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.

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.

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.

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.

The distribution of solar wind speeds during solar minimum: calibration for numerical solar wind modeling constraints on the source of the slow solar wind

It took the solar polar passage of Ulysses in the early 1990s to establish the global structure of the solar wind speed during solar minimum. However, it remains unclear if the solar wind is composed of two distinct populations of solar wind from different sources (e.g., closed loops which open up to produce the slow solar wind) or if the fast and slow solar wind rely on the superradial expansion of the magnetic field to account for the observed solar wind speed variation. We investigate the solar wind in the inner corona using the Wang-Sheeley-Arge (WSA) coronal model incorporating a new empirical magnetic topology–velocity relationship calibrated for use at 0.1 AU. In this study the empirical solar wind speed relationship was determined by using Helios perihelion observations, along with results from Riley et al. (2003) and Schwadron et al. (2005) as constraints. The new relationship was tested by using it to drive the ENLIL 3-D MHD solar wind model and obtain solar wind parameters at Earth (1.0 AU) and Ulysses (1.4 AU). The improvements in speed, its variability, and the occurrence of high-speed enhancements provide confidence that the new velocity relationship better determines the solar wind speed in the outer corona (0.1 AU). An analysis of this improved velocity field within the WSA model suggests the existence of two distinct mechanisms of the solar wind generation, one for fast and one for slow solar wind, implying that a combination of present theories may be necessary to explain solar wind observations.

Solar cycle evolution of dipolar and pseudostreamer belts and their relation to the slow solar wind

Dipolar streamers are coronal structures formed by open solar flux converging from coronal holes of opposite polarity. Thus the dipolar streamer belt traces the coronal foot print of the heliospheric current sheet (HCS), and it is strongly associated with the origin of slow solar wind. Pseudostreamers, on the other hand, separate converging regions of open solar flux from coronal holes of the same polarity and do not contain current sheets. They have recently received a great deal of interest as a possible additional source of slow solar wind. Here we add to that growing body of work by using the potential-field source-surface model to determine the occurrence and location of dipolar and pseudostreamers over the last three solar cycles. In addition to providing new information about pseudostreamer morphology, the results help explain why the observations taken during the first Ulysses perihelion pass in 1995 showed noncoincidence between dipolar streamer belt and the locus of slowest flow. We find that Carrington rotation averages of the heliographic latitudes of dipolar and pseudostreamer belts are systematically shifted away from the equator, alternately in opposite directions, with a weak solar cycle periodicity, thus keeping slow wind from the web of combined streamer belts approximately symmetric about the equator. The largest separation of dipolar and pseudostreamer belts occurred close to the Ulysses pass, allowing a unique opportunity to see that slow wind from pseudostreamer belts north of the southward-displaced dipolar belt was responsible for the noncoincident pattern.

Twenty-three cycles of changing open solar magnetic flux

This paper presents a comparison of various estimates of the open solar flux, deduced from measurements of the interplanetary magnetic field, from the aa geomagnetic index and from photospheric magnetic field observations. The first two of these estimates are made using the Ulysses discovery that the radial heliospheric field is approximately independent of heliographic latitude, the third makes use of the potential-field source surface method to map the total flux through the photosphere to the open flux at the top of the corona. The uncertainties associated with using the Ulysses result are 5%, but the effects of the assumptions of the potential field source surface method are harder to evaluate. Nevertheless, the three methods give similar results for the last three solar cycles when the data sets overlap. In 11-year running means, all three methods reveal that 1987 marked a significant peak in the long-term variation of the open solar flux. This peak is close to the solar minimum between sunspot cycles 21 and 22, and consequently the mean open flux (averaged from minimum to minimum) is similar for these two cycles. However, this similarity between cycles 21 and 22 in no way implies that the open flux is constant. The long-term variation shows that these cycles are fundamentally different in that the average open flux was rising during cycle 21 (from consistently lower values in cycle 20 and toward the peak in 1987) but was falling during cycle 22 (toward consistently lower values in cycle 23). The estimates from the geomagnetic aa index are unique as they extend from 1842 onwards (using the Helsinki extension). This variation gives strong anticorrelations, with very high statistical significance levels, with cosmic ray fluxes and with the abundances of the cosmogenic isotopes that they produce. Thus observations of photospheric magnetic fields, of cosmic ray fluxes, and of cosmogenic isotope abundances all support the long-term drifts in open solar flux reported by Lockwood et al. [1999a, 1999b].

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.

Long-term variations in the open solar flux and possible links to Earth’s climate

Recent paleoclimate studies provide strong evidence for an association between cosmogenic isotope production and Earth’s climate throughout the holecene. These isotopes are generated by the bombardment of Earth’s atmosphere by galactic cosmic rays, the fluxes of which vary in approximately inverse proportion to the total open magnetic flux of the Sun. This paper discusses how results from the Ulysses spacecraft allow us to quantify the open solar flux from observations of near-Earth interplanetary space and to study its long-term variations using the homogeneous record of geomagnetic activity. A study of the results and of their accuracy is presented. The two proposed mechanisms that could lead to the open solar flux being a good proxy for solar-induced climate change are discussed: the first is the modulation of the production of some types of cloud by the air ions produced by cosmic rays; the second is a variation in the total or spectral solar irradiance, in association with changes in the open flux. Some implications for our understanding of anthropogenic climate change are discussed.