The distribution of interplanetary dust between 0.96 and 1.04 au as inferred from impacts on the STEREO spacecraft observed by the heliospheric imagers

The distribution of dust in the ecliptic plane between 0.96 and 1.04 au has been inferred from impacts on the two Solar Terrestrial Relations Observatory (STEREO) spacecraft through observation of secondary particle trails and unexpected off-points in the heliospheric imager (HI) cameras. This study made use of analysis carried out by members of a distributed web-based citizen science project Solar Stormwatch. A comparison between observations of the brightest particle trails and a survey of fainter trails shows consistent distributions. While there is no obvious correlation between this distribution and the occurrence of individual meteor streams at Earth, there are some broad longitudinal features in these distributions that are also observed in sources of the sporadic meteor population. The different position of the HI instrument on the two STEREO spacecraft leads to each sampling different populations of dust particles. The asymmetry in the number of trails seen by each spacecraft and the fact that there are many more unexpected off-points in the HI-B than in HI-A indicates that the majority of impacts are coming from the apex direction. For impacts causing off-points in the HI-B camera, these dust particles are estimated to have masses in excess of 10−17 kg with radii exceeding 0.1 μm. For off-points observed in the HI-A images, which can only have been caused by particles travelling from the anti-apex direction, the distribution is consistent with that of secondary ‘storm’ trails observed by HI-B, providing evidence that these trails also result from impacts with primary particles from an anti-apex source. Investigating the mass distribution for the off-points of both HI-A and HI-B, it is apparent that the differential mass index of particles from the apex direction (causing off-points in HI-B) is consistently above 2. This indicates that the majority of the mass is within the smaller particles of this population. In contrast, the differential mass index of particles from the anti-apex direction (causing off-points in HI-A) is consistently below 2, indicating that the majority of the mass is to be found in larger particles of this distribution.

Open solar flux estimates from near-Earth measurements of the interplanetary magnetic field: comparison of the first two perihelion passes of the Ulysses spacecraft

Results from all phases of the orbits of the Ulysses spacecraft have shown that the magnitude of the radial component of the heliospheric field is approximately independent of heliographic latitude. This result allows the use of near- Earth observations to compute the total open flux of the Sun. For example, using satellite observations of the interplanetary magnetic field, the average open solar flux was shown to have risen by 29% between 1963 and 1987 and using the aa geomagnetic index it was found to have doubled during the 20th century. It is therefore important to assess fully the accuracy of the result and to check that it applies to all phases of the solar cycle. The first perihelion pass of the Ulysses spacecraft was close to sunspot minimum, and recent data from the second perihelion pass show that the result also holds at solar maximum. The high level of correlation between the open flux derived from the various methods strongly supports the Ulysses discovery that the radial field component is independent of latitude. We show here that the errors introduced into open solar flux estimates by assuming that the heliospheric field’s radial component is independent of latitude are similar for the two passes and are of order 25% for daily values, falling to 5% for averaging timescales of 27 days or greater. We compare here the results of four methods for estimating the open solar flux with results from the first and second perehelion passes by Ulysses. We find that the errors are lowest (1–5% for averages over the entire perehelion passes lasting near 320 days), for near-Earth methods, based on either interplanetary magnetic field observations or the aa geomagnetic activity index. The corresponding errors for the Solanki et al. (2000) model are of the order of 9–15% and for the PFSS method, based on solar magnetograms, are of the order of 13–47%. The model of Solanki et al. is based on the continuity equation of open flux, and uses the sunspot number to quantify the rate of open flux emergence. It predicts that the average open solar flux has been decreasing since 1987, as Correspondence to: M. Lockwood (m.lockwood@rl.ac.uk) is observed in the variation of all the estimates of the open flux. This decline combines with the solar cycle variation to produce an open flux during the second (sunspot maximum) perihelion pass of Ulysses which is only slightly larger than that during the first (sunspot minimum) perihelion pass.

On the evolution of the solar wind between 1 and 5 AU at the time of the Cassini Jupiter flyby: Multispacecraft observations of interplanetary coronal mass ejections including the formation of a merged interaction region

The Cassini flyby of Jupiter occurred at a time near solar maximum. Consequently, the pre-Jupiter data set reveals clear and numerous transient perturbations to the Parker Spiral solar wind structure. Limited plasma data are available at Cassini for this period due to pointing restrictions imposed on the instrument. This renders the identification of the nature of such structures ambiguous, as determinations based on the magnetic field data alone are unreliable. However, a fortuitous alignment of the planets during this encounter allowed us to trace these structures back to those observed previously by the Wind spacecraft near the Earth. Of the phenomena that we are satisfactorily able to trace back to their manifestation at 1 AU, two are identified as being due to interplanetary coronal mass ejections. One event at Cassini is shown to be a merged interaction region, which is formed from the compression of a magnetic cloud by two anomalously fast solar wind streams. The flux-rope structure associated with this magnetic cloud is not as apparent at Cassini and has most likely been compressed and deformed. Confirmation of the validity of the ballistic projections used here is provided by results obtained from a one-dimensional magnetohydrodynamic projection of solar wind parameters measured upstream near the Earth. It is found that when the Earth and Cassini are within a few tens of degrees in heliospheric longitude, the results of this one-dimensional model predict the actual conditions measured at 5 AU to an impressive degree. Finally, the validity of the use of such one-dimensional projections in obtaining quasi-solar wind parameters at the outer planets is discussed.

Non-radial solar wind flows induced by the motion of interplanetary coronal mass ejections

A survey of the non-radial flows (NRFs) during nearly five years of interplanetary observations revealed the average non-radial speed of the solar wind flows to be �30 km/s, with approximately one-half of the large (>100 km/s) NRFs associated with ICMEs. Conversely, the average non-radial flow speed upstream of all ICMEs is �100 km/s, with just over one-third preceded by large NRFs. These upstream flow deflections are analysed in the context of the large-scale structure of the driving ICME. We chose 5 magnetic clouds with relatively uncomplicated upstream flow deflections. Using variance analysis it was possible to infer the local axis orientation, and to qualitatively estimate the point of interception of the spacecraft with the ICME. For all 5 events the observed upstream flows were in agreement with the point of interception predicted by variance analysis. Thus we conclude that the upstream flow deflections in these events are in accord with the current concept of the large scale structure of an ICME: a curved axial loop connected to the Sun, bounded by a curved (though not necessarily circular)cross section.

A solar storm observed from the Sun to Venus using the STEREO, Venus Express, and MESSENGER spacecraft

The suite of SECCHI optical imaging instruments on the STEREO-A spacecraft is used to track a solar storm, consisting of several coronal mass ejections (CMEs) and other coronal loops, as it propagates from the Sun into the heliosphere during May 2007. The 3-D propagation path of the largest interplanetary CME (ICME) is determined from the observations made by the SECCHI Heliospheric Imager (HI) on STEREO-A (HI-1/2A). Two parts of the CME are tracked through the SECCHI images, a bright loop and a V-shaped feature located at the rear of the event. We show that these two structures could be the result of line-of-sight integration of the light scattered by electrons located on a single flux rope. In addition to being imaged by HI, the CME is observed simultaneously by the plasma and magnetic field experiments on the Venus Express and MESSENGER spacecraft. The imaged loop and V-shaped structure bound, as expected, the flux rope observed in situ. The SECCHI images reveal that the leading loop-like structure propagated faster than the V-shaped structure, and a decrease in in situ CME speed occurred during the passage of the flux rope.We interpret this as the result of the continuous radial expansion of the flux rope as it progressed outward through the interplanetary medium. An expansion speed in the radial direction of ~30 km s-1 is obtained directly from the SECCHI-HI images and is in agreement with the difference in speed of the two structures observed in situ. This paper shows that the flux rope location can be determined from white light images, which could have important space weather applications.

Forward modelling to determine the observational signatures of white-light imaging and interplanetary scintillation for the propagation of an interplanetary shock in the ecliptic plane

Recent coordinated observations of interplanetary scintillation (IPS) from the EISCAT, MERLIN, and STELab, and stereoscopic white-light imaging from the two heliospheric imagers (HIs) onboard the twin STEREO spacecraft are significant to continuously track the propagation and evolution of solar eruptions throughout interplanetary space. In order to obtain a better understanding of the observational signatures in these two remote-sensing techniques, the magnetohydrodynamics of the macro-scale interplanetary disturbance and the radio-wave scattering of the micro-scale electron-density fluctuation are coupled and investigated using a newly constructed multi-scale numerical model. This model is then applied to a case of an interplanetary shock propagation within the ecliptic plane. The shock could be nearly invisible to an HI, once entering the Thomson-scattering sphere of the HI. The asymmetry in the optical images between the western and eastern HIs suggests the shock propagation off the Sun–Earth line. Meanwhile, an IPS signal, strongly dependent on the local electron density, is insensitive to the density cavity far downstream of the shock front. When this cavity (or the shock nose) is cut through by an IPS ray-path, a single speed component at the flank (or the nose) of the shock can be recorded; when an IPS ray-path penetrates the sheath between the shock nose and this cavity, two speed components at the sheath and flank can be detected. Moreover, once a shock front touches an IPS ray-path, the derived position and speed at the irregularity source of this IPS signal, together with an assumption of a radial and constant propagation of the shock, can be used to estimate the later appearance of the shock front in the elongation of the HI field of view. The results of synthetic measurements from forward modelling are helpful in inferring the in-situ properties of coronal mass ejection from real observational data via an inverse approach.

Reconstruction and prediction of variations in the open solar magnetic flux and interplanetary conditions

Historic geomagnetic activity observations have been used to reveal centennial variations in the open solar flux and the near-Earth heliospheric conditions (the interplanetary magnetic field and the solar wind speed). The various methods are in very good agreement for the past 135 years when there were sufficient reliable magnetic observatories in operation to eliminate problems due to site-specific errors and calibration drifts. This review underlines the physical principles that allow these reconstructions to be made, as well as the details of the various algorithms employed and the results obtained. Discussion is included of: the importance of the averaging timescale; the key differences between “range” and “interdiurnal variability” geomagnetic data; the need to distinguish source field sector structure from heliospherically-imposed field structure; the importance of ensuring that regressions used are statistically robust; and uncertainty analysis. The reconstructions are exceedingly useful as they provide calibration between the in-situ spacecraft measurements from the past five decades and the millennial records of heliospheric behaviour deduced from measured abundances of cosmogenic radionuclides found in terrestrial reservoirs. Continuity of open solar flux, using sunspot number to quantify the emergence rate, is the basis of a number of models that have been very successful in reproducing the variation derived from geomagnetic activity. These models allow us to extend the reconstructions back to before the development of the magnetometer and to cover the Maunder minimum. Allied to the radionuclide data, the models are revealing much about how the Sun and heliosphere behaved outside of grand solar maxima and are providing a means of predicting how solar activity is likely to evolve now that the recent grand maximum (that had prevailed throughout the space age) has come to an end.

Relationship between the near-Earth interplanetary field and the coronal source flux: dependence on timescale

The Ulysses spacecraft has shown that the radial component of the heliospheric magnetic field is approximately independent of latitude. This has allowed quantification of the total open solar flux from near-Earth observations of the interplanetary magnetic field. The open flux can also be estimated from photospheric magnetograms by mapping the fields up to the ‘‘coronal source surface’’ where the field is assumed to be radial and which is usually assumed to be at a heliocentric distance r = 2.5R_{S} (a mean solar radius, 1R_{S} = 6.96x10^{8} m). These two classes of open flux estimate will differ by the open flux that threads the heliospheric current sheet(s) inside Earth’s orbit at 2.5R_{S} < r < 1R{1} (where the mean Earth-Sun distance, 1R_{1} = 1 AU = 1.5 x 10^{11} m). We here use near-Earth measurements to estimate this flux and show that at sunspot minimum it causes only a very small (approximately 0.5%) systematic difference between the two types of open flux estimate, with an uncertainty that is of order ±24% in hourly values, ±16% in monthly averages, and between -6% and +2% in annual values. These fractions may be somewhat larger for sunspot maximum because of flux emerging at higher heliographic latitudes.

Reconnection at the high-latitude magnetopause during northward interplanetary magnetic field conditions

The Polar spacecraft had a prolonged encounter with the high-latitude dayside magnetopause on May 29, 1996. This encounter with the magnetopause occurred when the interplanetary magnetic field was directed northward. From the three-dimensional electron and ion distribution functions measured by the Hydra instrument, it has been possible to identify nearly all of the distinct boundary layer regions associated with high-latitude reconnection. The regions that have been identified are (1) the cusp; (2) the magnetopause current layer; (3) magnetosheath field lines that have interconnected in only the Northern Hemisphere; (4) magnetosheath field lines that have interconnected in only the Southern Hemisphere; (5) magnetosheath field lines that have interconnected in both the Northern and Southern Hemispheres; (6) magnetosheath that is disconnected from the terrestrial magnetic field; and (7) high-latitude plasma sheet field lines that are participating in magnetosheath reconnection. Reconnection over this time period was occurring at high latitudes over a broad local-time extent, interconnecting the magnetosheath and lobe and/or plasma sheet field lines in both the Northern and Southern Hemispheres. Newly closed boundary layer field lines were observed as reconnection occur-red first at high latitudes in one hemisphere and then later in the other. These observations establish the location of magnetopause reconnection during these northward interplanetary magnetic field conditions as being at high latitudes, poleward of the cusp, and further reinforce the general interpretation of electron and ion phase space density signatures as indicators of magnetic reconnection and boundary layer formation.

Excess open solar magnetic flux from satellite data: 2. A survey of kinematic effects

We investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the kinematic effect on these open solar flux estimates of large-scale longitudinal structure in the solar wind flow, with particular emphasis on correcting estimates made using data from near-Earth satellites. We show that scatter, but no net bias, is introduced by the kinematic “bunching effect” on sampling and that this is true for both compression and rarefaction regions. The observed flux excesses, as a function of heliocentric distance, are shown to be consistent with open solar flux estimates from solar magnetograms made using the potential field source surface method and are well explained by the kinematic effect of solar wind speed variations on the frozen-in heliospheric field. Applying this kinematic correction to the Omni-2 interplanetary data set shows that the open solar flux at solar minimum fell from an annual mean of 3.82 × 1016 Wb in 1987 to close to half that value (1.98 × 1016 Wb) in 2007, making the fall in the minimum value over the last two solar cycles considerably faster than the rise inferred from geomagnetic activity observations over four solar cycles in the first half of the 20th century.

Characteristic magnetic field and speed properties of interplanetary coronal mass ejections and their sheath regions

Prediction of the solar wind conditions in near-Earth space, arising from both quasi-steady and transient structures, is essential for space weather forecasting. To achieve forecast lead times of a day or more, such predictions must be made on the basis of remote solar observations. A number of empirical prediction schemes have been proposed to forecast the transit time and speed of coronal mass ejections (CMEs) at 1 AU. However, the current lack of magnetic field measurements in the corona severely limits our ability to forecast the 1 AU magnetic field strengths resulting from interplanetary CMEs (ICMEs). In this study we investigate the relation between the characteristic magnetic field strengths and speeds of both magnetic cloud and noncloud ICMEs at 1 AU. Correlation between field and speed is found to be significant only in the sheath region ahead of magnetic clouds, not within the clouds themselves. The lack of such a relation in the sheaths ahead of noncloud ICMEs is consistent with such ICMEs being skimming encounters of magnetic clouds, though other explanations are also put forward. Linear fits to the radial speed profiles of ejecta reveal that faster-traveling ICMEs are also expanding more at 1 AU. We combine these empirical relations to form a prediction scheme for the magnetic field strength in the sheaths ahead of magnetic clouds and also suggest a method for predicting the radial speed profile through an ICME on the basis of upstream measurements.

Intermittent release of transients in the slow solar wind: 2. In situ evidence

In paper 1, we showed that the Heliospheric Imager (HI) instruments on the pair of NASA STEREO spacecraft can be used to image the streamer belt and, in particular, the variability of the slow solar wind which originates near helmet streamers. The observation of intense intermittent transient outflow by HI implies that the corresponding in situ observations of the slow solar wind and corotating interaction regions (CIRs) should contain many signatures of transients. In the present paper, we compare the HI observations with in situ measurements from the STEREO and ACE spacecraft. Analysis of the solar wind ion, magnetic field, and suprathermal electron flux measurements from the STEREO spacecraft reveals the presence of both closed and partially disconnected interplanetary magnetic field lines permeating the slow solar wind. We predict that one of the transients embedded within the second CIR (CIR‐D in paper 1) should impact the near‐Earth ACE spacecraft. ACE measurements confirm the presence of a transient at the time of CIR passage; the transient signature includes helical magnetic fields and bidirectional suprathermal electrons. On the same day, a strahl electron dropout is observed at STEREO‐B, correlated with the passage of a high plasma beta structure. Unlike ACE, STEREO‐B observes the transient a few hours ahead of the CIR. STEREO‐A, STEREO‐B, and ACE spacecraft observe very different slow solar wind properties ahead of and during the CIR analyzed in this paper, which we associate with the intermittent release of transients.

Cusp observations during a sequence of fast IMF B-Z reversals

In recent years, a large number of papers have reported the response of the cusp to solar wind variations under conditions of northward or southward Interplanetary Magnetic Field (IMF) Z-component (BZ). These studies have shown the importance of both temporal and spatial factors in determining the extent and morphology of the cusp and the changes in its location, connected to variations in the reconnection geometry. Here we present a comparative study of the cusp, focusing on an interval characterised by a series of rapid reversals in the BZ-dominated IMF, based on observations from space-borne and ground-based instrumentation. During this interval, from 08:00 to 12:00 UT on 12 February 2003, the IMF BZ component underwent four reversals, remaining for around 30 min in each orientation. The Cluster spacecraft were, at the time, on an outbound trajectory through the Northern Hemisphere magnetosphere, whilst the mainland VHF and Svalbard (ESR) radars of the EISCAT facility were operating in support of the Cluster mission. Both Cluster and the EISCAT were, on occasion during the interval, observing the cusp region. The series of IMF reversal resulted in a sequence of poleward and equatorward motions of the cusp; consequently Cluster crossed the high altitude cusp twice before finally exiting the dayside magnetopause, both times under conditions of northward IMF BZ. The first magnetospheric cusp encounter, by all four Cluster spacecraft, showed reverse ion dispersion typical of lobe reconnection; subsequently, Cluster spacecraft 1 and 3 (only) crossed the cusp for a second time. We suggest that, during this second cusp crossing, these two spacecraft were likely to have been on newly closed field lines, which were first reconnected (opened) at low latitudes and later reconnected again (re-closed) poleward of the northern cusp.

First imaging of corotating interaction regions using the STEREO spacecraft

Plasma parcels are observed propagating from the Sun out to the large coronal heights monitored by the Heliospheric Imagers (HI) instruments onboard the NASA STEREO spacecraft during September 2007. The source region of these out-flowing parcels is found to corotate with the Sun and to be rooted near the western boundary of an equatorial coronal hole. These plasma enhancements evolve during their propagation through the HI cameras’ fields of view and only becoming fully developed in the outer camera field of view. We provide evidence that HI is observing the formation of a Corotating Interaction Region(CIR) where fast solar wind from the equatorial coronal hole is interacting with the slow solar wind of the streamer belt located on the western edge of that coronal hole. A dense plasma parcel is also observed near the footpoint of the observed CIR at a distance less than 0.1AU from the Sun where fast wind would have not had time to catch up slow wind. We suggest that this low-lying plasma enhancement is a plasma parcel which has been disconnected from a helmet streamer and subsequently becomes embedded inside the corotating interaction region.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).