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Origin and Characteristics of the Southward Component of the Interplanetary Magnetic Field

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A Commentary to this article was published on 13 September 2022

Abstract

We investigate the rectified interplanetary magnetic field (IMF) components in two coordinate systems, GSEQ and GSM, focusing on the southward pointing component (\(B_{\text{s}}\)) in GSM within the period 1999 – 2017. The analysis is performed for different solar activity levels. The obtained results are valuable for the theoretical interpretation of IMF components variations and variations seen in geomagnetic indices. \(B_{\text{s}}\) ordered according to the polarity exhibits a “pair of spectacles” pattern. This reveals that \(B_{\text{s}}\) can also exist for toward/away field in fall/spring. The field is reduced, but it is not zero. Thus, in “unfavorable” seasons, geomagnetic activity can be due to reduced \(B_{\text{s}}\) and not because the field is northward pointing. We show that patterns of the experimental \(B_{\text{s}}\) fields are not in agreement with the Russell-McPherron model of \(B_{\text{s}}\) as widely assumed. The present study contributes in understanding the nature and behavior of \(B_{\text{s}}\), which is the important element that controls the reconnection process and has a great influence on terrestrial space weather over the solar cycle.

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Abbreviations

IMF:

interplanetary magnetic field

GSM:

Geocentric Solar Magnetospheric System

GSEQ:

Geocentric Solar Equatorial System

DOY:

day of the year (1 – 365)

HOY:

hour of the year (1 – 24 × 365)

\(B_{\text{s}}\) Contour plot:

a contour plot of \(B_{\text{s}}\) with two time axes:

DOY (1 – 365) and UT (1 – 24)

Favorable season:

toward/away IMF polarity in spring/fall

Unfavorable season:

toward/away IMF polarity in fall/spring

\(B_{i,{\scriptscriptstyle {\text{GS}}}}\) :

component \(i=(x,y,z)\) of the IMF given in GS = (GSM or GSEQ) coordinate system.

\(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >})\) :

positively rectified \(B_{i,{\scriptscriptstyle {\text{GS}}}}\); only positive values are considered

\(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle <})\) :

negatively rectified \(B_{i,{\scriptscriptstyle {\text{GS}}}}\); only negative values are considered

\(B_{\text{s}}\) :

special case of \(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle <})\) with \(i=z\) and GS = GSM

\(B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} >0)\) :

\(B_{\text{s}}\) value under away oriented IMF

\(B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} <0)\) :

\(B_{\text{s}}\) value under toward oriented IMF

\(\text{AVG}(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >}))\) :

yearly averages of \(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >})\)

\(\left \langle B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >}) \right \rangle \) :

HOY averages of \(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >})\)

\(\text{AVG}(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >}))_{\text{fin}}\) :

average of \(\text{AVG}(B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >}))\) over years

\(\left \langle B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >}) \right \rangle _{\text{fin}}\) :

average of \(\left \langle B_{i,{\scriptscriptstyle {\text{GS}}}}({\scriptstyle >}) \right \rangle \) over HOYs

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Acknowledgements

The authors thank Dr. Giovanni Piredda for helpful discussion. The used solar magnetic field data are the hour-averaged level-2 ACE (MAG) data given at http://www.srl.caltech.edu/ACE/ASC/level2/ and hour-averaged OMNI data from http://omniweb.gsfc.nasa.gov/form/dx1.html. The 13-month smoothed monthly total sunspot number data are available at https://wwwbis.sidc.be/silso/datafiles.

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Appendix: RM Model

Appendix: RM Model

RM explained how they obtained \(B_{\text{s}}\) without explicitly providing formulas to calculate \(B_{\text{s}}\). In the following, we present details about the calculations and predictions of the \(B_{\text{s}}\) model based upon the assumption set up by RM.

Generally, \(B_{\text{s}}\) can be derived from \(B_{y,\scriptscriptstyle {\text{GSEQ}}}\) and \(B_{z,\scriptscriptstyle {\text{GSEQ}}}\) using expressions 1 and 2. RM, who modeled a long-term \(B_{\text{s}}\), assumed that the average \(B_{z,\scriptscriptstyle {\text{GSEQ}}}\) is zero and that the magnetic field toward and away along the spiral angle (assumed to be 45) is 5 nT. So, toward and away \(B_{y,\scriptscriptstyle {\text{GSEQ}}}\) amounted to −5/\(\sqrt{2}\) and 5/\(\sqrt{2,}\) respectively, and represented averages over a long time span. The two \(B_{y,\scriptscriptstyle {\text{GSEQ}}}\) fields were transformed to GSM, and their northward part was set to zero. To obtain \(B_{\text{s}}\) the two fields were averaged.

According to our notation these steps can be written:

$$ \begin{aligned} \left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} < 0) \right \rangle & = & \left \langle B_{y,{\scriptscriptstyle {\text{GSEQ}}}}({ \scriptstyle < }) \right \rangle _{\text{fin}} \sin \alpha , \quad \sin \alpha > 0 ,\ (\alpha > 0) \\ \left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} >0) \right \rangle & = & \left \langle B_{y,{\scriptscriptstyle {\text{GSEQ}}}}({ \scriptstyle >}) \right \rangle _{\text{fin}} \sin \alpha , \quad \sin \alpha < 0 ,\ (\alpha < 0), \end{aligned} $$
(6)

where \(\left \langle B_{y,{\scriptscriptstyle {\text{GSEQ}}}}({\scriptstyle <}) \right \rangle _{\text{fin}} = -5/\sqrt{2}\) and \(\left \langle B_{y,{\scriptscriptstyle {\text{GSEQ}}}}({\scriptstyle >}) \right \rangle _{\text{fin}} = 5/\sqrt{2}\).

\(\left \langle B_{s} \right \rangle \) was postulated to be the average of \(\left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} <0) \right \rangle \) and \(\left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} >0) \right \rangle \). Taking into account that \(\left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} <0) \right \rangle \) and \(\left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} >0) \right \rangle \) do not overlap for any \(\alpha \), we can write \(\left \langle B_{s} \right \rangle \) as:

$$\begin{aligned} \left \langle B_{s} \right \rangle = \frac{1}{2} \textstyle\begin{cases} \left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} < 0) \right \rangle , \quad \alpha > 0 \\ \left \langle B_{\text{s}}({\scriptstyle B_{y,\text{GSEQ}}} >0) \right \rangle , \quad \alpha < 0. \\ \end{cases}\displaystyle \end{aligned}$$
(7)

Note that conditions \(\sin \alpha >0\) and \(\sin \alpha <0\) are a consequence of the constraint \(B_{z,\scriptscriptstyle {\text{GSM}}}<0\). Since \(\alpha >0\) around spring and \(\alpha <0\) around fall, it is clear that according to the RM model, toward/away \(B_{\text{s}}\) fields do not exist in fall/spring.

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Verbanac, G., Bandić, M. Origin and Characteristics of the Southward Component of the Interplanetary Magnetic Field. Sol Phys 296, 183 (2021). https://doi.org/10.1007/s11207-021-01930-1

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