Astron. Astrophys. 355, 365-374 (2000)

## 5. Conclusion

In this analysis, we have determined the profiles of the solar oblateness , as a function of radius and latitudes, from the core to the surface, and we have given its theoretical integrated value at the surface. The method used has consisted in the computation of the differential equation governing the fluids in hydrostatic equilibrium which depends on the latitude. The main quantities, taking part in this computation, are the mass and the density, which respect the helioseismic constraints, and the rotation given by a parametric model derived from helioseismic data.

The main results obtained are the following:

- The theoretical value, at the surface, of the solar oblateness is .

- From the model used, can be drawn as a function of the solar radius (assuming the Sun set up of successive homogeneous thin shells) and of the latitude. The variation of with the latitude shows that the properties of the tachocline, such as the width and the position of the center, vary with the latitude.

- The gradient which occurs in the profiles of , plotted for successive shells, from up to , sets borderlines of a new region located between the tachocline and the convection zone. This overshoot layer may have a joint zone with the tachocline, where the convective flux would be positive. The properties of this layer should also vary with the latitude.

- Beneath the surface, our model of oblateness gives changes of curvature in the profiles, which can be connected to solar events. The two first are located at and at . They are certainly linked to two types of flows: the zonal flows, represented by bands, and the meridional flows which circulate from the equator to the poles. The third change is located at and can be associated with the layer's borderline. Then, the fourth and fifth changes, which occur at and at , can be the signature of the region where the seismic events take place.

- A transition zone, characterised by the passage from a convective zone to a radiative one, exists inside the tachocline and within the subsurface. We assume that the structure of these two different transition layers may be similar. On this basis, we showed that the transition zone within the subsurface is composed of two layers, the first one has an extension in the range [, ]; the second one, where the magnetic field would be stored, extends in the range [, ].

- Finally, we were able to deduce from this study a global shape of the Sun, and we confirm that the solar diameter presents a dependence on the latitude.

The full study of a differential rotating body, such as the Sun, leads to the conclusion that the exact shape critically depends both on the rotation law from the subsurface to the tachocline and on the properties of its internal structure: shear, magnetic field, flux of matter, seismic events, etc... A motivating objective would be to monitor the solar parameters, like the oblateness, from space.

© European Southern Observatory (ESO) 2000

Online publication: March 17, 2000