Flux Lobes Research Articles

Elementary heating events – magnetic interactions between two flux sources

The magnetic field plays a crucial role in heating the solar corona – this has been known for many years – but the exact energy release mechanism(s) is(are) still unknown. Here, we investigate in detail, using resistive, non-ideal, MHD models, the process of magnetic energy release in a situation where two initially independent flux systems are forced into each other. Work done by the foot point motions goes into building a current sheet in which magnetic reconnection releases some of the free magnetic energy leading to magnetic connectivity changes. The scaling relations of the energy input and output are determined as functions of the driving velocity and the strength of fluxes in the independent flux systems. In particular, it is found that the energy injected into the system is proportional to the distance travelled. Similarly, the rate of Joule dissipation is related to the distance travelled. Hence, rapidly driven foot points lead to bright, intense, but short-lived events, whilst slowly driven foot points produce weaker, but longer-lived brightenings. Integrated over the lifetime of the events both would produce the same heating if all other factors were the same. A strong overlying field has the effect of creating compact flux lobes from the sources. These appear to lead to a more rapid injection of energy, as well as a more rapid release of energy. Thus, the stronger the overlying field the more compact and more intense the heating. This means observers need to know not only the flux of the magnetic fragments involved in an event, but also their rate and direction of movement, as well as the strength and orientation of the surrounding field to be able to predict the energy dissipated. Furthermore, it is found that rough estimates of the available energy can be obtained from simple models, starting from initial potential situations, but that the time scale for the energy release and, therefore its impact on the coronal plasma, can only be determined from more detailed investigations of the non-ideal behaviour of the plasma.

Continuous geomagnetic field models for the past 7 millennia: 2. CALS7K

We present two continuous global geomagnetic field models for recent millennia: CALS3K.2, covering the past 3000 years, and CALS7K.2, covering 7000 years from 5000 BC to 1950 AD. The models were determined by regularized least squares inversion of archeomagnetic and paleomagnetic data using spherical harmonics in space and cubic B splines in time. They are derived from a greatly increased number of paleomagnetic directional data, compared to previous efforts, and for the first time a significant amount of archeointensity data is used in this kind of global model, allowing the determination of evolution of geomagnetic dipole strength. While data accuracy and dating uncertainties remain a limitation, reliable low‐resolution global models can be obtained. The results agree well with previous results from virtual axial dipole moment (VADM) studies from archeomagnetic intensity data apart from a systematic offset in strength. A comparison of model predictions with the previous 3000 year model, CALS3K.1, gives general agreement but also some significant differences particularly for the early epochs. The new models suggest that the prominent two northern hemisphere flux lobes are more stationary than CALS3K.1 implied, extending considerably the time span of stationary flux lobes observed in historical models. Between 5000 BC and 2000 BC there are time intervals of weak dipole moment where dipole power is exceeded by low‐degree nondipole power at the core‐mantle boundary. Model coefficients and evaluation code can be obtained from the EarthRef Digital Archive (ERDA) together with animations and snapshots plots for every 100 years at http://www.earthref.org. Detailed URLs for the different material are listed in Appendix A.

Large-scale disturbance of the solar wind by a comet

Model calculations for the interaction of the solar wind with a comet are presented that extend 30 million km into the tail. It is shown that the disturbance of the interplanetary magnetic eld (IMF) (the draping) is limited to timescales of 10 to 50 hours and length scales of 10 to 50 million km. This is supported by a theoretical argument about the acceleration of the cometary ions. The distribution of ions and protons at the end of the model tails agrees with measurements made by Ulysses far in the tail of comet Hyakutake. It is shown that the ion tail is concentrated in the current sheet between two flux lobes as long as the draping persists. The far tail, however, is flat and concentrated in a plane parallel to the IMF.

Global geomagnetic field models for the past 3000 years: transient or permanent flux lobes?

PSVMOD1.0 is a compilation of globally distributed palaeodirectional data from archaeomagnetic artefacts, lava flows, and lake sediments at 24 sites evaluated at 100 year intervals from 1000 BC to AD 1800. We estimate uncertainty in these measures of declination and inclination by comparison with predictions from standard historical models in time–intervals of overlap, and use the 100–year samples and their associated uncertainties to construct a sequence of minimum structure global geomagnetic field models. Global predictions of radial magnetic field at the coremantle boundary (CMB), as well as inclination and declination anomalies at the Earth9s surface, provide an unprecedented view of geomagnetic secular variations over the past 3000 years, and demonstrate a consistent evolution of the field with time. Resolution of the models is poorest in the Southern Hemisphere, where only six of the 24 sites are located, several with incomplete temporal coverage. Low–flux regions seen in the historical field near the North Pole are poorly resolved, but the Northern Hemisphere flux lobes are clearly visible in the models. These lobes are not fixed in position and intensity, but they only rarely venture into the Pacific hemisphere. The Pacific region is seen to have experienced significant secular variation: a strong negative inclination anomaly in the region, like that seen in 0–5 Ma models, persists from 1000 BC until AD 1000 and then gradually evolves into the smaller positive anomaly seen today. On average between 1000 BC and AD 1800, the non–axial–dipole contribution to the radial magnetic field at the core–mantle boundary is largest in the north–central Pacific, and beneath Central Asia, with clear non–zonal contributions. At the Earth9s surface, average inclination anomalies are large and negative in the central Pacific, and most positive slightly to the east of Central Africa. Inclination anomalies decrease with increasing latitude. Average declinations are smallest in equatorial regions, again with strong longitudinal variations, largest negative departures are centred over Australia and Eastern Asia. Secular variation at the Earth9s surface is quantified by standard deviation of inclination and declination about their average values, and at the CMB by standard deviation in radial magnetic field. All three show significant geographical variations, but appear incompatible with the idea that secular variation in the Pacific hemisphere is permanently attenuated by greatly enhanced conductivity in D 00 beneath the region.

Anisotropic paleosecular variation models: implications for geomagnetic field observables

We present a family of statistical models for paleosecular variation (PSV) of the geomagnetic field that are compatible with paleodirectional and paleointensity variations in lava flows sampling the last 5 Ma, and explore what paleomagnetic observables might be used to discriminate among the various family members. We distinguish statistical models with axial anisotropy, which provide a suitable description for an earth with homogeneous boundary conditions at the core–mantle interface from those with more general anisotropy corresponding to geographically heterogeneous boundary conditions. The models revise and extend earlier ones, which are themselves descendants of CP88, devised by Constable and Parker [Constable, C.G., Parker, R.L., 1988. Statistics of the geomagnetic secular variation for the past 5 m.y. J. Geophys. Res. 93, 11569–11581]. In CP88, secular variation is described by statistical variability of each Gauss coefficient in a spherical harmonic description of the geomagnetic field, with each coefficient treated as a normally distributed random variable: the Gauss coefficients of the non-dipole part of the field exhibit isotropic variability, and the variances are derived from the present field spatial power spectrum. The dipole terms have a special status in CP88, with a non-zero mean for the axial-dipole, and lower variance than predicted from the spatial power spectrum. All non-dipole terms have zero mean except the axial-quadrupole. CP88 is untenable for two reasons: it fails to predict the observed geographic dependence of directional variability in the magnetic field, and it grossly underpredicts the variance in paleointensity data. The new models incorporate large variance in the axial-dipole, and in the non-axial-quadrupole Gauss coefficients, g 2 1 and h 2 1. The resulting variance in paleomagnetic observables depends only on latitude (zonal models), unless the variance in h 2 1 is different from that in g 2 1 (non-zonal models). Non-zonal (longitudinal) variations in PSV, such as the flux lobes seen in the historical magnetic field, are simulated using the non-zonal models. Both the zonal and non-zonal models fit summary statistics of the present dataset. We investigate the influence of persistent non-zonal influences in PSV on various paleomagnetic observables. It is shown that virtual geomagnetic pole (VGP) dispersion is rather insensitive to longitudinal variations in structure of PSV, and that inclination dispersion has the potential to be more informative given the right site distribution. There is also the possibility of using paleointensity and geographic variations in the frequency of occurrence of excursional directions to identify appropriate PSV models.

The time-averaged geomagnetic field: global and regional biases for 0-5 Ma

SUMMARY Palaeodirectional data from lava flows and marine sediments provide information about the long-term structure and variability in the geomagnetic field. We present a detailed analysis of the internal consistency and reliability of global compilations of sediment and lava-flow data. Time-averaged field models are constructed for normal and reverse polarity periods for the past 5 Ma, using the combined data sets. Nonzonal models are required to satisfy the lava-flow data, but not those from sediments alone. This is in part because the sediment data are much noisier than those from lavas, but is also a consequence of the site distributions and the way that inclination data sample the geomagnetic field generated in the Earth’s core. Different average field configurations for normal and reverse polarity periods are consistent with the palaeomagnetic directions; however, the differences are insignificant relative to the uncertainty in the average field models. Thus previous inferences of non-antipodal normal and reverse polarity field geometries will need to be re-examined using recently collected high-quality palaeomagnetic data. Our new models indicate that current global sediment and lava-flow data sets combined do not permit the unambiguous detection of northern hemisphere flux lobes in the 0-5 Ma time-averaged field, highlighting the need for the collection of additional high-latitude palaeomagnetic data. Anomalous time-averaged field structure is seen in the Pacific hemisphere centred just south of Hawaii. The location of the anomaly coincides with heterogeneities in the lower mantle inferred from seismological data. The seismic observations can be partly explained by lateral temperature variations; however, they also suggest the presence of lateral compositional variations and/or the presence of partial melt. The role of such heterogeneities in influencing the geomagnetic field observed at the Earth’s surface remains an unresolved issue, requiring higher-resolution time-averaged geomagnetic field models, along with the integration of future results from seismology, mineral physics and numerical simulations.

Palaeosecular variation recorded by lava flows over the past five million years

We present a new global palaeomagnetic database, comprising lava flows and thin intrusive bodies, suitable for studying palaeosecular variation and the time-averaged field. The database is presented in some detail in the appendix and is available on-line from the authors. We review palaeosecular variation models to date, emphasizing the assumptions required and the rather arbitrary construction of many of these models. Preliminary studies of the statistical properties of the new database suggest that existing palaeosecular variation models are inadequate to explain the long-term temporal variations in the field. It is increasingly apparent that data distribution and quality are pivotal in determining the characteristics of the secular variation. The work presented here demonstrates the need for revised models of the time-averaged field structure for both normal and reverse polarities before reliable models for palaeosecular variation can be made.

The time-averaged geomagnetic field as recorded by lava flows over the past 5 Myr

A recently compiled lava flow data base spanning the last 5 million years is used to investigate properties of the time-averaged geomagnetic field. More than 90 per cent of the power in the palaeofield can be accounted for by a geocentric axial dipole; however, there are significant second-order structures in the field. Declination and inclination anomalies for the new data base indicate that the main second-order signal is the ‘far-sided’effect, and there is also evidence for non-zonal structure. VGP (virtual geomagnetic pole) latitude distributions indicate that, over the last 5 million years, normal and reverse polarity morphologies are different, and that any changes in the normal polarity field morphology are undetectable, given the present data distribution. Regularized non-linear inversions of the palaeomagnetic directions support all these observations. We test the hypothesis that zonal models for the time-averaged field are adequate to describe the data and find that they are not. Non-zonal models are needed to fit the data to within the required tolerance level. Normal and reverse polarity field models obtained are significantly different. Field models obtained for the Brunhes epoch data alone are much smoother than those obtained from combining all the normal polarity data; simulations indicate that these differences can be explained by the less extensive data distribution for the Brunhes epoch. The field model for all of the normal polarity data (LN1) contains features observed in the historical field maps, although the details differ. LN1 suggests that, although the two northern hemisphere flux lobes observed in the historical field are stationary to a first-order approximation, they do show changes in position and amplitude. A third, less pronounced flux lobe is observed in LN1 over central Europe. The lack of structure in the southern hemisphere is due in part to the paucity of data. Jackknife estimates of the field models for different subsets of the data suggest that a few sites contribute significant structure to the final field models. More conservative estimates of the time-averaged field morphology are obtained by removing these sites.