Solar cycle evolution of the heliospheric magnetic field: The Ulysses legacy

Important contributions of Ulysses to understanding the solar cycle evolution of the heliospheric magnetic field (HMF) and solar wind are reviewed: a dramatic reorientation of the HMF as the solar dipole rotates between axial and equatorial orientations; solar cycle variation of the total heliospheric magnetic flux and its response to changes in solar magnetic fields; the unusual on-going solar minimum and its effects; a connection between magnetic flux and solar wind mass flux in the heliosphere and at the source; a recurrent north–south heliospheric asymmetry at solar minimum and the equatorial offset of the solar magnetic dipole.     

带电粒子在磁场中的运动区及其模型实验

本文讨论了带电粒子在电磁场中的运动区域.在计算过程中假定磁场是有势的,并且势函数分别考虑为轴对称与平面函数.计算结果表明:当磁场足够强时,粒子运动区的边界与磁力线是相似的.这个结果表明,我们可以根据磁力线图形确定带电粒子的运动区.此外,还将上述计算结果与模型实验做了对此,在磁场中的辉光放电实验里,放电中的辉光区部分相当于粒子的运动区,暗区部分相当于粒子禁区.对比结果表明,辉光区的边界与磁力线相似,其中有以下几个结果:（1）当磁场是一个偶极磁场,并且其磁短的大小大于其临界值时,则放电辉光将被捕获于偶极磁场中,其边界近似于磁力线;（2）当偶极磁场受到扰动时,设扰动场分别考虑为与赤道面上的偶极磁场方向相反的均匀磁场,以及位于捕获区之外在赤道面上的电流环磁场时,则偶极磁场磁力线将向外伸长,实验观测到被捕获于偶极磁场中的辉光将同时伸长,并且辉光区边界的变化与磁力线的变化是相似的;（3）根据中性线磁场中的辉光放电实验表明,辉光区的边界仍然与中性楱磁场的磁力线相似.由于气体放电中的现象比较复杂,因此要进行定量的计算是比较困难的,为此我们引进了一些简化假定,定量计算了辉光区在上进各种磁场中的边界,计算出来的辉光边界的大小和形状与实验结果是相同的.     

Small-scale magnetic buoyancy and magnetic pumping effects in a turbulent convection

We determine the nonlinear drift velocities of the mean magnetic field and nonlinear turbulent magnetic diffusion in a turbulent convection. We show that the nonlinear drift velocities are caused by three kinds of the inhomogeneities; i.e., inhomogeneous turbulence, the nonuniform fluid density and the nonuniform turbulent heat flux. The inhomogeneous turbulence results in the well-known turbulent diamagnetic and paramagnetic velocities. The nonlinear drift velocities of the mean magnetic field cause the small-scale magnetic buoyancy and magnetic pumping effects in the turbulent convection. These phenomena are different from the large-scale magnetic buoyancy and magnetic pumping effects which are due to the effect of the mean magnetic field on the large-scale density stratified fluid flow. The small-scale magnetic buoyancy and magnetic pumping can be stronger than these large-scale effects when the mean magnetic field is smaller than the equipartition field. We discuss the small-scale magnetic buoyancy and magnetic pumping effects in the context of the solar and stellar turbulent convection. We demonstrate also that the nonlinear turbulent magnetic diffusion in the turbulent convection is anisotropic even for a weak mean magnetic field. In particular, it is enhanced in the radial direction. The magnetic fluctuations due to the small-scale dynamo increase the turbulent magnetic diffusion of the toroidal component of the mean magnetic field, while they do not affect the turbulent magnetic diffusion of the poloidal field.     

From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.     

Geomagnetic polarity reversals in a turbulent core

The behavior of the main magnetic field components during a polarity transition is investigated using the α²-dynamo model for magnetic field generation in a turbulent core. It is shown that rapid reversals of the dipole field occur when the helicity, a measure of correlation between turbulent velocity and vorticity, changes sign. Two classes of polarity transitions are possible. Within the first class, termed component reversals, the dipole field reverses but the toroidal field does not. Within the second class, termed full reversals, both dipole and toroidal fields reverse. Component reversals result from long term fluctuations in core helicity; full reversals result from short term fluctuations. A set of time-evolution equations are derived which govern the dipole field behavior during an idealized transition. Solutions to these equations exhibit transitions in which the dipole remains axial while its intensity decays rapidly toward zero, and is regenerated with reversed polarity. Assuming an electrical conductivity of 3 × 10⁵ mho m^?1 for the fluid core, the time interval required to complete the reversal process can be as short as 7500 years. This time scale is consistent with paleomagnetic observations of the duration of reversals. A possible explanation of the cause of reversals is proposed, in which the core's net helicity fluctuates in response to fluctuations in the level of turbulence produced by two competing energy sources—thermal convection and segregation of the inner core. Symmetry considerations indicate that, in each hemisphere, helicity generated by heat loss at the core-mantle boundary may have the opposite sign of helicity generated by energy release at the inner core boundary. Random variations in rates of energy release can cause the net helicity and the α-effect to change sign occasionally, provoking a field reversal. In this model, energy release by inner core formation tends to destabilize stationary dynamo action, causing polarity reversals.     

Mantle-driven geodynamo features – Effects of compositional and narrow D″ anomalies

Lower mantle heterogeneity could cause deviations from axial symmetry in geodynamo properties. Global tomography models are commonly used to infer the pattern of core–mantle boundary heat flux via a linear relation that corresponds to a purely thermal interpretation of lower mantle seismic anomalies, ignoring both non-thermal origins and non-resolved small scales. Here we study the possible impact on the geodynamo of narrow thermal anomalies in the base of the mantle, originating from either compositional heterogeneity or sharp margins of large-scale features. A heat flux boundary condition composed of a large-scale pattern and narrow ridges separating the large-scale positive and negative features is imposed on numerical dynamos. We find that hot ridges located to the west of a positive large-scale core–mantle boundary heat flux anomaly produce a time-average narrow elongated upwelling, a flow barrier at the top of the core and intensified low-latitudes magnetic flux patches. When the ridge is located to the east of a positive core–mantle boundary heat flux anomaly, the associated upwelling is weaker and the homogeneous dynamo westward drift leaks, precluding persistent intense low-latitudes magnetic flux patches. These signatures of the core–mantle boundary heat flux ridge are evident in the north–south component of the thermal wind balance. Based on the pattern of lower mantle seismic tomography (Masters et al., 2000), we hypothesize that hot narrow thermal ridges below central Asia and the Indian Ocean and below the American Pacific coast produce time-average fluid upwelling and a barrier for azimuthal flow at the top of the core. East of these ridges, below east Asia and Oceania and below the Americas, time-average intense geomagnetic flux patches are expected.     

Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y ₂² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core.     

Buoyancy-driven perturbations in a rapidly rotating,electrically conducting fluid: part I – flow and magnetic field

The steady velocity, perturbation pressure and perturbation magnetic field, driven by an isolated buoyant parcel of Gaussian shape in a rapidly rotating, unconfined, incompressible electrically conducting fluid in the presence of an imposed uniform magnetic field, are obtained by means of the Fourier transform in the limit of small Ekman number. Lorentz and inertial forces are neglected. The solution requires at most evaluation of a single integral and is found in closed form in some spatial regions. The solution has structure on two disparate scales: on the scale of the buoyant parcel and on the scale of the Taylor column, which is elongated in the direction of the rotation axis. The detailed structures of the flow and pressure depend linearly on the relative orientation of gravity and rotation, with the solution for arbitrary orientation being a linear combination of two limiting cases in which these vectors are colinear (polar case) and perpendicular (equatorial case). The perturbation magnetic field depends additionally on the relative orientation of the imposed magnetic field, and three limiting cases of interest are presented in which gravity and rotation are colinear (polar–toroidal case), gravity and imposed field are colinear (equatorial–radial case) and all three are mutually perpendicular (equatorial–toroidal case). Visualization and analysis of the velocity and perturbation magnetic field vectors are facilitated by dividing these vector fields into geostrophic and ageostrophic protions. In all cases, the geostrophic and ageostrophic portions have different structure on the Taylor-column scale. The buoyancy force is balanced by a pressure force in the polar case and by a flux of momentum in the equatorial case. The pressure force and momentum flux do not decay in strength with increasing axial distance. Far from the parcel, the axial mass flux varies as the inverse one-third power of distance from the parcel. The velocity has a single geostrophic vortex in the polar case and two vortices in the equatorial case. The perturbation magnetic field has two, four and one geostrophic vortices in the polar–toroidal, equatorial–radial and equatorial–toroidal cases, respectively. To facilitate comparison of the present results with numerical simulations carried out in a finite domain, a set of boundary conditions are developed, with may be applied at a finite distance from the parcel.     

Axial and equatorial rotations of the Earth's cores associated with the Quaternary ice age

The differential axial and equatorial rotations of both cores associated with the Quaternary glacial cycles were evaluated based on a realistic earth model in density and elastic structures. The rheological model is composed of compressible Maxwell viscoelastic mantle, inviscid outer core and incompressible Maxwell viscoelastic inner core. The present study is, however, preliminary because I assume a rigid rotation for the fluid outer core. In models with no frictional torques at the boundaries of the outer core, the maximum magnitude of the predicted axial rotations of the outer and inner cores amounts to ∼2° year⁻¹ and ∼1° year⁻¹, respectively, but that for the secular equatorial rotations of both cores is ∼0.0001° at most. However, oscillating parts with a period of ∼225 years are predicted in the equatorial rotations for both cores. Then, I evaluated the differential rotations by adopting a time-dependent electromagnetic (EM) torque as a possible coupling mechanism at the core-mantle boundary (CMB) and inner core boundary (ICB). In a realistic radial magnetic field at the CMB estimated from surface magnetic field, the axial and equatorial rotations couple through frictional torques at the CMB, although these rotations decouple for dipole magnetic field model. The differential rotations were evaluated for conductivity models with a conductance of 10⁸ S of the lowermost mantle inferred from studies of nutation and precession of the Earth and decadal variations of length of day (LOD). The secular parts of equatorial rotations are less sensitive to these parameters, but the magnitude for the axial rotations is much smaller than for frictionless model. These models, however, produce oscillating parts in the equatorial rotations of both cores and also in the axial rotations of the whole Earth and outer and inner cores. These oscillations are sensitive to both the magnitude of radial magnetic field at the CMB and the conductivity structure. No sharp isolated spectral peaks are predicted for models with a thin conductive layer (∼200 m) at the bottom of the mantle. In models with a conductive layer of ∼100 km thickness, however, sharp spectral peaks are predicted at periods of ∼225 and ∼25 years for equatorial and axial rotations, respectively, although these depend on the strength of radial magnetic field at the CMB. While the present study is preliminary in modelling the fluid outer core and coupling mechanism at the CMB, the predicted axial rotations of the whole Earth may be important in explaining the observed LOD through interaction between the equatorial and axial rotations.     

Effects of convection instability due to incompatibility between ocean dynamics and surface forcings

The study demonstrates that an incompatibility between a surface temperature climatology and a given ocean model, into which the climatology is assimilated via Haney restoration, can cause model ocean climate drift and interdecadal oscillations when the ocean is switched to a weaker restoration. This is made using an idealized Atlantic Ocean model driven by thermal and wind forcing only. Initially, the temperature climatology is forcefully assimilated into the model, and an implied heat flux field is diagnosed. During this stage any incompatibility is suppressed. The restoring boundary condition is then switched to a new forcing consisting of a part of the diagnosed flux and a part of the restoring forcing in such a way that at the moment of the switching the heat flux is identical to that prior to the switching. Under this new forcing condition, the incompatibility becomes manifest, causing changes in convection patterns, and producing drift and interdecadal oscillations. The mechanisms are described.     

Helical core flow from geomagnetic secular variation

Fluid flow below the core-mantle boundary is inferred from geomagnetic secular variation data, assuming frozen magnetic flux and a new physical assumption termed helical flow, in which the tangential divergence correlates with the radial vorticity. Helical flow introduces streamfunction diffusion and removes non-uniqueness in the inversion of the magnetic induction equation. We combine helical flow with tangential geostrophy and compare the following physical assumptions: tangential geostrophy, strong helicity, weak helicity and columnar flow, using geomagnetic field models from the 2000 Oersted and 1980 Magsat satellites. Our solutions contain some features found in previous core flow models, such as large mid-latitude vortices, westward drift in most of the southern hemisphere, and suggested polar vortices. However, our solutions contain significantly more flow along contours of the radial magnetic field than previous core flow models.     

Geomagnetic secular variation from recent lake sediments,ancient fireplaces and historical measurements in southeastern Australia

Compilations of historical observations, archaeomagnetic data from ancient fireplaces and palaemagetic results from short cores of sediment from lakes in southeastern Australia, particularly Lake Keilambete, provide a detailed record of the geomagnetic secular variation during the last 3000 years. The independent sets of data are in good agreement if the radiocarbon time scale for the lacustrine record is about 450 years too old. The error is attributed to systematic incorporation of ancient carbon into the lake floor sediments, mainly through erosion of sediment on the crater walls at times of low water level. A significant lag between deposition and the acquisition of stable magnetic remanence is ruled out. Inclination has been abnormally steep during the last 500 years but remained fairly close to the axial dipole field value prior to that. During the last 1000 years the predominant sense of looping of the magnetic vector corresponds to westward drift of the nondipole field. Secular variations on a time scale of ～ 100 years can be resolved by the lacustrine record.     

Review of the geomagnetic secular variations on the historical time scale

In view of the classification of the geomagnetic field into its axisymmetric and non-axisymmetric parts, studies of geomagnetic secular variations on the historical time-scale are reviewed. The westward drift of the geomagnetic field, which is one of the most conspicuous features of its secular variation, is examined first. The non-axisymmetric field during the past several hundred years can be well approximated by the superposition of two constant-magnitude fields, a standing and a drifting field, whose lifetimes are supposed to be longer than 1000 years. It is pointed out that the sectorial term of the non-dipole standing field is small compared with the drifting one. The lack of the n = M = 2 term of the standing field is particularly remarkable.

On the other hand, the equatorial dipole field is likely to consist of two components which are both drifting. One drifts westwards with a normal velocity and the other eastwards with a small velocity.

Besides the pronounced westward drift in an east-west direction, the poleward movements of particular foci of the secular variation are noted. This may, however, be related to the rapid growth of the axisymmetric quadrupole field.

The time variation of the dipole field is briefly examined. As far as the data on the historical time scale are concerned, an antiparallel relationship seems to exist between the variations in the dipole and the quadrupole field. As the dipole moment decreases, the magnitude of the quadrupole moment increases. Finally, characteristic oscillation periods of the dipole field are examined. Although the data are few, a 60–70-year period, a 400–600-year and a 8000-year period emerge as the dominant periods.     

地磁场长期变化和日长十年尺度变化的周期特征

根据历史地磁场模型GUFM1、第10代国际参考地磁场（IGRF10）模型和日长资料,采用小波变换方法,分析了地磁场磁矩、能量、西向漂移等参数的长期变化和日长十年尺度变化的周期分量及其时变特征.结果表明,1800～2005年期间,偶极子磁场长期变化有82年和48年准周期分量,它们与日长变化的周期没有直接关系.非偶极子磁场参数的长期变化与日长变化有66年和32年准周期分量,66年准周期比32年准周期强.在66年准周期分量,西向漂移比日长变化超前8.8年,非偶极子磁场能量比日长变化滞后15.6年.日长十年尺度波动和地磁场长期变化的起源不存在因果关系.     

The ionospheric F2-region at low geomagnetic latitudes during the geomagnetic storms of 22–26 April 1990: Comparison of observed and modeled response

A comparison between the modeled NmF2 and hmF2 and NmF2 and hmF2, which were observed by the Kokubunji, Okinawa, Manila, Vanimo, and Darwin ionospheric sounders and by the middle and upper (MU) atmosphere radar, have been used to study the time-dependent response of the low-latitude ionosphere to geomagnetic forcing during a time series of geomagnetic storms from 22 to 26 April 1990. The reasonable agreement between the model results and data requires the modified equatorial meridional E×B plasma drift, the modified HWM90 wind, and the modified NRLMSISE-00 neutral densities. We found that changes in a flux of plasma into the nighttime equatorial F2-region from higher L-shells to lower L-shells caused by the meridional component of the E×B plasma drift lead to enhancements in NmF2 close to the geomagnetic equator. The equatorward wind-induced plasma drift along magnetic field lines, which cross the Earth equatorward of about 20° geomagnetic latitude in the northern hemisphere and about −19° geomagnetic latitude in the southern hemisphere, contributes to the maintenance of the F2-layer close to the geomagnetic equator. The nighttime weakening of the equatorial zonal electric field (in comparison with that produced by the empirical model of Fejer and Scherliess [Fejer, B.G., Scherliess, L., 1997. Empirical models of storm time equatorial zonal electric fields. J. Geophys. Res. 102, 24047–24056] or Scherliess and Fejer [Scherliess, L., Fejer, B.G., 1999. Radar and satellite global equatorial F region vertical drift model. J. Geophys. Res. 104, 6829–6842) in combination with corrected equatorward nighttime wind-induced plasma drift along magnetic field lines in the both geomagnetic hemispheres are found to be the physical mechanism of the nighttime NmF2 enhancement formation close to the geomagnetic equator over Manila during 22–26 April 1990. The model crest-to-trough ratios of the equatorial anomaly are used to study the relative role of the main mechanisms of the equatorial anomaly suppression for the 22–26 April 1990 geomagnetic storms. During the most part of the studied time period, a total contribution from geomagnetic storm disturbances in the neutral temperature and densities to the equatorial anomaly changes is less than that from meridional neutral winds and variations in the E×B plasma drift. It is shown that the latitudinal positions of the crests are determined by the E×B drift velocity and the neutral wind velocity.     

Reduced heat transfer in saltwater by a magnetic field: do oceans have a “geomagnetic brake”?

Seawater is the major heat transporter in our global environment, covering more than two-thirds of the surface of the earth. With an average salinity of ～3.5%, it is a moderate electric conductor, which is permanently in motion by thermal and hydrodynamic forces. A magnetic field exerts a Lorentz force on seawater that principally influences both the dissipation of turbulence and the flow properties by magnetic friction. Here we show by experiments on laboratory scale that convection in seawater is slowed down by an external static magnetic field and leads to a reduced heat flux resulting in an increased or decreased heat content in the volume in response to influx or drain of heat, respectively. Experimentally, the application of a vertical magnetic field of 60 mT reduces the convective heat transport on the liquid-air surface within in 5 min by about 8% perpendicular to the field and up to 14% parallel to it. The effect is strongly correlated with the magnetic interaction parameter of the system, which relates the magnetic to the viscous volume force. In the natural environment, the geomagnetic field is omnipresent. It is weaker by about three orders of magnitude compared with the magnetic field applied in the experiments. It has, however, an undisturbed and long-lasting impact on the convection, at low Reynolds numbers, in the large body of water in the deeper ocean below the mixed layer. There are no investigations regarding a possible contribution of this effect to natural saltwater flows, neither by proxy experiments nor by model calculations. The data presented raise the possibility that convective heat transport in the sea could be always slowed down by the geomagnetic field to a certain extent, besides it could be modulated by the geomagnetic secular variation on relatively short timescales like decades.     

Long wavelength thermal convection between non-conducting boundaries

Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection.     

Detecting thermal boundary control in surface flows from numerical dynamos

The geomagnetic field and secular variation exhibit asymmetrical spatial features which are possibly originating from an heterogeneous thermal control of the Earth's lower mantle on the core. The identification of this control in magnetic data is subject to several difficulties, some of which can be alleviated by the use of core surface flow models. Using numerical dynamos driven by heterogeneous boundary heat flux, we confirm that within the parameter space accessible to simulations, time average surface flows obey a simple thermal wind equilibrium between the Coriolis and buoyancy forces, the Lorentz, inertial and viscous forces playing only a secondary role, even for Elsasser numbers significantly larger than 1. Furthermore, we average the models over the duration of three vortex turnovers, and correlate them with a longer time average which fully reveals the signature of boundary heterogeneity. This allows us to quantify the possibility of observing mantle control in core surface flows averaged over a short time period. A scaling analysis is performed in order to apply the results to the Earth's core. We find that three vortex turnovers could represent between 100 and 360 years of Earth time, and that the heat flux heterogeneity at the core-mantle boundary could be large enough to yield an observable signature of thermal mantle control in a time average core surface flow within reach of the available geomagnetic data.     

Asymmetry of geomagnetic polarity: Equatorial dipole,Pangaea, and the Earth’s core

The paper presents the results of analyzing the set of dual-polarity paleomagnetic results the Global Paleomagnetic Database (GPMDB). The dataset was expanded by the results from the Paleomagnetic Data Catalogue for the USSR and with new data published after 2005. Some results were rejected to avoid the influence of overprints of ancient and recent magnetization. Overall, 59 dual-polarity results for the lithospheric plates of Baltica, Laurentia, and Siberia with their immediate framing were selected for the analysis in the interval of ages 207–359 Ma. The new data confirmed the model of the paleomagnetic field, according to which the field contains a long-lived component corresponding to the equatorial dipole which is responsible for the non-antipodal paleomagnetic directions in the zones of normal and reverse polarity in sedimentary and volcanic rock sequences. Retaining its value of 5–8% of the central axial dipole, the equatorial dipole changed its polarity a few times during the interval 359–207 Ma. The northern poles of the dipole formed two antipodal groups on the Earth’s surface, which lie within or near the subduction zones on the periphery of the Pangaea Supercontinent. Such localization of the equatorial dipole is suggested to be related to the ascending branches of the mantle convection and to the topography of both boundaries of the outer Earth’s core.