Structure of solar-wind streams at the maximum of solar cycle 23

We study the formation of solar-wind streams in the years of maximum solar activity 2000–2002. We use observations of the scattering of radio emission by solar-wind streams at distances of ～4–60R_S from the Sun, data on the magnetic field structure and strength in the source region (R ～ 2.5R_S), and observations with the LASCO coronagraph onboard the SOHO spacecraft. Analysis of these data allowed us to investigate the changes in the structure of circumsolar plasma streams during the solar maximum. We constructed radio maps of the solar-wind transition, transonic region in which the heliolatitudinal stream structure is compared with the structure of the white-light corona. We show that the heliolatitudinal structure of the white-light corona largely determines the structure of the solar-wind transition region. We analyze the correlation between the location of the inner boundary of the transition region R_in and the magnetic field strength on the source surface |B_R|. We discuss the peculiarities of the R_in = F(|B_R|) correlation diagrams that distinguish them from similar diagrams at previous phases of the solar cycle.     

Slow solar wind: Sources and components of the stream structure at the solar maximum

We study the sources and components of the solar-wind spatial stream structure at the maximum of the solar cycle 23. In our analysis, we use several independent sets of experimental data: radio-astronomical observations of scattered radiation from compact sources with the determination of the distance from the Sun to the inner boundary of the transonic-flow transition region (R_in); calculated data on the magnetic-field intensity and structure in the solar corona, in the solar-wind source region, obtained from optical measurements of the photospheric magnetic-field intensity at the Stanford Solar Observatory (USA); and observations of the white-light corona with the LASCO coronograph onboard the SOHO spacecraft. We show that at the solar maximum, low-speed streams with a transition region located far from the Sun dominate in the solar-wind structure. A correlation analysis of the location of the inner boundary R_in and the source-surface magnetic-field intensity |B _R | on a sphere R=2.5R_S (R_S is the solar radius) has revealed the previously unknown lowest-speed streams, which do not fit into the regular relationship between the parameters R_in and |B _R |. In the white-light corona, the sources of these streams are located near the dark strip, a coronal region with a greatly reduced density; the nonstandard parameters of the streams probably result from the interaction of several discrete sources of different types.     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.     

Stream Interactions and Interplanetary Coronal Mass Ejections at 0.72 AU

We present comprehensive surveys of 203 stream interaction regions (SIRs) and 124 interplanetary CMEs (ICMEs) during 1979 – 1988 using Pioneer Venus Orbiter (PVO) in situ solar-wind observations at 0.72 AU and examine the solar-cycle variations of the occurrence rate, shock association rate, duration, width, maximum total perpendicular pressure (P _t), maximum dynamic pressure, maximum magnetic field intensity, and maximum velocity change of these two large-scale solar-wind structures. The medians, averages, and histogram distributions of these parameters are also reported. Furthermore, we sort ICMEs into three groups based on the temporal profiles of P _t, and we investigate the variations of the fractional occurrence rate of three groups of ICMEs with solar activity. We find that the fractional occurrence rate of magnetic-cloud-like ICMEs declined with solar activity, consistent with our former 1-AU results. This study at 0.72 AU provides a point of comparison in the inner heliosphere for examining the radial evolution of SIRs and ICMEs. The width of SIRs and ICMEs increases by 0.04 and 0.1 AU, respectively, and the maximum P _t decreases to about 1/3 from Venus to Earth orbit. In addition, our work establishes the statistical properties of the solar-wind conditions at 0.72 AU that control the solar-wind interaction with Venus and its atmosphere loss by related processes. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Stream Interactions and Interplanetary Coronal Mass Ejections at 5.3 AU near the Solar Ecliptic Plane

We have performed a survey of the characteristics of two types of large spatial-scale solar-wind structures, stream interaction regions (SIRs), and interplanetary coronal mass ejections (ICMEs), near 5.3 AU, using solar-wind observations from Ulysses. Our study is confined to the three aphelion passes of Ulysses, and also within ± 10° of the solar ecliptic plane, covering a part of 1992, 1997 – 1998, and 2003 – 2005, representing three slices of different phases of the solar activity cycle. Overall, there are 54 SIRs and 60 ICMEs in the survey. Many are merged in hybrid events, suggesting that they have undergone multiple interactions prior to reaching Jovian orbit. About 91% of SIRs occur with shocks, with 47% of such shocks being forward – reverse shock pairs. The solar-wind velocity sometimes stays constant or even decreases within the interaction region near 5.3 AU, in contrast with the gradual velocity increase during SIRs at 1 AU. Shocks are driven by 58% of ICMEs, with 94% of them being forward shocks. Some ICMEs seem to have multiple small flux ropes with different scales and properties. We quantitatively compare various properties of SIRs and ICMEs at 5.3 AU, and study their statistical distributions and variations with solar activity. The width, maximum dynamic pressure, and peak perpendicular pressure of SIRs all become larger than ICMEs. Dynamic pressure (P _dyn) is expected to be important for Jovian magnetospheric activity. We have examined the distributions of P _dyn of SIRs, ICMEs, and general solar wind, but these cannot explain the observed bimodal distribution of the location of the Jovian magnetopause. By comparing the properties of SIRs and ICMEs at 0.72, 1, and 5.3 AU, we find that the ICME expansion slows down significantly between 1 and 5.3 AU. Some transient and small streams in the inner heliosphere have merged into a single interaction region. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Radial Evolution of Well-Observed Slow CMEs in the Distance Range 2 – 30 <Emphasis Type="Italic">R</Emphasis><Subscript>⊙</Subscript>

We performed a detailed analysis of 27 slow coronal mass ejections (CMEs) whose heights were measured in at least 30 coronagraphic images and were characterized by a high quality index (≥4). Our primary aim was to study the radial evolution of these CMEs and their properties in the range 2 – 30 solar radii. The instantaneous speeds of CMEs were calculated by using successive height – time data pairs. The obtained speed – distance profiles [v(R)] are fitted by a power law v = a(R−b) ^c . The power-law indices are found to be in the ranges a=30 – 386, b=1.95 – 3.92, and c=0.03 – 0.79. The power-law exponent c is found to be larger for slower and narrower CMEs. With the exception of two events that had approximately constant velocity, all events were accelerating. The majority of accelerating events shows a v(R) profile very similar to the solar-wind profile deduced by Sheeley et al. (Astrophys. J. 484, 472, 1997). This indicates that the dynamics of most slow CMEs are dominated by the solar wind drag.     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

The Solar Wind at 1 AU During the Declining Phase of Solar Cycle 23: Comparison of 3D Numerical Model Results with Observations

We present results of solar-wind parameters generated by 3D MHD models. The ENLIL inner-heliosphere solar-wind model together with the MAS or Wang – Sheeley – Arge (WSA) coronal models, describe the steady solar-wind stream structure and its origins in the solar corona. The MAS/ENLIL and WSA/ENLIL models have been tuned to provide a simulation of plasma moments as well as interplanetary magnetic-field magnitude and polarity in the absence of disturbances from coronal transients. To investigate how well the models describe the ambient solar wind structure from the Sun out to 1 AU, the model results are compared to solar-wind measurements from the ACE spacecraft. We find that there is an overall agreement between the observations and the model results for the general large-scale solar-wind structures and trends, such as the timing of the high-density structures and the low- and high-speed winds, as well as the magnetic sector structures. The time period of our study is the declining phase of Solar Cycle 23 when the solar activity involves well-defined stream structure, which is ideal for testing a quasi-steady-state solar-wind model.     

Spectro-Polarimetric Observations of Solar Magnetic Fields and the SOHO/MDI Calibration Issue

Comparisons of solar magnetic-field measurements made in different spectral lines are very important, especially in those lines in which observations have a long history or (and) specific diagnostic significance. The spectral lines Fe i 523.3 nm and Fe i 525.0 nm belong to this class. Therefore, this study is devoted to a comprehensive analysis using new high-precision Stokes-meter full-disk observations. The disk-averaged magnetic-field strength ratio R=B(523.3)/B(525.0) equals 1.97±0.02. The center-to-limb variation (CLV) is R=1.74−2.43μ+3.43μ ², where μ is the cosine of the center-to-limb angle. For the disk center, we find R=2.74, and for near-limb areas with μ=0.3, R equals 1.32. There is only a small dependence of R on the spatial resolution. Our results are rather close to those published three decades ago, but differ significantly from recent magnetographic observations. An application of our results to the important SOHO/MDI magnetic data calibration issue is discussed. We conclude that the revision of the SOHO/MDI data, based only on the comparison of magnetic-field measurements in the line pair Fe i 523.3 nm and Fe i 525.0 nm (increasing by a factor of 1.7 or 1.6 on average according to recent publications) is not obvious and new investigations are urgently needed.     

Penetration of coronal magnetic fields into solar-wind streams

The formation of solar-wind stream structure is investigated. Characteristic features of the solar and coronal magnetic-field structure, morphological features of the white-light corona, and radio maps of the solar-wind transition (transonic) region are compared. The solar-wind stream structure is detected and studied by using radio maps of the transition region, the raggedness of its boundaries, and their deviation from spherical symmetry. The radio maps have been constructed from radioastronomical observations in 1995–1997. It is shown that the structural changes in the transition region largely follow the changes occurring in regions closer to the Sun, in the circumsolar magnetic-field structure, and in the solar-corona structure. The correlations between the magnetic-field strength in the solar corona and the location of the inner (nearest the Sun) boundary of the transition region are analyzed. The distinct anticorrelation between the coronal magnetic-field strength and the distance of the transition region from the Sun is a crucial argument for the penetration of solar magnetic fields into plasma streams far from the Sun.     

Zonal structure and meridional drift of large-scale solar magnetic fields

Digitized synoptic charts of photospheric magnetic fields were analyzed for the past 4 incomplete solar activity cycles (1969–2000). The zonal structure and cyclic evolution of large-scale solar magnetic fields were investigated using the calculated values of the radial B _r, |B _r|, meridional B _θ, |B _θ|, and azimuthal B _φ, |B _φ| components of the solar magnetic field averaged over a Carrington rotation (CR). The time–latitude diagrams of all 6 parameters and their correlation analysis clearly reveal a zonal structure and two types of the meridional poleward drift of magnetic fields with the characteristic times of travel from the equator to the poles equal to ∼16–18 and ∼2–3 years. A conclusion is made that we observe two different processes of reorganization of magnetic fields in the Sun that are related to generation of magnetic fields and their subsequent redistribution in the process of emergence from the field generation region to the solar surface. Redistribution is supposed to be caused by some external forces (presumably, by sub-surface plasma flows in the convection zone).     

Relation between the Spatial Distribution and Spectral Index of Superthermal Electron Distribution in Solar cm-Radio Sources

A series of solar cm-radio bursts are analyzed by a new inverse method estimating spatial changes of the superthermal electron distribution in solar cm-radio burst sources. It is found that the measure of the spatial change of superthermal electrons in the radio source ν _n is always greater than that for the magnetic field ν _B and it is linearly dependent on the spectral index of the electrons δ as ν _n ≈0.5δ. This relation is explained in the simplified flare-loop model integrating the analytical solutions of the Fokker – Planck equation. The mean value of ν _B is found to be 0.36±0.04, which is very close to the value of ν _B =0.38±0.02 derived from the dependence of the magnetic field strength on the height in the active region measured by RATAN-600.     

Interplanetary Scintillation Observations of Stream Interaction Regions in the Solar Wind

We present a summary of results from ten years of interplanetary scintillation (IPS) observations of stream interaction regions (SIRs) in the solar wind. Previous studies had shown that SIRs were characterized by intermediate-velocity solar wind and – in the case of compressive interactions – higher levels of scintillation. In this study we considered all cases of intermediate velocities in IPS observations from the European Incoherent SCATter (EISCAT) radar facility made at low- and mid-heliographic latitudes between 1994 and 2003. After dismissing intermediate-velocity observations which were associated with solar-wind transients (such as coronal mass ejections) we found that the remaining cases of intermediate velocities lay above coronal structures where stream interaction would be expected. An improved ballistic mapping method (compared to that used in earlier EISCAT studies of interaction regions) was used to identify the regions of raypath in IPS observations which might be expected to include interaction regions and to project these regions out to the distances of in-situ observations. The early stages of developing compression regions, consistent with their development on the leading edges of compressive stream interaction regions, were clearly detected as close to the Sun as 30 R _⊙, and further ballistic projection out to the distances of in-situ observations clearly associated these developing structures with density and velocity features characteristic of developed interaction regions in in-situ data in the cases when such data were available. The same approach was applied to study non-compressive interaction regions (shear layers) between solar-wind streams of different velocities where the stream interface lay at near-constant latitude and the results compared with those from compressive interaction regions. The results confirm that intermediate velocities seen in IPS observations above stream boundaries may arise from either detection of intermediate-velocity flow in compression regions, or from non-compressive shear layers. The variation in velocity about the mean determined from IPS measurements (representing the spread in velocity across that part of the raypath associated with the interaction region in the analysis) was comparable in compressive and non-compressive regions – a potentially interesting result which may contain important information on the geometry of developing SIRs. It is clear from these results that compressive and non-compressive interaction regions belong to the same class of stream – stream interaction, with the dominant mode determined by the latitudinal gradient of the stream interface. Finally, we discuss the results from this survey in the light of new data from the Heliospheric Imagers (HI) on the Solar TErrestrial RElations Observatory (STEREO) spacecraft and other instruments, and suggest possible directions for further work.     

Interplanetary sector structure and the helliomagnetic equator

The magnetohydrodynamics of solar-wind flow lead logically to the formation of one warped annular neutral surface that apparently extends from ≈ 2r _⊙ (solar radii) to the boundary of the heliosphere. The most likely asymptotic configuration for this neutral sheet intersects the heliomagnetic equatorial plane along four corotating arcs. The observer sees a reversal of magnetic polarity on each crossing of the neutral surface, and so interprets each reversal as the crossing of a sector boundary.     

Stokes Diagnostics of 2D MHD-Simulated Solar Magnetogranulation

The properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes are studied. A synthetic infrared spectropolarimetric diagnostic based on a 2D MHD simulation of magnetoconvection is used for this. Analyzed are two time sequences of snapshots that likely represent two regions of the network fields with their immediate surroundings on the solar surface with unsigned magnetic flux densities of 300 and 140 G. In the first region from the probability density functions of the magnetic field strength it is found that the most probable field strength at log τ ₅=0 is equal to 250 G. Weak fields (B<500 G) occupy about 70% of the surface, whereas stronger fields (B>1000 G) occupy only 9.7% of the surface. The magnetic flux is −28 G and its imbalance is −0.04. In the second region, these parameters are correspondingly equal to 150 G, 93.3%, 0.3%, −40 G, and −0.10. The distribution of line-of-sight velocities on the surface of log τ ₅=−1 is estimated. The mean velocity is equal to 0.4 km s⁻¹ in the first simulated region. The average velocity in the granules is −1.2 km s⁻¹ and in the intergranules it is 2.5 km s⁻¹. In the second region, the corresponding values of the mean velocities are equal to 0, −1.8, and 1.5 km s⁻¹. In addition the asymmetry of synthetic Stokes V profiles of the Fe i 1564.8 nm line is analyzed. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude asymmetry is increased to 10% whereas the area asymmetry is only slightly varied.     

The Contribution of Sound Waves and Instabilities to the Penetration of the Solar Differential Rotation Below the Convection Zone

The response of a layer to a horizontal shear flow at its top the surface was studied numerically as an initial value problem. The geometry was Cartesian and the conservation equations were solved with the help of the Zeus-3D code. In the initial state, the pressure, p, and density, ρ, of the layer were assumed to be related by a polytropic equation of index 1.14, which best approximates the solar values in the region of interest. The values of p and ρ at the lower boundary of the layer, namely r=R _l=0.4 R _⊙, were taken to be the solar values. The upper boundary was chosen to be the base of the solar convection zone, r=R _c=0.7 R _⊙. The shear flow at the surface, v _φ(R _c), was proportional to the solar differential rotation, and acoustical oscillations were present in the layer. It is shown that if the initial state is stable, a dynamical coupling between sound waves and the shear flow transmits the surface flow to the inner regions of the layer, even in the absence of dissipation. The shear flow in the sublayer below the one at the surface is proportional to v _φ(R _c), to the time, and to the strength of the oscillations. The constant of proportionality is calculated from the numerical integrations, performed for times of the order of 100 hr. Extrapolation of these results to longer times shows that the surface shear flow is transmitted to the inner regions in a time of the order of of 30 000 years. If the initial state is unstable to the vertical shear, the region of maximum instability depends also on the horizontal shear, and is located away from the equator (where the vertical shear is maximum). As a consequence, the longitudinal flow below the surface shows two equidistant maxima across the equator, located at intermediate latitudes.     

The Magnetic Field at the Inner Boundary of the Heliosphere Around Solar Minimum

STEREO A and B observations of the radial magnetic field between 1 January 2007 and 31 October 2008 show significant evidence that in the heliosphere, the ambient radial magnetic field component with any dynamic effects removed is uniformly distributed. Based on this monopolar nature of the ambient heliospheric field we find that the surface beyond which the magnetic fields are in the monopolar configuration must be spherical, and this spherical surface can be defined as the inner boundary of the heliosphere that separates the monopole-dominated heliospheric magnetic field from the multipole-dominated coronal magnetic field. By using the radial variation of the coronal helmet streamers belts and the horizontal current – current sheet – source surface model we find that the spherical inner boundary of the heliosphere should be located around 14 solar radii near solar minimum phase.     

Coronal Field Opens at Lower Height During the Solar Cycles 22 and 23 Minimum Periods: IMF Comparison Suggests the Source Surface Should Be Lowered

The solar cycle 23 minimum period has been characterized by a weaker solar and interplanetary magnetic field. This provides an ideal time to study how the strength of the photospheric field affects the interplanetary magnetic flux and, in particular, how much the observed interplanetary fields of different cycle minima can be understood simply from differences in the areas of the coronal holes, as opposed to differences in the surface fields within them. In this study, we invoke smaller source surface radii in the potential-field source-surface (PFSS) model to construct a consistent picture of the observed coronal holes and the near-Earth interplanetary field strength as well as polarity measurements for the cycles 23 and 22 minimum periods. Although the source surface value of 2.5 R _⊙ is typically used in PFSS applications, earlier studies have shown that using smaller source surface heights generates results that better match observations during low solar activity periods. We use photospheric field synoptic maps from Mount Wilson Observatory (MWO) and find that the values of ≈ 1.9 R _⊙ and ≈ 1.8 R _⊙ for the cycles 22 and 23 minimum periods, respectively, produce the best results. The larger coronal holes obtained for the smaller source surface radius of cycle 23 somewhat offsets the interplanetary consequences of the lower magnetic field at their photospheric footpoints. For comparison, we also use observations from the Michelson Doppler Imager (MDI) and find that the source surface radius of ≈ 1.5 R _⊙ produces better results for cycle 23, rather than ≈ 1.8 R _⊙ as suggested from MWO observations. Despite this difference, our results obtained from MWO and MDI observations show a qualitative consistency regarding the origins of the interplanetary field and suggest that users of PFSS models may want to consider using these smaller values for their source surface heights as long as the solar activity is low.     

Average Thickness of Magnetosheath Upstream of Magnetic Clouds at 1 AU versus Solar Longitude of Source

Starting with a large number (N=100) of Wind magnetic clouds (MCs) and applying necessary restrictions, we find a proper set of N=29 to investigate the average ecliptic plane projection of the upstream magnetosheath thickness as a function of the longitude of the solar source of the MCs, for those cases of MCs having upstream shock waves. A few of the obvious restrictions on the full set of MCs are the need for there to exist a driven upstream shock wave, knowledge of the MC’s solar source, and restriction to only MCs of low axial latitudes. The analysis required splitting this set into two subsets according to average magnetosheath speed: slow/average (300 – 500 km s⁻¹) and fast (500 – 1100 km s⁻¹) speeds. Only the fast set gives plausible results, where the estimated magnetosheath thickness (ΔS) goes from 0.042 to 0.079 AU (at 1 AU) over the longitude sector of 0° (adjusted source-center longitude of the average magnetic cloud) to 40° off center (East or West), based on N=11 appropriate cases. These estimates are well determined with a sigma (σ) for the fit of 0.0055 AU, where σ is effectively the same as (chi-squared) for the appropriate quadratic fit. The associated linear correlation coefficient for ΔS versus |Longitude| was very good (c.c.=0.93) for the fast range, and ΔS at 60° longitude is extrapolated to be 2.7 times the value at 0°. For the slower speeds we obtain the surprising result that ΔS is typically more-or-less constant at 0.040±0.013 AU at all longitudes, indicating that the MC as a driver, when moving close to the normal solar wind speed, has little influence on magnetosheath thickness. In some cases, the correct choice between two candidate solar-source longitudes for a fast MC might be made by noting the value of the observed ΔS just upstream of the MC. Also, we point out that, for the 29 events, the average sheath speed was well correlated with the quantity ΔV[=(〈V _MC〉−〈V _UPSTREAM〉)], and also with both 〈V _MC〉 and 〈V _MC,T〉, where 〈V _MC〉 is the first one-hour average of the MC speed, 〈V _MC,T〉 is the average MC speed across the full MC, and 〈V _UPSTREAM〉 is a five-hour average of the solar wind speed just upstream of the shock.