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Convective Instabilities in the Sun

Convection is a heat transfer process in which the heat is transferred via the motion of fluid elements. This occurs in the sun, between 0.7 and 1 solar radii, in the area known as the ‘solar convective zone’. Hotter gas rises from the radiative zone of the sun, and as it is less dense than the surrounding sun, it is forced upwards by the buoyancy force. As it is rising, this ‘cell’ of gas breaks up, and we can observe what are known as ‘granules’ on the solar surface. These make up the mottled pattern on the surface, and are comprised of hot upwelling areas, and denser down welling areas. They are of the order of ~1x10^6m in scale.

What is unknown about these granulations, is at what depths and temperatures these cells form. My project plans on shedding some light on this question via a 1.5 dimensional computer simulation. A ‘cell’ is given initial conditions (such as mass, radial position and temperature), amidst the backdrop static conditions of the Sun (mass, radial position and temperature). The differences between the cell and the surroundings will initiate a motion in the cell upwards. This cell can be followed to the surface via the simulation, and depending on whether or not it breaks up, can be compared to observed granulations.

So far, I have successfully simulated an adiabatic cell with only gravity and buoyancy acting upon it. From this, the acceleration/velocity/position of the cell can be followed as it travels to the surface. However, this is a simplification of what actually occurs, and unrealistic speeds are reached. This is because neither drag, downdraft from descending dense plasma nor heat transfer have been taken into effect. Density gradients for cells at various temperatures have also been plotted.

What remains to be achieved in this project is to add more physical factors to the motion of the cell. These can include heat transfer between the cell and its surroundings, drag, and the total amount of energy carried by the convection in the sun can be calculated. These will give a more realistic motion of the cell.

1) At what depth do the supergranules form?


2) What are the expected properties of supergranules at the surface and sub-surface?
~10% ionized hydrogen -R.F. Stein and Nordlund, Simulations of Solar Granulation
Has a strongly horizontal velocity, in order to conserve mass.
Flows up at speeds up to ~8km/s, flows down at speeds ~ -4km/s
Downward moving intergranular lane plasma has low temperature, low entropy, very low ioniztion, and high density. Upward moving granule has high temperature, high entropy, high ionization, and low density.

Upflow temperatures ~10^4K
Downflow temperatures ~6000K

Upflows occupy ~ 2/3 of area under surface
Entropy is nearly constant under surface (upflows), varies greatly (downflows)
Downflow is very turbulent, mixing a lot.

Temperature gradient for ascending uplows ~100 K/km
Near surface, upflows and downflows transport approximately equal amounts of energy. With increased depth, downflows come to dominate the energy transport.


A fluid parcel cools adiabatically until it reaches optical depths of around tau= 30 - 100, where it begins to lose heat to radiation. As it cools, it loses even more heat quicker (~200K/s)


3) What is the statistical distribution of supergranules at the surface?