semianalytical method to derive the conditions required for burning 24Mg and producing Al via proton captures. The mixing inward of hydrogen at an abundance by mass X 0.001 is enough to ignite shell flashes. The deeper hydrogen is mixed and the more massive the core, the stronger is the resultant shell flash and the larger are the temperatures in the flashing region. The burning of 24Mg in the flash convective zone demands temperatures T 8.5 × 107 K because of short duration of the flash. The necessary depth of hydrogen mixing can be as small as ~1.5 times the pressure scale height for a core mass Mc = 0.45 M☉, while it must be twice this for Mc = 0.3 M☉. For Mc 0.25 M☉, the temperature never becomes large enough for 24Mg to burn during shell flashes. In stars in metal poor clusters with [Fe/H] < -1,27Al is produced via the subsequent burning of 25Mg,26Mg, and 26Al, while in stars in metal-rich clusters, the duration of a flash is too short for these burnings to occur. It is also predicted that significant enrichment of helium in the surface is necessarily attendant upon the Al/Mg abundance anomaly. In order to ignite shell flashes, the inward mixing of hydrogen has to take place on a timescale shorter than the lifetime of protons near the outer edge of the helium core; this lifetime varies from ~105 to ~104 yr, depending on the core mass. Hydrodynamical instabilities that are triggered by the inflow of angular momentum into the core are suggested as being responsible for the postulated inward mixing. The origin of this flow is attributed to star-star interactions in the dense environment of a globular cluster.