3D Numerical Simulations of Thermohaline Mixing in Low-Mass Red Giants Pavel Denisenkov, UVic

3D Numerical Simulations of Thermohaline Mixing in Low-Mass Red Giants Pavel Denisenkov, UVic A story about how important and difficult it is to take account of mixing in stars when studying stellar nucleosynthesis

(From Bania, T. M., Rood, R. T., and Balser, D. S. 2007, Space Science Review, 130, 53) The abundance of 3 He should have increased by an order of magnitude since the Big Bang Nucleosynthesis, but it has been remaining nearly constant

The incomplete pp-chain reactions produce a lot of 3 He far from the centre of a low-mass star on the main sequence, and low-mass stars are the most abundant species of stellar populations

Left: Evolution of a low-mass star in the HR diagram (M = 0.83M , Z = ) Right: Changes of abundance profiles inside the star that drive its evolution Data points are field stars with M = 0.8 – 0.9M , Z = – from Gratton et al. (2000) Arrow in the right panel shows the bottom of convective envelope

Left: Evolution of a low-mass star in the HR diagram (M = 0.83M , Z = ) Right: Changes of abundance profiles inside the star that drive its evolution on the MS, 3 He is produced in a wide pocket (blue curve in the right panel) after the MS, convection spreads 3 He all over the envelope (the 1 st dredge-up) mass-loss on the RGB and AGB will deliver this 3 He into ISM

Left: Evolution of a low-mass star in the HR diagram (M = 0.83M , Z = ) Right: Changes of abundance profiles inside the star that drive its evolution on the MS, 3 He is produced in a wide pocket (blue curve in the right panel) after the MS, convection spreads 3 He all over the envelope (the 1 st dredge-up) mass-loss on the RGB and AGB will deliver this 3 He into ISM

Low-mass red-giant-branch (RGB) stars show evidence of extra-mixing operating in their radiative zones between the hydrogen-burning shell and convective envelope that starts above the so-called “bump luminosity”. This RGB extra-mixing is most likely to reduce the envelope 3 He abundance back to its BBN value. How to explain the fact that the abundance of 3 He in the ISM has not changed since the BBN?

Left: Evolution in the HRD around the bump luminosity (M = 0.83M , Z = ) Right: H-burning shell erases abundance discontinuities What happens at the bump luminosity?

Left: Evolution in the HRD around the bump luminosity (M = 0.83M , Z = ) Right: H-burning shell erases abundance discontinuities What happens at the bump luminosity?

Left: Evolution in the HRD around the bump luminosity (M = 0.83M , Z = ) Right: H-burning shell erases abundance discontinuities What happens at the bump luminosity? On upper RGB, above the bump luminosity, the radiative zone has uniform chemical composition, which facilitates fluid buoyancy of any origin

Thermohaline convection as a mechanism for extra mixing in RGB stars Reaction 3 He( 3 He,2p) 4 He decreases µ locally byΔµ ≈ − Thermohaline convection is driven by a small difference in salinity S between a fluid element and its surrounding medium when the atomic diffusivity is much lower than the heat diffusivity K. In the ocean, it develops when both S and T decrease with depth and it takes a form of salt fingers, hence “salt-fingering convection” is another term for it. P ( µ *, ρ 1 *,T ) Double-diffusive (  K) instability leads to growing salt fingers in water

Thermohaline convection as a mechanism for extra mixing in RGB stars Reaction 3 He( 3 He,2p) 4 He decreases µ locally byΔµ ≈ − The RGB thermohaline convection is driven by a small difference in µ between a fluid parcel and its surrounding medium because the atomic diffusivity is much lower than the heat diffusivity K. It develops when µ decreases with depth (usually, µ increases with depth in stars)

Thermohaline convection as a mechanism for extra mixing in RGB stars The RGB thermohaline convection is driven by a small difference in µ between a fluid parcel and its surrounding medium because the atomic diffusivity is much lower than the heat diffusivity K. It develops when µ decreases with depth (usually, µ increases with depth in stars)

Thermohaline convection as a mechanism for extra mixing in RGB stars Reaction 3 He( 3 He,2p) 4 He decreases µ locally by |Δµ | ‹ (Eggleton et al. 2006) The RGB thermohaline convection is driven by a small difference in µ between a fluid parcel and its surrounding medium because the atomic diffusivity is much lower than the heat diffusivity K. It develops when µ decreases with depth (usually, µ increases with depth in stars)

2D numerical simulations of thermohaline convection in the oceanic and RGB cases (a change of color from red to blue corresponds to an increase of S and µ) Salinity fieldMean molecular weight field

3D numerical simulations of the oceanic and RGB thermohaline convection Ocean (S)RGB (µ)

The empirically constrained rate of RGB extra-mixing is D µ ≈ 0.01K which is a factor of 50 higher than the value estimated in our 2D and 3D numerical simulations Therefore, the physical mechanism of RGB extra-mixing is most likely to be different from thermohaline convection driven by 3 He burning A promising alternative mechanism is the buoyant rise of magnetic flux rings (Parker’s instability)

The End