Modeling of the temperature sensitivity of the apatite (U–Th)/He thermochronometer

Abstract

Apatite (U–Th)/He apparent ages will generally reflect residence for extended periods at temperatures where helium is neither quantitatively retained nor lost by diffusion. To characterize the response of apatite He ages to thermal histories involving partial He retention, we explored solutions to the He production–diffusion equation. Under thermally static conditions, the analytical solution to this equation, coupled with published diffusivity data, demonstrates that the zone of partial He retention extends from about ∼40°C to ∼85°C. This zone lies at temperatures ∼35°C cooler than the analogous fission track partial annealing zone. He ages within the partial retention zone ultimately achieve a balance between He production and loss, yielding a steady state age. Both the ultimate age and the time it takes to achieve this age are temperature dependent. For example, an apatite held at 75°C equilibrates to an age of ∼2 Ma after ∼17 Myr, regardless of whether equilibrium is approached from a higher or a lower initial He age. For representative dynamic thermal histories, we evaluated apatite He ages using a numerical solution to the ingrowth–diffusion equation. The results illustrate the sensitivity of He ages to various geologic histories and are useful for understanding He age–elevation relationships and for testing time–temperature paths derived from apatite fission track length distributions. In addition, although He diffuses rapidly from apatite at shallow crustal temperatures, modeling of ambient temperature fluctuations indicates that He ages are nearly unaffected by surficial processes.