Correlative
Study of Sunspot Number with Interplanetary Magnetic Field During Solar Cycle
24
Mansu Masram1*, Gopal Singh
Dhurve2
1 Assistant Professor
of Physics, Department of Physics, Govt. P. G. College Multai, Betul, M.P., India
m.b.masram@gmail.com
2 Assistant Professor
of Physics, Department of Physics, Rani Durgawati Govt. College Mandla, M.P.,
India
Abstract: The structure and dynamics of the heliosphere are
determined by the solar magnetic activity that has a powerful impact on the
near space conditions around the Earth. The sunspots number is a commonly used
measure of the magnetic activity of the solar surface and the interplanetary
magnetic field is the measure of the extension of this activity into space in
the form of the solar wind.In this paper, a correlative study of sunspots
numbers (SSN) and the magnitude of the interplanetary magnetic field (IMF) is provided,
with regard to the Solar cycle 24 (2008-2019), which has been marked by
exceptionally low magnetic activity. The correlation between the solar surface
magnetic activity and the heliospheric magnetic conditions around the earth was
studied by comparing monthly mean sunspot numbers of SILSO database and
interplanetary magnetic field data of OMNI database. Time-analysis comparison
of SSN and IMF reveals that both are affected by solar cycle variations, with
an even stronger IMF strength usually being observed when the sunspots are
active. The variability of IMF has however very large short-term oscillations
at the solar maximum, and declining phases, which suggests the effects of
transient and recurring solar wind structures. The statistical analysis done on
the basis of Pearson correlation coefficient shows a moderate positive
correlation between SSN and IMF magnitude during the whole cycle. Phase-wise
analysis indicates a higher correlation in rising phase and lower
correspondence in the maximum and declining phases owing to growth in the
contribution of coronal mass ejections and high-speed streams of the solar
wind. Such findings imply that although the sunspots numbers continue to be one
of the most important indicators of the solar magnetic activity, the behavior
of interplanetary magnetic fields is also dictated by the large-scale processes
taking place in the heliosphere particularly during the weak cycles. The
results also help in understanding solar-interplanetary coupling better, and
have significant implications on the modeling of the heliosphere as well as
space weather prediction.
Keywords: Sunspot number, Interplanetary magnetic field, Solar cycle
24, Solar activity,Heliospheric magnetic field, Solar wind, Space weather.
INTRODUCTION
Hydroelectric activity of the Sun is caused by the
complicated and changing magnetic field, which constantly evolves on various
temporal and spatial levels (Lockwood, 2013)[1]. Among the most apparent
results of this magnetic activity, the sunspots on the solar surface should be
mentioned. Sunspot number (SSN) is one of the most widely used indicators of
measuring solar activity as it is used to measure the intensity and structure
of the solar magnetic fields at the photosphere. Solar long-term variability and
impacts on the heliosphere since the time systematic observations were first
made have greatly depended on sunspot number. There is a temporal change in the
sun spot number with an approximate cycle of 11 years with variations between
the solar minimum and solar maximum. When the Sun has a high number of
sunspots, the Sun becomes more complex in terms of magnetism, experiences more
solar wind events, and eruptive events on the Sun, including solar flares and
eruptions known as coronal mass emissions (CMEs)(Zhang et al., 2021)[2]. These
processes play a large role in affecting the interplanetary environment and
also cause fluctuations of the interplanetary magnetic field.
The Interplanetary Magnetic Field (IMF) is formed by
the solar magnetic field, but it is expelled by the solar wind into the space
between planets. An overall interaction of solar rotation and plasma flow
causes the IMF to take a helical shape in the form of a Parker spiral as the
solar wind flows out radially away from the Sun(Clette& Lefèvre, 2016)[3].
The scale and direction of IMF are thus highly reliant on the large scale solar
magnetic field arrangement and the solar wind. Fluctuations in IMF parameters
are of importance in regulating the interaction of the solar wind and the
magnetospheres of the planets, especially that of Earth. Learning the
correlation between the number of the sunspots and the interplanetary magnetic
field is critical in explaining the mechanisms that convey solar magnetic
activity to the heliosphere. Although the sun spot number measures the activity
of the magnetism at the surface of the sun, IMF measures the spread of the
magnetic activity of the sun into space between earth and the sun.
Correlational study of these two parameters assists in closing the gap existing
between phenomena on the surface of the Sun and the dynamics of the heliosphere.
Ashutosh Kumar Tiwari et al. (2025) observed the correlation between
cosmic ray intensity CRI and a number of solar wind (SW) indicators, GSs,
IMF-B, Ap index, and SSN [4]. Kumar,
Ashok et al, (2024) found that the magnetic field in the Earth is generally
influenced by the numerous phenomenons that take place in the mental and core
part of the earth [5]. Goyal, Sanjay et al (2023) studied the correlation
between sunspots numbers (Rz), IMF and geomagnetic indices was positive. IMF, sun spot number and
indices are most variable between the onsets of cycle till the cycle conclusion
[6].Abha Singh et al. (2021) studied that the solar magnetic field causes all
the solar activities [7]. Jothe, M.et al. (2015) observed the CRI and
SSN have high and negative correlation coefficients (r= -0.78) that change
randomly each year Equally important, X-rays and UV radiations released by
solar flares [8].
Other previous studies have indicated that there are
some inconsistencies of coefficient of correlation among sunspot number and IMF
strength, solar wind speed, and geomagnetic indices. These relationships are
however not necessarily linear and can vary with each solar cycle. The observed
correlations can be affected by changes in the heliospheric structure,
transient solar events, and reversal of the polarity of the magnetic field of
the sun (Gonzalez &Tsurutani, 1987)[9]. Thus, a closer look at solar cycle
by cycle is significant in order to receive cycle-specific information. Solar
cycle 24 that lasted between around 2008 and 2019 was significantly less active
than previous solar cycles in sunspots and the general level of solar magnetic
activity. This abnormally low activity level gives a special background to its
study of solar-interplanetary interaction in a weak solar cycle. Analysis of
the relationship between the number of sunspots and the IMF parameters in this
period can be used to determine whether the decrease in solar activity results
in similar decreases or different behaviour of the interplanetary magnetic
field properties.
The main aim of our work is to carry out the
statistical correlation analysis of the parameters of the interplanetary
magnetic field and sunspots number during the Solar Cycle 24. This work will
measure the strength of association between these variables using long-term
observational data, which would study the temporal changes of these variables
during the cycle. It is hoped that the findings of this work will improve the
knowledge of the magnetic field propagation in the solar and can be used to
come up with better models of heliospheric variability and space weather
forecasting.
METHODS AND TECHNIQUES
Data Sources
The current research adopted long-term observational
records of sunspots number and interplanetary magnetic field (IMF) parameters in
Solar Cycle 24 to determine the correlation between these two parameters. Solar
Cycle 24 is typically deemed to stretch between January 2008 through December
2019 through the rising phase, the solar maximum, and the cycle decline stage
(Hathaway, 2015)[10].The World Data Centre of the Sunspot Index and Long-term
Solar Observations (SILSO), Royal Observatory of Belgium was used to acquire
the sunspot number (SSN) data. The SILSO dataset is a source of internationally
standardized continuously updated sunspots numbers, thus it is among the most
reliable sources of solar activity. In this study, the monthly mean sunspots
numbers were employed so as to minimize the short-term variations and focus on
the long-term variations in the solar cycles.The OMNI has NASA Space Physics
Data Facility as its keeper and provides the interplanetary magnetic field
(IMF) data. The OMNI database puts together near-Earth solar wind and IMF
measurements of various spacecrafts and time-shifts them to the bow shock of
the Earth to give a consistent and continuous data.(King &Papitashvili,
2005)[11]. The magnitude of the IMF total (IMF) was chosen as the main IMF
parameter to be used in this study because it is the overall strength of the
interplanetary magnetic field, and has been extensively deployed in
heliospheric studies.
Data Processing
Both IMF data and sunspot number have been collected
on similar time span to achieve similarity in the data sets. Means of IMF were
calculated every day and then averaged to get monthly averages which
corresponded with the time resolution of the sun spot number data. This method
can reduce the effect of the short-term fluctuation of the transient solar wind
and temporary variations that happen due to the individual occurrences like
coronal mass ejections.(Emery & Thomson, 2001)[12].The IMF data had gaps
and missing values and these were scrutinized. Months that had low data
coverage were not included in the analysis in order to prevent the introduction
of bias in the correlation results. The resultant time series was a continuous
monthly values series that covered the Solar Cycle 24 in its entirety.
Statistical Methods
The correlation analysis was used to determine the
relationship between the sunspot number and the interplanetary magnetic field.
To measure the level of linear relationship, Pearson correlation coefficient
(r) was used to determine the extent level of linear relationship between the
two variables. The Pearson technique is appropriate when the researcher is
seeking the strength and direction of the correlation between continuous
datasets and has mostly been applied in solar-terrestrial studies.(Bendat&
Piersol, 2010)[13].
The correlation coefficient has been calculated by
using the standard formula:
where
Graphical Representation
The relationship between IMF parameters and sunspots
number was studied visually by the help of graphical methods. Time-series plots
were created in order to compare the change in monthly mean sunspots number
with the IMF magnitude during Solar Cycle 24. Scatter plots were also made to
demonstrate the correlation between the two variables as well as evaluate the
nature of their relationship. The graphical representations are an add-on to
the statistical analysis, and they give an intuitive understanding of the relationship
between the interplanetary magnetic field behaviour and solar surface activity.
(Wilks,2011)[15].
Software Tools
All data calculation, statistics, and graphical
representation were done with conventional data analysis programs like
Python/MATLAB. These were used in averaging data, computing correlation and
creating publication quality figures.
RESULTS AND ANALYSIS
Temporal Evolution of Sunspot Number in Solar Cycle 24.
Figure 1 gives the temporal variation of the monthly
average sunspot number (SSN) of Solar Cycle 24. It starts with a long and
unusually deep sun minimum in 2008-2009 with very low levels of sunspots. This
long minimum is characteristic of the Solar Cycle 24 and it shows the poor
state of the magnetic field that the cycle started with (Pesnell, 2016)[16].
Figure
1: Monthly average sunspots number During Solar Cycle 24
The sun spot number, after this minimum, shows a slow
rise in the rising phase where a broad and asymmetric peak can be observed in
the period between 2013 and 2014. The Solar Cycle 24 unlike the earlier periods
exhibits a relatively smaller sunspot number which attests to it being a weak
solar cycle (Petrovay, 2020)[17]. The maximum phase is followed by the
declining phase during which the activity of the sun spots is steadily reduced
until the cycle is nearing the next minimum year around 2019. The measured
change in the number of sunspots gives the basic leading design of studying the
matched reaction of the interplanetary magnetic field because the sunspots are direct
evidence of the emergence of the magnetic flux of the sun.
Fluctuation of Interplanetary Magnetic Field Magnitude
Figure 2 illustrates the temporal behaviour of the
monthly mean interplanetary magnetic field magnitude (|B|) over the same
period. There is noticeable variability in the IMF magnitude across the Solar
Cycle 24, and both the long-term trends and short-term changes are overlaid on
the other (Smith & Balogh, 2008)[18].
Figure
2: Monthly average IMF Magnitude During Solar Cycle 24
At this stage of the solar minimum (2008-2009) the IMF magnitude is relatively small, which
marks the lack of solar magnetic flux and the weakening of the disturbances of
solar wind. With the cycle moving into the rising stage, there is gradual
strengthening of the IMF which is widely accompanied by the rising sunspots
activity. Higher average values of the IMF are achieved when the solar maximum
period is observed, showing that the solar magnetic effect is stronger than
normal in the interplanetary space. But, in contrast to the smoother variant of
the sunspots number, the IMF magnitude has strong oscillations, particularly
when the maximum and falling periods occur. Such variations may be explained by
the temporary interplanetary structures like coronal mass ejections,
interaction regions, and high-speed stream of solar winds(Borovsky &
Denton, 2006)[19]. This emphasizes the fact that the behaviour of IMF is
governed by solar activity in addition to being perturbed by dynamic processes
in the heliosphere.
Comparative Time-Series Analysis of SSN and IMF
The direct comparison of the profiles of SSN and IMF
magnitude time-series (Figure 3) shows that there are similarities and
differences in the development of them. On a larger time scale, it can be seen
that times of elevated sunspot activity are associated with large magnitudes of
the IMF indicating that there is a relationship between the magnetic activity
on the surface of the sun and the magnetic environment of the heliosphere
(Cliver & Ling, 2011)[20].
Figure
3: Comparison of time-series plot of monthly mean sunspot number and IMF
magnitude in Solar Cycle 24.
However, inconsistencies are also present. The IMF
magnitude is high in some periods especially at the falling phase when sunspots
number is low. This tendency is the sign of the impact of the large-scale
structures of solar wind like the coronal holes that become even more prominent
during the declining phase and contribute to the increased IMF strength
regardless of the sunspots (Grandin et al., 2019)[21].This comparative study
has shown that sunspot number records the world solar magnetic activity whereas
IMF magnitude records the world and local heliospheric events.
Correlation Analysis Between Sunspot Number and IMF
In order to obtain a quantitative estimate of the
dependence between the sun spot number and the magnitude of the interplanetary
magnetic field, a scatter plot of mean SSN per month and IMF magnitude is
presented in Figure 4. The trend in the distribution of data points has a
positive trend in general, with greater values of sunspots corresponding to the
greater values of IMF.
Figure
4: Scatter plot of the relationship between the interplanetary magnetic field
magnitude and the monthly mean sunspot number.
The obtained Pearson correlation coefficient
shows that there was a moderate positive correlation between SSN and IMF
magnitude at Solar Cycle 24. This has been confirmed that the changes in solar
magnetic activity in the surface are transferred to the interplanetary magnetic
field around Earth (Chifu et al., 2022)[22]. However, the data points that are
distributed around the regression line indicate that they are not directly
linear in nature. Outliers especially at the moderate sunspots and the
relatively high IMF values point to the contribution of the transient solar and
interplanetary processes that increase the strength of IMF without depending on
sunspots.
Phase-wise Correlation Behaviour
To have a greater understanding, the solar cycle was
further divided into three stages, which included rising stage, solar maximum,
and declining stage. At the rising stage, the SSN and IMF magnitude grow in a
coherent and gradual manner, which causes the relatively stronger association.
This is the period of the systematic accumulation of solar magnetic flux. The
correlation slightly weakens at the solar maximum phase because the scattering
is greater. This is credited to the common nature of coronal mass ejections and
complicated magnetic structures, which bring about high variability of IMF
magnitude in short periods (Owens et al., 2017) [23]. During the declining
phase, the number of sunspots in the solar system steadily gets lower, and the
IMF magnitude tends to be high as a result of frequent high-speed streams of
solar wind caused by long-lasting coronal holes. This means that the correlation
in this phase is weaker than in the rising phase due to the increasing
contribution by non-sunspots-related drivers of solar wind.
Weak-Cycle Characteristics Interpretation.
The middle-level correlation seen in Solar Cycle 24
should be seen within the framework of its low activity in terms of the
magnetism. The decrease in the number of sunspots suggests that the overall
emergence of magnetic flux decreases, but not in roughly the same proportion as
the number of sunspots. This implies that dynamics in large scales of open
magnetic flux and heliospheric current sheets are significant in maintaining
the strength of IMFs even in feeble solar cycles.
Figure
5.Smoothing of solar cycle 24 sunspots number and IMF magnitude with 12 months
running mean.
These results point to the fact that Solar Cycle 24 is
characterized by specific solar-interplanetary coupling properties in
comparison with more stronger cycles and it stresses the necessity to make
cycle-specific analyses during the development of heliospheric and space
weather models(Schrijver & Siscoe, 2010)[24]. The current paper is an
investigation of the correlation between sunspots number and the magnitude of
the interplanetary magnetic field in Solar Cycle 24 that can shed light on the
solar-interplanetary coupling in the weak solar activity conditions. These
findings indicate that despite the fact that Solar Cycle 24 is characterized by
much lower sunspot activity than the last several cycles, the interplanetary
magnetic field still possessed a noticeable response to the changes in the
magnetic activity of the solar surface(Hapgood, 2017)[25].
The time plot reveals that the IMF magnitude generally
obeys the long-term curve of the sun spot number, with lesser values during the
prolonged solar minimum of 2008-2009 and greater values during the solar
maximum of the years 2013-2014. This action confirms the opinion that the
sunspot number as a proxy of solar magnetic flux emerging is significant in the
formation of the heliospheric magnetic field. The IMF however show a lot of
variation in the short run compared to the sun spot number, especially at the
peak and the falling stages of the cycle. This means that the action of the IMF
is not only subject to world solar activities but it depends on the temporary
and repeated interplanetary actions. The positive linear relationship that was
found to be moderate between SSN and IMF magnitude is mirrored by previous
studies that solar magnetic activity is an enhancement factor to the
interplanetary magnetic field. However, the scatter of the correlation plots
shows the non-linear and multi-scale character of the solar-heliospheric
interactions. Cases in which IMF magnitude is still high when the sunspots
wells have decreased indicate the prevalence of high-speed solar wind streams
of the long-lived coronal holes, which are more common in the fading step of
the solar cycle. These constructions are used to augment the open magnetic flux
and give relatively high IMF conditions regardless of the presence of sunspots.
These differences are further stressed out by
phase-wise analysis. The systematic accumulation of solar magnetic flux causes
weaker correlation during the rising phase in the coherent increase of both SSN
and IMF magnitude. On the contrary, during the solar maximum period, the
scatter is greater because of the high rate of coronal mass ejections and
complicated magnetic fields that present some sudden increase in the strength
of IMF. The least strong correlation is experienced in the declining phase
which is characterized by the prevalence of recurrent structures of solar winds
in the heliospheric conditions. These results have a valuable context that is
the weak nature of Solar Cycle 24. The interplanetary magnetic field is
maintained despite the decline in sunspots activity due to the continuing
moderate level of IMF strength, which indicates that the large-scale solar
magnetic structure and heliospheric current sheet processes are important in
maintaining the interplanetary magnetic field. This discovery has major
consequences concerning the research of the space weather since it demonstrates
that weak sunspot cycles do not likely imply equally weak conditions in the
heliospheric magnetism. It can be concluded that the discussion shows the
weakness of using sunspot number to explain interplanetary magnetic variability
only. Multiple solar and heliospheric parameters have to be taken into account
to have a full picture of solar-terrestrial interactions. The findings of the
present research support the significance of an analysis by cycle and add to
the meaningful knowledge regarding the dynamics of the heliosphere during weak
solar cycles.
CONCLUSION
This paper is a correlative investigation of the
sunspots number (SSN) and interplanetary magnetic field (IMF) strength across
the Solar Cycle 24, which is a solar cycle with an abnormally weak magnetic
flux. Using long term observational data on a monthly scale, the connection
between solar surface magnetic activity and heliospheric magnetic conditions in
the vicinity of the earth has been studied in a systematic manner. The time
series analysis shows that sun spot number has the typical pattern of solar
cycle, where it has a long and mild minimum period, a weak solar maximum, and a
slow decaying period. The magnitude of the interplanetary magnetic field
follows a long-term variation that is seen to be generally similar, with
increased values tending to be at times when sunspots tend to increase in
activity. IMF variability is however characterized by high short-term
fluctuations and this is a result of the impact of the temporary and recurrent
structures of solar winds.
The correlation analysis shows that during Solar Cycle
24, sun spot number and IMF magnitude are positively correlated, though
moderately. This observation proves the fact that solar surface magnetic
activity is significant in the control of the strength of the interplanetary
magnetic field. Meanwhile, the non-linearity of the relationship and the
scatter in the correlation plots show that the IMF behavior is not the one that
can be attributed to sunspot number only. The solar cycle is analyzed
phase-by-phase and significant variations in solar-interplanetary coupling can
be seen. The highest alignment between SSN and IMF magnitude takes place during
the rising period whereas the low level is observed during the solar maximum
and falling period as a result of the growing impact of coronal mass ejections
and fast high-speed streams of solar wind generated by coronal holes. These
findings highlight the multi-scale and complicated aspects of modulation of the
heliospheric magnetic fields. The results of this paper indicate that in weak
solar cycles, like Solar Cycle 24 the Sun can still can support a considerable
strength in interplanetary magnetic fields through the intense dynamics of
large-scale open magnetic flux and heliospheric current sheaths. Such
implications are significant to the space weather research, since it highlights
the significance of incorporating various solar and heliospheric parameters in
the evaluation of near-Earth space conditions.
Future studies can also build upon this study by
considering other IMF components (such as
REFERENCES
1.
Lockwood, M. (2013). Reconstruction
and prediction of variations in the open solar magnetic flux. Living
Reviews in Solar Physics, 10(4). https://doi.org/10.12942/lrsp-2013-4
2.
Zhang, J., Temmer, M.,
Gopalswamy, N., Veronig, A. M., Shen, F., Wang, Y., & Chi, Y. (2021). Earth-affecting
solar transients. Progress in Earth and Planetary Science, 8(33). https://doi.org/10.1186/s40645-021-00426-7
3.
Clette, F., &
Lefèvre, L. (2016). The new sunspot number: Assembling all corrections. Solar
Physics, 291(9–10), 2629–2651. https://doi.org/10.1007/s11207-016-0980-2
4.
Ashutosh Kumar Tiwari,
Devendra Gautam, C.M. Tiwari, Sri Krishna Singh, Vidya Sagar Chaudhary (2025)
“Study of Cosmic Ray Intensity in relation with Interplanetary Magnetic Field
and Dst for Solar Cycle 23 & 24”. JETIR.. PP 90-06.
5.
Kumar, Ashok & Gupta,
Meera. (2024). International Journal of Engineering Research & Management
Technology Correlation of Sunspot number with Interplanetary magnetic field,
Solar wind velocityandDst.
6.
Goyal, Sanjay &
Chaurasiya, Deepak & Shrivastava, P. (2023). Study of solar parameter and
interplanetary medium with geomagnetic parameter on the solar cycle 24
Citation. 10.26671/IJIRG.2023.4.12.102.
7.
Abha Singh and Kalpana
Patel (2021) “Statistical Study of Solar Activity Parameters of Solar Cycle 24”
Journal of Scientific Research, Volume 65, Issue 1. pp-197-200
8.
Jothe, M. (2015).
Correlative Study of Cosmic Ray Intensity and Sunspot Number for the Period of
Solar Cycles 23 and Ascending Phase of 24. International Journal of Science and
Research (IJSR). https://doi.org/10.21275/V4I12.NOV152547.
9.
Gonzalez, W. D.,
&Tsurutani, B. T. (1987). Criteria of interplanetary parameters causing
intense magnetic storms. Planetary and Space Science, 35(9), 1101–1109. https://doi.org/10.1016/0032-0633(87)90015-8
10.
Hathaway, D. H. (2015). The
solar cycle. Living Reviews in Solar Physics, 12(4). https://doi.org/10.1007/lrsp-2015-4
11.
King, J. H.,
&Papitashvili, N. E. (2005). Solar wind spatial scales in and
comparisons of hourly Wind and ACE plasma and magnetic field data. Journal
of Geophysical Research: Space Physics, 110(A2). https://doi.org/10.1029/2004JA010649
12.
Emery, W. J., &
Thomson, R. E. (2001). Data analysis methods in physical oceanography.
Elsevier.
13.
Bendat, J. S., &
Piersol, A. G. (2010). Random data: Analysis and measurement procedures
(4th ed.). Wiley.
14.
Chatfield, C. (2004). The
analysis of time series: An introduction (6th ed.). Chapman & Hall/CRC
15.
Wilks, D. S. (2011). Statistical
methods in the atmospheric sciences (3rd ed.). Academic Press.
16.
Pesnell, W. D. (2016). Solar
cycle predictions (invited review). Solar Physics, 291, 1353–1364. https://doi.org/10.1007/s11207-016-0897-9
17.
Petrovay, K. (2020). Solar
cycle prediction. Living Reviews in Solar Physics, 17(2). https://doi.org/10.1007/s41116-020-0022-z.
18.
Smith, E. J., &
Balogh, A. (2008). Decrease in heliospheric magnetic flux in this solar
minimum: Recent Ulysses magnetic field observations. Geophysical Research
Letters, 35, L22103. https://doi.org/10.1029/2008GL035345
19.
Borovsky, J. E., &
Denton, M. H. (2006). Differences between CME-driven storms and CIR-driven
storms. Journal of Geophysical Research: Space Physics, 111, A07S08. https://doi.org/10.1029/2005JA011447
20.
Cliver, E. W., &
Ling, A. G. (2011). The floor in the solar wind magnetic field revisited.
Solar Physics, 274, 285–301. https://doi.org/10.1007/s11207-010-9657-6
21.
Grandin, M., Kalliokoski,
M., &Kilpua, E. K. J. (2019). Properties and geoeffectiveness of solar
wind high-speed streams. Journal of Geophysical Research: Space Physics,
124, 1–18. https://doi.org/10.1029/2018JA026396
22.
Chifu, I., Mackay, D. H.,
& Petrie, G. J. D. (2022). Coronal magnetic field evolution over solar
cycle 24. Astronomy & Astrophysics, 657, A62. https://doi.org/10.1051/0004-6361/202141804
23.
Owens, M. J., Crooker, N.
U., & Lockwood, M. (2017). How is open solar magnetic flux lost over the
solar cycle?Journal of Geophysical Research: Space Physics, 122, 6–19.
24.
Schrijver, C. J., &
Siscoe, G. L. (2010). Heliophysics: Space storms and radiation.
Cambridge University Press.
25.
Hapgood, M. (2017). Space
weather: Its impact on Earth and implications for business. Living Reviews
in Solar Physics, 14(1). https://doi.org/10.1007/s41116-017-0008-7