Looking inside stars and looking for planets

Asteroseismology and extrasolar planets are the main science goals of the Eddington mission, now approved by ESA for a 2007 launch. Alan Penny presents a summary of the January 2002 RAS meeting that discussed the sciences of this wide-field high-precision photometric space telescope. Since the date of this meeting, ESA has decided to implement the mission in the framework of a 2007–08 launch.     

Geophysical observations pertaining to solid-state convection in the terrestrial planets

We present a broad-based review of the observational evidence that pertains to or otherwise implies solid-state convection to be occurring (or have occurred) in the interiors of the terrestrial planets.For the Earth, the motion of the plates is prima facie evidence of large-scale mantle convection. Provided we understand upper-mantle thermal conductivity correctly, heat flow beneath the old ocean basins may be too high to be transported conductively from the upper mantle through the base of the lithosphere and therefore convection on a second smaller scale might be operative. The horizontal scale of plate dimensions implies, due to typical cell aspect ratios observed in convection, that the motion extends to the core-mantle boundary. Improved global data coverage and viscoelastic modeling of isostatic rebound due to Pleistocene deglaciation imply a uniform mantle viscosity, and thus indicate that whole-mantle convection could exist. Additionally, there is some seismic evidence of lithospheric penetration to depths deeper than 700 km. We discuss some salient features and assumption boundedness of arguments for convection confined to the upper mantle and for convection which acts throughout the mantle since the vertical length scale has a profound effect upon the relevance of geophysical observations. The horizontal form of mantle convection may be fully three-dimensional with complex planform and, therefore, searching for correlative gravity patterns in the ocean basins may not be useful without additional geophysical constraints. Many long-wavelength gravity anomalies may arise from beneath the lithosphere and must be supported dynamically, although thermal convection is not a unique explanation. Topography is an additional geophysical constraint, but for wavelengths greater than a few hundred kilometers, a general lack of correlation exists between oceanic residual gravity and topography, except at specific locations such as Hawaii. Theoretical calculations predict a complex relationship between these two observational types. Oceanic gravity data alone shows no regular planform and there is no correlation with any small-scale convective pattern predicted by laboratory experiments.All of the observational evidence argues against Martian plate tectonics occurring now or over much of the history of this planet, but lack of plate tectonics is not an argument against interior convection. The Tharsis uplift on Mars may have resulted from convective processes in the mantle, and the present-day gravity anomaly associated with Tharsis must be supported by the finite strength of the lithosphere or by mantle convection. Stresses imparted by the present topographic load would be greater than a kilobar, in excess of long-term finite strength. Observed fracture patterns are probably a direct result of this load, and the key question concerns the level of resultant strain relief. The global topographic and geomorphic dichotomy between the northern and southern hemisphere required a solid-state flow process to create the accompanying center-of-figure to center-of-mass offset.Lunar heat flow values, in analogy with oceanic heat flow on the Earth, strongly imply a convective mechanism of heat transport in the interior which, based on seismic Q values, is limited to the lower mantle. The presence of moonquakes in this region does not preclude solid-state convective processes. Lunar conductivity profiles provide no information on convection because of the difficulty in conductivity modeling, uniqueness of models, and the uncertainty in the conductivity-temperature relationship. The excess oblateness of the lunar figure over the hydrostatic value does not require convective support; in fact, such a mechanism is unlikely.The presence of a dipole magnetic field on Mercury does not provide a constraint on mantle convection unless its existence can be inextricably linked to a molten core. The non-hydrostatic shape of the equatorial figure, required for the observed $\text{3}\text{2}$ resonance between Mercury's rotational and orbital periods, is most likely related to surface processes, as opposed to convection. The $\text{3n}\text{2}$ resonance implies escape from a 2n resonance and, therefore, is related to the question of a molten core. Further dynamical data is needed to constrain interior models.Interpretation of limited radar imagery for the surface of Venus is enigmatic in terms of plate tectonics and therefore interior convection. Linear tensional and possibly compressional features are observed, but there are also crustal regions which appear to show large impact structures and are thus geologically old and may not have been recycled.     

A simple model of convection in the terrestrial planets

Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.     

Variational approach to modeling present-time mantle convection

Summary An analogy of the Hellinger-Reissner functional for the Stokes problem is constructed and the way of determining its minimum by means of spherical harmonic vectors and tensors is described. The variational method is applied to a Newtonian mantle in which the body forces were estimated on the basis of global inversion of gravitational and topographic data. The method is then generalized to the case of a realistic rheology (power-law creep), and prospects of the generalised method are briefly discussed.     

A model of thermal convection in the major planets with a strongly density-stratified atmospheric layer

Abstract

As an extension of a model by Busse (1983a), a two-layer model of thermal convection in the self-gravitating rotating spherical fluid is considered. The upper layer with arbitrary vertical distributions of density and potential temperature representing the atmospheric layer of major planets is imposed on the spherical Boussinesq fluid. The Prandtl number P and the ratio of the mass of the upper layer to that of the lower layer are used as small expansion parameters. The modification of the critical Rayleigh number by imposing the upper layer are clearly separated into two parts, proportional to (1) the mass of the upper layer and to (2) an integral representing a measure of convective instability of the upper layer. Some implications for atmospheric dynamics of the major planets are also presented.     

Edge-driven convection and thinning of craton lithosphere: Two-dimensional thermal-mechanical modeling

Science China Earth Sciences - There are usually abrupt changes in lithospheric thickness at the boundaries between ancient cratons and adjacent young mobile belts. Lateral variations in...     

A young person's guide to the planets

The UK Planetary Forum's Young Person's Planetary Meeting was a chance for young researchers to meet, speak and discuss their research with others from across the UK and to build new research contacts. The one-day symposium was organized by the UKPF with support from the RAS. Andrew Ball, Ingo Mueller-Wodarg and Tom Stallard report.     

Earth-mass planets in exoplanetary systems

No exoplanets with masses anywhere near as small as that of the Earth have yet been found. Barrie Jones considers whether they could, nevertheless, exist.     

Core formation in terrestrial planets

Calculations of the radial distribution of the energy released in core formation indicate that the cores of all the terrestrial planets may be expected to receive a disproportionate share of the gravitational energy released. Since the model of the process used in these calculations favors transfer of energy to the mantle, it is likely that other reasonable models of the process will result in even more energy being deposited in the cores of the early planets. The calculations also show that it is necessary for a certain amount of core phase to separate and accumulate, before the energy released by gravitational settling is sufficient to supply the latent heat of fusion of the core phase. The amount of melting required to reach this point varies according to the total mass of the planet, and mass fraction of core, but is not particularly great (<5% for the Earth to ～ 37% for the Moon). In the case of the Moon, this amount of segregation, although large, amounts to a surface layer about 260 km thick, similar to the proposed depth of early wholesale melting. Core separation in terrestrial planets appears to be a self-sustaining process even for fairly small bodies, provided that a small amount of a dense potential core phase is present. Although it seems likely to occur rapidly (within 10⁶–10⁷ years) even for small (Moon-size) bodies, detailed kinetic models will be necessary to specify the time scale.     

Ancient planets and cosmic vagabonds

Strange goings-on in space are revealed by powerful instruments in concert, observing the same phenomena at the same time and in consequence, revealing the inner workings of the stars. Peter Bond reports.     

Global electromagnetic induction in the Moon and planets

A summary of experiments and analyses concerning electromagnetic induction in the Moon and other extraterrestrial bodies is presented. Magnetic step-transient measurements made on the lunar dark side show the eddy current response to be the dominant induction mode of the Moon. Analysis of the poloidal field decay of the eddy currents has yielded a range of monotonic conductivity profiles for the lunar interior: the conductivity rises from 3·10^?4 mho/m at a depth of 170 km to 10^?2 mho/m at 1000 km depth. The static magnetization field induction has been measured and the whole-Moon relative magnetic permeability has been calculated to be $\text{μ}\text{μ}{}_0\text{= 1.01 ± 0.06}$. The remanent magnetic fields, measured at Apollo landing sites, range from 3 to 327 γ. Simultaneous magnetometer and solar wind spectrometer measurements show that the 38-γ remanent field at the Apollo 12 site is compressed to 54 γ by a solar wind pressure increase of 7·10^?8 dyn/cm². The solar wind confines the induced lunar poloidal field; the field is compressed to the surface on the lunar subsolar side and extends out into a cylindrical cavity on the lunar antisolar side. This solar wind confinement is modeled in the laboratory by a magnetic dipole enclosed in a superconducting lead cylinder; results show that the induced poloidal field geometry is modified in a manner similar to that measured on the Moon. Induction concepts developed for the Moon are extended to estimate the electromagnetic response of other bodies in the solar system.     

Minor planets and major X-ray finds

Yohkoh and Ulysses keep a watching brief on the Sun and the solar wind, comets and minor planets appear in close-up, auroral symmetry is confirmed and, elsewhere, X-ray observatories continue to uncover the workings of the high-energy universe. Peter Bond reports.     

Convection-driven zonal flows in the major planets

The major planets produce heat flux from their interiors that is comparable to the radiative flux they receive from the sun. The dynamics of convection flows carrying the heat flux are discussed, and the dominating effect of the Coriolis force is demonstrated. The characteristic high-velocity jets in the atmospheres of Jupiter and Saturn can be explained on the basis of Reynolds stresses generated by the fluctuating convective motions. A simple annulus model, which elucidates the more complex mathematical analysis of the spherical case given in an earlier paper (Busse, 1983), is considered in detail. Various aspects of the observational evidence are discussed in relation to the model.     

Structure and evolution of the terrestrial planets

Geo-scientific planetary research of the last 25 years has revealed the global structure and evolution of the terrestrial planets Moon, Mercury, Venus and Mars. The evolution of the terrestrial bodies involves a differentiation into heavy metallic cores, Fe-and Mg-rich silicate mantles and light Ca, Al-rich silicate crusts early in the history of the solar system. Magnetic measurements yield a weak dipole field for Mercury, a very weak field (and local anomalies) for the Moon and no measurable field for Venus and mars. Seismic studies of the Moon show a crust-mantle boundary at an average depth of 60 km for the front side, P- and S-wave velocities around 8 respectively 4.5 km s^–1 in the mantle and a considerable S-wave attenuation below a depth of 1000 km. Satellite gravity permits the study of lateral density variations in the lithosphere. Additional contributions come from photogeology, orbital particle, x-and -ray measurements, radar and petrology.The cratered surfaces of the smaller bodies Moon and Mercury have been mainly shaped by meteorite impacts followed by a period of volcanic flows into the impact basins until about 3×10⁹ yr before present. Mars in addition shows a more developed surface. Its northern half is dominated by subsidence and younger volcanic flows. It even shows a graben system (rift) in the equatorial region. Large channels and relics of permafrost attest the role of water for the erosional history. Venus, the most developed body except Earth, shows many indications of volcanism, grabens (rifts) and at least at northern latitudes collisional belts, i.e. mountain ranges, suggesting a limited plate tectonic process with a possible shallow subduction.List of Symbols and Abbreviations a=R _e mean equatorial radius (km) - A(r, t) heat production by radioactive elements (W m^–3) - A, B equatorial moments of inertia - b polar radius (km) - complex amplitude of bathymetry in the wave number (K) domain (m) - C polar moment of inertia - C _Fe moment of inertia of metallic core - C _Si moment of inertia of silicate mantle - C _p heat capacity at constant pressure (JK^–1 mole^–) - C _nm,J _nm,S _nm harmonic coefficients of degreen and orderm - C/(MR _e ² ) factor of moment of inertia - d distance (km) - d nondimensional radius of disc load of elastic bending model - D diameter of crater (km) - D flexural rigidity (dyn cm) - E Young modulus (dyn cm^–2) - E maximum strain energy - E energy loss during time interval t - f frequency (Hz) - f flattening - F magnetic field strength (Oe) (1 Oe=79.58A m^–1) - g acceleration or gravity (cms^–2) or (mGal) (1mGal=10^–3cms^–2) - mean acceleration - g _e equatorial surface gravity - complex amplitude of gravity anomaly in the wave number (K) domain - g free air gravity anomaly (FAA) - g Bouguer gravity anomaly - g _t gravity attraction of the topography - G gravitational constant,G=6.67×10^–11 m³kg^–1s^–2 - GM planetocentric gravitational constant - h relation of centrifugal acceleration (² R _e ) to surface acceleration (g _e ) at the equator - J magnetic flux density (magnetic field) (T) (1T=10⁹ nT=10⁹ =10⁴G (Gauss)) - J ₂ oblateness - J _nm seeC _nm - k ₍₀₎ (zero) pressure bulk modulus (Pa) (Pascal, 1 Pa=1 Nm^–2) - K wave number (km^–1) - K ^* thermal conductivity (Jm^–1s^–1K^–1) - L thickness of elastic lithosphere (km) - M mas of planet (kg) - M _Fe mass of metallic core - M _Si mass of silicate mantle - M(r) fractional mass of planet with fractional radiusr - m magnetic dipole moment (Am²) (1Am²=10³Gcm³) - m _b body wave magnitude - N crater frequency (km^–2) - N(D) cumulative number of cumulative frequency of craters with diameters D - P pressure (Pa) (1Pa=1Nm^–2=10^–5 bar) - P _z vertical (lithostatic) stress, see also _z (Pa) - P _n ^m (cos) Legendre polynomial - q surface load (dyn cm^–2) - Q seismic quality factor, 2E/E - Q _s ,Q _p seismic quality factor derived from seismic S-and P-waves - R=R ₀ mean radius of the planet (km) (2a+b)/3 - R _e =a mean equatorial radius of the planet - r distance from the center of the planet (fractional radius) - r _Fe radius of metallic core - S _nm seeC _nm - t time and age in a (years), d (days), h (hours), min (minutes), s (seconds) - T mean crustal thickness from Airy isostatic gravity models (km) - T temperature (°C or K) (0°C=273.15K) - T _m solidus temperature - T sideral period of rotation in d (days), h (hours), min (minutes), s (seconds), =2/T - U external potential field of gravity of a planet - V volume of planet - V _p ,V _s compressional (P), shear (S) wave velocity, respectively (kms^–1) - w deflection of lithosphere from elastic bending models (km) - z, Z depth (km) - z (K) admittance function (mGal m^–1) - thermal expansion (°C^–1) - viscosity (poise) (1 poise=1gcm^–1s^–1) - co-latitude (90°-) - longitude - Poisson ratio - density (g cm^–3) - mean density - ₀ zero pressure density - _m , _Si average density of silicate mantle (fluid interior) - average density of metallic core - _t , _top density of the topography - density difference between crustal and mantle material - electrical conductivity (^–1 m^–1) - _r , radial and azimuthal surface stress of axisymmetric load (Pa) - _z vertical (lithostatic) stress (seeP _z ) - _II second invariant of stress deviation tensor - latitude - angular velocity of a planet (=2/T) - ages in years (a), generally 0 years is present - B.P. before present - FAA Free Air Gravity Anomaly (see g - HFT High Frequency Teleseismic event - LTP Lunar Transient Phenomenon - LOS Line-Of-Sight - NRM Natural Remanent Magnetization Contribution No. 309, Institut für Geophysik der Universität, Kiel, F.R.G.     

Numerical approaches to solid-state convection in planetary bodies

Numerical methods suitable for the calculation of finite-amplitude thermal convection in planetary interiors are reviewed. Three methods of approach are described and compared; namely, finite-difference, finite-element and spectral procedures. Application of each approach to three-dimensional solid-state convection with complex rheology is examined. Finite-difference methods have enjoyed some success to date. However, future developments are likely to favor finite-element methods when rheology and boundaries are complex, and spectral methods when accuracy is paramount and rheology and boundaries are simple.     

Early physical conditions of the planets and satellites

An understanding of the origin of the Solar System is proving hard to achieve and there is still no finally accepted account. A wider range of reliable data, and especially for the outer Solar System, has become available over the last decade due to the use of space vehicles, and particularly the two Voyager probes which are now passing out of the Solar System. The planetary and satellite systems can, therefore, be viewed now more nearly as a whole than previously and consequences for the theory of the origin of the System should follow. The subject is here reviewed again but emphasis is placed on the relative planetology of the whole System. The only reliable data available to us are associated with the System as it is now and this will be the starting point for our discussion.     

Transition to two-dimensional turbulent convection in a rapidly-rotating annulus

Abstract

We study a semi-analytical model of convection in a rapidly-rotating, differentially-heated annulus with sloping top and bottom lids. Rapid rotation leads to a preservation of relatively simple, two-dimensional (2-D) structure in the experimentally-observed flow, while temporal complexity increases with the Rayleigh number. The model is, therefore, two-dimensional; it exhibits a sequence of bifurcations from steadily-drifting, azimuthally-periodic convection columns, also called thermal Rossby waves, through vacillation and a period-doubling cascade, to aperiodic, weakly-turbulent solutions.

Our semi-analytical results match to within a few percent previous numerical results with a limited-resolution 2-D model, and extend these results, due to the greater flexibility of the model presented here. Two types of vacillation are obtained, which we call, by analogy with classical nomenclature of the baroclinic annulus with moderate rotation rates, amplitude vacillation and tilted-trough vacillation. Their properties and dependence on the problem's nondimensional parameters are investigated. The period-doubling cascade for each type of vacillation is studied in some detail.