3.2 Convective driving

Convection is driven primarily by radiative cooling from a thin thermal boundary layer at the visible surface of the Sun, the layer from which most photons can escape to space. The most prominent intensity variations on the solar surface, aside from sunspots and faculae, are granules – the bright (hot) areas surrounded by dark (cooler) lanes that tile the Sun’s surface (Figure 2View Image). Their diameters are typically of order 1 Mm, and this is the horizontal scale on which radiative cooling drives the convective motions. The bright granules are the locations of upflowing hot plasma, while the dark intergranular lanes are the locations of downflowing cool plasma.

Plasma that reaches the layer where a typical photon’s mean free path equals the distance to space has some of its thermal energy carried away by photons. As a result the plasma cools, so that hydrogen ions capture electrons to become neutral hydrogen atoms and in the process release a large amount of ionization energy that is also carried away to space by photons. The escaping photons, as they remove energy, also remove entropy from the plasma that reaches the surface, producing overdense fluid which is pulled down by gravity (Figure 3View Image). Solar convective motions are driven by buoyancy work, primarily downward on the overdense, low entropy, cool fluid in the intergranular network, and partially upward on the underdense, high entropy, hot fluid in the granule interiors (Figure 4View Image). At increasing depths, more and more of the buoyancy work occurs in the cool downdrafts, rather than the warm upflows. Deeper into the convection zone the magnitude of the entropy fluctuations decreases because the diverging upflowing plasma all has nearly the same entropy, while the turbulent downdrafts entrain and mix with overturning fluid from the upflows which gradually increases their entropy (Figures 3View Image, 5View Image). The result is that, although the convecting plasma is heated at the bottom – as well as cooled at the top – of the convection zone, most of the buoyancy work is due to cooling at the surface which produces large entropy fluctuations, rather than heating at the bottom of the convection zone, which produces only small entropy fluctuations. The role of the lower boundary is to replenish the entropy of fluid parcels that reach the bottom of the convection zone – it is primarily a supplier of heat, and contributes to driving patterns of motion only on the largest, global convection zone scales.

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Figure 3: Temporal history of typical fluid parcels that reach the surface: height z (Mm), optical depth τ, log(ρ), radiative heating Qrad (103 erg/gm/s), internal energy E (105 erg/gm), specific entropy S (108 erg/gm/K), fraction ionization to total energy, and vorticity ω (10–2 s–1). Time is counted from when the parcel rises through unit optical depth. When fluid reaches optical depth τ ∼ 100, it begins to cool rapidly as the gas starts to recombine. Its entropy and energy drop so quickly that its density increases. As it passes above the surface a small amount of radiative reheating occurs and its entropy increases slightly. When it passes back down through optical depth unity it cools some more with a further drop in entropy. As it heads down into the interior it heats up by adiabatic compression and by diffusive energy exchange. The deeper it gets, the more adiabatic its motion becomes (from Stein and Nordlund, 1998Jump To The Next Citation Point).
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Figure 4: Buoyancy work at a depth of 0.5 Mm as a function of (a) vertical velocity (downflows are positive) and (b) fluid entropy. Most of the convective driving below the surface occurs in the low entropy downflows produced by radiative cooling at the surface (from Stein and Nordlund, 1998Jump To The Next Citation Point).
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Figure 5: Histogram of the entropy (logarithmic color scale with arbitrary units) as a function of depth. Most of the area of a horizontal plane below the surface is occupied by upward moving fluid with close to the maximum entropy. Entropy fluctuations are largest at the surface and decrease with increasing depth due to entrainment of entropy neutral material and, in the case of the simulations, numerical energy diffusion (which however is insignificant in this context – most of the entrainment is due to the overturning forced by mass conservation). Entropy increases above the surface because radiation from the surface heats the gas much above the temperature it would attain if moving adiabatically (from Stein et al., 1997).

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