I recall here how latitude-dependent rotation imposed by the solar convection zone on the top of the radiation zone would burrow deep into the interior, owing to thermal diffusion, in any laminar and purely hydrodynamic model. Since helioseismology has shown that this differential rotation remains confined in a thin boundary layer, the tachocline, it means that the radiative spread is inhibited by another physical process; this process may be purely hydrodynamic (non-MHD), which is the scope of this chapter, or it may involve magnetic fields: those are considered by Garaud in Chapter 7 of this book. I will show that the confinement of the tachocline can be achieved through an anisotropic turbulent viscosity, whose cause and plausibility are discussed. Other hydrodynamic mechanisms are examined, such as internal gravity waves, which may also play a role in the tachocline. An alternative possibility is that the tachocline is fully embedded in the layer of penetrative convection, in which case no differential rotation would be applied on to the radiation zone.

Introduction

In 1990, I was invited with Ed Spiegel to give the principal lectures at the Woods Hole summer school. The theme of that year, ‘Stellar Fluid Dynamics’, was covered extensively by Ed, and I chose to focus on problems related to the rotation of stars. My last lecture, as it happened, was devoted to ‘flow between the Sun's convection and radiation zones and transport of chemicals’.

It is natural to associate the tachocline with the region of generation of a strong toroidal field by the winding-up of a weaker poloidal component. Here I discuss the break-up and subsequent escape of such a field via magnetic buoyancy instabilities. I consider the different modelling approaches that have been employed and discuss which have the most relevance in a solar context.

Introduction

For many years, a controversial issue of solar magnetism has been that of the location of the site (or sites) of the generation and storage of the Sun's predominantly toroidal magnetic field, which eventually escapes and rises to the surface, leading to active regions and, ultimately, to much of the exotic magnetic behaviour observed in the photosphere, chromosphere and corona. For two rather different reasons, the idea had been put forward that the bulk of the toroidal field must be stored either at the base of, or just beneath, the convection zone. From estimates of the rise times of magnetic flux tubes through the convection zone, Parker (1975) argued that the dynamo must operate only in the ‘very lowest levels of the convective zone’. Golub et al. (1981) (see also Spiegel & Weiss 1980) proposed a similarly deep-seated layer of toroidal field, but from arguments based instead on the expulsion of magnetic fields by convective motions. The discovery of the tachocline by helioseismology provides probably the most compelling evidence for pinning down the location of the solar toroidal field.

Over the past 25 years helioseismology has at last enabled us to probe the internal structure and dynamics of our local star, the Sun. Perhaps its greatest triumph has been to determine how the rotation varies in the solar interior. Although the bulk of the radiative zone, occupying the innermost 70% by radius, rotates more or less uniformly, the known variation with latitude of angular velocity at the surface persists down to the base of the outer convective envelope. Since it had previously been supposed that the Sun rotates sufficiently rapidly for the angular velocity to be constant on cylindrical surfaces in the convection zone it was a surprise to find that it is actually constant on conical surfaces. It came as an even greater surprise to discover that the transition between the differentially rotating exterior and the uniformly rotating interior is effected through an extremely thin layer – the tachocline – whose thickness is less than 4% of the solar radius.

This unexpectedly abrupt transition has forced us all to refine our ideas on the interactions between turbulent convection, rotation and magnetic fields, for it seems that these last play a key role in preventing the tachocline from spreading downwards into the radiative zone. To describe the internal structure of the tachocline requires an understanding of convective penetration, turbulent diffusion, mixing and angular momentum transport.

The tachocline may be subject to a variety of instabilities leading to turbulent motion and angular momentum transport. This chapter reviews some approaches that have been found useful in the study of astrophysical accretion discs and discusses their possible application to the tachocline.

Introduction

The solar tachocline is a thin structure characterized by strong differential rotation, presumably in the presence of a magnetic field. It forms the interface between the radiative interior and the convective envelope of the Sun, which differ greatly in their dynamical properties, states of rotation and mechanisms of angular momentum transport. While the tachocline might have the character of a laminar boundary layer between these regions, it is more likely to be turbulent, at least in part, as a result of intrinsic instabilities or possibly because of forcing by the convective motions above.

Instabilities of the tachocline could derive from kinetic, gravitational or magnetic sources of free energy. Shear instabilities depend on the free kinetic energy in differential rotation, and may, as in the case of the magnetorotational instability, require the assistance of a magnetic field. Gravitational energy may be liberated through magnetic buoyancy (Parker) instabilities, while magnetic energy in non-potential configurations may be released in purely magnetic (Tayler) instabilities. To understand the existence and dynamics of the tachocline requires an appreciation of such instabilities and the transport effects, especially angular momentum transport, to which they give rise in a nonlinear regime.

The region near and just below the solar convection zone is characterized by a strong shear in rotation rate, between the latitudinally differential rotation in the convection zone and the nearly uniform rotation of the radiative interior. This so-called tachocline is also a region of substantial uncertainty in the modelling of solar structure, where convective overshoot and rotationally induced mixing may affect the thermal and compositional structure. Helioseismology led to the identification of the rotational shear and has provided fairly detailed information about the properties, structure and rotation of the tachocline, although unavoidably at somewhat limited resolution. Here we briefly discuss the techniques used in the helioseismic analyses and review the results of such analyses, as a background for the modelling of the properties of the tachocline and its effects on the generation of the solar magnetic field.

Introduction

As will be abundantly evident from other articles in this volume, knowledge of the solar internal rotation is essential for understanding solar magnetic activity, as it is for understanding important aspects of solar structure and evolution. Before the advent of helioseismology little was known about solar rotation below the surface, beyond the indication, from the surface latitudinal differential rotation, that it was non-uniform.

The physical processes causing the turbulent dissipation and mixing of momentum and magnetic fields in the solar tachocline are discussed in the context of a simple model of two-dimensional MHD turbulence on a β-plane. The mean turbulent resistivity and viscosity for this model are calculated. Special attention is given to the enhanced dynamical memory induced by small scale magnetic fields and to the effects of magnetic fluctuations on nonlinear energy transfer. The analogue of the Rhines scale for β-plane MHD is identified. The implications of the results for models of the solar tachocline structure are discussed.

Introduction

The tachocline is a thin, stably stratified layer of the solar interior situated in the radiative zone, immediately below the convection zone (Miesch 2005;Tobias 2005). This layer connects the latitudinal differential rotation of the solar convection zone to the expected solid body rotation of the solar interior (Schou et al. 1998; see also Chapter 3 in this book by Christensen-Dalsgaard & Thompson). Thus, flows in the tachocline are sheared (both poloidally and radially), with the predominant structure being that of a radially sheared toroidal flow. The stratification of the tachocline is strongly stable (with Richardson number Ri ≫ 1), and the magnetic field strength is significant, though magnetic pressure is still much smaller than thermal pressure, consistent with hydrostatic equilibrium, i.e. B2/8π ≪ p.

Introduction

The formation and evolution of Mars involved both physical and chemical processes that are revealed in the chemistry of the Martian meteorites, and in the chemistry of the surface of Mars determined by remote sensing from spacecraft in orbit and on the surface. The interpretation of the chemistry revealed by these studies has been strongly influenced by our knowledge of geochemical processes on the Earth, Moon, and asteroidal parent bodies. In a sense, the entire Earth, Moon, and a number of asteroid parent bodies can be considered Mars analogs! The most studied differentiated body (melted and chemically evolved) from the asteroid belt is the parent body of the Howardite, Eucrite, and Diogenite (HED) igneous meteorite classes, thought to be the asteroid 4 Vesta (Mittlefehldt et al., 1998). These HED meteorites are igneous rocks that are basaltic in nature with slightly different mineral assemblages (McSween, 1999). In this chapter we use data from samples on the Earth including the meteorites from the HED parent body and the Martian meteorites to understand the chemical fractionations that have affected Martian rocks and surface materials. These chemical fractionations are the changes in chemistry due to the different behavior of particular groups of chemical elements according to their properties. We will begin by looking at the evidence for the formation of Mars, the early differentiation of the planet, the later formation of igneous rocks by mantle melting, and end with surface processes leading to formation of the Martian fine-grained regolith OR soils.

Introduction

The major dynamic forces shaping the surfaces, crusts, and lithospheres of planets are represented by geological processes (Figures 1.1–1.6) which are linked to interaction with the atmosphere (e.g., eolian, polar), with the hydrosphere (e.g., fluvial, lacustrine), with the cryosphere (e.g., glacial and periglacial), or with the crust, lithosphere, and interior (e.g., tectonism and volcanism). Interaction with the planetary external environment also occurs, as in the case of impact cratering processes. Geological processes vary in relative importance in space and time; for example, impact cratering was a key process in forming and shaping planetary crusts in the first one-quarter of Solar System history, but its global influence has waned considerably since that time. Volcanic activity is a reflection of the thermal evolution of the planet, and varies accordingly in abundance and style.

The stratigraphic record of a planet represents the products or deposits of these geological processes and how they are arranged relative to one another. The geological history of a planet can be reconstructed from an understanding of the details of this stratigraphic record. On Mars, the geological history has been reconstructed using the global Viking image data set to delineate geological units (e.g., Greeley and Guest, 1987; Tanaka and Scott, 1987; Tanaka et al., 1992), and superposition and cross-cutting relationships to establish their relative ages, with superposed impact crater abundance tied to an absolute chronology (e.g., Hartmann and Neukum, 2001).

Just before I left to attend the June 2001 Geologic Society of London/Geologic Society of America Meeting in Edinburgh, Scotland, I received two e-mail messages. The first was from a UK-based freelance science writer, who was producing a proposal for a six-part television series on various ways that studies of the Earth produce clues about Mars. He requested locations where he might film, other than Hawaii. I was amazed that he seemed not to be aware of all of the locations on Earth where planetary researchers have been studying geologic processes and surfaces that they believe are analogous to those on Mars. In retrospect, his lack of knowledge is understandable, as no books were in existence on the topic of collective Earth locales for Martian studies and no planetary field guides had been published that included terrestrial analogs of the newly acquired data sets: Mars Global Surveyor, Mars Odyssey, Mars Exploration Rovers, and Mars Express. [Historically, NASA published a series of four Comparative Planetary Geology Field Guides with four locales having analog features for comparison with Mars, each book on a different subject and area (volcanic features of Hawaii, volcanism of the eastern Snake River Plain, aeolian features of southern California, and sapping features of the Colorado Plateau). However, all of these books were based on Viking data, intended for researchers in the field, were not widely distributed, and are now out of print (NASA has not published any more field guides).]

Introduction

Every solid-surfaced body in the Solar System except Io shows evidence of the impact cratering process, and Comet Shoemaker-Levy 9 showed that impacts can even temporarily leave their mark on gas planets. Earth's active geologic environment has erased much of its cratering record, particularly from the early episode of high impact rates known as the late heavy bombardment period (>3.8 Gyr ago). In comparison, ∼60% of the Martian surface preserves the late heavy bombardment record. Mars retains the most complete record of impact cratering in the entire Solar System (Barlow, 1988) and these craters display a range of morphologic features seldom seen on other solid-surface bodies. Comparison of terrestrial and Martian craters provides a more thorough understanding of impact structures: Mars preserves the pristine morphologic features which erosion has largely destroyed for terrestrial craters, but terrestrial studies allow us to understand subsurface structures and materials resulting from impact for which we currently have no information on Mars. Presence of an atmosphere and subsurface volatiles suggests that crater formation may be more similar on these two bodies than between Earth and Moon.

Understanding how impact craters form results from laboratory experiments, computer simulations, nuclear and chemical explosions, and terrestrial crater studies. Laboratory experiments were instrumental in realizing that high-velocity impacts create approximately circular craters except at low impact angles (Gault and Wedekind, 1979). Nuclear and large chemical explosions provided the first opportunity to study the physics of crater formation (Oberbeck, 1977).

Introduction

Eolian processes produce distinctive features and deposits on planetary surfaces where the atmosphere is sufficiently dense to allow interactions between the wind and sediments on the surface (Greeley and Iversen, 1985). Arid and semi-arid regions on Earth contain abundant evidence of wind–surface interactions (e.g., Lancaster, 1995a; Thomas, 1997), and the Martian surface shows a diverse array of eolian features across the planet (e.g., Greeley et al., 1992). The characteristics of several eolian localities (primarily sand dunes) in the western part of the United States have been used previously as analogs to features seen on Mars in data obtained from several spacecraft (e.g., Greeley et al., 1978; Greeley and Iversen, 1987; Golombek et al., 1995), yet the analog potential of other western eolian sites is relatively underutilized. Rather than attempting a comprehensive survey of all eolian features in the United States, this chapter will focus on several examples illustrative of a variety of dune forms and their potential applicability as analogs to eolian features observed on Mars. Dunes in the Great Plains, east of the Rocky Mountains, and all coastal dunes are excluded from this survey in order to concentrate on discrete sand accumulations in arid or semi-arid environments. Both traditional publications and selected internet sites (cited here as W#) are referenced throughout the text.

Eolian features in the western United States reflect varying climatic and drainage conditions that have directly contributed to the formation of the individual deposits.

Introduction

For reasons of cost and risk, planetary exploration since Apollo has been carried out by robots with the human input made from Earth. Given communication time delays and the manifest limitations of robots, the pace and quality of such exploration could be greatly improved if humans were more directly involved. Exploration continues using increasingly advanced robotic technologies including those intended to begin the subsurface exploration of the planets. Before such missions will be undertaken we need assurance that these new technologies work adequately under appropriate terrestrial analog conditions. Eventually, humans will re-enter the picture with in-depth exploration of the Moon and Mars as their principal focus. However, such human explorers will not be able to achieve the global reach needed to answer the many questions scientists pursue for a planet as large and diverse as Mars. So, how should humans and robots work together optimally? Can advanced robots tele-operated by humans at short light distances approach the scientific productivity of a trained, yet suit-encumbered, astronaut? To answer these questions, researchers must define scientific return and find ways to compare the productivity of different human–robot exploration systems. Analogs can be used to develop the full range of possible human and robotic exploration systems using metrics that allow us to quantify the effectiveness of each.

Some important outstanding exploration issues that high-fidelity analog missions can inform include:

• Development, testing, and demonstration of exploration hardware, including surface habitats and extra-vehicular activity (EVA) systems.

• Selection of landing sites that maximize access to resources and scientifically interesting terrain.

• […]

Introduction

In the 1970s, the two Viking spacecraft returned images of the surface of Mars in which numerous small domes, knobs, and mounds were visible. Based on the presence of summit depressions in many of these domes, they were interpreted to be rootless volcanic cones (Frey et al., 1979; Frey and Jarosewich, 1982), by analogy with similar features found in Iceland (Thoroddsen, 1894; Thorarinsson, 1951, 1953). Rootless cones (also called pseudocraters – a literal translation of the Icelandic gervigígar) form as a result of explosive lava–water interaction, whereby a flowing lava encounters a waterlogged substrate, causing violent vaporization of the water and expulsion of the lava from the explosion site (Thorarinsson, 1951, 1953). Repeated explosive pulses build a cone of disintegrated liquid and solid lava debris (Thordarson et al., 1992). As the activity at a given site within the flow wanes, explosions may be initiated elsewhere, leading to construction of a field of tens to hundreds of cones. Although they may bear a superficial resemblance to primary volcanic cones built over a subsurface conduit, Icelandic rootless cones are quite distinct, in that they are surface phreatomagmatic structures formed at the lava–substrate interface (Thordarson, 2000).

The identification of possible rootless cone fields at mid to low latitudes on Mars incited great interest because of the implication for the presence and distribution of volatiles (i.e., water or ice) in the near-surface environment on Mars (Frey et al., 1979; Frey and Jarosewich, 1982).