1. Evidence of early solar evolution in the tachocline and overshooting region below the present convective zone V.A.Baturin, A.B.Gorshkov, S.V.Ajukov Sternberg State Astronomical Institute of Moscow State University

2. Region of the Sun in focus of discussion
The region under the convection zone of the Sun, with width about 0.15R of solar radius from “classical” boundary of convection.
The terms “tachocline” and “overshooting” are used for marking the region and to refer on possible mixing processes there.
Why this region? That is because of “remarkable” deviation between the result of sound speed inversion and theoretical profile is still seen here (as discussed in previous report).

3. Mechanisms of hydrogen evolution
Several mechanisms determine a profile of the hydrogen in the envelope (in contrast to the core):
The outward drift (float) of hydrogen is present here as a result of thermo- and baro-diffusion. After interference of the float with full convective mixing, the region of gradient of hydrogen is appeared below the convection zone.
Convective overshooting, which is appeared as
thermal overshooting – that is extension of convective heat transfer outside of the region of convective instability;
mixing overshooting, that is extension of mixing effect (fast and convectively driven) outside the convective zone;
Non-convective mixing is likely present there. This “weak” mixing is not connected directly to convection zone and overshooting.

4. Evolution of hydrogen X(mr,t) near the bottom of convection zone

5. Evolution of hydrogen X below the convective zone (Model-S evolutionary sequence)
T-region
Fig1 X-prof (evolutionary sequence)

6. Evolutionary modeling of hydrogen profile
Modeling includes several “mixing” mechanisms
“classical” mechanisms of particle diffusion in plasma, including molecular (or “gradient”) diffusion, baro-diffusion and thermo-diffusion.
Possible “weak” mixing, which is modeled as artificially increased molecular diffusion coefficient.
Full or significant partial mixing of chemical composition inside the convective zone and closely connected with convection.
During solving of the evolutionary equation for X, the temperature and pressure distributions as functions of radius and time (i.e. T(r,t) and P(r,t)) are keep fixed. In the report, all T(r,t)- and P(r,t)- distributions are evolutionary sequence of the Model S.

7. Evolutionary equation for X profile

8. Flux of hydrogen JX near the bottom of convective zone (Model S)
Fig2_fluxes evolution of fluxes

9. Evolution of X and gradX in TB-diffusion model
Fig3

10. Evolution of hydrogen gradient X(mr,t) in model S

11. Evolution of X(mr,t) in a model with extented fully mixed region

12. Inversion of grad X
Inverted sound speed data has been taken from Vorontsov, et al., 2013, M.N.R.A.S., 430, 1636.

13. Adjusting of X to the inverted profile in T-region (for the standard early convective zone)

14. Adjusting of X in evolutionary sequence with heavier ZAMS CZ

15. Modeling of inverted X with adjusted overshooting mixing coefficient

16. Gradient of X as a function of radius
Fig6a_rad

17. Conclusions on early convective zone
The Sun is old enough, and gradient diffusion “irons out” (i.e. makes linear) the signature of earliest (ZAMS) convective zone, so we cannot see it in the present gradient profile.
2. Region of active convective mixing is presented under the convective zone. The evolutionary structure of GX-region almost completely was destroyed by modern convective mixing.
3. Structure of present T-region (where the gradient diffusion dominates) applies some restrictions on the depth of mixing in early Sun. The mass of early convective zone was hardly larger then 3.5% (in Model S it was exactly 3%). The question if the early convective zone maybe less massive then 3% is still open.

18. Conclusions about mixing under the convection zone
In the T-region a weak mixing (in addition to molecular diffusion) is definitely present, and source of such mixing is not convective overshooting.
2. The thickness of the mixing region (turbulent dissipation) under the present solar convection zone is about Hp/2 (d=0.038R). In this estimation the soft mixing region is included, whereas a possible region of full mixing is rather thin (about Hp/10?).
3. Width of thermal overshooting region is probably less but comparable to the width of mixing overshooting.