Long-term variations in the magnetic fields of the Sun and the heliosphere: their origin, effects, and implications

Recent studies of the variation of geomagnetic activity over the past 140 years have quantified the "coronal source" magnetic flux F-s that leaves the solar atmosphere and enters the heliosphere and have shown that it has risen, on average, by an estimated 34% since 1963 and by 140% since 1900. This variation of open solar flux has been reproduced by Solanki et al. [2000] using a model which demonstrates how the open flux accumulates and decays, depending on the rate of flux emergence in active regions and on the length of the solar cycle. We here use a new technique to evaluate solar cycle length and find that it does vary in association with the rate of change of F-s in the way predicted. The long-term variation of the rate of flux emergence is found to be very similar in form to that in F-s, which may offer a potential explanation of why F-s appears to be a useful proxy for extrapolating solar total irradiance back in time. We also find that most of the variation of cosmic ray fluxes incident on Earth is explained by the strength of the heliospheric field (quantified by F-s) and use observations of the abundance of the isotope Be-10 (produced by cosmic rays and deposited in ice sheets) to study the decrease in F-s during the Maunder minimum. The interior motions at the base of the convection zone, where the solar dynamo is probably located, have recently been revealed using the helioseismology technique and found to exhibit a 1.3-year oscillation. This periodicity is here reported in observations of the interplanetary magnetic field and geomagnetic activity but is only present after 1940, When present, it shows a strong 22-year variation, peaking near the maximum of even-numbered sunspot cycles and showing minima at the peaks of odd-numbered cycles. We discuss the implications of these long-term solar and heliospheric variations for Earth's environment.

The interconnection of the magnetic fields of the Earth and the sun

Magnetic reconnection facilitates the transfer of mass, energy, and momentum from the solar wind, through the Earth's magnetosphere and into the upper atmosphere. Recently, combined observations using both ground-based and satellite instruments have revealed much about how reconnection takes place. This new understanding has great signficance for systems which exploit, or operate within, the Earth's plasma environment, as well as for a wide variety of scientific studies.

In situ signatures of interchange reconnection between magnetic clouds and open magnetic fields: a mechanism for the erosion of polar coronal holes?

We outline a method to determine the direction of solar open flux transport that results from the opening of magnetic clouds (MCs) by interchange reconnection at the Sun based solely on in-situ observations. This method uses established findings about i) the locations and magnetic polarities of emerging MC footpoints, ii) the hemispheric dependence of the helicity of MCs, and iii) the occurrence of interchange reconnection at the Sun being signaled by uni-directional suprathermal electrons inside MCs. Combining those observational facts in a statistical analysis of MCs during solar cycle 23 (period 1995���������2007), we show that the time of disappearance of the northern polar coronal hole (1998���������1999), permeated by an outward-pointing magnetic field, is associated with a peak in the number of MCs originating from the northern hemisphere and connected to the Sun by outward-pointing magnetic field lines. A similar peak is observed in the number of MCs originating from the southern hemisphere and connected to the Sun by inward-pointing magnetic field lines. This pattern is interpreted as the result of interchange reconnection occurring between MCs and the open field lines of nearby polar coronal holes. This reconnection process closes down polar coronal hole open field lines and transports these open field lines equatorward, thus contributing to the global coronal magnetic field reversal process. These results will be further constrainable with the rising phase of solar cycle 24.

Do the legs of magnetic clouds contain twisted flux-rope magnetic fields?

Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs) characterised primarily by a smooth rotation in the magnetic field direction indicative of the presence of a magnetic flux rope. Energetic particle signatures suggest MC flux ropes remain magnetically connected to the Sun at both ends, leading to widely used model of global MC structure as an extended flux rope, with a loop-like axis stretching out from the Sun into the heliosphere and back to the Sun. The time of flight of energetic particles, however, suggests shorter magnetic field line lengths than such a continuous twisted flux rope would produce. In this study, two simple models are compared with observed flux rope axis orientations of 196 MCs to show that the flux rope structure is confined to the MC leading edge. The magnetic cloud ���legs,��� which magnetically connect the flux rope to the Sun, are not recognisable as MCs and thus are unlikely to contain twisted flux rope fields. Spacecraft encounters with these non-flux rope legs may provide an explanation for the frequent observation of non-magnetic cloud ICMEs.

Superhumps, magnetic fields and the mass ratio in AM Canum Venaticorum

We show that the observed K velocities and periodicities of AM CVn can be reconciled given a mass ratio q~0.22 and a secondary star with a modest magnetic field of surface strength B~1 T. We see that the new mass ratio implies that the secondary is most likely semidegenerate. The effect of the field on the accretion disc structure is examined. The theory of precessing discs and resonant orbits is generalized to encompass higher order resonances than 3:2 and shown to retain consistency with the new mass ratio.

A doubling of the sun's coronal magnetic field during the last 100 years

The solar wind is an extended ionized gas of very high electrical conductivity, and therefore drags some magnetic flux out of the Sun to fill the heliosphere with a weak interplanetary magnetic field(1,2). Magnetic reconnection-the merging of oppositely directed magnetic fields-between the interplanetary field and the Earth's magnetic field allows energy from the solar wind to enter the near-Earth environment. The Sun's properties, such as its luminosity, are related to its magnetic field, although the connections are still not well understood(3,4). Moreover, changes in the heliospheric magnetic field have been linked with changes in total cloud cover over the Earth, which may influence global climate(5), Here we show that measurements of the near-Earth interplanetary magnetic field reveal that the total magnetic flux leaving the Sun has risen by a factor of 1.4 since 1964: surrogate measurements of the interplanetary magnetic field indicate that the increase since 1901 has been by a factor of 2,3, This increase may be related to chaotic changes in the dynamo that generates the solar magnetic field. We do not yet know quantitatively how such changes will influence the global environment.

The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds

Magnetic clouds are a subset of interplanetary coronal mass ejections characterized by a smooth rotation in the magnetic field direction, which is interpreted as a signature of a magnetic flux rope. Suprathermal electron observations indicate that one or both ends of a magnetic cloud typically remain connected to the Sun as it moves out through the heliosphere. With distance from the axis of the flux rope, out toward its edge, the magnetic field winds more tightly about the axis and electrons must traverse longer magnetic field lines to reach the same heliocentric distance. This increased time of flight allows greater pitch-angle scattering to occur, meaning suprathermal electron pitch-angle distributions should be systematically broader at the edges of the flux rope than at the axis. We model this effect with an analytical magnetic flux rope model and a numerical scheme for suprathermal electron pitch-angle scattering and find that the signature of a magnetic flux rope should be observable with the typical pitch-angle resolution of suprathermal electron data provided ACE's SWEPAM instrument. Evidence of this signature in the observations, however, is weak, possibly because reconnection of magnetic fields within the flux rope acts to intermix flux tubes.

Solar induced climate effects

Solar electromagnetic radiation powers Earth���s climate system and, consequently, it is often naively assumed that changes in this solar output must be responsible for changes in Earth���s climate. However, the Sun is close to a blackbody radiator and so emits according to its surface temperature and the huge thermal time constant of the outer part of the Sun limits the variability in surface temperature and hence output. As a result, on all timescales of interest, changes in total power output are limited to small changes in effective surface temperature (associated with magnetic fields) and potential, although as yet undetected, solar radius variations. Larger variations are seen in the UV part of the spectrum which is emitted from the lower solar atmosphere (the chromosphere) and which influences Earth���s stratosphere. There is interest in���top-down��� mechanisms whereby solar UV irradiance modulates stratospheric temperatures and winds which, in turn, may influence the underlying troposphere where Earth���s climate and weather reside. This contrasts with ���bottom-up��� effects in which the small total solar irradiance (dominated by the visible and near-IR) variations cause surface temperature changes which drive atmospheric circulations. In addition to these electromagnetic outputs, the Sun modulates energetic particle fluxes incident on the Earth. Solar Energetic Particles (SEP) are emitted by solar flares and from the shock fronts ahead of supersonic (and super-Alfvenic) ejections of material from the solar atmosphere. These SEPs enhance the destruction of polar stratospheric ozone which could be an additional form of top-down climate forcing. Even more energetic are Galactic Cosmic Rays (GCRs). These particles are not generated by the Sun, rather they originate at the shock fronts emanating from violent galactic events such as supernovae explosions; however, the expansion of the solar magnetic field into interplanetary space means that the Sun modulates the number of GCRs reaching Earth. These play a key role in enabling Earth���s global electric (thunderstorm) circuit and it has been proposed that they also modulate the formation of clouds. Both electromagnetic and corpuscular solar effects are known to vary over the solar magnetic cycle which is typically between 10 and 14 yrs in length (with an average close to 11 yrs). The solar magnetic field polarity at any one phase of one of these activity cycles is opposite to that at the same phase of the next cycle and this influences some phenomena, for example GCRs, which therefore show a 22 yr (���Hale���) cycle on average. Other phenomena, such as irradiance modulation, do not depend on the polarity of the magnetic field and so show only the basic 11-yr activity cycle. However, any effects on climate are much more significant for solar drifts over centennial timescales. This chapter discusses and evaluates potential effects on Earth���s climate system of variations in these solar inputs. Because of the great variety of proposed mechanisms, the wide range of timescales studied (from days to millennia) and the many debates (often triggered by the application of inadequate statistical methods), the literature on this subject is vast, complex, divergent and rapidly changing: consequently the number of references cited in this review is very large (yet still only a small fraction of the total).

How is open solar magnetic flux lost over the solar cycle?

The Sun's open magnetic field, magnetic flux dragged out into the heliosphere by the solar wind, varies by approximately a factor of 2 over the solar cycle. We consider the evolution of open solar flux in terms of a source and loss term. Open solar flux creation is likely to proceed at a rate dependent on the rate of photospheric flux emergence, which can be roughly parameterized by sunspot number or coronal mass ejection rate, when available. The open solar flux loss term is more difficult to relate to an observable parameter. The supersonic nature of the solar wind means open solar flux can only be removed by near-Sun magnetic reconnection between open solar magnetic field lines, be they open or closed heliospheric field lines. In this study we reconstruct open solar flux over the last three solar cycles and demonstrate that the loss term may be related to the degree to which the heliospheric current sheet (HCS) is warped, i.e., locally tilted from the solar rotation direction. This can account for both the large dip in open solar flux at the time of sunspot maximum as well as the asymmetry in open solar flux during the rising and declining phases of the solar cycle. The observed cycle-to-cycle variability is also well matched. Following Sheeley et al. (2001), we attribute modulation of open solar flux by the degree of warp of the HCS to the rate at which opposite polarity open solar flux is brought together by differential rotation.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ��� X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Estimation of magnet separation for magnetic suspension applications

This thesis describes a form of non-contact measurement using two dimensional hall effect sensing to resolve the location of a moving magnet which is part of a ���magnetic spring��� type suspension system. This work was inspired by the field of Space Robotics, which currently relies on solid link suspension techniques for rover stability. This thesis details the design, development and testing of a novel magnetic suspension system with a possible application in space and terrestrial based robotics, especially when the robot needs to traverse rough terrain. A number of algorithms were developed, to utilize experimental data from testing, that can approximate the separation between magnets in the suspension module through observation of the magnetic fields. Experimental hardware was also developed to demonstrate how two dimensional hall effect sensor arrays could provide accurate feedback, with respects to the magnetic suspension modules operation, so that future work can include the sensor array in a real-time control system to produce dynamic ride control for space robots. The research performed has proven that two dimensional hall effect sensing with respects to magnetic suspension is accurate, effective and suitable for future testing.

A magnetometer for the Solar Orbiter mission

The magnetometer is a key instrument to the Solar Orbiter mission. The magnetic field is a fundamental parameter in any plasma: a precise and accurate measurement of the field is essential for understanding almost all aspects of plasma dynamics such as shocks and stream-stream interactions. Many of Solar Orbiter���s mission goals are focussed around the link between the Sun and space. A combination of in situ measurements by the magnetometer, remote measurements of solar magnetic fields and global modelling is required to determine this link and hence how the Sun affects interplanetary space. The magnetic field is typically one of the most precisely measured plasma parameters and is therefore the most commonly used measurement for studies of waves, turbulence and other small scale phenomena. It is also related to the coronal magnetic field which cannot be measured directly. Accurate knowledge of the magnetic field is essential for the calculation of fundamental plasma parameters such as the plasma beta, Alfv��n speed and gyroperiod. We describe here the objectives and context of magnetic field measurements on Solar Orbiter and an instrument that fulfils those objectives as defined by the scientific requirements for the mission.