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Spring 2009
Solar wind stream interfaces: The importance of time, longitude, and latitude separation between points of observation
Kristin Diane Commer Simunac University of New Hampshire, Durham
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Recommended Citation Simunac, Kristin Diane Commer, "Solar wind stream interfaces: The importance of time, longitude, and latitude separation between points of observation" (2009). Doctoral Dissertations. 487. https://scholars.unh.edu/dissertation/487
This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. SOLAR WIND STREAM INTERFACES: THE IMPORTANCE OF TIME, LONGITUDE, AND LATITUDE SEPARATION BETWEEN POINTS OF OBSERVATION
BY
KRISTIN DIANE COMMER SIMUNAC B.S. Astronomy, California Institute of Technology, 2001 M.S. Physics, University of Kansas, 2002
DISSERTATION
Submitted to the University of New Hampshire in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Physics
May, 2009 UMI Number: 3363731
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< /( K4Stfa Dissertatioissertationi Director, Lynn M. Kistler, Associate Professor, Physics and Institute for Earth, Oceans and Space A tJA//>u£ 1ame s J. CoJnell, Associate Professor, Physics and Institute for Earth, Oceans, andJSpace
Antoinette B. Galvin, Research Associate Professor, Physics and Institute for Earth, Oceans and s7> J
Karsten Pohl, Associate Professor, Physics
Charles W. Smith, Research Professor, Institute for Earth, Oceans and Space
^W J ^Q1 Date DEDICATION
To my always loving and supportive family. ACKNOWLEDGEMENTS
This work has been supported by NASA Contract NAS5-00132.
Thank you to K.W. Ogilvie (NASA GSFC) and A.J. Lazarus (MIT) for making WIND/SWE proton data available.
This work utilizes data obtained by the Global Oscillation Network Group (GONG) Program, managed by the National Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofisica de Canarias, and Cerro Tololo Interamerican Observatory.
iv TABLE OF CONTENTS
DEDICATION iii ACKNOWLEDGEMENTS iv LIST OF TABLES vii LIST OF FIGURES ix ABSTRACT xiv
INTRODUCTION 1
CHAPTER I: THE SUN AND SOLAR WIND 4 The Sun 4 The Corona 6 The Solar Wind 9 Solar Wind Source Regions 14 Corotating Interaction Regions 16 Fast-to-Slow Solar Wind Transitions 21 Numerical Models 23 Motivation and Application 26
CHAPTER II: INSTRUMENTATION AND PRE-FIGHT CALIBRATION 30 The STEREO Mission 30 The Plasma and Supra-Thermal Ion Composition Experiment 32 Pre-flight Calibration 35 Onboard Moments 39 Full Resolution Rate 48
CHAPTER III: DATA SELECTION AND IN-FIGHT CALIBRATION 50 Suspected Leakage 50 Calculating 1 -D Proton Bulk Parameters In-Flight 52
CHAPTER IV: OBSERVATIONS 74 Cam ngton Rotation 2054 76 Carr ngton Rotation 2055 79 Carr ngton Rotation 2056 83 Carr ngton Rotation 2057 86 Carr ngton Rotation 2058 89 Carr ngton Rotation 2059 92 Carri ngton Rotation 2060 95 Carri ngton Rotation 2061 98 Carr ngton Rotation 2062 101 Carr ngton Rotation 2063 104
V Carrington Rotation 2064 106 Carrington Rotation 2065 109 Carrington Rotation 2066 112
CHAPTER V: ANALYSIS AND DISCUSSION 115 Slow-to-Fast Solar Wind Transitions 115 Identification of the Solar Wind Source Regions 120 The Effects of Latitude Separation 133 The Effects of Time Separation 142 Additional Discussion: Carrington Rotation 2066 153 Fast-to-Slow Transitions 155
CHAPTER VI: CONCLUSIONS 159
APPENDIX A: EFFICIENCY AND INTERCALIBRATION 162 Rate Definitions 162 Changes Over Time 166 Noise 170 Azimuth Response 170 Triple Coincidence Proton Efficiency 171 Additional PLASTIC/A Efficiency Considerations 173 Inter-calibration of STEREO/PLASTIC with WIND/SWE 181
APPENDIX B: NORTH/SOUTH FLOW ANGLE 188
LIST OF REFERENCES 198
vi LIST OF TABLES
TABLE PAGE
1.1 Typical Solar Wind Properties Near 1 AU 14
2.1 STEREO/PLASTIC Calibration Summary 36 2.2 Analyzer Constants 36 2.3 Deflection Constants and Angular Acceptance Ranges 36
3.1 PLASTIC/AHEAD Velocity to ESA Step Correspondence 61 3.2 PLASTIC/BEHIND Velocity to ESA Step Correspondence 62
4.1 CR 2054 Slow-to-Fast Transitions 77 4.2 CR 2054 Fast-to-Slow Transitions 79 4.3 CR 2055 Slow-to-Fast Transitions 81 4.4 CR 2055 Fast-to-Slow Transitions 83 4.5 CR 2056 Slow-to-Fast Transitions 84 4.6 CR 2056 Fast-to-Slow Transitions 86 4.7 CR 2057 Slow-to-Fast Transitions 87 4.8 CR 2057 Fast-to-Slow Transitions 87 4.9 CR 2058 Slow-to-Fast Transitions 91 4.10 CR 2058 Fast-to-Slow Transitions 91 4.11 CR 2059 Slow-to-Fast Transitions 93 4.12 CR 2059 Fast-to-Slow Transitions 95 4.13 CR 2060 Slow-to-Fast Transitions 96 4.14 CR 2060 Fast-to-Slow Transitions 98 4.15 CR 2061 Slow-to-Fast Transitions 99 4.16 CR 2061 Fast-to-Slow Transitions 101 4.17 CR 2062 Slow-to-Fast Transitions 102 4.18 CR 2062 Fast-to-Slow Transitions 104 4.19 CR 2063 Slow-to-Fast Transitions 106 4.20 CR 2063 Fast-to-Slow Transitions 106 4.21 CR 2064 Slow-to-Fast Transitions 107 4.22 CR 2064 Fast-to-Slow Transitions 109 4.23 CR 2065 Slow-to-Fast Transitions 110 4.24 CR 2065 Fast-to-Slow Transitions 112 4.25 CR 2066 Slow-to-Fast Transitions 114 4.26 CR 2066 Fast-to-Slow Transitions 114
vii TABLE PAGE
5.1 Stream Interface Summary Table 118 5.2 Summary of Attempted Latitude Correction 141 5.3 Fast-to-Slow Transition Summary Table 157
viii LIST OF FIGURES
FIGURE PAGE
1.1 Differential Solar Rotation 6 1.2 Solar Eclipse 7 1.3 Sun in Extreme Ultra Violet 8 1.4 Parker Spiral 13 1.5 CIR Schematic 18 1.6 Shock Geometry 27 1.7 Effect of Radial Separation 28
2.1 PLASTIC Entrance System and Time-of-Flight Chamber 33 2.2 Pre-launch Azimuth Scan 37 2.3 PLASTIC/A Resistive Anode Response 38 2.4 PLASTIC/B Resistive Anode Response 39 2.5 Simulated Count Distribution 42 2.6 0th Moment from Simulated Data 43 2.7 1st Moment from Simulated Data 43 2.8 2nd Moment from Simulated Data 44 2.9 Modeled Instrument Response 45 2.10 Data Selection for Onboard Moments Calculation 47 2.11 Maxwellian Distribution Function 49
3.1 PLASTIC/AHEAD Deflection Distribution 52 3.2 PLASTIC/BEHIND Deflection Distribution 52 3.3 Background Subtraction Example 54 3.4 Deflection Wobble Correction Example 55 3.5 Density Comparison between PLASTIC/B and WIND/SWE 57 3.6 PLASTIC/A RA_Trig Efficiency versus MCP Setting 58 3.7 PLASTIC/B RA_Trig Efficiency versus MCP Setting 59 3.8 Kinetic Energy of PLASTIC and WIND/SWE 60 3.9 In-flight Estimated Proton Speed to ESA Step Correspondence 60 3.10 Sample Distribution Function 63 3.11 April 2007 Proton Data 65 3.12 May 2007 Proton Data 66 3.13 June 2007 Proton Data 67
ix 3.14 July 2007 Proton Data 68 3.15 August 2007 Proton Data 69 3.16 September 2007 Proton Data 70 3.17 October 2007 Proton Data 71 3.18 November 2007 Proton Data 72 3.19 December 2007 Proton Data 73
4.1 Carrington Rotation 2054 Bulk Speed 76 4.2 Stream Interface Arrives at STEREO/AHEAD 77 4.3 CR 2054 - PLASTIC/AHEAD 78 4.4 CR 2054 - PLASTIC/BEHIND 78 4.5 Carrington Rotation 2055 Bulk Speed 80 4.6 Stream Interface Arrives at STEREO/BEHIND 80 4.7 CR 2055 - PLASTIC/AHEAD 82 4.8 CR 2055 - PLASTIC/BEHIND 82 4.9 Carrinton Rotation 2056 Bulk Speed 84 4.10 CR 2056 - PLASTIC/AHEAD 85 4.11 CR 2056 - PLASTIC/BEHIND 85 4.12 Carrington Rotation 2057 Bulk Speed 87 4.13 CR 2057 - PLASTIC/AHEAD 88 4.14 CR 2057 - PLASTIC/BEHIND 88 4.15 Carrington Rotation 2058 Bulk Speed 89 4.16 CR 2058 - PLASTIC/AHEAD 90 4.17 CR 2058 - PLASTIC/BEHIND 90 4.18 Carrington Rotation 2059 Bulk Speed 93 4.19 CR 2059 - PLASTIC/AHEAD 94 4.20 CR 2059 - PLASTIC/BEHIND 94 4.21 Carrington Rotation 2060 Bulk Speed 96 4.22 CR 2060 - PLASTIC/AHEAD 97 4.23 CR 2060 - PLASTIC/BEHIND 97 4.24 Carrington Rotation 2061 Bulk Speed 99 4.25 CR 2061 - PLASTIC/AHEAD 100 4.26 CR 2061 - PLASTIC/BEHIND 100 4.27 Carrington Rotation 2062 Bulk Speed 102 4.28 CR 2062 - PLASTIC/AHEAD 103 4.29 CR 2062 - PLASTIC/BEHIND 103
x 4.30 Carrington Rotation 2063 Bulk Speed 104 4.31 CR 2063 - PLASTIC/AHEAD 105 4.32 CR 2063 - PLASTIC/BEHIND 105 4.33 Carrington Rotation 2064 Bulk Speed 107 4.34 CR 2064 - PLASTIC/AHEAD 108 4.35 CR 2064-PLASTIC/BEHIND 108 4.36 Carrington Rotation 2065 Bulk Speed 110 4.37 CR 2065 - PLASTIC/AHEAD 111 4.38 CR 2065 - PLASTIC/BEHIND 111 4.39 Carrington Rotation 2066 Bulk Speed 112 4.40 CR 2066 - PLASTIC/AHEAD 113 4.41 CR 2066 - PLASTIC/BEHIND 113
5.1 Idealized Stream Interface 116 5.2 Small Radial Separation 117 5.3 Expected - Actual SI Arrival versus Time 119 5.4 Carrington Rotation 2061 in situ data and GONG model 122 5.5 CR 2061 bulk speed and SECCHI synoptic images 125 5.6 Carrington Rotation 2061 PFSS 127 5.7 Bulk Speed and SECCHI maps CR 2054 - 2060 128 5.8 Bulk Speed and SECCHI maps CR 2061 - 2066 129 5.9 Expected - Actual Arrival versus Latitude Separation 134 5.10 Schematic of Latitude Separation Effect 135 5.11 GONG Synoptic Model and Slope Proxy 136 5.12 SECCHI Synoptic Image and Slope Proxy 140 5.13 Carrington Rotation 2062 in situ data and GONG model 144 5.14 SECCHI Images SI no. 27 Back-mapped 145 5.15 Carrington Rotation 2063 in situ data and GONG model 146 5.16 CR 2063 bulk speed and SECCHI synoptic images 147 5.17 SECCHI Images SI no. 28, 29, and 30 149 5.18 Carrington Rotation 2064 in situ data and GONG model 151 5.19 SECCHI Images SI no. 29 and 32a 152 5.20 Carrington Rotation 2066 in situ data and GONG model 154 5.21 CR 2066 bulk speed and SECCHI synoptic images 155 5.22 Expected - Actual Fast-to-Slow Arrival versus Time 156 5.23 Back-mapped Fast-to-Slow Transition and SECCHI Image 158
xi A.1 PLASTIC/B Proton Stop Efficiency versus MCP Voltage 163 A.2 PLASTIC/B Proton Start Efficiency versus MCP Voltage 164 A.3 PLASTIC/B Single Position Efficiency versus MCP Voltage 165 A.4 PLASTIC/B Total Proton Efficiency versus MCP Voltage 166 A.5 PLASTIC/B Efficiency Change with Time 167 A.6 PLASTIC/B Stop Efficiency versus Total Energy 168 A.7 PLASTIC/B Start Efficiency versus Total Energy 168 A.8 PLASTIC/B Single Position Efficiency versus Total Energy 169 A.9 PLASTIC/B Total Efficiency versus Total Energy 169 A. 10 Time-of-Flight Noise 170 A.11 PLASTIC/B Azimuth Scan 171 A. 12 Proton Triple Coincidence Efficiency versus MCP Voltage 172 A. 13 Proton Triple Coincidence Efficiency versus Total Energy 172 A. 14 PLASTIC/A Stop Efficiency versus MCP Voltage 173 A. 15 PLASTIC/A Single Position Efficiency versus MCP Voltage 174 A. 16 PLASTIC/A Threshold Change 174 A.17 PLASTIC/A Triple Coincidence Efficiency versus MCP Voltage 175 A. 18 PLASTIC/A Revised Stop Efficiency 176 A. 19 PLASTIC/A Revised Start Efficiency 177 A.20 PLASTIC/A Revised Single Position Efficiency 177 A.21 PLASTIC/A Revised Total Efficiency versus MCP Voltage 178 A.22 PLASTIC/A Revised Stop Efficiency versus Total Energy 178 A.23 PLASTIC/A Revised Start Efficiency versus Total Energy 179 A.24 PLASTIC/A Revised Single Position Efficiency versus Energy 179 A.25 PLASTIC/A Revised Total Efficiency versus Total Energy 180 A.26 Revised Triple Coincidence Efficiency 180 A.27 Revised Triple Coincidence Efficiency versus Total Energy 181 A.28 In-flight Density March 2007 PLASTIC and WIND/SWE 182 A.29 Thermal Speed March 2007 PLASTIC and WIND/SWE 183 A.30 In-flight Density April 2007 PLASTIC and WIND/SWE 184 A.31 Thermal Speed April 2007 PLASTIC and WIND/SWE 184 A.32 PLASTIC/B:SWE Density Ratio versus Speed 185 A.33 PLASTIC/A:SWE Density Ratio versus Speed 185 A.34 PLASTIC/B:SWE Revised Density Ratio 186 A.35 PLASTIC In-flight Proton Efficiency Curves 187
xii FIGURE PAGE
B.1 PLASTIC/A Deflection Distribution 189 B.2 PLASTIC/B Deflection Distribution 189 B.3 Small Channel Deflection Distribution 190 B.4 PLASTIC-A/SWE North/South Angle Comparison 190 B.5 PLASTIC-A/SWE North/South Difference versus Speed 191 B.6 PLASTIC-B/SWE North/South Difference versus Speed 192 B.7 North/South Angle versus Time 193 B.8 Back-mapped North/South Angle versus Time 193 B.9 North/South Angle versus Speed 194 B. 10 Modified North/South Angle versus Speed 195 B. 11 Modified PLASTIC-B/SWE Angle Difference versus Speed 196 B. 12 Calibrated PLASTIC-B North/South Angle versus Speed 197 B.13 Back-mapped Calibrated North/South Angle 197
xiii ABSTRACT
SOLAR WIND STREAM INTERFACES: THE IMPORTANCE OF TIME, LONGITUDE, AND LATITUDE SEPARATION BETWEEN POINTS OF OBSERVATION
by
Kristin Diane Commer Simunac
University of New Hampshire, May, 2009
Using data from the Plasma and Suprathermal Ion Composition
(PLASTIC) instruments onboard the Solar Terrestrial Relations Observatory
(STEREO), I have studied the evolution of solar wind stream interfaces in the
ecliptic plane near 1 AU over time scales of hours to a few days. STEREO
consists of two nearly identical satellites in orbits similar to the Earth's orbit about the Sun. One observatory leads the Earth (STEREO/A), and the other lags
behind (STEREO/B). The PLASTIC instruments, build by a team lead by A.B.
Galvin of the University of New Hampshire, measure solar wind and
suprathermal ion composition. In this work, the instruments were used to
determine the bulk properties of solar wind protons. The PLASTIC instruments
functioned somewhat differently than anticipated pre-launch, so it was necessary
to carry out an in-flight calibration for the bulk solar wind proton data. The proton
data were then used to identify transitions between slow and fast solar wind for
thirteen Carrington rotations covering March 2007 through February 2008. During
this interval the heliographic longitude separation between the two observatories
xiv grew from about 2 degrees to 45 degrees. After a solar wind transition was observed at STEREO/B, the expected time-of-arrival at STEREO/A was calculated assuming ideal corotation with the Sun and negligible source evolution. The difference between expected and actual arrival times was generally less than ten hours when heliographic longitude separation between the observatories was less than 20 degrees, and time separation was less than a day. Discrepancies of more than 40 hours occurred when heliographic latitude separation between the observatories exceeded 5 degrees. By propagating the solar wind data back to the sun, the source regions were identified for particular cases, and the sources were examined for both latitudinal differences and for source evolution. Both latitude differences and source evolution were reflected in the in situ solar wind proton data. In 32 of 41 cases the stream interface between slow and fast solar wind arrived earlier than predicted. This result is important to forecasting the arrival of high-speed streams at Earth, which are known to cause recurrent geomagnetic storms.
XV INTRODUCTION
In this dissertation I use data from the STEREO/PLASTIC instrument to identify solar wind stream interfaces observed by the two STEREO spacecraft.
The observed difference in arrival time is compared with the expected timing difference assuming corotation with the Sun. Changes in coronal holes, the sources of high-speed solar wind, are examined to potentially explain deviations from the expected timing between observations. I find that both changes in the coronal holes and latitudinal differences in the holes are related to the differences in observations between the two STEREO observatories.
This manuscript is divided into five chapters. The first is an introduction to the Sun and solar wind. An overview is given of the large-scale features of our
Sun including its activity cycle. The solar wind is introduced next, with descriptions of the large-scale geometry of the solar wind in the heliosphere, and the properties observed in situ near Earth. Techniques for identifying the most likely source regions of the different types of solar wind at the Sun are described.
The in situ signatures of transitions between slow and fast solar wind are then discussed. Numerical solar wind models and the key assumptions underlying them are described. My study tests the validity of two common assumptions: idealized corotation with the Sun and negligible source evolution.
Chapter 2 begins with an introduction to the STEREO Mission, its objectives, and the instruments onboard the observatories. The PLASTIC
1 instrument is described, and the results of pre-launch calibration testing are presented. I model the instrument response to test an onboard procedure designed to calculate the solar wind velocity, density, and temperature. A complementary technique for obtaining the 1-D bulk solar wind properties is also introduced.
Chapter 3 describes in-flight data selection and calibration. I revised estimates of the instruments' small channel geometric factors based on in-flight data. The ground-based data processing technique that I implemented for a single coincidence rate is presented next, including background subtraction techniques and corrections for dead time. Finally, the inter-spacecraft calibration that I carried out between STEREO/PLASTIC and WIND/SWE solar wind proton data is described.
Chapter 4 presents 1-D solar wind proton data from thirteen solar rotations, covering March 2007 through February 2008. I identify solar wind stream interfaces, as well as transitions from fast to slow solar wind.
Chapter 5 is analysis and discussion of the data presented in chapter 4.
Deviations from the idealized conditions used by the solar wind modelers are discussed. Two possible explanations for the discrepancies are examined: latitude separation between the observatories, and evolution of the solar wind source regions. Four solar rotations are studied in depth, with additional data including in situ observations of the magnetic field, remote observations of the corona at 195 A wavelength, and models of the magnetic field at the solar source
2 region. Finally the results and implications of the study are presented. I find that both latitude separation and time/longitude separation are important for predicting the arrival of the arrival of high-speed streams at Earth.
3 CHAPTER I
THE SUN AND SOLAR WIND
1.1 The Sun
Our Sun is a G-type yellow star. Its radius is 6.96 x 105 km, and it has a mass of 1.989 x 1031 kg. The Sun is made of hydrogen (about 90% by number, or 75% by mass), helium (about 10% by number, or 25% by mass), and the small remainder is heavier elements. The proton-proton chain converts hydrogen to helium in the Sun's innermost layer, the 1.5 x 107 K core.
+ lH+lH^lH + e + ve iH+lH—lHe+y A lHe+lHe-* 2He+2\H
The photons created by this reaction radiate outwards from the core (0.0 to 0.2
RSun) through the radiation zone (0.2 to 0.7 RSun) to the convection zone (0.7 to
1.0 RSun) by a random walk. Lang (1999) estimates the average time for photon to travel from through the radiation zone is 170,000 years. Large convection cells in the convection zone circulate hot material (about 2 x 106 K) to the Sun's surface, the photosphere, in about 10 days.
The photosphere is the visible surface of the Sun. Its temperature is about
6000 K. In visible (so-called "white") light, the photosphere appears to be granular. Each granule is the top of a convection cell. Dark sunspots are sometimes visible on the photosphere. They are cooler than the surrounding
4 material, and have intense magnetic fields on the order of 0.1 Tesla. (For reference, the Earth's magnetic field is on the order of 10"7 Tesla.) Sunspots often come in pairs (one of each polarity), and the area in the vicinity of these
intense magnetic fields is known as an "active region."
The number of sunspots visible at a given time varies with the solar activity cycle. The activity cycle is driven by changes in the Sun's magnetic field.
At times of minimal activity, "solar min," the field is roughly dipolar, like the
Earth's magnetic field. However, the polarity of the field reverses roughly every eleven years. The reversal does not happen instantaneously, but over a period of several years.
The heliographic equator rotates more rapidly than the poles. Newton and
Nunn (1951) observed the rotation of sunspots from 1934 to 1944. They found a
daily rotation rate of 14.38° - 2.96°sin2cp, where q> is heliographic latitude.
Snodgrass (1983) reported agreement with Newton and Nunn based on cross-
correlation of daily Mount Wilson magnetograms covering January 1967 to May
1982. From the point of view of an observer at Earth, the Sun's heliographic
equator completes a rotation in just under 27 days. At a latitude of 35° one
complete rotation takes nearly 29 days. The Sun's magnetic field is frozen-in to
the plasma because the conductivity is very large, so over time differential
rotation will cause a poloidal magnetic field to be warped into a toroidal field.
This is illustrated in Figure 1.1. Energy that is stored in the Sun's magnetic field
can be released by solar flares and coronal mass ejections.
5 Figure 1.1 Illustration of how differential rotation warps the Sun's magnetic field. Image courtesy of Windows to the Universe, http://www.windows.ucar.edu.
1.2 The Corona
Above the photosphere is the chromosphere, which can sometimes be viewed as a narrow red band about the edges of the Sun during a solar eclipse.
The temperature of the chromosphere is about 104 K. Above the chromosphere is the Sun's corona (from the Latin for "crown"). The corona is the outermost layer of the solar atmosphere. It is rarified and hot, about 106 K. The mechanism by which the corona is heated is an ongoing topic of study (c.f. Aschwanden et al.
2007 and references therein).
6 The line separating regions of opposite magnetic polarity at the Sun is called the neutral line. In the vicinity of the magnetic neutral line fields are typically closed. Plasma inhabits the magnetic loops, resulting in the appearance of coronal streamers when the sun is eclipsed (see Figure 1.2 below). This region near the neutral line is called the streamer belt. When the Sun's magnetic field is roughly dipolar the streamer belt is near the heliographic equator.
Figure 1.2 1991 eclipse image courtesy of Rhodes College, Memphis, Tennessee, and High Altitude Observatory (HAO), University Corporation for Atmospheric Research (UCAR), Boulder, Colorado. UCAR is sponsored by the National Science Foundation.
From space the corona can be viewed in X-ray and extreme ultraviolet
(EUV) wavelengths. Figure 1.3 shows an extreme ultra violet image (195 A) of the Sun in November 2007. Near the center of the disk is a dark region with very
low density. This is called a coronal hole. The first regular observations of coronal holes took place in 1973 with the X-ray imager on Skylab. Coronal holes
7 are almost always present near the heliographic poles of the Sun, and extensions of polar coronal holes sometimes reach equatorial latitudes (c.f. Timothy et al.
1975, Wang and Sheeley 1993).
Figure 1.3 Extreme ultraviolet image of the Sun from STEREO/SECCHI/BEHIND. Near disk center is a coronal hole.
Timothy, Krieger and Vaiana (1975) described a coronal hole extending from the northern polar region to about 20° latitude south. The coronal hole rotated rigidly, even though the photosphere underneath rotated differentially.
Wang and Sheeley (1993) reported observations of a coronal hole that first rotated rigidly, and later became sheared. They related the tendency for a coronal hole to shear with the magnetic neutral line's topology. The rotation period of a coronal hole depends on a variety of factors including its age and its latitude.
8 1.3 The Solar Wind
The corona expands into the heliosphere as the solar wind: a continuous stream of quasi-neutral magnetized plasma. The most abundant ions in the ambient solar wind are protons and alpha particles. Because it was created from a neutral gas, the net charge of a sample of plasma is very near to zero, so it can be described as quasi-neutral.
The primary reason the solar wind exists is the pressure difference between interstellar space and the corona (Hundhausen 1995). The gravitational force of the Sun opposes this exodus of material, and the overall change in the Sun's mass is negligible, even over billions of years. The actual rate of mass loss is about 5.0 x 1016 kg/year, small compared to the Sun's mass of about 2.0x1030 kg.
In the late 1950's Parker derived equations describing the expansion of the solar wind into space. Parker assumed that mass and momentum are conserved quantities, but that the corona is not in equilibrium (described in
Hundhausen 1972). The equations for conservation of mass and momentum are given below.
9 — + V • pu = 0 (conservation of mass)
p— + pu • Vu = -Vp + j x B + pFg (conservation of momentum) where: p = mass density u = velocity p = pressure = 2nkT (n = number density, k = Boltzmann constant, T = temperature) j = current B = magnetic field
F = gravitational force due to sun = -r^- r r (G = gravitational constant, Msun = mass of Sun)
Assuming a steady-state flow, the time derivatives can be set to zero. For simplicity, assume the solution is spherically symmetric with radial outflow. The mass conservation equation is simplified as follows:
V»pu = 0
r drv ' 2 r pur = Constant
2 4nr pur = 0 (A constant flux)
In other words, the mass flux is conserved through a spherical shell, which has surface area 4jtr2.
Neglecting the Lorentz force by setting E = -v x B, the conservation of momentum equation can also be significantly simplified:
10 pu • Vu = - Vp + pF du dp -GM„ dr dr du, dP PGM sun (u = u r) pur dr dr r2 r du d{2nkT) mnGM r (p = mn) mnu. dr dr r du 2kT dn -GMm r — 2 dr m dr r Going back to the conservation of mass equation:
2 4jtr pur = O 2 4jtr mnur =
n = 4JVT mur dn dn Substituting this back into the conservation of momentum equation: du 2kTJ Gravity keeps most of the material bound to the Sun, but at a critical radius r = Msunm/4kT the thermal pressure exceeds the force of gravity and material must flow out and away from the Sun. 11 Even before in situ measurements of the solar wind were possible (with the Russian probes of the late 1950's, and Mariner 2 in the early 1960's), Biermann (1951) suggested particles were leaving the Sun continuously. He based his assumption on observations of comet tails: the ion tail of a comet is directed away from the Sun, regardless of the comet's direction of motion. The coronal material has a very large conductivity, and magnetic flux is frozen-in to the plasma. As a parcel of plasma changes shape, the magnetic flux through it remains constant. In other words, as plasma expands into space the magnetic field from the Sun is carried with it, but the magnitude of the field decreases with distance. Looking down onto the plane of the solar system, the magnetic field lines appear to extend from the Sun and form an Archimedean spiral, usually referred to as the Parker spiral. The spiral pattern is formed because the solar wind sources rotate with of the Sun. (It is important to remember that the emitted plasma is not rotating, but traveling radially away from the Sun!) By the time the solar wind reaches Earth, a stream moving at 400 km/s makes an angle of 45° with respect to the Sun-Earth line (see Figure 1.4). The winding of the Parker spiral becomes tighter as the radial velocity of the plasma decreases, and similarly less tight as the speed increases. At a distance r, the "garden hose angle" between the parker spiral and a radial vector is given by: tana = Qsunr/ur a = angle 6 Qsun = the sun's angular roation speed - 2.9x10 rad/sec ur = solar wind speed (assumed to be radial) 12 Forsyth etal. 1996 found that within 60° latitude of the heliographic equator the magnetic field is "in approximate agreement with the Parker model." Figure 1.4 Illustration of the Parker-spiral curvature of both interplanetary magnetic field lines and corotating solar wind structures. The green circle has radius 1 AU, and the grey curve is an Archimedean spiral for solar wind with speed 400 km/s. Neugebauer and Snyder (1966) described the average properties of the solar wind based on in situ data from Mariner 2, launched in 1962. Observations covered positive ions with energy per charge between 0.231 and 8.224 keV/e (protons with speeds between 210 and 1250 km/s). The electrostatic spectrometer collected a continuous flow of material for about 3 months, giving the first clear observational evidence that the solar wind is not intermittent. Observed protons had an average speed of 500 km/s, and had an average temperature of 1.7x105 K. Fast moving, hot streams (up to 830 km/s and 9x105 K) alternated with slower streams having lower temperatures (down to about 300 13 km/s and 3x104 K). The fast streams were seen to recur with the Sun's rotation period of about 27 days. At the leading edge of the fast streams were density enhancements, but outside of these times the density and velocity were inversely related. Typical properties at 1 AU are summarized in the table below, from Hundhausen (1995) and Kallenrode (2004). The properties of the solar wind vary with the solar cycle. TABLE 1.1 Typical Solar Wind Properties Near 1 AU Proton Density (np) Overall Average 6.6 cm"3 Fast Solar Wind 3 cm3 Slow Solar Wind 8 cm"3 3 Electron Density (ne) 7.1 cm" Alpha Density (nj Fast Solar Wind 0.25 cm'3 (4% by number) Slow Solar Wind Variable, usually between 2% and 4% Speed (vsw) Overall Average 450 km/s Fast Solar Wind 400 to 800 km/s Slow Solar Wind 250 to 400 km/s Proton Temperature (Tp) Overall Average 1.2x105K Fast Solar Wind 2x105K Slow Solar Wind 3x104K 5 Electron Temperature (Tej 1.4x10 K Magnetic Field Strength (B) 7x10"9Tesla 1.4 Solar Wind Source Regions It has been reported since the 1970s that the fast solar wind originates from coronal holes (c.f. Krieger era/. 1973, Nolte etal. 1976, Sheeley era/. 14 1976). Nolte etal. 1976 reported a linear relationship between the area of coronal holes and the maximum observed solar wind speed. The slow solar wind streams originate nearer to the sun's streamer belt, where the magnetic field pattern is typically closed. The properties of the slow solar wind vary much more than the fast wind. The exact source (or sources) of the slow solar wind is an ongoing topic of study, but will not be discussed in detail here. A simple technique for estimating the source longitude of a solar wind stream is "ballistic" back-mapping. The distance from the source surface to the observation point is divided by the measured solar wind speed to obtain a travel time. The travel time is then divided by the Sun's equatorial angular speed to obtain the difference in longitude between the source and the observer. This technique assumes the bulk solar wind travels with constant speed and radial trajectory. Effects of non-radial flow near the Sun are roughly canceled by flow sheer in the ecliptic plane. Nolte and Roelof (1973a) found the error in this method to be less than or equal to 10° longitude. Ballistic back-mapping is only useful for estimating a source longitude. To identify the most likely source at the photosphere the results from ballistic back-mapping can be combined with a potential-field source-surface (PFSS) model (c.f. Neugebauer etal. 1998 and 2002). PFSS solves a boundary value problem with the conditions that the magnetic field must be radial at a spherical surface some few solar radii above the photosphere, and the foot-points must agree with the measured photospheric magnetic field. 15 In addition to the continuous flow of solar wind there are transient plasma flows. These come from sources including solar flares and coronal mass ejections. Studying coronal mass ejections is one of the primary science goals of the STEREO mission (described in the next chapter), but during 2007 and early 2008 solar activity was minimal, so recurring patterns of fast and slow streams dominated the in situ data. 1.5 Corotating Interaction Regions The Sun's magnetic field is roughly dipolar, particularly during the minimum activity portion of the solar cycle. The extension of the magnetic neutral line into the heliosphere is a plane of magnetic neutrality called the heliospheric current sheet (HCS). The HCS and streamer belt are located near the Sun's heliographic equator during solar minimum. The Sun's equator is tilted approximately 7° with respect to the ecliptic plane in which the planets travel. A stationary observer in the ecliptic plane would thus see alternating patterns of fast (coronal hole) and slow (streamer belt region) solar wind as the Sun rotates. As stated earlier, the curvature of the Parker spiral pattern created by the solar wind depends on speed. The spirals resulting from fast solar wind are less tightly wound than slow-stream Archimedean spirals. Near the ecliptic plane the fast solar wind can catch-up-to and try to overtake pre-existing slow solar wind flows. Because magnetic fields are frozen into the plasma, the structures are • prevented from merging together. (Magnetic field lines do not cross each other.) The faster moving plasma is forced to slow down, and it both compresses and 16 deflects the slower-moving stream in its path. This region of interacting flows appears to corotate with Sun, and thus is usually referred to as a corotating interaction region (CIR). Jian etal. 2006 defined a CIR specifically as a recurring feature, while a non-recurring interaction region is referred to as a stream interaction region (SIR). The interaction between slow and fast solar wind increases with radial distance from the Sun, eventually leading to the formation of shocks. CIRs form at about 10 solar radii; nearer to the Sun the corona's magnetic field guides the plasma so the streams do not interact. The schematic illustration found frequently in CIR/SIR literature (shown in Figure 1.5) is from Pizzo (1978). The small arrows show the velocity of the plasma parcels, which is radial in direction. The solid curves show the interplanetary magnetic field lines being dragged away from the Sun by the solar wind. The large arrows on either side of the compression region indicate the propagation direction of pressure waves, which accelerate and deflect the ambient solar wind plasma. 17 Figure 1.5 CIR schematic sketch from Pizzo, V., J. Geophys. Res., 83, 5563-5572 (1978). Within the compression region is found the boundary between slow and fast solar wind streams: the stream interface (SI), a term first defined by Burlaga in 1974. "At 1 AU there is a distinct boundary...characterized by an abrupt (approximately a factor of 2 change in <106 km) drop in density, a similar increase in temperature, and a small increase in speed." Burlaga presented data from Explorer 34, showing that shocks are sometimes associated with the stream interfaces. While there may not always be a shock associated with the transition from slow to fast solar wind, there is always an interface (though not necessarily well enough defined to meet Burlaga's criteria). Gosling etal. 1978 used data from IMP 6, 7 and 8 to study 23 stream interfaces (occurring from 1971 to 1974). They further characterize the general properties of Sis with a superposed epoch analysis. They observed that Sis usually follow 2 to 36 hours after a magnetic field reversal. The interface separates dense, slow moving plasma from fast, less dense plasma. In the co- 18 rotating reference frame, there is a velocity shear at the interface, which decreases with radial distance from the sun as momentum is transferred across the interface. The electron temperature rises by about 40%, and the alpha particle abundance usually increases. Gosling etal. 1978 suggested the fast and slow solar wind streams have different origins. This was supported by later studies such as Borrini etal. 1981 and Wimmer-Schweingruber etal. 1997, which showed that solar wind composition changed with the passage of a stream interface. Freezing-in temperatures for carbon and oxygen decrease, as do the proton to alpha and magnesium to oxygen ratios. Multipoint observations of stream interfaces are sparse, except in the vicinity of L1. Nolte and Roelof (1973b) studied a stream interaction region using data from Pioneer 8, Pioneer 9, and Vela. They found evidence for time evolution at the interaction region. Data from Helios 1 and Helios 2, combined with IMP 7/8 in the 1970s and 1980s, provided an opportunity to study several dozen CIR stream interfaces from multiple observation points. Schwenn 1990 summarizes the results of 45 such observations. The IMP satellites were in Earth orbit near 1 AU, while the Helios probes were much closer to the sun, and often at very different longitudes from the Earth. Schwenn reports that the stream interfaces observed by two spacecraft followed a "Parker-type spiral" that could be defined by an effective radial propagation speed. 19 _Qam{Rl-R2) propagation fa - (pj where: Qsun = sun's angular speed R{ = spacecraft l's radial distance from sun 99, = spacecraft l's Carrington longitude R2 = spacecraft 2's radial distance from sun cp2 = spacecraft 2's Carrington longitude The average propagation speed for the 45 events studied by Schwenn is 420 ± 60 km/s. Stream interfaces and CIRs are not limited to the in-ecliptic plane, though that is where most in situ observations have been made. The superposed epoch analysis of Gosling etal. 1978 shows the plasma in the vicinity of the stream interface undergoes deflection in the ecliptic plane (again, to avoid crossing magnetic field lines). The dense plasma ahead of a stream interface is deflected westward (i.e. in the same direction as planetary motion), while the less dense plasma following the interface is deflected eastward. CIRs can be tilted out of the ecliptic plane, which can result in a flow deflection to the north or south. This was confirmed with observations from Ulysses' first excursion away from the ecliptic plane (Gosling etal. 1993). The tilt of the sun's dipole in conjunction with differential rotation gives rise to a three-dimensional CIR structure resembling the heliospheric current sheet's "ballerina skirt" shape (see V.J. Pizzo 1991). Neugebauer etal. (1998) combined measurements from the Ulysses and Wind spacecraft to determine the latitudinal dependences of structures in the solar wind. They also mapped solar wind streams to the corona using different 20 source-surface models for solar activity minimum time periods. Neugebauer et al. (2002) extended this analysis to active times, using data from the Ulysses and ACE spacecraft. Radial evolution of the CIR leads to steepening of the velocity gradient and eventually to the formation of a shock pair (one forward and one reverse) that sandwiches the stream interface. This takes place because the interface is being squeezed tighter and tighter with increasing radial distance. Eventually, the speed transition becomes so steep that shocks form. Shocks have sometimes formed by 1 AU, but often not. Jian etal. (2006) reported on 365 stream interaction regions (SIRs) observed by WIND and ACE. About one fourth of the SIRs had developed at least one shock by 1 AU. 1.6 Fast-to-Slow Solar Wind Transitions The stream interaction resulting from a transition from slow to fast solar wind at 1 AU is obvious. Identifying the interaction associated with the opposite transition from fast to slow solar wind is more difficult. The fast streams can over-expand into the rarefaction region that develops behind a CIR/SIR. A gap naturally forms between the ambient, non-compressed fast stream and the following flow of slow solar wind. Burton et al. (1999) suggests the fast-to-slow, or "trailing" interface can be identified by an increase in the ratio Mg/O, and by a corresponding sudden drop in the specific entropy argument of protons: T/nv1. T is the proton temperature, n is the proton number density, and y is the ratio of specific heats. Using y = 3/2 (after Totten etal. 1995), Burton etal. find the 21 specific entropy drops by about one third at the trailing edge interface. Clear identification of the trailing edge interface is useful in trying to identify the coronal source(s) of the plasma. Proton entropy has been used to identify the fast-to-slow transition in several other studies: Burlaga etal. 1990 and Siscoe and Intriligator 1993. Burlaga etal. note that the fast-to-slow interface is essentially the mirror image of a leading edge SI; density increases, while the temperature and bulk speed decrease. However, the data presented shows the magnitude of these changes is small compared to the CIR/SIR leading edge interface. Thus, the change in proton entropy is easier to spot than looking for the fast-to-slow interface in the temperature and density as separate quantities. Both Siscoe and Intriligator and Burlaga etal. identify the material with lowest entropy as coming from the streamer belt. Zurbuchen etal. 1999 studied eight fast-to-slow solar wind transitions using the composition instrument SWICS aboard Ulysses. The iron to oxygen ratio was obtained with time resolution of about an hour. They observed a typical timescale for the fast-to-slow transition of 40 or more hours. This is quite long compared to the slow-to-fast transition time of just a few hours. They also observed smooth transitions in the iron to oxygen ratio. In none of the observed cases was there a distinct discontinuity between the fast and slow streams. They suggest this is indicative of magnetic reconnection, which would allow slow and fast streams of different origins to mix. 22 The Coronal Hole Boundary Layer (CHBL) was identified by McComas et al. 2002 as the source of rarefied solar wind based on observations from Ulysses/SWICS. In the CHBL the freezing-in temperature drops with increasing acceleration of the solar wind. Note: The McComas etal. study focused on solar wind from high-latitude coronal holes. Schwadron etal. 2005 modeled both the slow-to-fast and fast-to-slow solar wind transition for an observation point at 20° heliographic latitude during solar minimum conditions. In addition to polar coronal hole and equatorial streamer regions, their model included the CHBL. Foot-point motion across coronal holes was also considered, since coronal holes can rotate rigidly while the photospheric material underneath rotates differentially (Wang and Sheeley 1993). This model was able to replicate the smooth transition in freezing-in temperature observed by Zurbuchen et al. With foot-point motion across the polar coronal holes, a magnetic field configuration that threaded the stream transitions could be obtained, suggesting the mixing of fast and slow solar wind could be observed. This model does not explain the mixing of fast and slow solar wind when both originate near the Sun's heliographic equatorial plane. Foot-point motion across rigidly rotating equatorial coronal holes is expected to be minimal. 1.7 Numerical Models Three-dimensional numerical models of corotating interaction regions are described by various publications, including Gosling and Pizzo 1999, and Riley 23 2007. The first major assumption in 3-D models is that there exists a reference frame rotating with the Sun where the fast and slow solar wind pattern is everywhere fixed. For small time scales this is not too bad an assumption, but it must be remembered that the rotation rate of the sun varies with latitude. The second assumption in the numerical models is the applicability of the magnetohydrodynamic (MHD) equations. The MHD equations are used to describe the conditions of mass, energy, momentum, and magnetic flux conservation in the idealized corotating frame. Outside the corona the ideal MHD description seems to work well, and often the models are restricted to radial distances outside 30 solar radii. The MHD calculations are carried out over successive spherical shells, beginning with an input set of conditions at the inner boundary surface: velocity, density, gas pressure, and magnetic field strength. These inner boundary conditions can be the output of models such as potential field source surface (PFSS), which uses maps of the photospheric magnetic field as an input. Comparing the results with actual data shows large-scale structures can sometimes be reproduced, but sometimes not. Riley 2007 notes several possible reasons for model failure. First, the assumption of perfectly corotating solar wind structure is not realistic. Second, the source regions on the Sun undergo evolution on time scales less than the solar rotation period. Finally, the specifications of the inner boundary conditions (at about 30 solar radii) are an 24 approximation based on observations of the photosphere. Errors in the starting conditions can propagate through the entire simulation. Biesecker etal. 2008 suggest using multi-point observations from STEREO (described in the next chapter) to validate the Wang-Sheeley(-Arge) model and the Hakamada-Akasofu-Fry version 2 (HAFv2) model. The Wang- Sheeley-Arge (WSA) model is described by Arge et al. 2004. WSA models the solar wind from the inner corona to the inner heliosphere. It can be used to predict solar wind speed and the polarity of the interplanetary magnetic field at Earth. The input to the WSA model is the Sun's photospheric magnetic field. This is obtained from ground based line-of-sight observations (magnetograms). The magnetograms are fed into the WSA model, which solves a boundary value problem with the condition that the field is radial at a spherical, Sun-centered surface at 2.5 solar radii. At this point the output of WSA can be coupled to other models such as ENLIL or HAFv2 to project the solar wind's trajectory and characteristics outward. Arge modified the original Wang-Sheeley model and extended it to model the solar wind out to the L1 Lagrange point (and beyond). One model to which WSA has been coupled is called ENLIL, described by Osdstrcil 2004. ENLIL is a three-dimensional ideal magnetohydrodynamic (MHD) code. It solves the usual set of MHD equations: continuity, momentum conservation, energy conservation, and diffusion (magnetic induction) given a set of boundary conditions. 25 Another model to which WSA can be coupled is HAFv2. Fry etal. 2001 describe the HAFv2 model as "modified kinematic." Fry etal. 2003 highlights one of the differences between HAFv2 and ideal MHD codes: "Wheras MHD solutions integrate the equations of motion to obtain velocity, the kinematic model begins with...the fluid parcel positions; velocity then comes from dx/dt." The solar wind speed is continually being computed, updating the background conditions through which a structure such as a CIR shock propagates. 1.8 Motivation and Application The idea for this study began with a puzzle. In early May 2007 a CIR associated shock was observed by at least four spacecraft: WIND, SOHO, STEREO/AHEAD, and STEREO/BEHIND. Figure 1.6 shows that all four spacecraft were near 1 AU radial distance from the sun, but they were spread across almost 7° of in-ecliptic longitude. Assuming the shock is a structure that corotates with the Sun and that the spacecraft's radial separation is negligible, the shock would have first been seen at STEREO/BEHIND, then at SOHO and WIND (both near the L1 Lagrange point), and lastly at STEREO/AHEAD. If the longitudinal separation is ignored and only the small radial separation taken into account, the expected order of arrival would be STEREO/AHEAD, then SOHO and WIND, and lastly STEREO/BEHIND. The actual observation sequence was the L1 satellites, followed by STEREO/AHEAD and lastly by STEREO/BEHIND. This demonstrates that calculating the arrival time of a shock or solar wind stream at Earth after it has been observed at STEREO/BEHIND is not as simple 26 as dividing the longitudinal separation by the solar rotation speed. Figure 1.7 shows the small radial separation between Earth and the STEREO observatories is important because corotating structures are expected to have Archimedean spiral geometry. -2000 RF ©STEREO/ AHEAD t SOHO TO SUN OR, « WIND SHOCK 4 • I STSTEREOI / BEHIND +2000 Ri +2000 RE 0RE -2000 RE Figure 1.6 In-ecliptic positions of STEREO/AHEAD, STEREO/BEHIND, SOHO, and WIND on 6 May, 2007, just before the arrival of a CIR shock. The estimated shock plane is shown in purple. 27 ..•• .• •. • • *. • • • - • \ *••.. V--' / Figure 1.7 A stream interface in the Carrington coordinate system. The grey curve is the SI, which is static. The red and blue circles represent STEREO/A and STEREO/B, which move clockwise in this representation. Stream interfaces are well-defined structures that are expected to have Parker spiral geometry under the modeler's assumptions of ideal corotation and negligible source evolution. This is a study of both slow-to-fast and fast-to-slow stream interfaces, primarily using in situ observations of solar wind protons from PLASTIC/AHEAD and PLASTIC/BEHIND. The heliocentric orbits of the two STEREO satellites are similar in radius and ecliptic latitude, with separation in longitude increasing by about 45 degrees per year. This arrangement provides a unique opportunity to study the evolution of stream interfaces near 1 AU over time scales of hours to a few days, much less than the period of a Carrington rotation. The results of this study will provide insight into the applicability of existing solar wind modeling techniques, particularly testing the time-scale over 28 which the modelers' basic assumptions of ideal corotation and non-evolving sources are valid. If these assumptions hold it should be possible to predict the arrival time and location of an interface at one observatory after it has been observed at the other. Causes of discrepancies between the expected and actual times and longitudes of arrival will be explored. Recurring fast solar wind streams are associated with geomagnetic storms, so the results of this study are important to space weather forecasting. 29 CHAPTER II INSTRUMENTATION AND PRE-FLIGHT CALIBRATION 2.1 The STEREO Mission STEREO, the Solar TErrestrial REIations Observatory, is composed of two three-axis stabilized spacecraft. Each spacecraft has four suites of instruments, described in brief below. The two spacecraft are in orbit about the sun at slightly different radii. The "Ahead" (A) spacecraft is just inside 1 AU, while the "Behind" (B) spacecraft is just outside 1 AU. As a result, the orbital period of A is slightly less than one Earth year, and the orbital period of B is slightly more than one Earth year. From the perspective of an observer on the Earth they are drifting in opposite directions. Longitudinal separation from A to B increases at a rate of about 45° per year. Both A and B are very near to the ecliptic plane. It is important to note that the sun's heliographic equator is tilted about 7° out of the ecliptic plane, so in terms of solar latitude the A and B spacecraft can be separated by up to 14°. The primary science objective of the STEREO mission (Kaiser era/. 2008) is to study coronal mass ejections (CMEs). Goals include identification of the initiation mechanism, and tracking CME propagation through the interplanetary medium. Additional science objectives are locating energetic particle acceleration sites and mechanisms, and better characterizing the ambient solar 30 wind. As STEREO was launched near solar minimum, this study focuses on the ambient solar wind. The four major instrument suites on STEREO are SECCHI, SWAVES, IMPACT, and PLASTIC. SECCHI (Sun Earth Connection Coronal and Heliospheric Investigation) is described in Howard etal. 2008. It consists of five imagers. There are two white light coronagraphs (COR 1:1.5 - 4 RSun, COR2: 2.5-15 RSun) an ultraviolet imager (EUVI: 1 - 1.7 RSun), and two heliospheric imagers (HI-1: 15-84 RSun, HI-2: 66-318 RSun). This combination of instruments is designed to track coronal mass ejections from their origin on the Sun to their arrival at Earth. SA/VAVES (STEREOA/VAVES) investigates radio and plasma waves (Bougeret etal. 2008). It can track radio bursts from the Sun to 1 AU. Instruments include both low- and high-frequency receivers, and a fixed 30 MHz receiver, all on booms outside the field of view of the imaging instruments. In addition to tracking, SAA/AVES can be also used to measure the temperature and density of electrons found in interplanetary shocks and CMEs. IMPACT (In-situ Measurements of Particles and CME Transients) collects data on electrons, energetic particles, and the local magnetic field (Luhmann et al. 2008). There are seven IMPACT instruments, which can be divided into two groups. The first group is located on a boom six meters in length: a solar wind electron experiment, a magnetometer, and a supra-thermal electron telescope. The other four instruments are located on the body of the spacecraft, and are 31 designed to study energetic particles (MeV and greater energies). Between IMPACT and PLASTIC (described in the next section) a large regime of energies is covered, sufficient to meet the science objectives of the STEREO mission. 2.2 The Plasma and Supra-Thermal Ion Composition Experiment The PLASTIC (PLAsma and Supra-Thermal Ion Composition) instruments provide data on solar wind and supra-thermal ions. Each PLASTIC unit contains an electrostatic analyzer (ESA), a time-of-flight (TOF) chamber, and solid state detectors (SSDs). For an extensive description, see Galvin etal. 2008. Figure 2.1 shows a schematic of the PLASTIC entrance system. Solar wind ions travel radially outwards from the sun, so the solar wind sector (SWS) of the entrance system is always kept sunward facing. The wide-angle partition (WAP) accepts ions from the vicinity of the ecliptic plane, but more than 22° away from the Sun-spacecraft line in the ecliptic plane. This includes particles streaming along the interplanetary magnetic field (IMF) lines. There are two apertures in the solar wind sector: the "main" channel and the "s" (small aperture) channel. When flux rates exceed a pre-set (but command-able) threshold during an ESA stepping cycle, the main channel is electronically gated closed and the s channel is opened for the remainder of the sequence. This aperture switch is intended to reduce the incoming flux and protect the solid-state detectors from the bulk solar wind protons (which have energy below the solid state detector threshold). The entrance system for the solar wind sector includes deflectors, which electronically steer in ions from up to 32 20° out of the ecliptic plane (both above and below). The instantaneous field of view is about 1.9° FWHM (full width half maximum) for the main channel, and 0.3° FWHM for the s channel. The WAP has a fixed aperture with a field of view that is just over 3° FWHM in the out-of-ecliptic plane. Just inside the entrance apertures is the ESA. This is used to select ions by energy per charge (E/q). The observable E/q range covers 86 keV/e (on both PLASTIC/A and /B) down to about 0.3 keV/e on PLASTIC/B and 0.2 keV/e on PLASTIC/A. The energy per charge of an incident ion is determined from the electro-static analyzer (ESA) step during which it enters the analyzer. There are 128 (nominally logarithmically spaced) ESA steps, which are stepped through from high to low energy per charge. T \ l Polar -». -f angle Smafl Channel J *20* \ „ , i .Polar WAP Main Channel •*» -f *»«•« Jf +20* — T ost Jlcceleration - TO SUN *"-Carbon foil \. Elections / Tteie —. \ c fligta p»r !HE*™ ) Start, Stop Start Stop Figure 2.1 Side view of PLASTIC entrance system and time-of- flight chamber. Figure courtesy of A.B. Galvin. 33 It takes about 1 minute to go through an entire ESA cycle because the deflectors must step through their 32 steering voltages for each of the ESA's energy per charge settings. There are 12.8 ms of accumulation time for each combination of ESA and deflection steps. 12.8 x 10"3 seconds * 32 deflection steps * 128 ESA steps = 52.4 seconds There is a bit of extra time required to set the voltages and to ramp the ESA up at the beginning of each cycle, so that brings the time to just less than a minute per ESA cycle. After passing through the ESA, an ion undergoes a post-acceleration (PAC) of about -20 keV before hitting a carbon foil. This impact knocks off electrons, which are electrostatically steered to a micro-channel plate (MCP). The resulting electron shower triggers a start signal in the time-of-flight (TOF) system. In the solar wind sector the (slower-moving) ion encounters a solid- state detector, and backscatter electrons hit the MCP. The shower from the MCP triggers a stop signal. Most of the wide-angle partition does not have solid-state detector coverage, so in that case the ion hits a second micro-channel plate which showers charge onto a stop grid. The resulting time-of-flight (TOF) measurement can be combined with the energy/charge (E/Q) measurement to estimate the mass per charge (M/Q). Q \Q ' ' Q A L ) 34 The energy loss (E,oss) in the carbon foil is estimated based on density and thickness of the foil, and the energy and mass of the incident particle. "L" is the length of the time-of-flight chamber. In the solar wind sector the solid-state detector measures the residual energy of the ion (if it is greater than the detector threshold), which can be used (in combination with above information) to determine mass (M) and charge (Q) as separate quantities in the solar wind sector. M = 2| Eresidua> IfT0F I { phd ){ L ) With both M and M/Q the charge can now be found. J Q- residual E ' {PM)(^ + \PAC\- Q ) The pulse height defect (phd) is species dependent. For more details on pulse height defect see Leo, chapter 10. Without solid-state detectors, mass and charge cannot be separated for counts registered in the WAP section. 2.3 Pre-Flight Calibration Much of the pre-flight entrance system testing was carried out at the University of Bern, Switzerland. For a comprehensive description see the Ph.D. dissertation of Reto Karrer (2007). Karrer's results are summarized in Tables 2.1, 2.2, and 2.3. 35 TABL E 2.1 STEREO/PLASTIC Calibration Summary S Channel Main Channel WAP Measured Species H, He He-Fe H-Fe Energy Range [keV/e] 0.2-15 0.2-100 0.2-100 AE/E AHEAD 0.06 0.06 0.07 BEHIND 0.06 0.06 0.07 Geometrical Factor per 22.5° sector [cm2 sr keV/keV] C O b AHEAD 3x10"7 X 3x10"3 BEHIND 3x10"7 3x10"3 Active Area [cm2] AHEAD 1.4 x10"3 0.9 1.12 BEHIND 1.5 x10"3 0.8 0.94 Instantaneous 45° x 0.3° 45° X 2° 315° x ±3° Field-of-View TABLE 2.2 Analyzer Constants AHEAD BEHIND SPARE AHEAD BEHIND SPARE Channel Electrode Analyzer Analyzer Analyzer FWHM FWHM FWHM Constant Constant Constant SCO-L 3.23(1) 10.40% 3.25(1) 10.64% 3.19(1) 10.40% S SCI-U 3.68(1) 13.20% 3.64(1) 10.75% 3.59(2) 13.80% Channel ESA 8.46(1) 6.35% 8.46(2) 6.26% 8.38(3) 6.12% Main ESA 8.26(1) 6.12% 8.26(2) 6.48% 8.25(2) 6.30% Channel WAP ESA 8.25(4) 6.77% 8.26(1) 7.30% 8.28(1) 6.67% Table 2.3 Deflection Constants and Angular Acceptance Ranges AHEAD AHEAD BEHIND BEHIND SPARE SPARE Channel Deflection Angular Deflection Angular Deflection Angular Constant FWHM Constant FWHM Constant FWHM s 0.117(1) 0.37 0.114(1) 0.27 0.112(1) 0.27 Main 0.128(3) 1.9 0.127(3) 1.8 0.126(7) 1.9 WAP - 3.2 - 3.1 - 3.2 36 The azimuth (nominally in-ecliptic) angle of ions entering through either the solar wind sector or the first quadrant of the WAP is registered on a resistive anode, which is divided into 64 segments, or position bins. The central 32 bins are defined as belonging to the solar wind sector, while the outer bins are defined as belonging to the supra-thermal section. The incident solar wind is spread across multiple position bins, with the width being proportional to temperature. Ideally, knowing the bin number corresponding to the peak of the count distribution is enough to determine the East/West flow angle. Pre-calibration testing of the resistive anode response showed the distribution of counts is bifurcated (see Figure 2.2 below) when ions enter near the center of the solar wind sector. This is due to scattering caused by a carbon foil support spoke. Thus, more information about the distribution of counts than just the peak step is needed to accurately determine the flow angle. 50 45 40 35 30 & 25 S 20 V 15 E I 10 5 0 -45 -35 -25 -15 -5 5 15 25 35 45 FM1-041Z15-1726 Beam Azimuth (deg) !_:. Figure 2.2 PLASTIC/AHEAD peak channel responses to azimuth scan at Bern. (Figure courtesy of Mark Popecki.) 37 Examining the entire distribution of counts shows a more unique correspondence between input angle and resistive anode response. Figures 2.3 and 2.4 show the percentage of counts in each position channel for a given input angle (for A and B respectively). The bright orange cells contain at least 10% of the total counts for a given angle. The grey cells contain less than 1%. The green cells indicate a secondary peak for the same input angle. The resistive anode table used for FM1 during pre-flight testing was reversed from its in-flight orientation. The up-to-date distribution is a mirror image of the one shown. The FM2 table is unchanged since calibration testing. Figure 2.3 PLASTIC/AHEAD resistive anode response distribution - position step numbers (horizontal axis) are reversed from in-flight orientation. Incident angle is the vertical axis. Azimuth scan conducted at University of Bern. 38 RACh-> 16 17 | 18 | 19 [ 20 1 21 | 22 | 23 | 24 | 25 26 27 28 29 30 31 32 33 34 35 36 37 1 38 1 39 1 40 1 41 1 42 1 43 1 44 1 45 I 46 1 47 POSStep-> 0 1 1 2 3|4l5|6|7IB|9 10 11 12 13 14 15 16 17 18 19 20 21 22 I 23 { 24 25 26 27 | 28 29 30 31 -22 0.02 0.03.003 £06 t!$t-Q.ffi 0.0? 0.07 00$ 0 04 0.03 0.03 0.02 0.02 0.0? 0.01 0.01 0.01 0.01 0.01 0.01 Wm 0-01 W^MmS^^mSM^m^^^mB -21 0.01 0.03J 0 04 ao^tMW am, ao&'&ar os$ O 04 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 -ZO 0.02 0.04 &Q5 CM»aHBH|4<$ 007- COS 0.04 0.03 0.02 0.02 0.01 0.01 0.01 -19 0.02 0.04 Oj)5,aoe^HHtt.09 0.0? Q.05 0.03 0.03 0.02 0.01 0.01 0.01 -18 tt02 0.04 o.oe o.09B^^Bao£ e.o? aos 0 03 0.0? 0.0? 0.01 0.01 -17 0.02 0.03 0.0410.03 0.02 0.01 0.01 -16 0.02 0.03 0.03 002 0.01 0.01 -15 0.01 0.03 0.03 0 02 0 01 0.01 0.01 -14 0.02 0.0210.04 4 -•HDWBB Note that the entire PLASTIC/AHEAD distribution is shifted away from the center of the solar wind sector (position steps 16 through 47 on the 0 to 63 scale). This means some of the counts that should be going into the distribution used for the onboard moments calculations (described below) are being "lost." As a result, the calculated solar wind density may be too low when the East/West flow angle is large. 2.4 Onboard Moments PLASTIC has two complementary proton data products: onboard velocity moments and Maxwellian fits to the full resolution rate. Data is classified onboard using time-of-flight. During each 1-minute ESA cycle a matrix of counts is collected in energy, position (aximuth angle), and deflection (polar angle) 39 space. The characteristics of the bulk solar wind protons are then calculated onboard as distribution function moments (Kistler 2005). If the distribution of counts in velocity and angle is known, it can be integrated to obtain density, velocity, and temperature. 0th Moment: Density fff /(v,0, 1st Moment: Velocity x - component: 2 mvr = — ffff(v,d,cp)(mvjv cosddddcpdv Substituting the general relation vx = vcosd: 3 2 vx =—Jjff(v,d,(p)v cos dcoscpdddcpdv The other two components are found similarly. 2nd Moment: Momentum Flux (Pressure and Temperature) 2 mlT^ = JjJ f(v,d,cp)(mvx)(mvx)v cosddddcpdv Substituting in the general relation vx = vcos0 4 3 2 nn = mjjj f(v,d,cp)v cos 0cos cpdddcpdv To obtain the pressure tensor's xx - component: To obtain the xx - component of the temperature tensor: Ta = %BL (because P = nkT) nk The other 5 components are found similarly. The integrals can be approximated as summations over the range of energies and angles accepted by the PLASTIC entrance system. The distribution function is obtained by dividing the count rate at each combination of energy and angle by accumulation time, geometric factor, and velocity to the fourth power. 40 .. „ . Number of Counts f(v,6, v Gtacc G = geometric factor tacc = accumulation time The number of counts must be corrected for background, dead time, and efficiency before a realistic distribution function can be obtained. See Appendix A for further explanation. To see how well the summations approximate the integrals, I carried out simulations assuming the solar wind has an ideal Maxwellian distribution function: 2kT n = density m = mass of species k = Boltzmann's constant T = temperature v = velocity corresponding to a specific energy step u = solar wind velocity The combinations of azimuth and polar angles are divided into a 32 by 32 grid. The number of counts in each grid bin is estimated based upon the input distribution, the geometric factor, and the accumulation time. Figure 2.5 shows some of the plots that were created for each energy step showing the expected distribution of counts. 41 Figure 2.5 A simulated distribution of counts around the peak energy step. 9 of 128 energy steps are shown. The input parameters are density = 5.8 cm3, velocity = 562 km/s, thermal speed = 60 km/s (temperature = 2.16 x 105 K), azimuth angle = 0°, polar angle = 0°. I tested the onboard moments calculations using idealized Maxwellian distributions as input. Counts in each bin were rounded to the nearest integer, since fractional counts are not physically possible. This means the edges of the distribution dropped to exactly zero, and thus the calculated density was expected to be somewhat lower than the input. This effect was lessened by increasing the accumulation time to simulate multiple ESA cycles (so that the counts around the edges will round up, and not to zero), and then taking an average. Simulations were carried out for azimuth angles covering the entire solar wind sector, and the results are shown below in Figures 2.6 though 2.8. 42 Density vs. Input Azimuth Angle Ideal Input - Moment Calculated from All Bins H*KX**XK»tt a a a a a c n a a n r ; - Input ; a1 cycle | : x 25 cydes I -16 •4 0 4 input Azimuth Angle [degrees] Figure 2.6 Moment 0 calculated for input with density = 5.8 cm"3, v = 400 km/s, T = 216,098 K, polar angle = 0°, and varying azimuth angle. Velocity vs. Input Azimuth Angle ideal Input - Moment Calculated from All Bins 450 ] ..s. 2 Q fi S 5J s c a o 5 . * * s i I-Input ; I jo 1 Cycle. I | ;i 10 cycles ! {xzsCyclas: 1 -18 -4 0 4 « 16 Input Azimuth Angle [degrees] Figure 2.7 Moment 1 calculated for input with density = 5.8 cm"3, v = 400 km/s, T = 216,098 K, polar angle = 0°, and varying azimuth angle. Figure 2.6 shows the input and calculated density (0th moment). There is a drop off in the calculated value near the edges of the SWS. This is because part of the distribution is landing outside the portion of the grid designated for the 43 solar wind sector. Figure 2.7 shows the input and calculated velocity (1st moment). This is determined by the energy step in which the count distribution peaks, so agreement should be very good for all input angles. Temperature Component vs. Input Azimuth Angle Ideal Input — Moment Calculated from All Bins 5?200000' ^Kxx£gjpgft|sS*Ma8xB«*>K8M^ i Q V *A**-D- a U - • to o £) '"Q-Sju | B a B ej a. Q - Input Temp {KJ tiTempXX(K) i TempYY (K) x TempZZ (K) -4 0 4 Input Azimuth Angle [degrees] Figure 2.8 2nd moment calculated for n = 5.8 cm'3, v = 400 km/s, T = 216,098 K, polar angle = 0°, and varying azimuth angle. The second moment is momentum flux density, from which the temperature is obtained. The ideal input is isotropic, so the expected result is Tx = Tyy = Tzz. Figure 2.8 is for one accumulation cycle, so the calculated temperature is expected to be a bit lower than the input value (because of the counts at the edges of the distribution rounding to zero). For typical solar wind parameters the velocity component with the largest magnitude is the in the x- direction. The input velocity's y-component is small, and the z-component is zero. There is more scatter in Txx than in the other components because the value calculated for vx is large, and a large number is subtracted from another 44 large number when converting from flux density to pressure and temperature. Averaging over multiple accumulation cycles reduces the amount of scatter and alleviates the rounding problem. Figure 2.9 Simulated instrument response to incoming stream. Top: n = 5 cm3, v = 562 km/s, T = 1000 K, azimuth angle = 0°, polar angle = 0°. Bottom: n = 5.8 cm3, v = 400 km/s, T = 216,098 K, azimuth angle = 7°, polar angle = 0°. 45 The next step in the simulation process was to include the instrument response, including the spreading of the input distribution across position steps. Using the STEREO/AHEAD table as a guide, I simulated the instrument response to the idealized Maxwellian distribution inputs. In addition to the spread across the azimuth angle bins, there is a small amount of spread across the polar angle deflection steps. I generated a response table similar to the one for the azimuth position bins for the simulation of deflector response. Compact (cold) streams entering near center are distorted the most, as shown in the top of Figure 2.9. Such a cold, compact distribution is not typical of the solar wind. The distribution shown at the bottom of Figure 2.9 is physically realistic. The final consideration in the simulation is the limitation on telemetry. PLASTIC is typically operated in "science mode". Because of telemetry limitations the full 32 by 32 grid distribution of counts is not available in science mode. A reduced distribution of 16 azimuth angle bins (position steps), 8 polar angle bins (deflection steps), and 20 energy steps surrounding the count peak (+4/-15) can be telemetered. The original plan was to take a box (16 azimuth steps by 8 deflection steps) centered on the bin with maximum counts. Due to the distortion of the distribution at the resistive anode this plan was modified. The in-flight selection (illustrated in Figure 2.10) is the 8 deflection steps centered about the peak, and the 16 odd position steps (to get an idea of the entire azimuth distribution). Taking only the odd position steps results in approximately half the incoming 46 counts being lost (summing pairs of position steps was not an option). As a result, the original equation for calculating the density must be multiplied by a factor of about 2. In addition to the spread of the beam, another factor that needs to be included in the final moments calculation is instrument efficiency. Pre-launch efficiency calibration information is given in Appendix A. In-flight calibration will be discussed in the next chapter. (mm)Expected Counts Expected Counts 30 25 ' -III __. 0) * 20 krijiiMfc O o 15 RA Position Step Q_ RA Position Step Qv Expected Counts Expected Counts < 10 0 5 10 15 20 25 30 0 5 10 15 20 25 30 RA Position Step QQ RA Position Step 1 nf~ Figure 2.10 The data from 4 (of 20) energy steps that would actually be received is shown within the red box. The ideal input is centered at 0° azimuth and 0° polar, with n = 5.8 cm'3, v = 400 km/s, and T = 216,098 K. 47 2.5 Full Resolution Rate The "full resolution rate" data from STEREO/PLASTIC is a selected rate reported once per minute. From March 2007 to present (March 2009) the selected full resolution rate is the single coincidence RA_Trigger. Whenever counts are registered on the resistive anode, the rate is incremented. This rate has the smallest dead time, and the greatest dynamic range. Data are collected from all of the 32 deflection (defl) steps, and from 64 of the 128 energy/charge (ESA) steps. The incident in-ecliptic (EastA/Vest) angle cannot be determined from this rate. To obtain 1-D solar wind proton parameters of density, speed, and kinetic temperature the counts are summed across all the deflection steps. This results in a distribution of counts versus energy per charge. This can be converted into a distribution function versus speed (which is described in Chapter 3), and fit with a Maxwellian distribution function, shown in Figure 2.11. The center of the distribution function is the bulk solar wind speed, the full width half maximum is twice the thermal speed (proportional to the square root of the temperature), and the area under the curve is proportional to density. 48 Maxwellian Distribution for solar wind speed 400 km/s 0 100 200 300 400 500 600 700 800 900 velocity [km/s] Figure 2.11 Maxwellian Distribution Function. 49 CHAPTER III DATA SELECTION AND IN-FLIGHT CALIBRATION 3.1 Suspected Leakage STEREO was successfully launched in October 2006. Both PLASTIC instruments were commissioned over the following months, with regular operation of the entrance systems beginning in January 2007. Based on pre- flight calibration testing, the active area of the small aperture channel on both flight units was estimated to be about 1/600 of the main channel active area. From early in-flight count rates I determined the change in active area between the main and s channel is only on the order of 120 for PLASTIC/A, and 65 for PLASTIC/B. The distribution of counts across azimuth angle bins also showed a bifurcation when the s channel was engaged, even when the ions entered away from the center support spoke. The most likely explanation for these observations was leakage through the main channel when the s channel was engaged. The bifurcation in azimuth angle suggests the electric gating field works as expected in the center of the main channel, but it is less effective along the sides. In addition to the higher than expected s channel flux, the calculated bulk speeds were consistently lower than expected when the pre-launch conversion 50 from ESA step to E/q was applied. I compared PLASTIC and WIND/SWE solar wind proton data, and found the PLASTIC values for kinetic energy were too low. Tests on the flight spare entrance system showed that leakage is greatest when test beams are incident from below the ecliptic plane (L. Blush and R. Karrer, private communication, 2007). STEREO/B is oriented upside-down with respect to STEREO/A (and the PLASTIC flight spare), so it is expected that solar wind incident from above the ecliptic plane on PLASTIC/B would have more main channel leakage than from solar wind incident from below the ecliptic plane. Plotting the in-flight distribution of deflection counts (Figures 3.1 and 3.2) confirms this. The procedure I developed to calculate a corrected North/South (deflection) flow angle is described in Appendix B. 51 Cantor of Dally Ejection Distribution PLASTIC AftetM am NOT corrected for roil. -AHEAD Main Channel -AHEAD S Channel !-' 3I*M*f-07 S-AfK-Or 10-AfW-O? lS*A(X*m 30;-AFu0? 25-Apr-G? 30~Apr-07 DRV Figure 3.1 Center of deflection distribution in the RA_Trigger full resolution rate (summed over 24 hour days) on STEREO/AHEAD for both main and small entrance apertures. Center of Daily DsRactian Distribution PLASTIC Angles are NOT corrected for roll. 4 *~» i j •*- BEHIND Main Channel | - BEHIND S Channel U-Mar-O? S-A1K.07 10-Apr47 lS-Anr-07 2Mfr47 25-APS-07 3O-A»f07 Figure 3.2 Center of deflection distribution in the RA_Trigger full resolution rate (summed over 24 hour days) on STEREO/BEHIND for both main and small entrance apertures. 3.2 Calculating 1-D Proton Bulk Parameters In-Fliqht 3.2.1 Data Rate. The full resolution rate reports counts from 64 of the 128 ESA steps on a minute-by-minute basis. The E/q step range is command-able, and is set to the second half of the ESA cycle (steps 64 through 127): 4 keV/q down to the minimum, about 0.3 keV/q. (Equivalent proton speeds are 880 km/s 52 to about 270 km/s.) Counts are recorded for each combination of ESA step and deflection step. This results in a matrix of 64 x 32 values for each minute of the day when operating in science mode (which is the usual mode of operation). Before any calculations take place, the matrix is checked for a value that designates data overflow. As of February 2009 there have been no instances of data overflow in the full resolution RA_Trigger rate. 3.2.2 Background Subtraction. Two background subtraction techniques have been used for data analysis. The first assumes a background level based on the average number of counts from deflection bins 0, 1, 30, and 31 of ESA step 127 (the lowest E/Q setting). (These bins were chosen because they are not expected to contain counts during times of ambient, non-transient solar wind.) This average value or 3 counts (whichever is larger) is subtracted out on a minute-by-minute basis from each combination of ESA and defl steps. If subtraction of background results in a negative number of counts, the result is set to zero. The second single coincidence background subtraction technique uses the average of the counts in defl bins 0 and 31, calculated for each ESA step individually. This second technique was created to help identify solar energetic particle events and time periods when counts from the first quadrant of the Wide Angle Partition (WAP) were making a significant contribution to the RA Trigger rate (and were consequently being multiplied by an incorrect geometric factor). The result of this technique is shown in figure 3.3. 53 Contour Plot of Counts Contour Plot of Counts 30 30 - 25 25 - - • - c 4 /fPM 1. - - ^ IP'* 10 Lr^,.! t 5 - 1 - imTiiliiiTuuiiiiniMiliiitui•llll 0 i Energy per Charge Figure 3.3 This figure shows counts from the PLASTIC full resolution rate. Each color represents a factor of 5 in counts. The ESA Steps have been plotted so that low energy/charge is on the left. The deflection bins correspond to angles of about -20° to +20c degrees from bottom to top. The gap is the aperture switch from main to small channel. The left panel shows the "raw" distribution of counts, and the right panel shows the results of background subtraction number 2. 3.2.3 Deflection Wobble. The right-hand plot in Figure 3.3 shows a "saw tooth" pattern in the deflection distribution. This pattern is observed on both spacecraft, and is likely a consequence of differences in the two power supplies for the deflectors. Shifting the deflection bin number assignment by one for every other ESA step (Figure 3.4) results in a smoothed distribution that can be more easily fit by Gaussian curve in deflection space. 54 Contour Plot of Counts 127 00:00 T f • 0.0 0.36 0.52 0.80 1.26 1.99 3.21 Enetgy/Ctiafge [KeWq] Figure 3.4 RA_Trigger count distribution corrected for deflection wobble. The small red triangle indicates the switch from main to small entrance aperture in the solar wind sector. 3.2.4 Dead Time Correction and Unit Conversion. The RA_Trigger rate has a dead time of about 5 microseconds for both PLASTIC/A and PLASTIC/B. The accumulation time for a single combination of ESA step and deflection step is 0.0128 seconds. Dividing the recorded counts through by this value gives a rate in terms of counts per second, or Hertz. Using the standard correction for non-paralyzable dead time (see Leo chapter 5), the "true" count rate can be calculated from the recorded rate: true rate = recorded rate/(1-recorded rate*dead time) The results of this calculation are checked to ensure the true count rate is greater than zero. Should a negative value be found (which would indicate the dead time 55 estimate is too large), the data analysis program is designed to halt. This has not occurred using the dead time estimate of 5 microseconds. 3.2.5 In-flight Geometric Factor. The count distribution is not continuous due to the aperture switch from main to small channel. Dividing through by the relative geometric factors takes care of this. Unfortunately, the in-flight small channel geometric factors on both PLASTIC/A and PLASTIC/B do not agree with the values found during pre-flight calibration testing. This is most likely due to leakage from the main channel as described above in section 3.1. I estimated the actual In-flight geometric factors in two steps. First, I determined a nominal value by trying different multiplicative factors to create a smooth distribution function across the aperture switch for varying solar wind conditions. Then I made a higher order correction based on inter-calibration of density with the WIND/SWE instrument (see Appendix A). The PLASTIC/A effective in-flight geometric factor ratio (main to small channel) is approximately 120. The PLASTIC/B geometric factor ratio is dependent on energy. The nominal value is 65. Figure 3.5 shows the energy dependence of the PLASTIC/B S channel geometric factor. 56 Density Ratio versus Bulk Speed -- 3 hour offset Hourly Averaged Data from April 2007 |y = 3.11E+06xz'47E+0° I R2 = 7.25E-01 J 5 ,14 c'2 * j _ 200 300 400 500 600 700 800 PLASTIC B Proton Speed [km/s] Figure 3.5 Ratio of densities from PLASTIC B and WIND (assuming a geometric factor ratio of 65) plotted against the proton bulk speed from PLASTIC B. In order to account for spacecraft separation, the hourly averaged PLASTIC B density values have been time shifted by about 3 hours. After dividing through by the appropriate geometric factors, the next step in the analysis is to sum over all the deflection bins. A one-dimensional distribution function is obtained, which can be fit by a Maxwellian distribution function. (A factor of cosine deflection angle is also included in the summation, but this is very close to 1 since the deflectors do not scan more than about 20° outside the ecliptic plane.) 3.2.6 In-Flight Efficiency Calibration. The next thing to consider is instrument efficiency. Figures 3.6 and 3.7 show the RA_Trigger pre-launch efficiency versus MCP voltage. The RA_Trigger rate is less susceptible to changes in MCP voltage than the double coincidence rates. In fact, the curves in Figures 3.6 and 57 3.7 are nearly flat. The efficiency curves used for data processing post launch were revised from the pre-launch values using inter-spacecraft data comparison. Both PLASTIC/A and PLASTIC/B experience leakage, so I used data from WIND/SWE to cross-calibrate. The final efficiency tables (given in Appendix A) are a convolution of the instrument efficiency and the energy dependence of the leaky s channel geometric factor. PLASTIC A: RAJTRXG Efficiency versus MCP Voltage Bern Pre-flight Tests, December 2004 1.0 0.9 0.8 0.7 0.6 0.S 0.4 -2keVH+, PAC20 0.3 20 keV H-f, PAC 20 0.2 0.1 0.0 2850 2900 2950 3000 3050 3100 3150 3200 MCP [Volt*] Figure 3.6 PLASTIC A pre-launch RA Trigger proton efficiency versus MCP voltage settings. 58 PLASTIC B: RA_Trig Efficiency versus MCP Voltage Bern Prc-flight Testing, June 2005 1.0 0.9 i--2keVH+, PAC18I I 0.8 3 0.7 t • 0.6 | 0.4 X• 0.- 3. { °-2 0.1 0.0 2200 2300 2400 2500 2600 2700 2800 2900 3000 MCP [Volts] Figure 3.7 PLASTIC B pre-launch RA Trigger proton efficiency versus MCP voltage settings. Energy/charge must be converted to speed before fitting a Maxwellian curve to the distribution function. The proton velocities corresponding to the ESA step numbers do not agree with pre-launch calibration values. Figure 3.8 shows a simple linear fit against data from WIND/SWE. The fit is forced to zero at the origin. Using the pre-launch speed to ESA step conversion, the proton kinetic energies were too low by about 7% and 17% respectively on PLASTIC/A and PLASTIC/B. The energy per charge definition corresponding to a particular ESA step was modified to account for this. (Note: The velocity of the spacecraft has not been taken into account.) Closer inspection and inter-comparison (again with WIND) shows the percentage offset in velocity is largest at the lowest E/q steps, and least at the highest energy per charge steps. Revisions in the table of velocity to ESA step correspondence for the small channel are listed in Tables 3.1 and 3.2, and plotted in Figure 3.9. With these revisions there is much better 59 agreement between PLASTIC/A, PLASTIC/B, and WIND/SWE bulk proton speeds. PLASTIC proton KE versus WIND proton KE Hourly Averaged Data from February and March 2007 ; ! ! • AHEAD • BEHIND i 1 ^^C^ . ,-* I 2.0 a ! ^^^^ ; =zr y = 0.93x 5 1 : 2 rfffp - ' 1 R = 0.98 * • * .! y = 0,83x| R2 = 0.96 1.0 1.5 2.0 WIND proton KE [keV] Figure 3.8 PLASTIC bulk speeds plotted against bulk speeds from WIND when the spacecraft are near one another. Speed versus ESA Step (27 June, 2007) AHEAD BEHIND X Original Table % *tf* Vg 600 tJ E \. " 500 *H Ht*tu> --*****, *4^^m>- 200 •:••»». 100 90 100 ESA Stap Numbar Figure 3.9 Revised proton speed corresponding to each ESA step number. 60 TABLE 3.1 PLASTIC A Velocil y to ESA Step Correspondence Proton Proton E/q E/q ESA STEP Speed ESA STEP Speed [keV/e] [keV/e] [km/s] [km/s] 64 905 4.271 96 429 0.960 65 884 4.072 97 419 0.917 66 863 3.882 98 410 0.876 67 843 3.701 99 401 0.838 68 823 3.528 100 392 0.801 69 803 3.363 101 383 0.766 70 784 3.206 102 375 0.732 71 766 3.057 103 367 0.700 72 748 2.914 104 359 0.670 73 730 2.778 105 351 0.641 74 713 2.648 106 343 0.614 75 696 2.525 107 336 0.588 76 680 2.407 108 329 0.563 77 664 2.295 109 322 0.540 78 648 2.188 110 315 0.518 79 633 2.085 111 309 0.497 80 618 1.988 112 303 0.477 81 603 1.895 113 297 0.459 82 589 1.807 114 291 0.441 83 575 1.723 115 285 0.425 84 562 1.646 116 280 0.409 85 550 1.575 117 275 0.394 86 538 1.506 118 270 0.381 87 526 1.441 119 266 0.368 88 514 1.377 120 261 0.356 89 503 1.317 121 257 0.344 90 491 1.259 122 253 0.334 91 480 1.203 123 249 0.324 92 470 1.150 124 246 0.315 93 459 1.099 125 243 0.307 94 449 1.051 126 240 0.299 95 439 1.004 127 237 0.292 61 TABLE 3.2! PLASTIC B Velocily to ESA Step Correspondence Proton Proton E/q ESA STEP Speed ESA STEP Speed E/q [keV/e] [keV/e] [km/s] [km/s] 64 908 4.298 96 440 1.007 65 889 4.119 97 430 0.963 66 870 3.946 98 420 0.920 67 852 3.779 99 411 0.880 68 833 3.619 100 402 0.842 69 815 3.464 101 393 0.806 70 798 3.316 102 385 0.772 71 780 3.173 103 377 0.740 72 763 3.035 104 369 0.710 73 746 2.903 105 361 0.681 74 730 2.776 106 354 0.654 75 714 2.653 107 347 0.629 76 698 2.536 108 341 0.605 77 682 2.424 109 334 0.582 78 667 2.316 110 328 0.562 79 651 2.212 111 322 0.542 80 637 2.113 112 317 0.524 81 622 2.018 113 312 0.507 82 608 1.927 114 307 0.491 83 594 1.840 115 302 0.476 84 580 1.756 116 298 0.463 85 567 1.676 117 294 0.450 86 554 1.600 118 290 0.439 87 541 1.527 119 287 0.428 88 529 1.458 120 283 0.419 89 517 1.392 121 281 0.410 90 505 1.328 122 278 0.403 91 493 1.268 123 276 0.396 92 482 1.211 124 274 0.391 93 471 1.156 125 272 0.386 94 460 1.104 126 271 0.382 95 450 1.054 127 269 0.378 62 3.2.7 Distribution Function. Finally, the distribution function f(v) is calculated. i \1/2 _. . Adkw counts m \ m (v - uf •Av)' 77-1 = n Exp K2xkT) 2kT tGv counts = counts(v) t = accumulation time = 0.0128 seconds G = geometric factor = Active Area * Angular Extent of Slit * Bandwidth/2 AHEAD main channel: 8.9 x 10_5m2 *(0.033 rad) * (0.785 rad)*(0.0612 eV/eV)/2 = 7.1xlO'8m2sreV/eV BEHIND main channel: 7.5x10"5m2 * (0.031 rad) * (0.785 rad) * (0.0648 eV/eV) 12 = 6.0;dO~8m2sreV/eV v = bulk speed A0A(p = angular bin size = (0.0218 rad) * (0.7854 rad) n = density u = speed corresponding to ESA step T = temperature k = Boltzmann constant = 1.38x10 B J/deg K PIASTIC/B f(v) versus v 2007 MAY 4 11:37 UT 8.0E+06 ; , { ; ; i -+-f{v) 7.0E+06 — fit with 5% delta _eff •1 • j \ 6.DE+06 i .; | AT i ; ! \ 5.0EHJ6 "'£."{'• •••|4 [•••• \ S 4.06+06 1 [ 4 1 Xr\ 1 A. 1 ; .vJ 3.0E+OS ' T """" • " Jn I 2.0E+06 ; I Reduced j •|v :ChiA2= 1.10 S 1.0E+05 ! kr-- : j/-i J Q.0E+OO i : 1 »-» »< » • 2.SE+0S 2.7E+0S 2.9E+0S 3.1E+05 3.3E+0S 3.5E+05 3.7E+0S 3.SE+05 4.1E+0S 4.3E+0S 4.SE+05 » (rn/.J Figure 3.10 The black dots are the distribution function for each ESA step as calculated above. The red curve is the fit obtained with the IDL gaussfit routine. 63 The IDL gaussfit routine is used to fit the curve and obtain bulk parameters. Figures 3.11 through 3.19 show month-by-month comparisons of 1 - D, hourly-averaged proton bulk parameters from PLASTIC/A, PLASTIC/B, and WIND/SWE. WIND data is courtesy of K.W. Oligvie, A.J. Lazarus, and M.R. Aellig. 64 BEHIND — WIND — AHEAD 800 •3-700 4/1 4/6 4/11 4/16 4/21 4/26 5/1 4/1 4/6 4/11 4/16 4/21 4/26 5/1 lOO 4/1 4/6 4/11 4/16 4/21 4/26 5/1 Figure 3.11 April 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 65 — BEHIND —WIND —AHEAD SOO •S770° 5/1 5/6 5/11 5/16 5/21 5/26 5/31 70 SO [a so 2,40 Q 20 I i i 1 lO o 5/1 5/6 5/11 5/16 5/21 5/26 5/31 5/1 5/6 5/11 5/16 5/21 5/26 5/31 Figure 3.12 May 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 66 — BEHIND —WIND AHEAD 800 6/1 6/6 6/11 6/16 6/21 6/26 7/1 45 40 i_i35 O 30 Ei25 I J as §15 uZtlZZtl ill L "".'' ,1A la CI IO 5 O 6/1 6/6 6/11 6/1© 6/21 6/26 7/1 IOO ,—. 90 *j|- SO •o ©O !« g 30 *^ IO O 6/1 6/6 6/11 6/16 6/21 6/26 7/OJ Figure 3.13 June 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 67 — BEHIND —WIND —AHEAD 800 7/1 7/6 7/11 7/16 7/21 7/26 7/31 SO ; j 70 7T6° -••---•-{-•--•- I •'••'•' ! | •••!•:• • [ I' ' ' i i g 2300 11 j fit J jEf lO O 7/1 7/6 7/11 7/16 7/21 7/26 7/31 7/1 7/6 7/11 7/16 7/21 7/26 7/31 Figure 3.14 July 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 68 — BEHIND —WIND —AHEAD 800 •—1700 (A JJ600 "S500 ^400 "5 "'soo 8/1 8/6 8/11 8/16 8/21 8/26 8/31 200 SO AS a 35 ^5*30 S*25 "g 20 10 LijQyl 5 8/1 8/6 8/11 8/16 8/21 8/26 8/31 O 8/1 8/6 8/11 8/16 8/21 8/26 8/31 Figure 3.15 August 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 69 — BEHIND —WIND —AHEAD 800 9/1 9/6 9/11 9/16 9/21 9/26 lO/l 9/1 9/6 9/11 9/16 9/21 9/26 lO/l 100 | go en so I 70 .L. ; 60 1? - 'A"T"L'»—J 8. SO Ml 40 fO E 30 f r\ E If 'P* .2 20 1— Mui io O 9/1 9/6 9/11 9/16 9/21 9/26 lO/l Figure 3.16 September 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 70 BEHIND WIND AHEAD 800 200 10/1 10/6 10/11 10/16 10/21 10/26 10/31 35 ! i 30 •• 1 1725 n,2o •'•JhjlJK t! ••§15 il S io y^tteij^l • J \ . , 5 itt^^Bt^s^^1 j 1—i^mJix, i \- H AH « lO/l lO/S lO/ll 10/16 10/21 10/26 10/31 lO/l lO/S lO/ll 10/16 10/21 10/26 10/31 Figure 3.17 October 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 71 — BEHIND —WIND —AHEAD 800 <5?700 11/6 11/11 11/16 11/21 11/26 12/1 40 35 7730 O "gl5 01 $$m ^ I I 1 Q lO 5 On/ i 11/6 11/11 11/16 11/21 11/26 12/1 lOO "E" SO llM-w it k HL g. 50 i liilAs it t\Jyjujl J fesj 'V i|fra| £ 3° ^ff^yk Figure 3.18 November 2007 proton bulk parameters from WIND/SWE, STEREO/AHEAD, and STEREO/BEHIND. 72 Thermal Speed [km/s] H Density [1/cc] Bulk Speed [km/s] U £ Ul 01 M 03 •n MM U W * * 111 £ 00000000000 WO01OU1OU1O o O O O O O O z <5" o o o o o o D c3 ERE O H M 7\ NJ z 03 v. N **^ 0) o CD 3 H CD m i—i- i CD 2 0) v. z O M O-^ 01 0 3 Ul CHAPTER IV OBSERVATIONS March 2007 through February 2008 was an exceptionally quiet period in terms of transient solar activity. Recurring patterns of fast and slow solar wind dominated the in situ proton data, as shown in the sections that follow. Bulk proton speeds varied from about 250 km/s to 750 km/s. All of the PLASTIC data used in this study are from the RA_Trigger full resolution rate (described in chapter 3). The plots shown in the following sections are bulk proton parameters that have been averaged over one hour. Ten minute averaged data was used to determine the arrival times of the solar wind transitions at each spacecraft with greater precision, but the large-scale features used for identification of stream interfaces are easily recognized in the hour averaged data set. The first in situ data plot shown for each Carrington rotation (CR) is the bulk proton speed versus time. Displaying the data in this format emphasizes the time separation between observations. As the longitudinal separation between the observatories increases, so does the offset in the speed profiles. The remaining plots display the in situ proton density, bulk speed, thermal speed, and entropy argument separately for both observatories. These plots use spacecraft Carrington number (CR No.) for the x-axis. This is convenient because the 74 Carrington coordinate system corotates with the Sun. This allows for easy comparison of data between the two spacecraft without distortions that would result from time-shifting techniques. Each integer Carrington number corresponds to one solar rotation. In March 2007 both STEREO spacecraft were near Earth. The longitudinal separation between the AHEAD and BEHIND spacecraft was less than 2°. The radial separation was about 0.03 AU. Time separation was minutes to a few hours. The data presented here ends in February 2008, when STEREO/AHEAD and STEREO/BEHIND were separated by about 45°, and time lags between observations were on the order of a few days. The slow-to-fast solar wind transitions are defined for this study as the leading edge Stream Interface (SI), as described in chapter 1. To very briefly review: a drop in density accompanies an increase in temperature and solar wind speed. Forty-one Sis observed in 2007 and early 2008 are presented below. They are highlighted in the in situ data plots with a transparent grey box. The fast-to-slow solar wind interface is like a smaller-scale mirror image of an SI. As described in chapter 1, identification can be made easier by combining the density and temperature information into a single parameter, the proton specific entropy argument. For convenience, the plots of the proton entropy argument below have all been scaled by a factor of 10"4. Thirty-five examples of fast-to-slow interfaces are presented. They are highlighted in the plots with a transparent blue box. 75 4.1 Carrington Rotation 2054 Figure 4.1 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2054. Figure 4.1 shows the in situ solar wind speed measured by PLASTIC/A and PLASTIC/B during Carrington rotation 2054. The longitude separation between the observatories was less than 2°, and the time separation was on the order of minutes. Careful examination shows that the transitions from slow to fast solar wind occur first at STEREO/AHEAD, and later at STEREO/BEHIND, as illustrated in Figure 4.2. There were at least two stream interfaces (Sis) observed between the third and seventh of March, 2007. These are shown in Figures 4.3 and 4.4 as interfaces 1a and 1b. The next slow-to-fast transition also has two interfaces. These are labeled as 2a and 2b, and they occurred at the end of the eleventh and at the beginning of the twelfth of March 2007. The third slow-to-fast 76 transition takes place on the twenty-fifth of March. It is labeled as interface 3. There is another possible interface just prior to SI 3, but it does not meet the identification criteria at PLASTIC/B so it will not be evaluated further. Table 4.1 lists the arrival time and location of the stream interfaces at both observatories during CR 2054. )le 4.1 Slow-to-Fias t TransituDn s for C arrington Rotation 2CI5 4 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 03/04/2007 1a AHEAD 0.967 89.320 -7.346 350.569 23:30 03/05/2007 1a BEHIND 1.006 88.029 -7.275 347.751 02:05 03/06/2007 1b AHEAD 0.967 90.721 -7.344 332.910 07:45 03/06/2007 1b BEHIND 1.007 89.398 -7.286 329.666 11:00 03/11/2007 2a AHEAD 0.967 96.607 -7.288 260.588 23:10 03/11/2007 2a BEHIND 1.010 94.885 -7.290 256.709 23:25 03/12/2007 2b AHEAD 0.967 97.238 -7.277 250.824 13:40 03/12/2007 2b BEHIND 1.011 95.514 -7.286 248.509 14:40 03/25/2007 3 AHEAD 0.965 110.223 -6.869 87.391 00:10 03/25/2007 3 BEHIND 1.019 108.029 -7.030 80.419 08:15 Figure 4.2 6 March, 2007 07:45 UT. Stream interface 1 b arrives at spacecraft A. 77 E WOHi f< * 400 : 2/"\^i j '<*n J 200 205' X 30 t" 10: \f\ m "Xi. •'VM z 0 i#M "-. s» ' 205*» 2054.4 ;»54.8 < 100 | 75 •Z- 50 A r LE-r^i/^yv"/^ H>X „ ,A/1«\*^ U~-~Vvi,^ V A"1-*^. *l 25 -.A, ^M^v^- > 0 2054.6 M54.8 a,b 2a,b ii: Al jPlw/fc \\ Kf Af-J "i ^ fc^' •v vv'\,4 i5 2054,0 2054.4 2054.6 STEREO/AHEAD Corrington Number 1 Figure 4.3 PLASTIC/AHEAD data for Carrington Rotation 2054. I 600 ^ 400 "V ~i~m 200 m 205' S 30 t 10 Hi-" M V v w l iK®T.;S'»V •-vn^V^V^^'^Vi^1^V%^ ~- ^y * .A >H I ° 2054.4 2054.6 •» in 205' v. 100 I 75 JfxA pv* fcjV /**A v-vV ~! 25 '^V,/%j 0 P" ni m 20547T 2054.6 2654* la,b 2 a,b MilA |P 10 Ml ij fli; A/V' ^Nvu^ \J ^ "I 0 '•^VvM ^r*Awv/ tvN u 2054.0 2054.2 2054.4 2054.6 2054.8 STEREO/BEHW0 Carrington Number 1 2 Figure 4.4 PLASTIC/BEHIND data for Carrington Rotation 2054. 78 Even though the separation between the three spacecraft is small, the proton entropy argument plots already show some differences. There is a spike in entropy observed by PLASTIC/AHEAD between interfaces 2 and 3 that is not seen by PLASTIC/BEHIND. }le4 L.2 Fast-to-S ow Transit ons for Carrington Rotation 2054 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 03/08/2007 1 AHEAD 0.967 93.101 -7.330 305.122 14:30 03/08/2007 1 BEHIND 1.008 91.784 -7.296 302.420 20:30 03/17/2007 2 AHEAD 0.966 102.276 -7.162 187.220 09:30 03/17/2007 2 BEHIND 1.014 100.323 -7.228 180.968 11:30 03/28/2007 3 AHEAD 0.965 113.914 -6.688 40.944 13:00 03/28/2007 3 BEHIND 1.021 111.502 -6.898 33.213 22:00 4.2 Carrington Rotation 2055 The longitude separation between the STEREO observatories grew to about 5° during Carrington Rotation 2055. Figure 4.6 shows that the time separation is still small, on the order of minutes to a few hours. The solar wind speeds measured in situ are similar, but PLASTIC/A recorded noticeably faster winds on the ninth and twenty-third of April. On 27 April, 2007 the first observation took place where a stream interface arrived at STEREO/B before STEREO/A, seen at the right-hand edge of Figure 4.6 and illustrated in Figure 4.7. That signaled the change between propagation dominated by radial separation, and propagation dominated by longitudinal separation. 79 Car ring ton Rotation 2055 BOO AHEAD —BEHIND 200 03/31/2007 04/05/2007 04/10/2007 04/15/2007 04/20/2007 04/25/2007 Month/Day/Year Figure 4.5 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2055. Figure 4.6 27 April, 2007 15:00 UT. The stream interface arrives at STEREO/BEHIND. There are four obvious stream interfaces during this Carrington rotation, with a possible fifth around Carrington number 2055.6. The increase in speed corresponding with stream interface number 5 takes place in several steps, but 80 only one dramatic change in density is observed. Interface number 7 straddles Carrington rotations 2055 and 2056. )le 4.3 Slow-to-Fast Transitions for Carrington Rotation 2055 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 04/01/2007 4 AHEAD 0.965 117.637 -6.477 354.085 02:35 04/01/2007 4 BEHIND 1.023 114.646 -6.758 350.258 04:00 04/09/2007 5 AHEAD 0.964 126.208 -5.890 246.177 07:40 04/09/2007 5 BEHIND 1.029 122.569 -6.315 241.011 10:15 04/22/2007 6a AHEAD 0.962 140.124 -4.661 70.820 15:55 04/22/2007 6a BEHIND 1.038 135.156 -5.366 64.227 18:40 04/23/2007 6b AHEAD 0.962 140.573 -4.612 64.614 02:15 04/23/2007 6b BEHIND 1.039 135.567 -5.330 58.383 05:15 04/27/2007 7 AHEAD 0.962 145.374 -4.121 4.606 16:50 04/27/2007 7 BEHIND 1.042 139.698 -4.957 359.423 16:00 81 B»r -^v. •+4l V : 35§,ft' 2055.6 2*5»' o|pi Ayu ,* r-i „#w... ,.A~ ffit. ,'josio 'W M- i-AA -vH-"'' Mft^v TOW 2055.2 '—' 2055.4 2W515" "W.0 6 a,b 7 h.,. V-\L >A>-^' ^\/M 11 2055.6 STEREO/AHEADffiarrinjton Number Figure 4.7 PLASTIC/AHEAD data for Carrington Rotation 2055. 6*0 .^v-- ;.* /K-w/^ ?i ./M^-~~ 2tei.8 4 l , sJ /M ' ~ A»_,~ JVy-v. Wv^ I.> A A>1 KSiT 2055.2 l>2055. 4 2J65S N 1 E L*v^* W^V*!,! (W^V AAI »v -^yV*Vk/ iNyv vV^Wv 205ST 2055.2 2055.4 20*551 "ZOM.O 6 a,b 7 »1,5 If 10 )W \M•4'w v «>. 5 A) M_!*V -JVv K b^A 5 -2055.0 2055.4 2055.6 2055.8 STEREO/BEHIND Corrinjton Number 6 Figure 4.8 PLASTIC/BEHIND data for Carrington Rotation 2055. 82 Table 4.4 Fast-to-S ow Transit ons for Carrington Rotation 2055 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] RfAUl [degrees] [degrees] [degrees] 04/05/2007 4 AHEAD 0.964 121.918 -6.201 300.200 05:00 04/05/2007 4 BEHIND 1.026 118.775 -6.543 293.511 11:00 04/13/2007 5 AHEAD 0.963 130.417 -5.552 193.156 08:30 04/13/2007 5 BEHIND 1.032 126.457 -6.052 186.832 12:30 04/23/2007 6 AHEAD 0.962 141.278 -4.546 56.263 18:30 04/23/2007 6 BEHIND 1.039 136.159 -5.279 49.962 20:30 4.3 Carrington Rotation 2056 Carrington Rotation 2056 covered most of May 2007. HCI longitude separation grew to 9°, and HCI latitude separation increased to more than 1.5°. Figure 4.11 shows an obvious difference in the in situ speed profiles near 22 May. This corresponds to at least one interplanetary coronal mass ejection (ICME). The transition from slow-to-fast wind immediately following the ICME will not be evaluated. The SI near 27 April at the far left of Figure 4.11 was discussed with CR 2055. Slow-to-fast transition number 8 included a shock before the stream interface. The peak density at STEREO/A was nearly double the maximum density observed at STEREO/B. This disparity may not be real. While the density trends are consistent between the spacecraft, the absolute values are somewhat questionable as different background subtraction techniques yield different results during CIR compression regions. (See Appendix C.) Stream 83 interface number 9 is less well defined in the STEREO data than the previous cases, particularly on STEREO B, where there are a number of jumps in thermal speed, but the most significant does not correspond to a drop in density. Carrington Rotation 2056 800 | —AHEAD—BEHIND | 600 400 i^_ \ If f-W 200 i 1 04/27/2007 05/02/2007 05/07/2007 05/12/2007 05/17/2007 05/22/2007 Month/Day/Year Figure 4.9 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2056. Table 4.5 Slow-to-Fast Transitions for Carrington Rotation 2056 Date and Orbital HCI Long. HCI Lat. Carr Long. Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 05/07/2007 AHEAD 0.961 155.701 -2.961 234.320 14:45 05/07/2007 BEHIND 1.049 148.849 -4.040 227.173 15:15 05/18/2007 AHEAD 0.960 167.154 -1.560 89.795 14:40 05/18/2007 BEHIND 1.056 158.483 -2.961 85.556 07:10 84 ^ BOO V. >w ,-""' °. 400 > 200 2056.0 2057.0 >20 1 L'^Uw ! ?- i. s/U m. 2J56.B < 100 I 75 r v i 5oK " V.. rK i. J *%V VW ^ 2056.6 n IV i Iffl v^«»«i WW H f\ lwVv' 1" 2056.2 2056.4 2056.6 £ 2056.0 STEREO/AHEAD Carrington Number Figure 4.10 PLASTIC/AHEAD data for Carrington Rotation 2056. £ 600 = ^ 400 J •w J i 200 2016.4 8 30 1- 10 "V, LrAAv^ LAv* K}¥-A 0 ."•^.yA. w CD 2036.4 imx, < 100 I '5 i^v/i /ft VA3 k/^S A. vv rrv.w^/ u S|-wV ^"»K V W J ">, 5 ^K.\r m °f 0PMZJ ^ ,j-.AA... Jl wn u 2056.0 2056.4 2056.6 STERE0/SEHWD Carrington Number 8 Figure 4.11 PLASTIC/BEHIND data for Carrington Rotation 2056. 85 Die 4k 6 Fast-to-S ow Transit ons for Carrington Rotation 2056 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 05/02/2007 7 AHEAD 0.961 150.460 -3.564 300.445 14:00 05/02/2007 7 BEHIND 1.045 144.516 -4.489 290.068 21:30 05/10/2007 8 AHEAD 0.961 158.771 -2.595 195.576 13:30 05/10/2007 8 BEHIND 1.051 151.717 -3.730 185.271 19:00 05/21/2007 9 AHEAD 0.960 170.077 -1.190 52.922 10:00 05/21/2007 9 BEHIND 1.058 161.606 -2.592 39.132 19:00 4.4 Carrington Rotation 2057 CR 2057 covers the end of May through most of June 2007. During this time the HCI longitudinal separation between the observatories grew to about 14°, and the latitude separation increased to about 2°. Figure 4.15 shows the bulk speed profiles are definitely not identical between the two spacecraft. The high-speed peak during the first week of June is wider at STEREO/B than at STEREO/A. The opposite is true for the high-speed peak ten days later. SI number 10 is another case where the stream interface is not terribly well defined. The increase in speed is very small at the times when density drops and thermal speed increases. There is a PLASTIC/B data gap around the 14th of June, so the SI occurring at that time has been excluded from this study. 86 Carrington Rotation 2057 800 | 600 400 a to 200 05/24/2007 05/29/200? 06/03/2007 06/08/2007 06/13/2007 06/18/2007 Month/Day/Year Figure 4.12 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2057. Table 4.7 Slow-to-Fast Transitions for Carrington Rotation 2057 Date and Orbital HCI Long. HCI Lat. Carr Long. Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 06/02/2007 10 AHEAD 0.958 182.975 +0.467 250.387 18:50 06/02/2007 10 BEHIND 1.066 172.170 -1.290 240.370 17:30 Table 4.8 Fast-to-Slow Transitions for Carrington Rotation 2057 Date and Orbital HCI Long. HCI Lat. Carr. Long. Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 06/06/2007 10 AHEAD 0.958 186.942 +0.975 200.473 14:00 06/06/2007 10 BEHIND 1.068 175.621 -0.852 187.970 16:00 87 ^ BOO ^w--v-^ 1 600 x ./''' "^ ^_^ —/••• " ^A^^, ^ 400 j^ .,,„. ^* a'' ^ > 200 2057.0 2057.2 2057.4 ' 2057.6 2057.8 205B.0 ^ 30 >20 * I 1- 10 ,/A. Z 0 ft' . ^/v .."•V -Jk^ ~~S 2057.0 2057.2 2057.4 2057.6 2057.8 2058.0 < 100 75 ! 4. w ^A'^v. fv '"A VW 50 ^.^•r^s. ^ VvV'" "' ^ '*~W-A,n • -} 25 > 0 205/,u iw!.z 2057.4 2057.6 2057.8 20iC O 10 c If,0 «>. 5 (^r*-».. V U/^VV4^„„^ -v.....,^'~-^'»' V 6o v i, °kv "- "\ y.^/1^ £20 — 1 to — fAL Jtf 2057.4 2057.8 2056.0 v. 100 E 75 a 5»PvAvJ0 \ .if' //" f^A^/''^'VVvAVi 25 U WV^^^J* Awl v*V 0 \yt° 03 2057.0 2058,0 10 HjjfPl ,A , ">*• 5 \j** iW/Hv v> rV WW WvVU '-rv.,/^ ki~v 88 4.5 Carrington Rotation 2058 The HCI longitude separation between the STEREO observatories grew to about 19° during CR 2058. Figure 4.19 shows the time separation between SI observations has increased to nearly a full day. There are five well-defined stream interfaces during CR 2058. The speed profiles for SI numbers 11 and 12 vary between the two spacecraft. Bulk speeds at PLASTIC/B reach 650 km/s, while at PLASTIC/A do not quite reach 550 km/s. The other three stream interfaces show less variation from STEREO/B to STEREO/A. Carrington Rotation 2058 j ! [ — AHEAD—BEHIND « | | | 600 | Am •• MA f-. •fi. *\ Rif V. 1 ML pee d 1 1 \A I 'I N& 2 400 "5 m ! 200 i i '< 1 1 1 06/20/2007 06/25/2007 06/30/2007 07/05/2007 07/10/2007 07/15/2007 07/20/2007 Month/Day/Year Figure 4.15 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2058. 89 t 900 j soo _ -• .••-/K^_," "•*—~ V. ( . (OC '^\^^ /•• },.. WS# J 200 ' 4 ; 105 .0 2058.2 2358.4 2058.6 2053. !'•;."'••; 2059.0 F* ~ > 20 ! - , \ "' 'W^' v' 1 % ; oi l^A-" !• i .0 2058.2 ?J58.* 2058.6 2058.1/;;'^ 2059.0 ! 1 j • «r '' • K r-fv* / ' i "V/-V u '^^v /Jm. • *J**W ^ *" \^r 2058.0 2058.2 1 2058.8 2059. 0 2053.4 2058.6 i -11 12 13 14 15 7-'wv,j- n V j ' V> v lA, j! •—-v„„ w„J L V'" 5 205 2058.2 2058.4 2053.6 2058,8 2059.0 1 STEREO/AHEAD Carrington Number 11 12 13 14 15 Figure 4.16 PLASTIC/AHEAD data for Carrington Rotation 2058. | 600 — ^ 400 —"' i*?.'. * 200 — 2058.0 g 30 > 20 t 10 v* Wyl'V* V-^l—^ M M at 2059.0 2058.0 < 100 I » •M. 50 J^'lvA 7 vAt' Uv i^^Vx. XwwyjjWi^ v~wwv\] £i 25 ' ^Vvr^wT^. ww»" 0 m m 2058.0 20&8.4 2058.6 2059.0 11 12 13 14 15 y W\ 'wk M • (J 4S^ si: iVifi^vfyfA) /w VJP /^K yj* ^i s^ ,.,J K 5 2058.0 205S* 2058.? SIERE0/8EHIND Corrirtgion Number ii 12 13 14 15 Figure 4.17 PLASTIC/BEHIND data for Carrington Rotation 2058. 90 Table 4.9 Slow-to-Fast Transitions for Carrington Rotation 2058 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 06/22/2007 11 AHEAD 0.957 203.299 +2.995 355.199 05:00 06/22/2007 11 BEHIND 1.076 189.001 +0.859 342.674 02:00 06/30/2007 12 AHEAD 0.957 211.804 +3.957 248.898 07:15 06/29/2007 12 BEHIND 1.079 195.468 +1.675 242.462 14:30 07/04/2007 13 AHEAD 0.957 216.256 +4.427 193.363 12:45 07/03/2007 13 BEHIND 1.080 199.035 +2.116 186.977 18:25 07/11/2007 14 AHEAD 0.957 223.564 +5.137 102.414 11:00 07/10/2007 14 BEHIND 1.082 205.100 +2.846 92.372 20:45 07/15/2007 15 AHEAD 0.957 227.549 +5.489 52.912 05:30 07/14/2007 15 BEHIND 1.083 208.172 +3.203 44.370 11:10 >le 4.10 Fast-to-Slow Trans tions for Carrington Rotation 2058 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 06/25/2007 11 AHEAD 0.957 206.471 +3.363 316.160 05:30 06/25/2007 11 BEHIND 1.077 192.337 +1.282 290.213 23:00 07/01/2007 12 AHEAD 0.957 212.955 +4.081 234.535 09:30 07/01/2007 12 BEHIND 1.079 196.665 +1.824 223.860 00:00 07/06/2007 13 AHEAD 0.957 218.222 +4.625 168.880 09:30 07/05/2007 13 BEHIND 1.081 200.838 +2.336 158.884 21:00 07/13/2007 14 AHEAD 0.957 225.633 +5.323 76.705 10:00 07/12/2007 14 BEHIND 1.083 206.709 +3.034 67.237 18:00 07/15/2007 15 AHEAD 0.957 228.276 +5.551 43.887 22:00 07/15/2007 15 BEHIND 1.083 209.107 +4.194 29.742 13:30 91 4.6 Carrington Rotation 2059 Carrington rotation 2059 begins with a high-speed stream (S116) that is very different between PLASTIC/B and PLASTIC/A. The solar wind speed measured by PLASTIC/B reaches 600 km/s, while at PLASTIC/A the peak speed is just 440 km/s. Figure 4.23 shows the other high-speed streams during this Carrington rotation show some differences between BEHIND and AHEAD, but not as obvious as S116. Stream interface number 16 is surprising well defined at STEREO/A given that the change in speed is not that large. Transition 17 takes place in two steps, with two interfaces. There is a possible transition after number 18, but it is not obvious in the data from PLASTIC/B, so it will not be analyzed. By the end of CR 2059, the HCI longitude separation between BEHIND and AHEAD had reached 25°, and the latitudinal separation had decreased to about 1.5°. 92 Carrington Rotation 2059 BOO — AHEAD --BEHIND | 600 400 1 200 i : 07/17/2007 07/22/2007 07/27/2007 08/01/2007 06/06/2007 08/11/2007 08/16/2007 Month/Day/Year Figure 4.18 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2059. )le 4.1 1 Slow-to-Fast Transitions for Carrington Rotation 2 D59 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 07/21/2007 16 AHEAD 0.957 233.753 +5.984 335.979 02:10 07/20/2007 16 BEHIND 1.084 213.057 +3.752 327.941 04:45 07/27/2007 17a AHEAD 0.957 240.242 +6.426 255.638 05:05 07/26/2007 17a BEHIND 1.085 218.474 +4.329 243.129 13:25 07/29/2007 17b AHEAD 0.957 242.663 +6.571 225.701 11:50 07/29/2007 17b BEHIND 1.086 220.810 +4.565 206.557 07:15 08/07/2007 18 AHEAD 0.957 252.031 +7.016 109.971 07:30 08/06/2007 18 BEHIND 1.086 227.535 +5.202 101.334 04:40 93 I 600 r..^"\. ^"^X ,^^ ^ 400 < 200 2053.0 20J9.4 8 30 > 20 1 10 A S » ^•J^^^A /" 2059.0 2059.8 < 100 E 75 ^ 50 r 'Ay^v v-\4-y-v "vv,,. *i 25 ~> 2059.0 0 16 17a,b 18 5 .I'0 If' m ,vH, 5 <£ ** *i •wv-4, H % ° M ^. #V^ n. 5 2059.0 2059.2 2059.4 2059.6 STEREO/AHEAD Ccrnmjton Number 16 17 18 Figure 4,19 PLASTIC/AHEAD data for Carrington Rotation 2059. < aoo J^ 600 f 400 "xt Vr"" * 200 1' 10 U.,lfe yM wfc 1 * o ^A .f-^/V/ L^---.^^ 2059.0 Mi < 100 I 75 ~ 50 tt£ .OT^V~<-v A r ICiA v -, 25 ^K ^Wv m Ww^ * 0 ^H^wsJ 2059.0 2059.2 2060.0 16 17a,b 18 ~i^mE «> 5 /v K-A m! o kJ'Hk 5 2059.0 2059.4 "2099.5 2«wr STEREO/BEHIND Carrington Number 16 17 18 Figure 4.20 PLASTIC/BEHIND data for Carrington Rotation 2059. 94 )le 4.12 Fast-to-Slow Trans tions for Carrington Rotation 2059 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 07/24/2007 16 AHEAD 0.957 237.587 +6.255 288.493 17:00 07/23/2007 16 BEHIND 1.085 216.206 +4.092 278.637 21:30 08/04/2007 17 AHEAD 0.957 248.777 +6.882 150.156 06:00 08/03/2007 17 BEHIND 1.086 225.274 +4.995 136.700 13:00 08/09/2007 18 AHEAD 0.957 254.755 +7.111 76.347 21:00 08/08/2007 18 BEHIND 1.086 229.787 +5.399 66.154 20:00 4.7 Carrington Rotation 2060 Carrington rotation 2060 begins in mid-August 2007. HCI longitude separation grows to about 30°, and latitude separation decreases to less than 0.5°. Figure 4.27 shows the high-speed peaks observed by PLASTIC/B are clearly narrower than those observed by PLASTIC/A. SI number 19 is well- defined on both STEREO spacecraft, in spite of the small change in bulk speed. The AHEAD spacecraft sees a large drop in density resembling an interface prior to interface number 20, but it is not accompanied by the requisite increase in temperature and bulk speed. 95 Carrington Rotation 2060 800 ! —AHEAD—BEHIND j ! | 600 NtyuA ZkAu 400 3 10 200 i ; : : L. 08/13/2007 08/18/2007 08/23/2007 08/28/2007 09/02/2007 09/07/2007 09/12/2007 Month/Day/Year Figure 4.21 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2060. )le 4.1 3 Slow-to-Fast Transitions for Carrington Rotation 2 360 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 08/16/2007 19 AHEAD 0.957 261.666 +7.281 351.059 09:00 08/15/2007 19 BEHIND 1.085 235.560 +5.866 336.084 14:10 08/26/2007 20 AHEAD 0.958 272.744 +7.333 214.877 19:10 08/24/2007 20 BEHIND 1.084 243.592 +6.416 211.236 23:00 09/01/2007 21 AHEAD 0.958 279.194 +7.239 134.545 21:00 08/31/2007 21 BEHIND 1.083 249.447 +6.738 120.656 18:10 96 jir-.,,,„,^,,^. .tf j-r i v LA,/-. '^^Hvv—,.>< Ml v •* v.... A 2060.8 I, 19 20 21 * If- ,,/*> nJ 5 "r^tw \A j/W 2060.4 2060.8 '4 2061.0 STEREO/AHEAD Carrington Number 19 20 21 Figure 4.22 PLASTIC/AHEAD data for Carrington Rotation 2060. S 600 F^A jt^*^ cj. «0t m mi •&•••••< 206( 20&W £20 1 AA--AI' f 10 .-VW^^^y^-lA^y/V . *uyiV. . .^yx^. 2060.2 20*0.+ 2061.0 100 1 »+- M /•^~v r Vv-v^i^v^r ^ 50;- 0 *s>-v ,vv, AW/V _^>^ rf^ ^r ~H*tV 97 Table 4.14 Fast-to-Slow Transitions for Carrington Rotation 2060 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 08/21/2007 19 AHEAD 0.958 267.557 +7.342 278.345 22:00 08/20/2007 19 BEHIND 1.085 240.158 +6.196 264.539 23:00 08/31/2007 20 AHEAD 0.958 277.647 +7.270 153.683 10:00 08/29/2007 20 BEHIND 1.083 247.823 +6.656 145.727 21:00 09/06/2007 21 AHEAD 0.959 284.296 +7.100 71.384 16:30 09/05/2007 21 BEHIND 1.081 253.474 +6.919 58.589 10:00 4.8 Carrington Rotation 2061 During CR 2061 the HCI latitude separation between the observatories begins to increase again, reaching just over 2° by the first week of October 2007 when the HCI longitude separation reaches 35°. Figure 4.31 shows a "high speed" stream on the 14th and 15th of September, though the peak speed recorded by PLASTIC/B is less than 450 km/s. The high-speed streams show fewer disparities, though STEREO/AHEAD appears to see two interfaces associated with transition number 24 while STEREO/BEHIND sees just one. 98 Carrington Rotation 2061 800 1 ; —AHEAD—BEHIND >y^ v | 600 j 1} my\ /\|V/* \ n 400 v IAJ JL/. jXAMi^ a 200 j ! i 1 09/09/2007 09/14/2007 09/19/2007 09/24/2007 09/29/2007 10/04/2007 10/09/2007 Month/Day/Year Figure 4.24 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2061. Table 4.15 Slow-to-Fast Transit ons for Carrington Rotation 21D6 1 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 09/15/2007 22 AHEAD 0.959 293.367 +6.716 318.804 06:20 09/14/2007 22 BEHIND 1.078 261.323 +7.173 298.171 10:50 09/21/2007 23 AHEAD 0.960 300.396 +6.303 231.271 22:20 09/20/2007 23 BEHIND 1.076 266.187 +7.264 224.199 00:25 09/28/2007 24 AHEAD 0.961 307.671 +5.776 140.387 20:25 09/26/2007 24 BEHIND 1.073 272.156 +7.305 133.784 19:30 10/04/2007 25 AHEAD 0.961 313.446 +5.290 68.000 08:40 10/03/2007 25 BEHIND 1.069 277.754 +7.272 49.546 03:30 99 — """ <>— , 800 |_ 600 /^---V^ v'~ "'~^-^.. "V _ ^ 400 r ^ .r-' ,./•" > 3L —_ 200 -j 2061.0 2061.2 20! 1.4 2C1V5 618 2062.0 _.. 8 30 li > 20 X. 100 I 75 ) Vv,,, ^ j vVw -.- *• " 50 "^-.^rt ^ _ -, 25 """"W.W- h ^-/"-V'l..., ..N N > 0 * 2061.0 2061.2 TB51.4 2061.8 2061.8 2062.0 ? 22 23 24 25 | „E 15 ^o> 10 — i } 1 A g< ^\ 1 5 i ? X u f v "* 4 ... .N oV " -"..,^»^x < 2iS 2061.0 0 2061.2 20*1.4 2061.6 2061,8 2062.0 S'fffiEQ/AHEAD Ccrritigton Number 22 23 24 25 Figure 4.25 PLASTIC/AHEAD data for Carrington Rotation 2061 : N—K. A/v. kr •ir^' ^— 11 400 m ^JJi«/;.:.i ** 200 m.u\ 8 30 / t 10 ,.«v^A-' VTAJWV~^_. Wvu, * o rv- U~- 206 2 '2061.4! 2*8 x 100 I » \H^v^»« ,•> 1 " 50 ;f||AAv^A,-~~---'f •TV \4^ r. rvwwy 3 25 > 0 •"58$ .2 255tt 2061.6 22 23 24 25 ,0 ? If 4\Jk "$: 5 A. «V_ P wwp«r % '4»/»Aj '4*Vw 7 LJ 2061.0 2061.2 2065.4 2061.6 2061,8 2062.0 S1ERE0/3EHIND Corrington Number 22 23 24 25 Figure 4.26 PLASTIC/BEHIND data for Carrington Rotation 2061. 100 )le 4.16 Fast-to-Slow Trans tions for Carrington Rotation 2061 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] Ft [All] [degrees] [degrees] [degrees] 09/17/2007 22 AHEAD 0.960 295.815 +6.583 289.264 14:00 09/16/2007 22 BEHIND 1.077 263.238 +7.215 269.073 15:30 09/27/2007 23 AHEAD 0.961 306.559 +5.862 158.949 10:30 09/25/2007 23 BEHIND 1.073 271.184 +7.304 148.473 17:00 10/02/2007 24 AHEAD 0.961 311.519 +5.458 92.177 12:30 09/30/2007 24 BEHIND 1.071 275.282 +7.295 86.673 08:30 10/05/2007 25 AHEAD 0.961 314.964 +5.153 48.932 19:30 10/04/2007 25 BEHIND 1.069 279.066 +7.254 29.878 15:00 4.9 Carrington Rotation 2062 Carrington rotation 2062 covers most of October and the begging of November 2007. The HCI latitude separation increased to more than 4° during this solar rotation, and the longitude separation grew to about 39°. Figure 4.35 shows the in situ speed profiles are similar between the two spacecraft, but not identical. The high-speed streams are wider at PLASTIC/AHEAD than at PLASTIC/BEHIND. There is a data gap on STEREO B during slow-to-fast transition 26. It appears that the stream interface is just after the gap. Transition 27 takes place in two steps at STEREO/B, but appears to be one smooth step on at STEREO/A. The final high-speed peak following SI 27 has a well-defined interface at PLASTIC/A, but not at PLASTIC/B. 101 Carrington Rotation 2062 BOO -AHEAD—BEHIND | 600 400 3 200 10/06/2007 10/11/2007 10/16/2007 10/21/2007 10/26/2007 10/31/2007 11/05/2007 Month/Day/Year Figure 4.27 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2062. Table 4.17 Slow-to-Fast Transit ons for Carrington Rotation 2 D62 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 10/19/2007 26 AHEAD 0.963 329.063 +3.720 231.148 08:10 10/17/2007 26 BEHIND 1.061 290.437 +6.945 220.693 08:30 10/26/2007 27 AHEAD 0.963 336.295 +2.890 139.483 07:30 10/24/2007 27 BEHIND 1.056 297.224 +6.630 120.802 21:00 102 1 1"- ! - J,. 5 v.. A s ^ -A - _ *^f~ ^l,./'" Vw,„,"'"' 2062.0 2062.2 2062.4 :062i 2062.8 2063.0 < 100 1 '5 J •'> w 50 V"Vv^.A/y^ v ^ vv ^h $ 25 jUw •-,/xA— . -v^W MA7 \a- > 0 :- 2.0 2062.2 2062.'! 2062.6 2062.8 2oe3. 0 26 27 ji;: - y M- wv V, ,>i 4 \A fi2oe 2.0 2062.2 2062.4 2062.6 2062.8 2063.0 1 STEREO/AHEAD Carragtorc Number 26 27 Figure 4.28 PLASTIC/AHEAD data for Carrington Rotation 2062. """v Cf 400 ^/~~°~*~ * 200 :.'2W2.4 o 30 J^ Vl f 10 P-vi 'AOJ \ v^A AJ * o 3*hw ,/i /v .''•2M2.4 <. 100, I Til " 50 iWWH .c K V^SJVV^ "N^V^vA-UK''^WAM* . 1 25 A ^->n' ':¥ 4A TO > 0 KA- —SW2.4 26 27 ,1 '5 TFMT !?,0 ft* ! 5 A' Kj, A ""» •^K^y V Figure 4.29 PLASTIC/BEHIND data for Carrington Rotation 2062. 103 Table 4.18 Fast-to-Slow Transitions for Carrington Rotation 2062 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 10/24/2007 26 AHEAD 0.963 334.698 +3.078 159.753 18:30 10/22/2007 26 BEHIND 1.058 295.188 +6.735 150.680 15:00 10/29/2007 27 AHEAD 0.963 339.487 +2.508 98.939 09:30 10/27/2007 27 BEHIND 1.055 299.189 +6.522 92.034 01:00 4.10 Carrington Rotation 2063 Carrington rotation 2063 covered most of November 2007. HCI longitude separation was about 40°, and latitude separation was more than 5°. Figure 4.39 shows the high-speed streams were wider at STEREO/A than STEREO/B, and the peak observed speeds were obviously larger at the AHEAD observatory. In fact, PLASTIC/B sees just a very small increase in speed around the tenth of November, while PLASTIC/A clearly observes a high-speed stream. Carrington Rotation 2063 800 — AHEAD—BEHIND , j | 600 i ft Ifff^ \i if Vi JTv X v a i r\ i f \ \in / \ \ ; 01 400 200 1 ; i L_ 11/03/2007 11/08/2007 11/13/2007 11/1S/2007 11/23/2007 11/28/2007 12/03/2007 Month/Day/Year Figure 4.30 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2063. 104 ^ 800 I 600 v-. ;' --.„,..,.. 8 30 >20 <\ 10 — '» K ^. „ , :'.. " ^As I o %~J~~-__y'V. ,,-.-' 206 3.0 2C6 1.2 2063.4 2(J =3.6 2063.8 206 < 100 75 1 /A ; -?: A- \ w ~s/«~ W\ '- 50 I'vw ,.,Vv / v,a VWZ ~! 25 > 0 2063.2 2063.4 2063.8 2064.0 28 29 30 4 I ^4wt\ iwWi/v ' V.JH,/, V\ f ' W 2063._i_2L 2063.L 4 __:^s;~ 2063.1 6 2063,8 2064.0 STEREO/AHEAD Carrinqton Number 28 29 30 Figure 4.31 PLASTIC/AHEAD data for Carrington Rotation 2063. £ 600 y\. o- 400 S 2063.2 20RA6 2C63.8 H 30 ^w\^W -A* 'Vv> 20R3.C' \ 100 I '» %-M ~ 50 — ^v^ y ^^v^•tw^fA 3 2jjpx— -A- 2063.2 »3.4 20S3X 2063.8 28 If,0 ^ M <">, 5 ^ KM v ^iL^ w 4A. -4-A' »**VK. 2063.4 2063.6 2063.8 S7ERE0/8EHW0 Carrington Number 28 29 30 Figure 4.32 PLASTIC/BEHIND data for Carrington Rotation 2063. 105 Table 4. 9 Slow-to-Fast Transitions for Carrington Rotation 2063 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 11/14/2007 28 AHEAD 0.965 356.001 +0.432 248.404 09:40 11/12/2007 28 BEHIND 1.043 315.139 +5.369 221.135 10:40 11/21/2007 29 AHEAD 0.966 2.949 -0.464 159.558 03:45 11/20/2007 29 BEHIND 1.038 321.489 +4.788 130.461 06:50 11/26/2007 30 AHEAD 0.966 7.950 -1.104 95.559 00:30 11/24/2007 30 BEHIND 1.035 325.225 +4.418 77.459 06:50 Tat >le 4.20 Fast-to-Slow Trans tions for Carrington Rotation 2063 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 11/18/2007 28 AHEAD 0.965 360.303 -0.123 193.407 14:00 11/16/2007 28 BEHIND 1.041 317.544 +5.156 186.701 01:00 11/24/2007 29 AHEAD 0.966 6.858 -0.965 109.537 23:00 11/22/2007 29 BEHIND 1.037 323.634 +4.578 100.001 14:00 11/28/2007 30 AHEAD 0.966 10.113 -1.379 67.875 03:00 11/25/2007 30 BEHIND 1.034 326.578 +4.279 58.323 17:30 4.11 Carrington Rotation 2064 The final complete Carrington rotation of 2007 was 2064. The HCI latitude separation between the observatories peaked near the middle of the month at 5.7°. Longitude separation increased to about 43° by the end of December. In spite of the large separations in both time and latitude, the bulk speed plots in Figure 4.43 look quite similar. 106 Carrington Rotation 2064 800 — AHEAD—BEHIND | 600 400 3 a 200 11/30/2007 12/05/2007 12/10/2007 12/15/2007 12/20/2007 12/25/2007 12/30/2007 Month/Day/Year Figure 4.33 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2064. Table 4.21 Slow-to-Fast Transit ons for Carrington Rotation 2064 Date and Orbital HCI Long. HCI Lat. Carr Long. # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 12/12/2007 31 AHEAD 0.967 25.078 -3.203 236.378 16:20 12/09/2007 31 BEHIND 1.025 339.900 +2.795 231.586 20:00 12/18/2007 32a AHEAD 0.967 31.562 -3.931 153.520 23:30 12/16/2007 32a BEHIND 1.021 346.228 +2.031 143.942 11:00 12/20/2007 32b AHEAD 0.967 33.586 -4.198 127.668 22:40 12/18/2007 32b BEHIND 1.020 348.173 +1.790 117.125 11:40 107 5 600 «f 400 b; _^ N > 2001 r »6*,S\. S 30 >20 t 10 ,jf ; o ^_.^>-^n v U---^"' ''"""•"• ?06».& N. too E 75 J( - 50 r ••MWu L -^ r-^v.,- "•---..,;^/V»d *1 25 AJ^--^ > 0 -2064.6 , 2064.8 31' 32a,b „E '5 |? 10 r*a IT S< \/i THp "& 5 VAV v H ^L. •^-w- ? o 2064.4 2064.6 2065.0 STEREO/AHEAD Cofringtor, Number 3f 32 Figure 4.34 PLASTIC/AHEAD data for Carrington Rotation 2064. 60 £ ° rkv ~~y" <^ 400 v„ * 200 I 2064.0 2064.2 20fe*-6,-. 30 X_ 20 V i V t 10 ^l^Uw/^VV ^V HA1: \«,V*n4-, y-A„ / V: 2064,0 N 100 J ?S w 50 ,^Wt\Wv< r H^^-vwf^' HAA JWAAW 1 25 W^-wJ W --. > 0 2065.0 31' 2064'32 a,b *E, '5 1 If '° Pi Vrt Vt\U H ">>, 5 R- f\ Vv ^ *° 0 w—v. /->"M. ./ TV %v UUvMVy^ 2064.6 STEREO/BEHIND Corrington Number 32 Figure 4.35 PLASTIC/BEHIND data for Carrington Rotation 2064. 108 Table 4.22 Fast-to-Slow Transitions for Carrington Rotation 2064 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 12/14/2007 31 AHEAD 0.967 27.251 -3.452 208.606 19:00 12/11/2007 31 BEHIND 1.024 341.925 +2.554 203.469 23:00 12/25/2007 32 AHEAD 0.967 37.896 -4.593 72.679 03:00 12/23/2007 32 BEHIND 1.017 352.560 +1.241 56.893 01:00 4.12 Carrington Rotation 2065 Carrington rotation 2065 began at the very end of December 2007 and covered most of January 2008. During this time the HCI longitudinal separation grew to almost 45°, and the latitude separation decreased to about 4°. Figure 4.47 shows that both observatories saw two high-speed streams, and observed similar peak speeds. However, the detailed speed profiles are clearly not identical. PLASTIC/B recorded a multi-step transition from slow to fast solar wind in the middle of the Carrington rotation, but a few days later PLASTIC/A recorded a single transition. 109 Carrington Rotation 2065 BOO — AHEAD—BEHIND | J 600 t \ f\ All i\ I (fl 400 V—'—' ^^ 200 i i 12/27/2007 01/01/200B 01/06/2008 01/11/2008 01/16/2008 01/21/2008 01/26/2008 Month/Day/Year Figure 4.36 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2065. Table 4.23 Slow-to-Fast Transiltion s for Carrington Rotation 2 065 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 01/07/2008 33 AHEAD 0.967 51.248 -5.793 262.717 01:10 01/03/2008 33 BEHIND 1.011 3.954 -0.214 261.818 18:40 01/14/2008 34 AHEAD 0.967 58.688 -6.328 168.305 05:30 01/10/2008 34 BEHIND 1.008 10.710 -1.076 170.761 16:10 110 <, BOO I 600 <\ 4001—.—'VJ" -—-..J-I.,.^ '•Vv-,_v > 200 2*5.6 8 3o >20 v. 100 | 75 ^ 50 °ih r k>/v^-v,,*, ' ^'HAj, ,/-V"w\,>t1 ~i 25 W, > 0 2065.2 W5.6 33 34 li» MI MPfi c ."Ail^k^i' v iH- :/VVJ tX*'*/^Jx r*. ui 2065.0 2065.4' 2065.6 2066.0 STEREO/AHEAD Carrington Number 33 34 Figure 4.37 PLASTIC/AHEAD data for Carrington Rotation 2065. J! 800 V--A"y^K . f\ 1^1 2 "hvy1! Ai m i «4-WY Aw.^.^y^w „^"-* x 100 | 75 A w /V 50 A ./ Kvv\ r •\nrjw\sA M Vf V '\vw''' ./-W^^/^/U-^ -| 25 -yVrW wv K > 0 2065.0 33 34 ilS MTYJTV1, p ^ ,i ! Ifji.W /J%*M ^ S/Mul i5 2065.0 2065.4 2065.6 2065,8 2066.0 STEREO/BEHIND Corrington Number 33 34 Figure 4.38 PLASTIC/BEHIND data for Carrington Rotation 2065.' Ill Table 4.24 Fast-to-Slow Transitions for Carrington Rotation 2065 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 01/11/2008 33 AHEAD 0.967 55.513 -6.112 208.570 04:00 01/09/2008 33 BEHIND 1.008 9.516 -0.924 186.805 11:00 01/23/2008 34 AHEAD 0.967 67.947 -6.844 51.087 03:30 01/19/2008 34 BEHIND 1.004 19.646 -2.191 51.249 17:30 4.13 Carrington Rotation 2066 The last Carrington rotation in this study is number 2066. During February 2008 the HCI longitudinal separation between the STEREO observatories exceeded 45°, and the latitudinal separation waned to less than 2°. Figure 4.51 shows somewhat higher peak speeds recorded at STEREO/BEHIND compared to STEREO/AHEAD. Time separation between stream interface observations was more than two days. The entropy drop following stream interface 36 did not occur until Carrington Rotation 2067, so it does not appear in the figures below. Carrington Rotation 2066 800 — AHEAD—BEHIND 200 4 01/23/2008 01/28/2008 02/02/2008 02/07/2008 02/12/2008 02/17/2008 02/22/2008 Month/Day/Year Figure 4.39 Proton bulk speed measured in situ by STEREO/PLASTIC plotted versus time for Carrington Rotation 2066. 112 v 800 | 600 <} 400 * 200 2C66.6 2066.8 8 M >20 t 10 ! o \il/^ ||.S 2066.0 8*6.6 X 100 E 75' «V*VVW 2066.8 2067.0 35 36 rr «>>. shvv"\ lA 'Vf.,^-J""v>'U 1 U ¥n \<*VW*vA^ ..7 y' f^\l 2066.4 2066.6 2067.0 STEREO/AHEAD Ccfringtor, Number 35 Figure 4.40 PLASTIC/AHEAD data for Carrington Rotation 2066. < 800 1 e0° Cj, 400 * 200 20BM i Nj J '°k^wv*iJ "•Vif-lV-W ~AV-/ \*nri'^j^~*"r 2066.0 206K 2MJ < 100 I 75 rtA w.w\zi*^ y~u'^» **..'•^-v'V-yu-A'vviAJ t ^.^vL 'nyvt^^v^'N d 2066.0 206fci 20WS 2066.S 2067.0 35 36 I' k%M^V , '^A-^AjW^ W*Wu \A^V>\/ *w h 0 J <4\„~r 2066.4 2066,6 2066.8 2067,0 SiEREO/BEHMD Carrington Number 35 Figure 4.41 PLASTIC/BEHIND data for Carrington Rotation 2066. 113 Table 4.25 Slow-to-Fast Transiltion s for Carrington Rotation 2066 Date and Orbital HCI Long, HCI Lat. Carr Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 02/02/2008 35 AHEAD 0.967 78.691 -7.221 275.456 11:10 01/30/2008 35 BEHIND 1.001 29.957 -3.407 274.496 02:20 02/11/2008 36 AHEAD 0.966 88.441 -7.345 152.622 19:30 02/09/2008 36 BEHIND 1.000 40.289 -4.513 138.452 10:00 Table 4.26 Fast-to-Slow Transiltion s for Carrington Rotation 2066 Date and Orbital HCI Long, HCI Lat. Carr. Long, # Spacecraft Time [UT] R[AU] [degrees] [degrees] [degrees] 02/07/2008 35 AHEAD 0.966 84.180 -7.317 206.280 17:30 02/03/2008 35 BEHIND 1.001 34.566 -3.917 213.699 17:00 114 CHAPTER V ANALYSIS AND DISCUSSION 5.1 Slow-to-Fast Solar Wind Transitions Modeling a stream interface (SI) as a Parker-like spiral requires two major assumptions: an ideal corotating reference frame exists, and the source of the solar wind undergoes negligible evolution. Modelers admit these assumptions are unrealistic over the scale of a Carrington rotation (c.f. Riley 2007), but for smaller time intervals they may be reasonable. The STEREO/PLASTIC data set presented in Chapter IV covers a range of separations in time and space. From March 2007 through February 2008 the longitude separation between the STEREO observatories grew from less than 2° to just over 48°. The separation in heliographic latitude varied, but never exceeded 6°. The difference in orbital radii varied from 0.03 AU to 0.13 AU. The temporal separation between stream interface observations ranged from 10 minutes to 3.5 days, allowing us to study the evolution of stream interfaces over periods much shorter than a complete solar rotation. The longitude where STEREO/AHEAD is expected to encounter a stream interface can be calculated based on the solar wind speed measured by PLASTIC/B at the time STEREO/BEHIND observes the interface. The speed measured by PLASTIC/B is assumed to be the radial propagation speed of the 115 interface. The radial propagation speed is used to infer the idealized Parker spiral geometry. The curvature of the interface is needed for an accurate estimate of the time-of-arrival because of the radial separation between the observatories (see Figure 5.1). Latitude separation between the observatories may have an effect (Lee 2000), but for now this is neglected. The calculation (Equation 5.1) is carried out in the Carrington coordinate system, using the sidereal photospheric equatorial angular speed QSun = 14.38 degrees per day (Newton and Nunn, 1951). ^A.expected = ^B " ^SUHC^B'RAV VB_SW [5.1] The time corresponding to the expected arrival longitude is then obtained using the STEREO orbit tool (available at http://stereo-ssc.nascom.nasa.gov/where/). Figure 5.1 Idealized geometry of a stream interface. The longitude separation between the observatories is greater than the longitude that must be covered between observations of the interface. Table 5.1 lists the interface arrival times at STEREO/BEHIND, the solar wind speed measured at that time by PLASTIC/BEHIND, the time difference between arrivals at the two observatories (time differences less than zero indicate that STEREO/AHEAD was the first observer), the latitude and longitude 116 separations of the observatories in Heliocentric Inertial (HCI) coordinates, the difference in orbital radii in AU, the difference between the expected and actual longitude of arrival at STEREO/A, and the difference between the expected and actual arrival time at STEREO/A. Stream interfaces 1 through 6b and 8 were observed first at STEREO/AHEAD and later at STEREO/BEHIND. This is not unexpected. While an idealized stream interface appears to corotate with the Sun, in reality the plasma travels radially outwards (as illustrated in Figure 5.2). When the longitude separation between the observatories is small, the radial separation is more significant than the longitudinal separation. Figure 5.2 When longitude separation is small, the radial separation is particularly important. 117 TABLE 5.1 Slow to Fast Solar Wind Stream Interfaces Exp.- Exp.- Time Obs. Obs. V_sw AHCI AHCI Interface Arrival from B AR Carr. Arrival No. atB Lat. Long, time at B [UT] to A [AU] Long, Time at [km/s] [deg.] [deg.] [hours] at A A [deg.] [hours] 1a 2007 Mar. 5 02:05 370 -2.58 -0.07 1.4 0.039 -0.2 -0.4 1b 2007 Mar. 6 11:00 445 -3.25 -0.06 1.5 0.040 -1.0 -1.9 2a 2007 Mar. 11 23:45 385 -3.92 0.00 1.7 0.043 -1.1 -1.9 2b 2007 Mar. 12 14:40 500 -1.00 0.01 1.8 0.044 -0.1 -0.3 3 2007 Mar. 25 08:15 360 -8.08 0.18 2.5 0.053 -3.3 -6.0 4 2007 Apr. 1 04:00 400 -1.42 0.29 3.1 0.058 -0.2 -0.3 5 2007 Apr. 9 10:15 310 -2.58 0.43 3.8 0.065 0.1 0.1 6a 2007 Apr. 22 18:40 365 -2.75 0.72 5.1 0.076 -1.4 -2.6 6b 2007 Apr. 23 05:15 380 -3.00 0.73 5.1 0.076 -1.2 -3.2 8 2007 May 7 15:15 425 -0.50 1.08 6.9 0.088 -2.0 -3.7 7 2007 Apr. 27 16:00 500 0.83 0.83 5.6 0.080 -1.2 -2.2 9 2007 May 18 07:10 380 7.50 1.36 8.3 0.096 2.1 4.0 10 2007 Jun. 2 17:30 405 1.33 1.75 10.7 0.107 -3.4 -6.3 11 2007 Jun. 22 02:00 445 3.00 2.12 14.2 0.118 -5.9 -10.8 12 2007 Jun. 29 14:30 420 16.75 2.20 15.6 0.122 0.8 1.5 13 2007 Jul. 3 18:25 530 18.33 2.23 16.4 0.123 -0.6 -1.1 14 2007 Jul. 10 20:45 390 14.25 2.23 17.8 0.126 -2.0 -3.7 15 2007 Jul. 14 11:10 460 18.33 2.22 18.6 0.127 -1.7 -3.1 16 2007 Jul. 20 04:45 375 21.42 2.16 19.8 0.128 0.4 0.8 17a 2007 Jul. 26 13:25 385 15.67 2.05 21.1 0.129 -4.2 -7.7 17b 2007 Jul. 29 07:15 450 4.58 1.99 21.7 0.129 -12.0 -22.0 18 2007 Aug. 6 04:40 330 26.83 1.77 23.3 0.129 1.1 2.0 19 2007 Aug. 15 14:10 470 18.83 1.40 25.3 0.128 -8.2 -14.9 20 2007 Aug. 24 23:00 410 44.17 0.93 27.2 0.126 4.0 8.4 21 2007 Aug. 31 18:10 350 26.83 0.52 28.6 0.124 -5.1 -9.2 22 2007 Sep. 14 10:50 370 19.50 -0.41 31.2 0.119 -12.6 -23.3 23 2007 Sep. 20 00:25 435 45.92 -0.83 32.2 0.116 -0.4 -0.8 24 2007 Sep. 2619:30 430 48.92 -1.36 33.4 0.112 -0.1 -0.2 25 2007 Oct. 3 03:30 540 29.17 -1.87 34.4 0.108 -13.5 -24.6 26 2007 Oct. 17 08:30 440 47.67 -3.00 36.6 0.099 -4.9 -8.9 27 2007 Oct. 24 21:00 515 34.50 -3.57 37.6 0.093 -14.2 -25.9 28 2007 Nov. 13 10:40 480 23.00 -4.81 39.9 0.078 -23.2 -42.4 29 2007 Nov. 20 06:50 410 20.92 -5.14 40.6 0.073 -24.7 -45.1 30 2007 Nov. 24 06:50 510 41.67 -5.30 40.9 0.070 -14.7 -26.7 31 2007 Dec. 9 20:00 530 68.33 -5.66 42.3 0.058 -2.1 -3.8 32a 2007 Dec. 1611:00 490 60.50 -5.68 42.7 0.054 -6.8 -12.4 32b 2007 Dec. 18 11:40 520 59.00 -5.67 42.9 0.052 -8.0 -14.7 33 2008 Jan. 3 18:40 450 78.50 -5.30 43.9 0.043 1.5 2.7 34 2008 Jan. 10 16:10 435 85.33 -5.00 44.3 0.040 4.8 8.7 35 2008 Jan. 30 02:20 360 80.83 -3.72 45.2 0.035 1.4 2.6 36 2008 Feb. 9 10:00 465 57.50 -2.82 45.7 0.034 -12.4 -22.6 118 Stream interface 7 is the first instance when STEREO/B was the first observer and STEREO/A the second. It was seen in late April 2007 when the observatories' longitudinal separation was about 6°. Interfaces 9 through 36 were also dominated by the separation in longitude rather than the separation in radii. The final two columns of Table 5.1 list the difference between the expected and actual arrival longitude and time at STEREO/AHEAD. Up through the end of July 2007 the interfaces were observed within 10° (or 11 hours) of the expected Carrington longitude. After that time the difference between expected and actual time-of-arrival (and longitude-of-arrival) shows more variation, as shown in Figure 5.3. Difference between Expected and Actual Arrival Time at STEREO/A 10 i ! <[ i i'" • # o «^ '* *7 ~ > 1 "*•" 1 " TT ] * * J * • |1* *-: -* ! - ! 1 • I • # r : " • • u i t o o Differenc e -40 i ' i ; • ! '•3U ' ' ! ' 03/01/07 04/30/07 06/29/07 08/28/07 10/27/07 12/26/07 02/24/08 Motith/Day/Year Figure 5.3 Difference between expected and actual time when STEREO/A encounters each stream interface plotted against time. 119 Possible explanations for the discrepancy between expected and observed times (or longitudes) include latitude separation of the observatories, and evolution of the source regions. These will be explored in the following sections. Note that the interface arrives at STEREO/A earlier than expected in the majority of cases. Possible explanations and implications will be discussed later in the chapter. 5.2 Identification of the Solar Wind Source Regions The first step to studying the possible evolution of a source region is to identify the source. A simple approach is to use "ballistic" back-mapping. The ballistic back-mapping technique assumes the solar wind has traveled with constant speed radially outward from the solar source surface, as described by Nolte and Roelof (1973a). (The source surface is usually chosen to be a spherical shell centered about the Sun at a few solar radii.) The distance from the spacecraft to the source surface is divided by the measured solar wind speed to obtain a travel time. The Sun's equatorial angular speed is divided by the travel time to obtain the difference in longitude between the source and the observatory. This method of estimating the source longitude has been used in previous studies including Nolte and Roelof 1973a and 1973b; Neugebauer etal., 1998, and Neugebauer etal., 2002. Nolte and Roelof (1973a) found the error in the source longitude calculated using this technique is £ 10 degrees. They show that the effects of interplanetary acceleration and corotation near the Sun, which 120 would cause the biggest distortions from the assumed radial flow, tend to cancel one another. Once the source longitude has been estimated, the back-mapped in situ data can be lined up with remote images and/or magnetograms to identify the most likely source for a given stream. This technique is demonstrated in Figures 5.4 and 5.5. The top panel in Figure 5.4 is the back-mapped bulk solar wind speed corresponding to Carrington Rotation 2061 (September 2007). At this time the observatories were separated by about 30° in longitude, and by about 2 days in time. The red trace is from PLASTIC/AHEAD and the blue trace is from PLASTIC/BEHIND. Time goes from right to left in order to match the in situ data with the synoptic map in the second panel. The speed profiles match up very well. The longitudinal extents of the back-mapped high-speed streams agree between the two observatories, and the peak speeds differ by less than 80 km/s from PLASTIC/B to PLASTIC/A. 121 25 24 23 800 U*tifaLJ 2062 2061.75 2061.5 2061.25 2061 Figure 5.4 Carrington Rotation 2061. Top panel: Back-mapped in situ solar wind proton data. Middle panel: GONG modeled magnetic field and projection of spacecraft trajectories. Bottom panels: Back-mapped in situ radial magnetic field polarity. Vertical lines over all panels are back-mapped longitudes of stream interfaces. 122 The second panel in Figure 5.4 shows a synoptic plot of the modeled coronal holes obtained from the Global Oscillation Network Group (GONG) for Carrington Rotation 2061. To create this plot, a potential-field source surface model with the source surface fixed at 2.5 solar radii (RSun) is determined from hourly synoptic solar magnetograms. Purple and orange shading represent regions of open fields (i.e. coronal holes) with opposite magnetic polarity. The solid black curve is the location of the modeled heliospheric current sheet (HCS). Green lines indicate fields that are closed out to just less than 2.5 RSun. Plotted over the GONG map is a projection of the spacecraft trajectories; red for AHEAD, blue for BEHIND. In this representation the observatories travel from right to left. The bottom two panels show the back-mapped polarity of the radial magnetic field measured in situ by STEREO/IMPACT. Negative polarity corresponds to the purple (mostly northern) regions in the GONG plot, and positive polarity corresponds to the orange (mostly southern) regions. The high-speed stream with negative polarity matches up with the equatorial extension of the northern polar coronal hole, near CR 2061.35. The high-speed streams with positive polarity line up with the large equatorial extension of the southern polar coronal hole. Regions of slow solar wind and mixed polarity correspond to material from the vicinity of the current sheet - the neutral line separating the two magnetic polarities. Plotted over all the panels are vertical lines indicating the back-mapped longitudes of the stream interfaces. 123 Figure 5.5 shows the same back-mapped proton bulk speed as in Figure 5.4. The middle and bottom panels of Figure 5.5 show synoptic plots created from STEREO/SECCHI remote images at 195 A. This band is sensitive to Fe XII, or iron with a charge state of +11. The dark regions correspond to coronal holes, which have less density than the surrounding corona. The coronal holes observed by SECCHI agree fairly well with the modeled coronal holes pictured in the GONG synoptic plot in Figure 5.4. The vertical lines indicating the stream interfaces match up with the edges of the coronal holes near 270° (SI 23) and 180° (SI 24). The third interface (SI 25) near 90° is near a small extension of the south polar coronal hole. The SECCHI synoptic maps are separated by about 2.5 days in time, but qualitatively they are nearly identical. 124 800 £600 5 « 400 "5 " 200 Figure 5.5 Carrington Rotation 2061. Top panel: Back-mapped in situ solar wind proton data. Middle and Bottom panel: Synoptic maps constructed from 195 A STEREO/SECCHI images. The vertical lines over all the panels correspond to the back-mapped longitude of the stream interfaces. The nearly horizontal lines correspond to the projection of the observatory trajectories. 125 An additional step is to take the results from the ballistic back-mapping technique and extend it from the source surface to the surface of the Sun with the potential field source surface (PFSS) model. PFSS (code written by Janet Luhmann) is available as a package that can be downloaded with SolarSoft, a library of software, utilities, and databases for solar physics applications. Coronal magnetic fields are calculated by solving a boundary value problem with spherical harmonics (c.f. Jackson, Chapter 3). The fields must agree with the photospheric magnetogram at 1 RSun, and they must be radial at the source surface. The recommended source surface radius is 2.5 RSun. The model assumes no currents and satisfies VxB = 0. The stream interface at STEREO/A near 180° Carrington longitude in Figures 5.4 and 5.5 (SI 24) is estimated to have left the source surface on 24 September, 2007 at about 16:30 UT. The left-hand panel of Figure 5.6 shows a SECCHI/A 195 A image taken at about 12:00 UT on 24 September, 2007. The right-hand panel of Figure 5.6 shows the output of a PFSS simulation for the same time. (12:00 UT was the closest time to the back-mapped time for which a magnetogram was available.) The pink and green traces represent magnetic field lines of opposite polarity. The starting points are equally spaced about the heliographic equator at a radius of 2.5 RSun. The PFSS code maps them down to regions of open magnetic flux at the photosphere. The bottom panel of Figure 5.6 is an overlay of the PFSS output on the SECCHI image. The magenta field lines map to the equatorial coronal hole in the northern hemisphere with negative 126 polarity. The green field lines map to regions of positive polarity, such as the southern coronal hole extension. All the field lines originating in the ecliptic plane are mapping to the equatorial coronal holes and coronal hole extensions. This is consistent with the results from the simple ballistic technique. The PFSS results also show that a field line that is at the center of the disk at 2.5 Ro„n can be connected to longitudes and latitudes that are off-center. Figure 5.6 Top left: 195 A STEREO/SECCHI image from 12:05 UT on 24 September, 2007. Top right: Results of PFSS simulation with the source surface at 2.5 solar radii and the photospheric magnetogram from about 12:00 UT on 24 September, 2007. Bottom panel: Overlay of remote image and PFSS result. 127 _800 I 600 $400 2054.75 2054.5 2054.25 i 600 1400 1... 2056 205S.75 2055.5 2055.25 2055 aach-nnppmirf CarrlngM* Number „aoo ieoo J 400 rV\:.i....A;...... 2056.75 20S6.5 2056.25 2056 Mck-m«p»e«4 Cwninsten number #400 r '-wS*^* \,~ iftft .1 ; 2058 2057.75 2057.5 2057.25 2057 •eckineiieMe' Carrineten Numfaer £600 2059 2058.75 2058.5 2058.25 •ecfc.nwvppeee' CBrrlngtnn Number 800 2060 2059.75 2059.5 2059.25 2059 B*ck-m*tfM*d Cantnoten Nembtr 800 2060.75 2060.5 2060.25 2060 Figure 5.7 Left: Bulk speed measured in situ by STEREO/PLASTIC versus back-mapped Carrington number. The red traces are from PLASTIC/AHEAD, and the blue traces are from PLASTIC/BEHIND. Right: SECCHI/AHEAD 195 A synoptic image. 128 Figure 5.8 Left: Bulk speed measured in situ by STEREO/PLASTIC versus back-mapped Carrington number. The red traces are from PLASTIC/AHEAD, and the blue traces are from PLASTIC/BEHIND. Right: SECCHI/AHEAD 195 A synoptic image. Ballistic back-mapping of the in situ data was carried out for all the Carrington rotations presented in Chapter IV. Figures 5.7 and 5.8 show the results for the bulk solar wind speed during Carrington rotations 2054 through 129 2066. The data from Carrington Rotation 2054 (March 2007) lines up almost exactly between the two observatories. As time separation between the observations grows, the differences in the speed profiles become more noticeable. The right-hand columns of Figures 5.7 and 5.8 are the synoptic maps created from 195 A SECCHI/AHEAD observations. The top right-hand panel of Figure 5.7, CR 2054, has at least three major equatorial coronal holes. The largest is near 270° Carrington longitude (equivalent to CR No. 2054.25). There is a long, narrow hole extending roughly between 90° and 120° longitude. The third major hole is near 30° longitude, and is adjacent to an active region. These three coronal holes correspond to the three high-speed streams in the left hand panel's back-mapped in situ solar wind speed. Studying the hole centered near 270° (highlighted with the yellow boxes in Figure 5.7), it decreases in area from CR 2054 to CR 2055. The corresponding back-mapped solar wind stream in CR 2055 has a lower peak than in CR 2054. In CR 2056 the same hole has decreased further in longitudinal extent, but has developed a new equator-ward extension. An active region has also emerged adjacent to the western (right-hand) edge. The corresponding in situ data shows a narrower, but higher speed peak. From CR 2056 to 2059 the coronal hole decreases in area. The in situ data shows correspondingly narrower high-speed streams with decreasing peak speeds. By CR 2060 the hole is nearly gone from the SECCHI image, and can no longer be identified in the back-mapped in situ 130 data. Between CR 2054 and CR 2059 the center of the coronal hole has moved westward (i.e. in the same direction as solar rotation) from about 270° to about 290°. This drift is reflected by the left-to-right movement of the peaks in the back- mapped data plots. A small equatorial coronal hole emerges adjacent to an active region near 230° Carrington longitude during CR 2058. This hole is highlighted with magenta boxes in Figures 5.7 and 5.8. Between CR 2058 and 2059 the hole extends eastward (to the left). The back-mapped solar wind speed shows a corresponding wider high-speed peak. From CR 2059 to 2060 the hole shrinks in longitude and grows in latitude, apparently linking to the north polar coronal hole. During CR 2061 the connection to the north polar hole remains. The equatorial boundaries of the hole extend westward, to about 270° Carrington longitude. Similarly the back-mapped speed shows the increase in speed occurring sooner during CR 2061 than in CR 2060. The following rotation, number 2062, shows the coronal hole's area has decreased, and the shape appears to be a ring. The in situ speed profiles are different between PLASTIC/A and PLASTIC/B. PLASTIC/A shows two speed peaks, but PLASTIC/B shows just one corresponding to this coronal hole. In CR 2063 the westward (right-hand) extent of the coronal hole has grown again. PLASTIC/A again records two high-speed peaks while PLASTIC/B again sees one. The back-mapped speed profile shows an increase in speed at larger (further to the west) longitudes at STEREO/A than STEREO/B. In addition, the peak speed recorded by PLASTIC/A is higher than 131 that at PLASTIC/B by more than 100 km/s. Skylab observations showed that the peak solar wind speed is well correlated with the area of equatorial coronal holes (Nolte et al. 1976). This in turn can be modeled in terms of magnetic flux tube expansion (c.f. Wang and Sheeley 1990). The flux tubes nearest the center of a coronal hole expand the least, resulting in higher in situ measured speeds than flux tubes that originate near the coronal hole boundaries. This may explain the difference in observed in situ solar wind speeds. The area of the coronal hole decreases again between CR 2063 and CR 2064. The back-mapped speeds in CR 2064 once again agree well between the two observatories. The transition from slow to fast solar wind back-maps from both observatories in CR 2064 to the longitude from back-mapped from PLASTIC/A in CR 2063. The hole continues to shrink through CR 2065 and CR 2066. Compared to its emergence in CR 2058, the coronal hole has drifted westward (to the right) by about 30 degrees. These two examples clearly show that the coronal holes evolve over time, and that the high-speed streams reflect both changes in area and shifts in location. However, with a single observation point it is not possible to see if the changes are occurring gradually during a Carrington rotation, or with an abrupt shift. Comparing observations from STEREO/A and STEREO/B within a rotation will yield further insight into how much change can take place over the time scale of a few days. 132 The greatest discrepancies between back-mapped solar wind speeds within a single solar rotation are observed during Carrington Rotation 2063 (November 2007), when the longitude separation between the observatories was about 40°, and latitude separation was about 5°. Possible explanations for the differences in both the measured speeds and the longitudinal extent of the high speed streams include movement of the source (i.e., non-ideal corotation), evolution of the source (such as shrinking or growing surface area) which can result in a change in the radial speed at which material leaves the source (c.f. Nolte etal. 1976, Wang and Sheeley 1990), and back-mapping to different source latitudes at the Sun. According to the STEREO/IMPACT level 3 event list (available at http://www-ssc.igpp.ucla.edu/forms/stereo/stereo_level_3.html), no ICMEs were observed during CR 2063, so transient events will not be explored as a possible cause for the differences in the bulk speed measured by PLASTIC/B and PLASTIC/A. Latitude separation will be studied first, then possible movement and evolution of the source regions. Carrington rotations 2061 through 2064 will be examined in detail. They cover HCI latitude separations from less than 1 ° to more than 5° between the STEREO observatories. 5.3 The Effects of Latitude Separation Figure 5.9 is a plot of the difference between expected and actual stream interface arrival times (as calculated with Equation 5.1) versus the latitude separation between STEREO observatories. As latitude separation increases, so 133 does the spread in the data. The largest differences between the expected and actual arrival times correspond to cases where latitude separation exceeds 4°. Difference between Expected and Actual Arrival Time at STEREO/A 20 10 •! [ j * • | : • 3 " *•• •*""!•"* * r1 • O • • * * -10 j [•«• 8 : • i g-20 • "i »f • 8) £ -30 Q -40 _ , -50 1 : '; • 12 3 4 5 Difference in HC1 Latitude [degrees] Figure 5.9 Difference between expected and actual time when STEREO/A encounters each stream interface plotted against the STEREO observatories latitude separation. If a stream interface at the Sun is not vertical (i.e. oriented North-South), then the slope of the interface combined with the latitudinal separation between the observatories can result in an apparent longitudinal offset in the observations. This idea is illustrated in Figure 5.10, and was described before by Lee (2000). Leske et al. (2008) and Mason et al. (2009) note the importance of latitude separation when comparing CIR energetic particle data between the STEREO observatories. Schwenn (1990) reported 3° latitude separation as an upper limit for reliable stream interface forecasting. He used data from Helios to predict the arrival of solar wind streams at IMP 8 (near Earth). The radial separation 134 between Helios and IMP 8 was large, up to 0.7 AU. Taking his entire set of 50 cases with corotation times greater than 10 days, he found good correlation about half the time. In 9 of the 11 cases when latitude separation was less than 3° Schwenn found a good correlation between expected and actual Carrington longitude-of-arrival. U Figure 5.10 Simple illustration to demonstrate the importance of the slope of the stream interface when the two observatories are separated in latitude. Each panel shows the out-of-ecliptic plane orthogonal to the Sun-Observer line. The interface is the solid black line. The projected spacecraft trajectories are the red and blue arrows. Because the interface slope is not measured remotely, a proxy is needed to calculate the effect of latitude separation. A potential proxy is the slope of the modeled heliospheric current sheet (HCS) at the longitude where it was crossed. (The GONG consortium models the neutral line at the source surface.) As Gosling etal. (1978) noted, Sis are generally observed several hours after a current sheet crossing. This technique to correct for latitude separation was 135 tested. The following paragraphs summarize the results for a recurring high speed stream that back-maps to the coronal hole near 180° Carrington longitude (Sis no. 24, 27, 29, 32a) during rotations 2061 through 2064. Figure 5.11 GONG synoptic maps for Carrington Rotations 2061 through 2064. The tangents to the modeled neutral line are indicated in yellow and magenta. 136 Figure 5.11 shows the GONG synoptic maps for Carrington Rotations 2061 through 2064. The tangents to the points where the observatories cross the modeled neutral line are indicated in yellow and magenta as the proxies being used for the stream interface slope at the source surface. Both STEREO observatories crossed the current sheet just before encountering SI number 24 in the middle of CR 2061. The slope of the yellow line tangent to the modeled current sheet is about -1.80. The observatories were separated by 1.5° HCI latitude at this time. The extra back-mapped longitude (Acp) that would have to be covered by spacecraft B before encountering the interface is 7.3°, calculated (using Equation 5.2) following Lee (2000). Q A(p= s»n{RB-RA) + dA-eB [52] Vsw slope The actual offset in Carrington longitude is 6.6°. During CR 2062 the observatories crossed the current sheet at about 200° back-mapped Carrington longitude, just before encountering SI no. 27. The slope of the yellow modeled neutral line is approximately -1.68. The expected offset in longitude is 6.8°. The actual offset in back-mapped Carrington longitude is 18.7°, which is more than double the value calculated using equation 5.2. One Carrington rotation later (2063) the slope of the yellow line tangent to the modeled current sheet has changed such that it is less steep, about -1.00. The HCI latitude separation between the two spacecraft has increased to about 5.25°. The same calculation as above yields an expected longitude offset of 9.6°. The actual offset in back-mapped Carrington longitude for SI 29 is about 29.1 °, 137 more than three times the calculated value. The interface slope would need a magnitude of 0.21 to obtain the larger offset, which is possible. However, from CR 2061 through 2064 the slope of the modeled neutral line only varies from -1.0 to -1.82. Either latitude separation is not the only cause for the offset in back- mapped longitude, or the neutral line slope is not a good substitute for the interface slope in this case. Finally, the modeled current sheet prior to SI 32 in the middle of CR 2064 has a slope of about -1.82, similar to the slope during CR 2062, but steeper than in CR 2063. The expected offset in back-mapped Carrington longitude is 6.0°. The actual offset is 9.6°. Figure 5.11 also shows the proxy slopes for the interfaces corresponding to the northern hemisphere coronal hole. The slope shown in magenta is at the left of each synoptic map, and is applied to the interface for the following Carrington rotation. (The observatories projected trajectories go from right to left across the maps.) The slopes shown are used to calculate the expected longitude offset for Sis no. 26, 28, 31, and 33. In three of four cases, the slope required to obtain the actual offset in Carrington longitude has the opposite sign of the proxy slope. Table 5.2 lists the difference in HCI latitude between the observatories, the estimated slope for each interface from the GONG model, the expected difference in Carrington longitude between observations (calculated with equation 5.2), the actual difference in Carrington longitude between the observations, and the slope that would be required to obtain the observed offset. 138 Using the modeled neutral line as a proxy for the interface slope does not work well. A better proxy for stream interface slope might be obtained from the observed edges of the coronal holes. Figure 5.12 shows the SECCHI synoptic images for Carrington rotations 2061 through 2064. Over-plotted are vertical lines indicating the back-mapped longitudes of the stream interfaces. The solid, nearly-horizontal, lines are the projections of the observatory trajectories. The dotted lines indicate tangents to the western edges of the coronal holes (and coronal hole extensions) nearest to the back-mapped interface longitude. The slope can vary significantly depending on where the tangent line is drawn. For example, the dotted magenta line in CR 2061 (corresponding to SI 23) is drawn tangent to a small westward (to the right) extension of the main coronal hole. If the slope had been chosen as a tangent to the larger central region of the coronal hole, then the slope would be of the opposite sign. Like the proxies obtained with the modeled neutral line, some of the slopes shown in Figure 5.12 have the opposite sign from what is required to obtain the observed difference in Carrington longitude. These include the slopes corresponding to SI no. 28, 30, and 31, or 3 cases out of 11. This is better than using the modeled neutral line's slope, but it is still not reliable. 139 UmgHudw fD#g.,l CR 2062, East Unto. 1.0 Rsun EIWI A 1»S Lotvaltud* IDea.l CR 2063, East llmo. 1.0 Rsun EWIA19S iotMKude flO*a.l CR 2064. East liffiix 1.0 Rsun J Figure 5.12 SECCHI synoptic maps for Carrington Rotations 2061 through 2064. Tangents to the coronal hole boundaries near the back-mapped stream interface longitudes are indicated with dotted lines. 140 BLE 5.2 Interface Slope Expected Slope Observed Offset needed to Difference in AHCI Lat. Estimated calculated agree with SI Carrington [deg.] Slope with latitude back- Longitude and slope mapped [degrees] [degrees] offset 1a -0.07 2.00 2.57 2.82 -0.34 1b -0.06 2.00 2.19 3.24 -0.06 2a 0.00 -0.53 2.81 3.88 0.00 2b 0.01 -0.53 2.17 2.32 0.07 3 0.18 -0.54 3.37 6.97 0.05 4 0.29 1.57 3.81 3.83 1.46 5 0.43 -0.39 4.13 5.17 -8.02 6a 0.72 -0.39 3.37 6.59 0.50 6b 0.73 -0.39 3.15 6.23 0.58 8 1.08 -1.29 4.32 7.15 0.54 7 0.83 1.60 4.50 5.18 0.70 9 1.36 -0.78 4.51 4.24 -0.68 10 1.75 -0.42 2.38 10.02 0.51 11 2.12 2.14 7.62 12.53 0.36 12 2.20 -0.57 3.23 6.44 -2.90 13 2.23 0.83 8.57 6.39 3.94 14 2.23 -1.45 6.45 10.04 1.14 15 2.22 -1.45 5.28 8.54 1.36 16 2.16 1.44 10.03 8.04 -4.97 17a 2.05 -0.95 6.12 12.51 0.50 17b 1.99 1.05 9.04 19.14 0.17 18 1.77 -1.33 8.37 8.64 -1.66 19 1.40 0.82 8.52 14.98 0.17 20 0.93 -1.36 6.99 3.64 -0.23 21 0.52 -1.71 8.54 13.89 0.10 22 -0.41 1.40 7.66 20.63 -0.04 23 -0.83 1.40 5.94 7.07 -2.14 24 -1.36 -1.80 7.33 6.60 -12.48 25 -1.87 -1.80 6.09 18.45 -0.15 1 MB 1 — $sm 27 -3.57 -1.67 •6.7I4 18.68 -0.26 H — If Hi nm 1 29 -5.14 -1.00 9.66 29.10 -0.21 30 -5.30 -1.00 8.92 18.10 -0.38 H — 11 mm i MM1 32a -5.68 -1.82 6.01 9.58 -0.87 32b -5.67 -1.82 5.78 10.54 -0.74 H — 1 HI MB BHl 34 -5.00 -2.33 4.55 -2.46 1.10 35 -3.72 0.93 -1.71 0.96 2.65 36 -2.82 -2.20 3.09 14.17 -0.23 141 In summary, the combination of latitude separation and interface slope can explain some, but not all, of the discrepancies between the expected and observed stream interface locations. Two proxies for stream interface slope were used in an attempt to calculate quantitatively the offset expected due to the difference in HCI latitude between the observatories. Neither the slope of the modeled neutral line nor the edge of the observed coronal hole worked reliably, though the slopes obtained from the coronal hole observations could vary substantially depending on what point of the hole was chosen for drawing the tangent line. PFSS models have shown, like in Figure 5.6, that the solar wind source regions are often at different heliographic latitudes than the observatories themselves. This is further supported by the stream interfaces that back-map to about 110° Carrington longitude in Figure 5.12. Both observatories record high speed streams from this extension of the south polar coronal hole, even though the projected spacecraft trajectories do not fall within the hole's observed boundaries. Three-dimensional solar wind velocity vectors and/or custom runs of PFSS are really needed to obtain a realistic estimate of the stream interface slope for cases such as this. 5.4 The Effects of Time Separation Figures 5.4 and 5.5 show the back-mapped in situ data and the remote observations for Carrington Rotation 2061. In CR 2061 the velocity profile for the middle peak, corresponding to the southern coronal hole and SI no. 24, is very 142 similar between spacecraft A and spacecraft B. Stream interface no. 24 was back-mapped to 195° Carrington longitude from STEREO/AHEAD, and to 190° from STEREO/BEHIND. The interface was observed shortly after a region of mixed polarity indicating current sheet material. There is reasonable agreement between the back-mapped current sheet crossing longitude of about 200° Carrington longitude, and the predicted longitude from the GONG modeled current sheet. The SECCHI synoptic images show coronal holes with the same locations and boundaries as the GONG model indicates. There are no obvious differences between the SECCHI/A and SECCHI/B images. The HCI latitudinal separation of the two spacecraft in this case was 1.5 degrees. In Figure 5.13 (CR 2062) the difference between the STEREO/A and STEREO/B back-mapped longitudes of SI no. 27 (the recurrence of SI no. 24) has increased to about 8°. As mentioned earlier, the high-speed observed by STEREO/A back-maps to a larger range of Carrington longitudes than from STEREO/B. The latitude separation between the spacecraft is 3.7°. Figure 5.14 shows the 195 A observations from SECCHI at the times corresponding to the stream interface departing the source surface (based on ballistic back-mapping) during CR 2062. The images have been scaled so that the apparent disk size is the same for both observatories. A qualitative comparison of the images from STEREO/B and STEREO/A show the boundaries of the coronal hole do not appear to change substantially in the 2 days between SECCHI/B and SECCHI/A observations. 143 Figure 5.13 Same as Figure 5.4, but for CR 2062. 144 Figure 5.14 SECCHI 195 A images. Left: BEHIND. 2007/10/21 07:47 UT. Right: AHEAD. 2007/10/23 03:56 UT. Figure 5.15 shows the back-mapped bulk speed, the GONG modeled coronal holes, and the back-mapped radial magnetic field polarity for Carrington Rotation 2063. Vertical lines indicate the back-mapped longitude of the stream interfaces. The projection of the spacecraft trajectories on the GONG map shows they are very near to the modeled neutral line. Mixed magnetic field polarity is observed for much of the Carrington rotation, indicating the in situ instruments are sampling plasma from the heliospheric current sheet (HCS), which is the interplanetary extension of the neutral line at the Sun. 145 110 f| {stereo) +1 I 2064 2063.75 2063.5 2063.25 2063 Figure 5.15 Same as Figure 5.4, but for CR 2063. 146 2007/12/03 06:49:01 Figure 5.16 Same as Figure 5.5, but for CR 2063. Figure 5.16 shows the back-mapped solar wind speed and the SECCHI 195 A synoptic maps. The vertical lines marking the back-mapped stream interfaces do lie near the edges of the coronal holes. A qualitative comparison of the SECCHI images does not show a striking change in the coronal hole 147 boundaries. However, the time at which a strip of the synoptic image was taken does not necessarily agree with the time obtained from ballistic back-mapping. For a more careful comparison the full-disk SECCHI images of the coronal holes are shown in Figure 5.17. The top row is the hole near 270° longitude (SI 28). The middle row shows the coronal hole near 180° Carrington longitude (SI 29). The bottom row shows the coronal hole extension near 130° Carrington longitude (SI 30). The images from A and B have been scaled so that the apparent disk size is the same. The images from SECCHI/B in the left-hand column correspond to the back-mapped stream interface time. The center and right- hand columns contain images from SECCHI/A. The center column images correspond to the back-mapped stream interface time from STEREO/A. The right-hand column images from SECCHI/A were chosen to match the view of the coronal hole from STEREO/B. The coronal hole near 270° does not show any signs of dramatic evolution in the three images across the top row of Figure 5.17, though the Carrington longitude to which the stream interface back-maps is obviously different between the two observatories. The SECCHI/B image shows the coronal hole near disk center. In the central image (from SECCHI/A) the coronal hole is closer to the Sun's East limb. The bottom row of images from CR 2063 picture the extension of the southern polar coronal hole near 130° longitude. All three images show the narrow extension is near disk center, and there are no obvious signs of evolution. 148 Figure 5.17 SECCHI 195 A full-disk images of the coronal holes adjacent to the stream interfaces during CR 2063. The left hand column images are from SECCHI/B, and the center and right-hand column images are from SECCHI/A. The images have been scaled so that the apparent disk size is the same for both AHEAD and BEHIND images. The left and center column images correspond to the back-mapped stream interface times at the source surface. The times for the right-hand images were chosen to give a similar view of the coronal hole from both observatories. 149 The coronal hole near 180° longitude, and corresponding to SI no. 29, does show apparent evolution. In the time between the SECCHI/B and SECCHI/A images an active region emerges, and the northernmost extension of the coronal hole disappears. This area is hi-lighted with a yellow box in all three images. Figure 5.18 shows that in Carrington rotation 2064 the back-mapped high speed streams have better agreement between the two observatories than in CR 2063. Interface no. 32a, the recurrence of no. 29, maps to about 195° Carrington longitude from both A and B. This is the same longitude as the mapping from A the previous rotation. The GONG synoptic map shows that the boundary of the modeled coronal hole has moved to the right, i.e. in the direction of solar rotation, by about 15° since CR 2063. Figure 5.20 shows SECCHI/A and SECCHI/B full- disk 195 A images for the coronal hole associated with SI 29 and 32a. The two images from CR 2064 in the bottom row look very similar to each other, but they are clearly different from the previous solar rotation images in the top row. The northernmost portion of the coronal hole has sheared westward (to the right) compared to the SECCHI/B image from CR 2063. This is consistent with the GONG model, and with the back-mapped solar wind speeds. 150 32b 32a 31 800 Figure 5.18 Same as Figure 5.4, but for CR 2064. 151 Figure 5.19 SECCH1195 A full-disk images of the coronal hole associated with SI numbers 29 (CR 2063, top) and 32a (CR 2064, bottom). In summary, we find that the source region does change in the days between observations for our example with the largest discrepancy between expected and actual arrival at STEREO/AHEAD, SI 29. However, latitude separation is almost certainly the cause of the different in situ speeds measured during Carrington rotations 2062 and 2063, particularly for the cases when there was no apparent change in the source, such as SI 28. One more example is now presented in order to better distinguish between the effects of latitude and separation and source evolution. 152 5.5 Additional Discussion: Carrington Rotation 2066 During Carrington Rotation 2066 (February 2008) the radial magnetic polarities line up fairly well between the two spacecraft, as shown in the bottom two panels of Figure 5.20. The HCI latitude separation between the spacecraft decreased from 3.5° to 1.5°, and the modeled current sheet was not between the observatories. Even so, the profile of the high-speed stream following SI no. 35 (near CR no. 2066.15) is obviously different between the two spacecraft. SI number 36 in the middle of the Carrington rotation also arrives at STEREO/A more than 22 hours earlier than expected. With such a small difference in latitude, evolution of the source between the two observations seems to be the most likely cause. This is supported by the SECCHI synoptic images in Figure 5.21. The coronal hole near 270° longitude decreases in area between the observations by SECCHI/B and the observations by SECCHI/A. The western (right-hand) boundary Also, the northernmost extension of the southern coronal hole, near longitude 190° moves a few degrees westward between the SECCHI/B and SECCHI/A images. 153 36 35 800 Figure 5.20 Same as Figure 5.4, but for Carrington Rotation 2066. 154 800 200 CR 2066, East limb, 1.0 Rsun EUVI B 19S 200B/01/23 1*44:06 CR 2065, tast limb, 1.0 Rsun EUVI A 19& Figure 5.21 Back-mapped in situ bulk speed and SECCH1195 A synoptic images for Carrington Rotation 2066. 5.6 Fast-to-Slow Transitions Thirty-five fast to slow solar wind transitions were presented in Chapter IV. Based on the order-of-arrival, longitudinal separation was more important than radial separation for slow-to-fast stream interfaces beginning in May 2007, when 155 longitude separation between STEREO/A and STEREO/B was about 7°. The fast-to-slow solar wind transitions were dominated by radial separation for another three months, until July 2007, when the longitudinal separation between the STEREO observatories was more than 14°. This is consistent with tighter winding of the Parker spiral expected with slower solar wind speeds. The longitude and time at which a spacecraft is expected to encounter a fast-to-slow transition can be calculated in the same way as the stream interface (Equation 5.1), assuming ideal corotation and negligible source evolution. The results are plotted versus time in Figure 5.22, and listed in Table 5.3. The average difference between the expected and observed arrival longitudes is about -5°, or about 9 hours early arrival. This would be equivalent to a small non- radial velocity component in the ecliptic plane. Fast-to-Slow Transitions ! - •- "! ! 1 ! • • • **i •• • . •• • • i -io ••••'• r* • ••- ^—4-i— i • • ! : ! ! 03/01/2007 04/30/2007 06/29/2007 08/28/2007 10/27/2007 12/26/2007 02/24/2008 Month/IMy/Yosr Figure 5.22 Difference between expected and actual time at which spacecraft A encounters the fast-to-slow interface versus time. 156 TAB LE 5.3 Fast-to-Slow Transitions Exp.- Time V_sw AHCI Obs. Interface Arrival from B AR No. atB Lat. Arrival time at B [UT] to A [AU] Time at A [km/s] [deg.] II I [hours] [hours] 1 03/08/2007 12:35 505 -2.08 -0.04 1.5 0.041 -1.5 2 03/17/2007 17:30 540 -7.67 0.06 1.7 0.047 -7.2 3 03/28/2007 22:00 460 -9.00 0.21 2.4 0.056 -8.5 4 04/05/2007 11:00 400 -6.00 0.34 3.1 0.062 -5.0 5 04/13/2007 12:30 405 -4.00 0.50 4.0 0.068 -4.0 6 04/23/2007 20:30 440 -2.00 0.73 5.1 0.077 -3.5 7 05/02/2007 21:30 355 -7.50 0.93 5.9 0.084 -8.0 8 05/10/2007 19:00 435 -5.50 1.14 7.1 0.090 -9.5 9 05/21/2007 19:00 495 -9.00 1.40 8.5 0.099 -16.0 10 06/06/2007 16:00 355 -2.00 1.83 11.3 0.110 -9.0 11 06/26/2007 00:30 390 -20.17 2.07 14.0 0.120 -33.7 12 07/01/2007 00:00 495 9.50 2.26 16.3 0.122 -8.5 13 07/05/2007 21:00 450 12.50 2.29 17.4 0.124 -5.5 14 07/12/2007 18:00 490 16.00 2.29 18.9 0.126 -5.5 15 07/15/2007 13:30 550 8.50 2.24 19.2 0.127 -15.5 16 07/23/2007 21:30 385 19.50 2.16 21.4 0.128 0.0 17 08/03/2007 13:00 440 17.00 1.89 23.5 0.129 -11.0 18 08/08/2007 20:00 445 25.00 1.71 25.0 0.129 -5.5 19 08/20/2007 23:00 310 23.00 1.15 27.4 0.127 -6.5 20 08/29/2007 21:00 445 37.00 0.61 29.8 0.125 -2.0 21 09/05/2007 10:00 450 30.50 0.18 30.8 0.122 -11.0 22 09/16/2007 15:30 355 20.83 -0.63 32.5 0.118 -23.7 23 09/25/2007 17:00 440 41.50 -1.44 35.4 0.113 -7.5 24 09/30/2007 08:30 515 52.00 -1.84 36.2 0.110 -0.5 25 10/04/2007 15:00 440 28.50 -2.10 35.9 0.107 -23.5 26 10/22/2007 15:00 390 51.50 -3.66 39.5 0.095 -5.5 27 10/27/2007 01:00 495 56.50 -4.01 40.3 0.091 -4.5 28 11/16/2007 01:00 480 61.00 -5.28 42.8 0.076 -5.0 29 11/22/2007 14:00 450 57.00 -5.54 43.2 0.071 -10.0 30 11/25/2007 17:30 520 57.50 -5.66 43.5 0.068 -11.5 31 12/11/2007 23:00 530 68.00 -6.01 45.3 0.057 -4.5 32 12/23/2007 01:00 610 50.00 -5.83 45.3 0.050 -25.0 33 01/09/200811:00 440 41.00 -5.19 46.0 0.041 -35.5 34 01/19/200817:30 545 82.00 -4.65 48.3 0.037 3.5 35 02/03/2008 17:00 500 96.50 -3.40 49.6 0.034 16.5 Figure 5.23 shows the back-mapped locations of the fast-to-slow transitions during Carrington rotation 2061 (no. 23, 24, 25) plotted over the SECCHI/A synoptic image. Fast-to-slow transition 23 is near the eastern (left) boundary of the northern hemisphere coronal hole, as expected. The other fast- 157 to-slow transitions are east (left) of the equator-ward extensions of the southern polar coronal hole. CR 2061, East limt^ 1.0 Rsun EWI A IS 2007/09/12 0*01:09 Figure 5.23 SECCHI synoptic image for CR 2061. Dotted vertical lines indicate back-mapped longitudes of fast-to-slow transitions. 158 CHAPTER VI CONCLUSIONS In this study forty-one stream interfaces and thirty-five fast-to-slow solar wind transitions were studied. They were observed in situ with the STEREO/PLASTIC experiment between March 2007 and February 2008, which included Carrington rotations 2054 through 2066. During this time the STEREO observatories separated in longitude from 2° to 45°, which corresponds to time separations ranging from minutes to about three days. After a stream interface (or fast-to-slow transition) was observed by PLASTIC/B, its expected time- and location-of-arrival at STEREO/A was predicted assuming ideal corotation and negligible source evolution. Ballistic back-mapping was used to identify the sources of the observed high-speed streams. Evolution of the observed coronal holes was compared to changes in the streams measured in situ. Below are the main results of this study. First, changes in the in situ solar wind speed from one Carrington rotation to the next are clearly correlated with changes in coronal holes. New high-speed streams are observed in situ when new coronal holes appear in the remote observations. When the longitudinal extent of an existing hole expands or contracts, this is reflected in the back-mapped longitude covered by the in situ stream. When the area of a hole changes, so does the peak speed observed by 159 STEREO/PLASTIC. These results are consistent with previous studies, such as Nolteefa/. 1976. Several high-speed streams (and their associated coronal holes) were observed that gradually drifted from east to west, (the direction of solar rotation). The movement during a single Carrington rotation is on the order a few degrees, which is not striking, but over the course of 5 or more solar rotations this adds up to a shift of tens of degrees. Zhao, Hoeksema, and Scherrer (1999) reported on a large, boot-shaped coronal hole observed during the Whole Sun Month of 1996. They observed a rotation rate consistent with a drift of 5° with respect to the equatorial photosphere during one Carrington rotation. Heliographic latitude separation between the STEREO observatories was found to be significant. A latitude difference of 5° was enough to result in obviously different in situ solar wind stream profiles. The back-mapped locations of the solar wind stream interfaces did not agree, and the predicted arrival times were off by more than three days in some cases. However, latitude separation does not always result in substantially different in situ solar wind measurements. In December 2007 and January 2008 (Carrington Rotations 2064 and 2065) latitude separation exceeded 5°, and there was good agreement between the back-mapped speed profiles from the high-speed stream associated with the northern hemisphere coronal hole. This disagrees with Schwenn (1990), who said "...two spacecraft traveling there at more than about 5° latitudinal separation have almost no chance of observing similar structures." 160 Attempts to compensate for latitude separation using two different proxies for stream interface slope (modeled neutral lines and the edges of coronal holes) were unsuccessful. Temporal evolution started becoming noticeable when the longitude separation between the STEREO observatories exceeded 20°. Coronal hole evolution over the scale of a few days was enough to cause a stream interface to arrive nearly two days ahead of the predicted time, even though latitude separation at the time was less than 3°. Coronal hole evolution taking place over days or even hours has been previously reported (c.f. Nolte et al. 1978, Kahler and Moses 1990), but the prompt in situ response has not. Slow-to-fast solar wind transitions were the primary focus of this study, but the transitions from fast to slow solar wind were also identified. Compared to an ideal Parker spiral the fast-to-slow transitions were encountered on average 5° Carrington longitude earlier than expected at STEREO/AHEAD, which corresponds to nine hours early in time. Ballistic back-mapping of the fast-to- slow transitions showed their source longitudes were west of the equatorial coronal holes and coronal hole extensions, as expected. 32 of 41 stream interfaces and 33 of 35 fast-to-slow transitions arrived earlier than expected at STEREO/AHEAD. This result is important to forecasting the arrival of compression regions and high-speed streams at Earth, which are known to cause recurrent geomagnetic storms. 161 APPENDIX A EFFICIENCY AND INTERCALIBRATION A.1 Rate Definitions There are three basic efficiencies that are combined to estimate the PLASTIC solar wind sectors' total efficiencies for detecting doubly coincident solar wind ions. A.1.1 Double Coincidence "Stop" Efficiency: SFR/SF The ratio of the start-stop coincidence rate ("start flag reset" (SFR)) to the start rate ("start flag" (SF)) is effected by the active area, gain, and voltage of the Micro-Channel Plates (MCPs); and by signal threshold and scattering. In Figure A.1 the pre punch PLASTIC/B Solar Wind Sector (SWS) double coincidence stop efficiency is shown for protons at several beam energies and post-acceleration voltages (PACs). The SFRO/SFO ratio increases with MCP voltage until it levels off around 2900 V. (The "0" following the rate name "SFR" indicates it is from TAC board 0.) The 2 keV proton beam data was collected just a few days after PLASTIC/B was installed in the vacuum chamber at University of Bern, and has a higher than expected double coincidence stop efficiency. Had the 2 keV beam test been repeated later, it is likely the stop efficiency curve would nearly agree with the 1 keV proton beam curves. 162 FM2: Bern H* SFRD/SFO versus MCP i 1.0 • 2 keV beam + 18 kV PAC (050617) I 0.9 -2 keV beam + 18 kV PAC (050618) : 0.8 - 60 keV beam + 20 kV PAC (050624) 7 i °- 1 keV beam + 15 kV PAC (050624) 0.6 -1 keV beam + 18 kV PAC (050624) ! £ 1 keV beam + 20 kV PAC (050624) i S°-s i % o.< i 0.3 i °-2 i al I 0.0 , 2000 2300 2600 2900 3200 3500 I MCPIV] | Figure A.1 PLASTIC/B SWS proton stop efficiency. A.1.2 "Start" Efficiency: SF/(incident ion frequency) = SF/(active area * frequency/cm2) A beam scanner was used to estimate the frequency per square centimeter of the incoming test beams. The rate of ions incident on the time-of- flight (TOF) chamber was estimated by multiplying the average frequency per square centimeter value by the active area of the entrance system (i.e. the electrostatic analyzer). The active areas were measured to be 0.897 cm2 for the main channel of PLASTIC/A, and 0.755 cm2 for PLASTIC/B (Karrer, 2005). Dividing the start rate (SF) by the incident ion rate gives the start efficiency. Similar to the stop efficiency, the start efficiency plotted in Figure A.2 shows an increase with MCP voltage and then a plateau. The start efficiency levels out around 2700 V, which is less than the voltage required for maximum stop efficiency. (Because beam scans were not available for all files in this document, start efficiency is not always included.) 163 FM2: BernH* Start Efficiency versus MCP 1,0 i..._. . . <-2keVbeam + 18 kv 0.9 PAC (050617) »~2 keV beam + 18 kv 0.3 PAC (050618) •-60 keV beam + 2i I a, PAC (050624) 1 keV beam + 15 I PAC (050624) -1 keV beam + 18 | 0.6 PAC (050624) go.5 - 1 keV beam + 20 PAC (050624) i 0.2 • i 0.1 : o.o | 2000 2300 2600 2900 3200 3500 j j MCP [VI I Figure A.2 PLASTIC/B SWS proton start efficiency. A.1.3 "Single Position" Efficiency: (S E NOT REQ-S NO POS- S MULT POS)/SFR The number of counts registered at a single position divided by the start-stop coincidence rate is the "single position" effieciency. "S_E_NOT_REQ" indicates than an energy measurement is not required for an event to be counted, though it does require both a start (SF) and start-stop coincidence (SFR). "S_NO_POS" is an event that registered without a position indication, while "S_MULT_POS" is an event that triggered multiple position responses. (The position rates do not require SFR.) The single position efficiency is particularly susceptible to changes in the MCP voltage, as cross-talk between the pixels will cause multiple position triggers for the same event. Figure A.3 shows the single position efficiency rises to nearly 1.0, and then drops off as multiple position triggers increase at the higher MCP settings. 164 FM2: BernH' Single Position Efficiency versus MCP - 2 keV beam + 18 kV PAC (050617) - 2 keV beam + 18 kV PAC (050618) - 60 keV beam + 20 kV PAC (0S0624) -1 keV beam + 15 kV PAC (050624) fi 0.2 -1 keV beam + 18 KV PAC (050624) Bl'O.l -1 keV beam + 20 kV PAC (050624) o.o 2000 2300 2600 MCP [VI Figure A.3 PLASTIC/B SWS proton single position efficiency. A.1.4 "Total" Efficiency: Stop * Start * Single Position Taking the product of the above three efficiencies gives the total efficiency for a double coincidence event recorded at a single position. This value is plotted versus MCP voltage in Figure A.4. 165 FM2: BeraH* Total Efficiency versus MCP 1.0 -*- 2 keV beam + 18 kV PAC (050617) 0.9 -»- 2 keV beam + 18 kV PAC (050618) -*- 60 keV beam + 20 kV PAC (050624) E - 0.7 c •-»- 1 keV beam + 15 kV PAC (050624) o S £ 0.6 — 1 keV beam + 18 kV PAC (QS0624) •fO.5 -» 1 keV beam + 20 kV PAC (050624) t t 0.4 i » J0.3 2 0.2 MCI»[V] Figure A.4 PLASTIC/B SWS Total efficiency for doubly coincident protons registering at a single position. An optimal MCP voltage setting would maximize the three separate efficiencies, but such a setting does not necessarily exist. Thus, a voltage is chosen that maximizes the total efficiency. Once the MCP voltage has been selected, the total efficiency can be plotted against total energy (beam energy plus post acceleration). Efficiency estimates for a range of energies can then be obtained by fitting a curve to the plot. Separate curves must be obtained for hydrogen (protons), light ions (such as helium), and heavier ions (such as argon and neon). A.2 Changes Over Time Another important issue must be considered: the response of the MCPs varies with time. The plots in section A.1 were created from data acquired at the test facility at the University of Bern in June 2005. Figure A.5 shows the 166 efficiency curves from testing at UNH in 2005 agrees with the curve from Bern 2005. The stop efficiency curve for testing at UNH in 2006 shows a change in instrument response. For example, the efficiency for an MCP voltage of 2600 V at Bern in 2005 would require setting the MCP voltage to more than 3000 volts at UNH the following year during the final calibration tests. FM2 Quadrant O: Stop Efficiency Final Testing at UNH i 1.00 - 2006 May, UNH (Post-Bern): 2 keV beam + 18 kV PAC i 0.90 i 0.80 — 2005 June, Bern: 2 keV H+ beam + 18 kV PAC ; 0.70 »- 2005 June, UNH (Pre-Bem): 2 keV beam + 18 kV PAC ;oo.« to i o oso ; o: : u. • w O.AO ^ \ 0.30 I 0.20 ; 0.10 : o.oo ! 2000 2200 2400 2600 2800 3000 3200 3400 MCP[VJ | Figure A.5 PLASTIC/B stop efficiency from Bern 2005 calibration, and UNH calibration in 2005 and 2006. Taking the most-recent calibration curve, the best MCP voltage setting is at least 3100 volts. (No significantly higher voltages were tested.) The in-flight MCP voltage is about 3000 V. Because the stop efficiency at 3000 V at the final UNH test is about the same as the stop efficiency at 2650 V at Bern, the stop, start and single position data from the Bern tests at 2650 V will be used to estimate the total efficiency. 167 FM2: H+ Bern, MCP ~ 2650 V (equivalent to ~ 3100 V at UNH summer 2006) SFR0/SF0 versus Total Energy Figure A.6 PLASTIC/B SWS proton stop efficiency. FM2: H* Bern, MCP ~ 2650 V (equivalent to ~ 3100 V at UNH summer 2006} Start Efficiency versus Total Energy Figure A.7 PLASTIC/B SWS proton start efficiency. 168 FM2-. H+ Bern, MCP ~ 2650 V (equivalent to ~ 3100 V at UNH summer 2006) Single Position Efficiency versus Total Energy 40 50 Beam + PAC [kV] Figure A.8 PLASTIC/B SWS proton single position efficiency. FM2: H* Bern, MCP ~ 2650 V (equivalent to ~ 3100 V at UNH summer 2006} Total Efficiency versus Total Energy 40 50 Beam + PAC [kV] Figure A.9 PLASTIC/B FM2 SWS proton single position total efficiency. 169 A.3 Noise Figure A. 10 shows the time of flight spectra for the files used to generate the total efficiency estimates. There is a small noise peak around channel 21. This accounts for 1% or less of the total counts for each file. FM2: Bern H\ MCP ~ 2650 V -— 1 keV beam + 15 kV PAC 1 (050624-1658) — 1 keV beam + 18 kV PAC (0S0624-1938) — 2 keV beam + 18 kV PAC il (050617-1609) 2 keV beam + 18 kV PAC i\ (050618-0651) — 1 keV beam + 20 kV PAC (050624-2003) - 60 keV beam + 20 kV PAC j! ; (050624-1413) | j\^ 400 600 Tim* at Flight Chaftn«l Figure A.10 PLASTIC/B SWS Time of Flight Spectra for protons at most likely MCP setting. A.4 Azimuth Response Examining the total efficiency across the solar wind sector (Figure A.11) shows a drop near the center of the section (azimuth angle = 0°). There is a spoke that supports the carbon foil at this location, and it scatters the incoming beam. This results in a decrease in the single position efficiency at that particular position. 170 FM2: Bern H* (MCP ~ 3000 V} Single Position Total Efficiency versus Azimuth Angle 0.9 - 2 keV beam + 18 kV PAC (050617-1808) ! 0.8 -60 keV beam + 18 kV PAC (050624-1449) ; 0.7 ! 0.6 « 0.4 Azimuth Angle [degrees] Figure A.11 PLASTIC/B SWS proton single position efficiency plotted over the possible range of azimuth angles. A.5 Triple Coincidence Proton Efficiency "Triple Coincidence" Efficiency: S E REQ/SFR Another rate of interest is the "triple coincidence efficiency." This is similar to the stop efficiency, except that in addition to SFR and SF it requires a single energy measurement. This depends on the solid state detector threshold and the pulse height defect for protons in that detector. Multiple energy events and events with no energy measurement are excluded. 171 FM2: BOTH* Triple Coincidence Efficiency versus MCP 1.0 i 0.9 —~ 2 keV beam + 18 kV PAC (050617) -*- 2 keV beam + 18 kV PAC (050618) 0.8 -*- 60 keV beam + 20 kV PAC (050624) 0.7 1 1 keV beam + 15 kV PAC (050624) -*-1 keV beam + 18 kV PAC (050624) •••»•• 1 keV beam + 20 kV PAC (050624) !- MCP £V] Figure A.12 PLASTIC/B SWS proton triple coincidence stop efficiency. FM2: H* Bern, MCP ~ 2650 V {equivalent to ~ 3100 V at UNH summer 2006) Triple Coincidence Efficiency versus Total Energy Figure A.13 PLASTIC/B SWS proton triple coincidence stop efficiency. 172 A.6 Additional PLASTIC/A Efficiency Considerations The procedure for determining the efficiency curves for PLASTIC/A is generally the same as for PLASTIC/B. However, the SF and SFR thresholds were decreased following calibration testing at Bern. This means some additional scaling of the efficiencies (obtained from Bern testing) is required. The absolute flux was not measured for the UNH test beams, so while stop, single position, stop * single position , and triple coincidence efficiencies can be compared between the test locations, start efficiencies can not. FMl: SFRO/SFO versus MCP Voltage: | Before and After Threihold Change I 1.0 --*- Bern: 2 keV H+ beam + 20 kV PAC (041220) i 0.9 ••*-•-Bern: 10 keVH+beam + 20 kV PAC (041221) -*- Bern: 20 keV H+ beam + 20 kV PAC (041221) I 0,8 -*- Bern: 60 keV H-t- beam + 20 kV PAC (041221) j 0,7 •- UNH: 2 keV H+ beam + 15 kV PAC (0S0418) -*- UNH: 20 keV H+ beam + 18 kV PAC (050601) ; 0.6 : 8 ; »> • iQS ! ft 0.+ f , - • " - ; °-3 ; 0.2 [ [ .' ! .1^ / /'" I 0-1 i o.o i 2000 2300 2600 2900 3200 3500 j MCP m 1 Figure A.14 PLASTIC/A stop efficiency before and after threshold change. 173 FM1: Single Position Efficiency versus MCP Voltage: Before and After Threshold Change HCP [V] Figure A.15 PLASTIC/A single position efficiency before and after threshold change. FM1: SFRO/SFO • Single Position Efficiency versus MCP Voltage: Before and After Threshold Change -*•-. Bern. 2 keV H+ beam + 20 kV PAC (041220) -»- Bern: 10 keV H+ beam + 20 kV PAC (041221) -«- Bern: 20 keV H+ beam + 20 kV PAC (041221) 0 7 -«- Bern: 60 keV H+ beam + 20 kV PAC (041221) I - ,.„,.. UNH. 2 keV H+ beam + 15 kV PAC (050418) *0.6 -*- UNH: 20 keV H+ beam + 18 kV PAC (050601) 1 "> 0,5 $0.3 0.2 JT /' —_^r- 2600 2900 MCP[V] Figure A.16 PLASTIC/A stop*single position efficiency before and after threshold change. 174 FM1: Triple Coincidence Efficiency versus MCP Voltage: Before and After Threshold Change 0.9 - Bern: 2 keV H+ beam + 20 kV PAC (041220) - Bern: 10 keV H+ beam + 20 kV PAC (041221) 0.8 - Bern: 20 keV H+ beam + 20 kV PAC (041221) - Bern: 60 keV H+ beam + 20 kV PAC (041221) 0.7 UNH; 2 keV H+ beam + IS kV PAC (050418) |« - UNH: 20 keV H+ beam + 18 kV PAC (050601) O* go.s -! in 0.4 Figure A.17 PLASTIC/A triple coincidence stop efficiency before and after threshold change. The threshold setting at Bern was high, so a high MCP voltage was necessary to get appreciable counts (above the threshold). This is similar to operating at a low MCP voltage with a low threshold. In other words, more particles exceed the threshold as MCP voltage increases. Assuming the relationship between valid counts and change in MCP voltage is similar no matter what the threshold value, the Bern data that requires valid events can simply be shifted to lower MCP settings until it matches up with the data taken after the threshold change. For example, if the Bern stop efficiency curves in Figure A. 14 are shifted to the left by 400 V, then they are in good agreement with the post- Bern data. Unlike PLASTIC/B, where the micro-channel plate's response changed over time, the change in threshold should not affect the position rates (S_NO_POS and S_MULT_POS) because they do not require SFR. Shifting the 175 PLASTIC/A single position efficiency curve does not make sense. Instead, it is simply assumed that in the region of interest the single position efficiency is equal to 1 (based on the post-threshold change single position efficiency curves). The total efficiency curves can now be recalculated with the assumption that post- Bern start efficiencies follow the same trends as the values from Bern (with the MCP shift). FM1: SFRO/SFO versus MCP Voltage -- Adjusted Subtracted 400 V from Barn MCP totting. •*- Bern: 2 keV H+ beam + 20 IcV PAC (041220) • - Bern: 10 keV H+ beam + 20 kV PAC (041221) -*- Sam: 20 keV H+ beam + 20 kV PAC (041221) -*-Bern: 60 keV H+ beam + 20 kV PAC (041221) •-*•• UNH: 2 keV H+ beam + 15 kV PAC (050418) ~*~UNH: 20 keV H+ beam + 18 kV PAC (050601) - y - 0.3 0.2 J/ 0.1 /.j^/.,„ 2600 2900 MCP [V] Figure A.18 Revised PLASTIC/A stop efficiency. 176 FMl: Start Efficiency versus MCP Voltage -- Adjusted * V from Bern MC* fetUng, and aaauraed poat-Eern amctattetet hava saifta profile as Seen K -*- Bern: 2 keV H+ beam + 20 kV ••» • Bernr lOTceV H+ beam + 20 kV -BernriOlceV H+ beam + 20 kV I- PAC (041221) -*-Bern: 60 keV H+ beam + 20 kV PAC (041221) UNH: 2TseV H+ beam + 15 kV PAC (050418) -UNH: 20keV H+ beam + 18 kV PAC (050601} MCP £V1 Figure A.19 Revised PLASTIC/A start efficiency. FMl: Sinigs Position Efficiency versus MCP Voltage — Adjusted Subtracted 400 V from Bern MCP setting, and auumad Bern single position efficiency -> 1. j;,,~'--->»» - J? 0.8 I; 0.7 3 :z:---::rhr «l'0.6 - lo.S s -...- Bern: 2 keV H+ beam + 20 kV PAC (041220) J0.4 -•-Bern: 10 keVH+ beam + 20 kV PAC (041221) O -*- Bern: 20 keV H+ beam + 20 kV PAC (041221) 2 0.2 ~*~ Bern: 60 keV H+ beam + 20 kV PAC (041221) - UNH: 2 keV H+ beam + 15 kV PAC (050418) a o.i -•-UNH: 20 keV H+ beam ¥ 18 kV PAC (050601) MCPtV] Figure A.20 Revised PLASTIC/A single position efficiency. 177 FM1: Total Efficiency versus MCP Voltage ~ Adjusted — Bern: 2 keV H+ beam + 20 kV PAC (041220) 8o.9 -.- Bern: 10 keV H+ beam + 20 kV PAC (041221) •o -*- Bern: 20 keV H+ beam + 20 kV PAC (041221) 1 0.8 -*- Bern: 60 keV H+ beam + 20 kV PAC (041221) i - - UNH: 2 keV H+ beam + 15 kV PAC (050418) s -"- UNH: 20 keV H-t- beam + 18 kV PAC (050601) S 0.6 s f o.s * i l0.3 2 Si O0.2 I ^m&yt.. w0.1 ^stS*/*' MCPrVJ Figure A.21 Revised PLASTIC/A total double coincidence proton efficiency. FMl: SFRO/SFO versus Total Energy - Adjusted (Adjusted Bern MCP ~ 2660 V) Bram + PAC [kV] Figure A.22 Revised PLASTIC/A stop efficiency. 178 FM1: Adjusted Start Efficiency versus Total Energy (Adjusted Bern MCP ~ 2660 V) 40 50 Beam + PAC [kV] Figure A.23 Revised PLASTIC/A start efficiency. FMl: Single Position Efficiency versus Total Energy — Adjusted (Adjusted Bern MCP ~ 2660 V) Beam + PAC [kV] Figure A.24 Revised PLASTIC/A single position efficiency. 179 FM1: Total Efficiency versus Total Energy - Adjusted (Adjusted Bern MCP ~ 2660 V) 40 SO Bom + PAC [kV] Figure A.25 Revised PLASTIC/A total double coincidence proton efficiency. FM1: Triple Coincidence Efficiency versus MCP Voltage — Adjusted Subtrwcad 400 V from B*m MCP sotting. ~*~ Bern: 2 keV H+ beam + 20 kV PAC (041220) 0: » Bern: 10 keV H+ beam + 20 kV PAC (041221) 0.: -*- Bern: 20 keV H+ beam + 20 kV PAC (041221) -*- Bern: 60 keV H+ beam + 20 kV PAC (041221) 0 — UNH: 2 keV H+ beam + 15 kV PAC (050418) go -»- UNH: 20 keV H+ beam + 18 kV PAC (050601) - -- „ rlfTf*-* *"" 2600 Z9D0 MCP £v) Figure A.26 Revised PLASTIC/A triple coincidence stop efficiency. 180 FM1: Triple Coincidence Efficiency versus Total Energy — Adjusted (Adjusted Bern MCP ~ 2660 V) Figure A.27 Revised PLASTIC/A trip coincidence stop efficiency. A.7 Inter-calibration of STEREO/PLASTIC with WIND/SWE After determining an average Main to S Channel Geometric Factor Ratio (120 for PLASTIC/AHEAD, and 65 for PLASTIC/BEHIND), the higher order corrections were implemented through efficiency tables. While the pre-launch efficiency estimates were reasonable for the main channel, the small channel tables had to be recreated more-or-less from scratch by inter-calibration with WIND/SWE. Thank you to Keith Ogilvie, Al Lazarus, and M.R. Aellig for making the WIND/SWE data available to the public! In March and April 2007 both STEREO spacecraft were near Earth and the L1 satellites. Separation in time was just a few hours, so it was expected that STEREO/AHEAD, WIND/SWE, and STEREO/BEHIND would all observe the same solar wind features. The plot below shows density versus time assuming 181 the STEREO/AHEAD S to Main Channel area ratio is 1:120, and the STEREO/BEHIND S to Main Channel area ratio is 1:65. 3/1/07 3/26/0? 3/31/07 Figure A.28 Density versus time with 0th order correction for leakage. When the density is high (usually during slow solar wind), the PLASTIC/A values agree fairly well with the WIND/SWE densities. When the density is low (usually during high speed streams), the STEREO/A density is obviously less than the WIND/SWE proton density. The STEREO/B densities are similar to WIND/SWE values during times of moderate speed solar wind. Otherwise, the STEREO/B densities tend to be larger than the WIND/SWE values. Figure A.29 shows thermal speeds, which are calculated from the full width half maximum of the Maxwellian distribution function. The STEREO/A thermal speeds look very similar to the WIND values in most cases. The 182 STEREO/B values are mostly larger than the WIND/SWE thermal speeds. This suggests the distribution functions for PLASTIC/BEHIND are too broad. 0 I , . : _» 3/1/07 3/6/07 3/11/07 3/16/07 3/11/07 3/2«/07 3/31/07 Time Figure A.29 Thermal speed versus time with 0th order correction for leakage. The micro-channel plate (MCP) voltages were being manipulated on PLASTIC/BEHIND during March 2007, so the offsets in density and thermal speed compared to WIND are not constant. Making similar plots for the month of April shows that the solar wind streams observed between the three satellites are still similar, but the variations between PLASTIC/B and WIND/SWE are less complicated than in March. 183 PLASTIC B - - - PLASTIC A WIND _ so 8 1 I e 2 sUSHwsi JW^C'-S*' l/i V^J^W"«'2lFlSi*tf ^|^%w w v^fc^Ja 04/01/07 04/06/07 04/U/07 04/16/07 04/21/07 04/26/07 05/01/07 TIm« Figure A.30 Density versus time with 0th order correction for leakage. — PLASTIC B — PLASTIC A — WIND 04/01/07 04/06/07 04/11/07 04/16/07 04/21/07 04/26/07 05/01/07 Day Figure A.31 Thermal speed versus time with 0th order correction for leakage. Figures A.32 and A.33 are plots of the ratios of density versus solar wind speed. 1ST order corrections to the efficiency estimates were obtained for both PLASTIC/A and /B small channels by fitting curves to the plots. The 184 PLASTIC/BEHIND to WIND/SWE density ratios show a much stronger dependence on bulk speed (kinetic energy) compared to PLASTIC/AHEAD. Note that the PLASTIC data was time shifted by a few hours to minimize scatter. Density Ratio versus Bulk Speed — 3 hour offset Hourly Averaged Data from April 2007 * y = 3E+06X-*"71' Rz = 0.7254 * A J 5 * M J 4 A*^ :, J 2 *. ^^Sffi. V * *« * ****** * •. *^ *.. * * * 3r* *•£.* raw* J i.:^": ."-—*r*£ 200 300 400 500 600 700 800 PLASTIC B Proton Speed [km/s] Figure A.32 Ratio of the 0th order corrected density from PLASTIC/B to the density at WIND/SWE versus solar wind speed. Density Ratio versus Bulk Spaed — 2 hour offset Hourly Averaged Data from April 2007 3J 3 400 500 600 PLASTIC A Proton Sp»«d [km/*] Figure A.33 Ratio of the 0th order corrected density from PLASTIC/A to the density at WIND/SWE versus solar wind speed. 185 To obtain a higher-order correction to the efficiency tables for STEREO/BEHIND, the first order correction was implemented, and then fits were made to smaller ranges of solar wind speed as shown in Figure A.34. N_PLASTIC_B/N_WIND vs E/q Hourly Averaged Data from May, 2007 (PLASTIC Data Tima Shifted for Minimum Scatter) 275.95X* 576.01X1 + 414.82X2 - 116.24X + 10.253 3.S [v- 3 jy = -74.375x' + 321.13X - 513.61X* + 360.23X - 92.361 3.0 -8.1884X3 + 41.931X* - 71.121X + 40.769J 4 5 2 F 2.3794X - 8.8205X - 15.299X + 93.916X - 93.482 • < 0.8 keV/q I" ]Y- . » V .. • 0,8tol.4keV/q • t „ rattffl * • 1.4 to 2 keV/q tj * i» • ** * , » • > 2 keV/q r JM *v>* *«/• & 1.5 ^04^0:?™**..^..™..™f . — 1.0 JLJae/ *•"• • •» * i 0.5 i n n0. 0 0.5 1.0 1.5 2.0 2.5 3.0 j Energy per Charge [keV/q] Figure A.34 PLASTIC/B to WIND/SWE density ratio versus energy per charge after 1st order correction. The end results were the efficiency curves shown in Figure A.35. (Discontinuities can cause some analysis problems, and the curves will almost certainly be revised later!) When the original Maxwell distribution function algorithm was implemented, it was missing a factor of 2K (due to an IDL syntax error). Correcting for this mistake, the efficiencies are greater than 1.0 for many ESA steps. This does not seem to be contrary to logic given that most of the counts coming in when the small channel is enabled (particularly on PLASTIC/BEHIND) 186 are actually leaking through the main channel, resulting in count rates 10 to 20 times higher than expected from pre-launch calibration. Efficiency versus Energy/Charge 27 June, 2007 * •AHEAD -» t - - * BEHIND IX - - A A A 4 A A \ *****•*, ,, * A A A A A * A A '* * A * • I * * * I » * 4 * * * 0.0 0.5 1.0 l.S 2.0 2.5 3.0 3.5 4.0 Ermroy par Ctiarg* [kaV/q] Figure A.35 In-flight efficiency curves. Since April 2007, the MCP gain has changed on both spacecraft. On PLASTIC/AHEAD this has had little effect on the RAJTrigger rate. On PLASTIC/B the efficiency tables had to be scaled on a month-by-month bases until August 2007, from which time on the efficiency has not seen a noticeable change. 187 APPENDIX B NORTH/SOUTH FLOW ANGLE The main and s channel deflection (out-of-ecliptic angle) distributions are offset from one another by several degrees on both spacecraft, as shown in Figure B.1 and B.2. This is likely due to main gate leakage, which is more prevalent when ions are coming in from below the horizontal on PLASTIC/A, and above the horizontal on PLASTIC/B. (Remember that STEREO/BEHIND is upside down with respect to STEREO/AHEAD.) The deflection bin to angle conversion is different for main and S channel, with a larger angular size for main channel stepping. In addition to the leakage effect, the deflector voltages are larger than planned at the lowest E/q steps. This causes the deflectors to steer in ions from farther out of the ecliptic plane than the nominal bin number to angle conversion would suggest, and artificially narrows the out-of-ecliptic spread at the lowest solar wind speeds, as shown in Figures B.3 and B.4. 188 Center of Dally Deflection Distribution PLASTIC Angles are NOT corrected for roll. -AHEAD Main Channel -AHEAD S Channel * w± fcr*CV/ •*^^> ar-X-e^ ******** •V^ 3l-Mar-0? S-Apr-07 iO-Apr-07 l$-Apr-07 2Q~Apr-07 25-Apr-07 30-Apr-07 0*y Figure B.1 Daily averaged PLASTIC/A main and s channel out-of- ecliptic angles calculated with idealized bin to angle conversion. Center of Dally Deflection Distribution PLASTIC Angle* are NOT corrected for roll. A " , f\ / /l , - X rt I \ \ -*- BEHIND Main Channel —- BEHIND S Channel S-Apr-07 lMpr-07 15-Apr-07 JO-Apr-07 25^Apr-07 30-Af>r-07 Day Figure B.2 Daily averaged PLASTIC/B main and s channel out-of- ecliptic angles calculated with idealized bin to angle conversion. 189 S Channel Deflection Distribution Peak versus Bulk Speed * * * " " ~~ r~ i —r * -*~ -y— A - * _ • ~ _ — A A . A 1 »» * * A *A * 1 * « I. . . . •... «. . ..| * < -2 : • • • : * • AHEAD S Channel * BEHIND S Channel 400 450 500 550 Approximate Bulk Speed [km/»] Figure B.3 Daily averaged s channel out-of-ecliptic angle versus solar wind speed for both PLASTIC/A and PLASTIC/B. WIND N/S Angle versus PLASTIC N/S Angle Hourly Averaged Data from April 2007 PLASTIC data time shifted by 2 hours muKMb'iflb ,*» JOiCSJm.*-*'—-A • 5. . , *«- » * * • • AHEAD Main Channel «5-%»^"»'" AHEAD S Channel -8 -2 0 2 PLASTIC N/S Angle [deflrtes] Figure B.4 WIND North/South flow angle versus PLASTIC/A flow angles from the main and s channels' calculated with the idealized bin to angle conversion. 190 The first step in finding the "real" small channel deflection angle is to center and stretch the distribution. The multiplicative constants were chosen so that the final range of angles covered is similar to that observed on WIND for the time periods used for calibration. A: theta_stretched = 3*(theta + 1.72°) B: theta_stretched =1.75*(theta - 4.43°) (where theta is the peak of a Gaussian fit to the count distribution). The second step is to correct for the speed dependence. Figures B.5 and B.6 are plots of the difference between the WIND North/South angle and the PLASTIC North/South angle versus speed. The trends are similar, though mirror imaged (as expected). The fits shown in Figure B.5 and B.6 were implemented in the bin to angle conversion, with one modification. WIND N/S - modified PLASTIC AHEAD N/5 versus Speed * ** * % i- , ** * 7t_ %V +A• ** ^— ~—^_.* .. „... . ,™ ~- ^—-~nr-. • • * * # * 2 -• • *+ iy =-3.6613E-0SX + S.2914E-02X- ! 1.5385E+01 *** * # i R2 » 5.6146E-01 40Q 500 SfMMrf (km/«] Figure B.5 Difference between WIND and PLASTIC/A small channel north/south angle versus solar wind speed. 191 WIND N/S - modified PLASTIC BEHIND N/S versus Bulk Speed * !y « 4.549E-05X2 - 5.344E-02X + 1.469E+01 R2 = 4.355E-01 4 * J. . . *» T^.A t- 7.. A IJ» »*» * .4 4 * » *• * *' " " A. A 400 SCO 600 Bulk Speed [km/s) Figure B.6 Difference between WIND and PLASTIC/B small channel north/south angle versus solar wind speed. After the above curves were found, a correction for deflection "wobble" was added. This shifted the distribution, so an additive constant is used to re- center the resulting small channel angles. In summary: A: reaLtheta = theta_stretched - (3.6613E-5)*v2+ (5.2914E-2)*v-13.385 [degrees] B: reaLtheta = theta_stretched + (4.549E-5)V - (5.344E-2)*v+13.690 [degrees] (where v is the speed in km/s). STEREO/B was rolled away from the nominal north/south configuration until the second half of 2007. The North/South flow angle calibration for spacecraft B was updated using 1 -hour-averaged data from September 2007. At that time, STEREO/B and WIND were separated by about 13° in longitude and by several hours in time. In order to compare the north/south flow angles from 192 the same solar source regions, both data sets were mapped back in time using a simple ballistic technique. North/South Flow Angle versus Time -**«% m %£••* .• v« * ' *- i-' 4-1 ** &*!?,•%• : •» MK| .m m m*k ,^....*... &. ± M • WIND • STEREO B -10 W/01/2007 09/11/2007 09/21/2007 10/01/2007 Montii/Day/Ycar Figure B.7 WIND and PLASTIC/B small channel (idealized bin to angle conversion) North/South flow angles for September 2007. North/South Flow Angle versus Back-mapped Carrington Number 2060.9 2061.1 20S1.3 Back-nwppad Carrinoton Numbar Figure B.8 WIND and PLASTIC/B small channel (idealized bin to angle conversion) North/South flow angles for September 2007, time-shifted for easier comparison. 193 Comparing the back-mapped North/South flow angles in Figure B.8 the two spacecraft are seeing similar trends. However, the STEREO-B data is shifted above nearly all of the WIND data, and does not cover as wide an angular range. Making a plot of North/South Flow angle versus measured solar wind speed (Figure B.9) shows this even more clearly. N/S Flow Angle versus Solar Wind Speed WIND 400 500 600 Solar Wind Spent from STEREO B [km/a] Figure B.9 North/South flow angle versus solar wind speed. Just as was done before, the first modification to the STEREO B data is to re-center and stretch the distribution. theta_stretched =1.75*(theta - 4.62°) The multiplicative factor of 1.75 is the same as the previous calibration. Previously a value of 4.43° was used for the offset from center, different by 0.19° from the updated value of 4.62°. A plot of the North/South distribution versus solar wind speed with the centered and stretched B distribution is shown below. 194 N/S Flow Angle versus Solar Wind Speed 400 500 600 Solar Wind Sp»d from STEREO B [km/.] Figure B.10 Revised 0th order corrected STEREO/B North/South flow angle and WIND flow angle versus solar wind speed. Figure B.10 shows the centered and stretched B distribution covers a similar angular range as WIND, but the WIND angular distribution is roughly flat across all speeds, while the B angles show a definite trend when the measured solar wind speed is less than about 400 km/s. To quantify this, Figure B.11 shows a plot of the difference in angles between B and WIND versus speed. 195 WIND N/S -Stretched STEREO B N/S versus Solar Wind Speed Hourly Averaged Data (Time Shifted) from September 2007 jy = -2.640E-07x3 + 4.373E-04X* - 2.392E-01X + 4.264E+01 i R2 = 3.650E-01 a 5 !C?* .t • . . • • *?: 1 • • !•*•*.. , * •* •» •.*!•• 400 500 600 Solar Wind Spaed from STEREO B {km/*] Figure B.11 Difference between WIND and PLASTIC/B 0th order corrected North/South flow angle versus solar wind speed. The difference in N/S flow angle between the two spacecraft can be well fit with a third-order polynomial in speed. Applying this to the stretched B distribution results in the following. realjheta = theta_stretched + (-2.640E-07)V + (4.373E-04) V - 0.2392 + 42.6394 [degrees] 196 N/S Flow Angle versus Solar Wind Spaed s STEREO B final modification WIND 6 T i» ?* * * A, w * 1 2..SS—--^ ^.•«....A, *...... «X«. f * 400 500 600 Solar Wind Speed from STEREO B [ton/*] Figure B.12 Corrected PLASTIC/B and WIND North/South flow angle versus solar wind speed. North/South Flow Angle versus Back-mapped Carrington Number 6 i ii i 1*1 I! I* J 1*1**. 1 1 1 lIA11 a 2 ij y^Kv ii i i * ! 1 ° S p I" — WIND — STEREO B Modified 2060.9 2061.1 2061.3 Back-mappad Carrington Number Figure B.13 Corrected PLASTIC/B flow angle plotted with flow angle from WIND/SWE and time shifted for comparison. 197 LIST OF REFERENCES Arge, C.N., J.G. Luhmann, D. Odstrcil, C.J. Schrijver, and Y. Li, Stream structure and coronal sources of the solar wind during the May 12th, 1997 CME, J. Atmos. Sol. Terr. 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