1 Introduction

Convection is of central importance to the structure and appearance of the Sun, both with respect to its average internal structure and secular evolution, and with respect to the detailed structure and dynamics of the many diverse phenomena that occur at the solar surface. In this review we discuss convection in those layers of the Sun that directly influence what may be observed at the solar surface. In practice, this means that we consider layers ranging from the temperature minimum down to about 20 Mm below the visible surface. Over this range of depths hydrogen ionization goes from essentially zero, with electrons instead supplied mainly by the most abundant metals, to essentially unity. Helium (2nd) ionization is also nearly complete near the bottom of this range of depths.

As illustrated by Figure 1View Image, a depth of 20 Mm corresponds to roughly half the range of pressure or density spanned by the solar convection zone. Thus, even though this layer corresponds to only about 3% of the solar radius, and only about 10% of the geometrical depth of the solar convection zone, mass density and pressure vary by factors of about 105 and 106 across it, respectively.

In these surface and near-surface layers the equation of state of the solar plasma is strongly influenced by the effects of ionization and molecular dissociation. Deeper down the solar plasma is nearly fully ionized, the equation of state is nearly ideal and, hence, the vertical structure of the lower part of the convection zone (90% by depth) is close to that of a perfect polytrope.

The physics of convection near the surface of the Sun is also greatly influenced by the fact that the solar surface is a radiating surface, where the mode of energy transport all of a sudden changes from convective – with energy being carried by moving fluid – to radiative – with energy carried by essentially free-streaming photons.

Each one of these complications – extreme density stratification, ionization and molecule dissociation, and transition to radiative energy transfer – would by itself be sufficient to render analytical treatments impossible and, hence, major progress in modeling these layers could only be achieved via computer simulations and modeling. The subject area was thus truly opened up for study and revolutionized when computer capacity became large enough for realistic simulations to be performed.

Conversely, because of the proximity and large apparent luminosity of the Sun, it is one of the most ideal objects for quantitative and accurate comparisons between numerical simulations and observations – arguably in five dimensions: one has, to a rather unique extent, access to both the time domain and the spatial domain, over a large range of scales, and the available photon flux is large enough to also essentially fully resolve the wavelength domain, from the extreme ultra-violet to the far infrared.

In addition, the Sun is an ideal object for studying magneto-hydrodynamics in an astrophysical context, in that it displays a variety of magnetically related phenomena, ranging in strength from very weak and kinematic, where the evolution of the magnetic field is almost entirely controlled by the fluid motions to the opposite extreme, where the gas pressure is so feeble that fluid motions are totally dominated by the magnetic field.

The comparison of models and observations is thus both particularly challenging and particularly rewarding in this context, and the evolution of the subject area over the last few decades has amply illustrated this state of affairs.

In this review we try to summarize, in a necessarily incomplete and biased way, our current understanding of solar surface convection.

The review is organized as follows: In Section 2 we discuss the principles of hydrodynamics as they apply to solar convection. In Section 3 we discuss the manifestations and properties of the main energy carrying scales, and the granulation pattern that they give rise to. In Section 4 we discuss how larger scale convective patterns arise and are driven, and how they interact with smaller scale patterns. We introduce the concept of a velocity spectrum, and address the question the extent to which the traditional concepts of meso- and supergranulation represent distinct scales of motion. In Section 5 we discuss how spectral line synthesis and comparisons with observed spectral line profiles may be used to asses the accuracy of numerical simulations, and how the resulting spectral line profiles may be used to accurately determine solar chemical abundances. In Section 6 we discuss applications to global and local helioseismology: wave excitation and damping, the influence of convection on the mean structure, and helioseismic diagnostics related to convective flow patterns. In Section 7 we discuss the interaction of convection and solar magnetic fields and, finally, in Section 8 we discuss open questions and directions for future work. Section 9 ends the review with a summary and concluding remarks.

Previous reviews related to this subject include: Bray et al. (1984); Nordlund (1985aJump To The Next Citation Point); Zahn (1987); Spruit et al. (1990); Nordlund et al. (1996); Spruit (1997); Stix (2004), and Asplund (2005Jump To The Next Citation Point).

View Image

Figure 1: Schematic figure showing the average pressure and mass density stratification of the Sun.

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