## Stars and latte macchiato

What do stars and latte macchiato have in common? Inquisitive coffee drinkers may have noticed a pretty 'layering' phenomenon that sometimes occurs in a glass of latte macchiato (see Fig. 1). A series of numerical simulations recently completed at the Max-Planck-Institute for Astrophysics demonstrates how the same layering process happens inside stars. The results of the simulations settle an open issue in the theory of stellar evolution that has been under investigation for half a century.

 Fig 1: Layered convection in a glass of coffee with milk. Fig 2: Convective flow pattern inside a double-diffusive layer. The top image shows the temperature distribution (red is warm, blue is cold), the bottom image the helium concentration (dark means high concentration). The flow structures in the temperature image appear wider than those seen in the helium. This blurring is due to thermal conduction (movie). Fig 3: Flow structures at the interface between two layers of a double-diffusive set of layers (movie).

Let’s do a little experiment: When you put hot coffee in a glass - not in a mug, since you want to see what's happening inside the liquid — the coffee cools at the top, sinks to the bottom, and is replaced by rising hot fluid - this is called a convective flow. (Side note: If you stir milk into your coffee, then the rising and sinking pattern shows nicely — especially if the milk you added was slightly off.)

If you add milk and do not stir the coffee, the flow pattern is interrupted: the convection is not strong enough to lift the milk, which is slightly heavier than water from the bottom of the glass. However, this is not the end: after a few minutes one can observe that thin layers have formed in the transition region between the milk and the coffee (this works especially well with low-fat condensed milk). Convection continues, but separately inside each of the layers without larger-scale mixing. This phenomenon is called double diffusive convection and occurs also in Nature, for example in the Arctic Ocean, where cold fresh water under the ice sheet forms layers above warm sea water, or in the volcanic lakes of East Africa.

Double diffusive convection can also occur in stars, which burn hydrogen into helium at their cores. Here, the convection driven by the heat from nuclear fusion is impeded by accumulating helium 'ashes'. The resulting layers interfere with the convective mixing of helium outward — it more or less stays in the centre.

The detailed distribution of helium throughout the star, however, has a strong impact on its further evolution. Over the long life of the star, even minor amounts of mixing can become important. Therefore the question of how much residual mixing might take place needs to be investigated.

Scientists at the MPA have now measured this rate of mixing with an extensive set of numerical simulations of the layering phenomenon. Just like in the geophysical examples mentioned above, the scientists found that the mixing of helium produced in nuclear reactions inside the star is quite low, much lower than what is usually assumed in theories of stellar evolution. Even over the star's entire life time, its effects are probably negligible.

F. Zaussinger, H. Spruit