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.

The formation of large-scale current sheets within magnetic clouds

Magnetic clouds are a class of interplanetary coronal mass ejections (CME) predominantly characterised by a smooth rotation in the magnetic field direction, indicative of a magnetic flux rope structure. Many magnetic clouds, however, also contain sharp discontinuities within the smoothly varying magnetic field, suggestive of narrow current sheets. In this study we present observations and modelling of magnetic clouds with strong current sheet signatures close to the centre of the apparent flux rope structure. Using an analytical magnetic flux rope model, we demonstrate how such current sheets can form as a result of a cloud’s kinematic propagation from the Sun to the Earth, without any external forces or influences. This model is shown to match observations of four particular magnetic clouds remarkably well. The model predicts that current sheet intensity increases for increasing CME angular extent and decreasing CME radial expansion speed. Assuming such current sheets facilitate magnetic reconnection, the process of current sheet formation could ultimately lead a single flux rope becoming fragmented into multiple flux ropes. This change in topology has consequences for magnetic clouds as barriers to energetic particle propagation.

Excess open solar magnetic flux from satellite data: 1. Analysis of the third perihelion Ulysses pass

We use the third perihelion pass by the Ulysses spacecraft to illustrate and investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the potential effects of small-scale structure in the heliospheric field (giving fluctuations in the radial component on timescales smaller than 1 h) and kinematic time-of-flight effects of longitudinal structure in the solar wind flow. We show that the flux excess is explained by neither very small-scale structure (timescales < 1 h) nor by the kinematic “bunching effect” on spacecraft sampling. The observed flux excesses is, however, well explained by the kinematic effect of larger-scale (>1 day) solar wind speed variations on the frozen-in heliospheric field. We show that averaging over an interval T (that is long enough to eliminate structure originating in the heliosphere yet small enough to avoid cancelling opposite polarity radial field that originates from genuine sector structure in the coronal source field) is only an approximately valid way of allowing for these effects and does not adequately explain or account for differences between the streamer belt and the polar coronal holes.

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.

The accuracy of using the Ulysses result of the spatial invariance of the radial heliospheric field to compute the open solar flux

We survey observations of the radial magnetic field in the heliosphere as a function of position, sunspot number, and sunspot cycle phase. We show that most of the differences between pairs of simultaneous observations, normalized using the square of the heliocentric distance and averaged over solar rotations, are consistent with the kinematic "flux excess" effect whereby the radial component of the frozen-in heliospheric field is increased by longitudinal solar wind speed structure. In particular, the survey shows that, as expected, the flux excess effect at high latitudes is almost completely absent during sunspot minimum but is almost the same as within the streamer belt at sunspot maximum. We study the uncertainty inherent in the use of the Ulysses result that the radial field is independent of heliographic latitude in the computation of the total open solar flux: we show that after the kinematic correction for the excess flux effect has been made it causes errors that are smaller than 4.5%, with a most likely value of 2.5%. The importance of this result for understanding temporal evolution of the open solar flux is reviewed.

Space physics for graduate students: an activities-based approach

The geospace environment is controlled largely by events on the Sun, such as solar flares and coronal mass ejections, which generate significant geomagnetic and upper atmospheric disturbances. The study of this Sun-Earth system, which has become known as space weather, has both intrinsic scientific interest and practical applications. Adverse conditions in space can damage satellites and disrupt communications, navigation, and electric power grids, as well as endanger astronauts. The Center for Integrated Space Weather Modeling (CISM), a Science and Technology Center (STC) funded by the U.S. National Science Foundation (see http://www.bu.edu/cism/), is developing a suite of integrated physics-based computer models that describe the space environment from the Sun to the Earth for use in both research and operations [Hughes and Hudson, 2004, p. 1241]. To further this mission, advanced education and training programs sponsored by CISM encourage students to view space weather as a system that encompasses the Sun, the solar wind, the magnetosphere, and the ionosphere/thermosphere. This holds especially true for participants in the CISM space weather summer school [Simpson, 2004].

Conservation of open solar magnetic flux and the floor in the heliospheric magnetic field

The near-Earth heliospheric magnetic field intensity, |B|, exhibits a strong solar cycle variation, but returns to the same ``floor'' value each solar minimum. The current minimum, however, has seen |B| drop below previous minima, bringing in to question the existence of a floor, or at the very least requiring a re-assessment of its value. In this study we assume heliospheric flux consists of a constant open flux component and a time-varying contribution from CMEs. In this scenario, the true floor is |B| with zero CME contribution. Using observed CME rates over the solar cycle, we estimate the ``no-CME'' |B| floor at ~4.0 +/- 0.3 nT, lower than previous floor estimates and below |B| observed this solar minimum. We speculate that the drop in |B| observed this minimum may be due to a persistently lower CME rate than the previous minimum, though there are large uncertainties in the supporting observational data.

Suprathermal electron evolution in a Parker spiral magnetic field

Suprathermal electrons (>70 eV) form a small fraction of the total solar wind electron density but serve as valuable tracers of heliospheric magnetic field topology. Their usefulness as tracers of magnetic loops with both feet rooted on the Sun, however, most likely fades as the loops expand beyond some distance owing to scattering. As a first step toward quantifying that distance, we construct an observationally constrained model for the evolution of the suprathermal electron pitch-angle distributions on open field lines. We begin with a near-Sun isotropic distribution moving antisunward along a Parker spiral magnetic field while conserving magnetic moment, resulting in a field-aligned strahl within a few solar radii. Past this point, the distribution undergoes little evolution with heliocentric distance. We then add constant (with heliocentric distance, energy, and pitch angle) ad-hoc pitch-angle scattering. Close to the Sun, pitch-angle focusing still dominates, again resulting in a narrow strahl. Farther from the Sun, however, pitch-angle scattering dominates because focusing is effectively weakened by the increasing angle between the magnetic field direction and intensity gradient, a result of the spiral field. We determine the amount of scattering required to match Ulysses observations of strahl width in the fast solar wind, providing an important tool for inferring the large-scale properties and topologies of field lines in the interplanetary medium. Although the pitch-angle scattering term is independent of energy, time-of-flight effects in the spiral geometry result in an energy dependence of the strahl width that is in the observed sense although weaker in magnitude.

Ambient solar wind's effect on ICME transit times

Most empirical and numerical models of Interplanetary Coronal Mass Ejection (ICME) propagation use the initial CME velocity as their primary, if not only, observational input. These models generally predict a wide spread of 1 AU transit times for ICMEs with the same initial velocity. We use a 3D coupled MHD model of the corona and heliosphere to determine the ambient solar wind's effect on the propagation of ICMEs from 30 solar radii to 1 AU. We quantitatively characterize this deceleration by the velocity of the upstream ambient solar wind. The effects of varying solar wind parameters on the ICME transit time are quantified and can explain the observed spread in transit times for ICMEs of the same initial velocity. We develop an adjustment formula that can be used in conjunction with other models to reduce the spread in predicted transit times of Earth-directed ICMEs.

Metrics for solar wind prediction models: Comparison of empirical, hybrid, and physics-based schemes with 8 years of L1 observations

Space weather effects on technological systems originate with energy carried from the Sun to the terrestrial environment by the solar wind. In this study, we present results of modeling of solar corona-heliosphere processes to predict solar wind conditions at the L1 Lagrangian point upstream of Earth. In particular we calculate performance metrics for (1) empirical, (2) hybrid empirical/physics-based, and (3) full physics-based coupled corona-heliosphere models over an 8-year period (1995–2002). L1 measurements of the radial solar wind speed are the primary basis for validation of the coronal and heliosphere models studied, though other solar wind parameters are also considered. The models are from the Center for Integrated Space-Weather Modeling (CISM) which has developed a coupled model of the whole Sun-to-Earth system, from the solar photosphere to the terrestrial thermosphere. Simple point-by-point analysis techniques, such as mean-square-error and correlation coefficients, indicate that the empirical coronal-heliosphere model currently gives the best forecast of solar wind speed at 1 AU. A more detailed analysis shows that errors in the physics-based models are predominately the result of small timing offsets to solar wind structures and that the large-scale features of the solar wind are actually well modeled. We suggest that additional “tuning” of the coupling between the coronal and heliosphere models could lead to a significant improvement of their accuracy. Furthermore, we note that the physics-based models accurately capture dynamic effects at solar wind stream interaction regions, such as magnetic field compression, flow deflection, and density buildup, which the empirical scheme cannot.

The heliospheric magnetic field over the Hale cycle

The concept that open magnetic flux of the Sun (rooted with one and only one footpoint at the Sun) is a conserved quantity is taking root in the heliospheric community. Observations show that the Sun's open magnetic flux returns to the baseline from one solar minimum to the next. The temporary enhancement in the 1 AU heliospheric magnetic flux near solar maximum can be accounted for by the temporary creation of closed magnetic flux (with two footpoints at the Sun) during the ejection of coronal mass ejections (CMEs), which are more frequent near solar maximum. As a part of the International Heliophysical Year activities, this paper reviews two recently discussed consequences of open flux conservation: the reversal of open magnetic flux over the solar cycle driven by Coronal Mass Ejections and the impacts of open flux conservation on the global structure of the heliospheric magnetic field. These studies demonstrate the inherent linkages between coronal mass ejections, footpoint motions back at the Sun, and the global structure and evolution of the heliospheric magnetic field.

Predicting magnetospheric dynamics with a coupled sun-to-Earth model: challenges and first results

Results from the first Sun-to-Earth coupled numerical model developed at the Center for Integrated Space Weather Modeling are presented. The model simulates physical processes occurring in space spanning from the corona of the Sun to the Earth's ionosphere, and it represents the first step toward creating a physics-based numerical tool for predicting space weather conditions in the near-Earth environment. Two 6- to 7-d intervals, representing different heliospheric conditions in terms of the three-dimensional configuration of the heliospheric current sheet, are chosen for simulations. These conditions lead to drastically different responses of the simulated magnetosphere-ionosphere system, emphasizing, on the one hand, challenges one encounters in building such forecasting tools, and on the other hand, emphasizing successes that can already be achieved even at this initial stage of Sun-to-Earth modeling.