Parameter Study of Geoeffective Active Regions

Abstract

Geomagnetic storms (GSs) are major disturbances in the terrestrial atmosphere caused by the reconnection process between the incoming plasma ejecta in the solar wind and the planetary magnetosphere. The strongest GSs can lead to auroral displays even at lower latitudes, and cause both satellite and ground-based infrastructure malfunctions. The early recognition of geoeffective events based on specific features on the solar photosphere is crucial for the development of early warning systems. In this study, we explore 16 magnetic field parameters provided by the Space-weather HMI Active Region Patch (SHARP) database from the SDO/HMI instrument. The analysis includes 64 active regions that produced strong GS during solar cycle (SC) 24 and the ongoing SC25. We present the statistical results between the SHARP and solar parameters, in terms of Pearson and Spearman correlation coefficients, and discuss their space weather potential.

1. Introduction

Active regions (ARs) are commonly regarded as the area of magnetic field concentrations roughly centered over a sunspot or sunspot group, visible on magnetograms and uniquely enumerated by the National Oceanic and Atmospheric Administration (NOAA). An updated definition was introduced by [1] as ‘…the totality of observable phenomena in a 3D volume represented by the extension of magnetic field from the photosphere to the corona…’ including electromagnetic (EM) emissions and strong twisted magnetic field emergence. Although the AR hallmarks are the loops connecting oppositely magnetic polarities and stretching out into the solar corona, ARs have been also recognized as the origin of diverse solar activity phenomena, including both EM emissions (from small-scale brightenings to solar flares, SFs [2,3]) and plasma motions (from jets to coronal mass ejections, CMEs [4,5]). Although SFs are usually regarded as the detected signatures across the EM spectrum, the underlying process of magnetic reconnection includes major reconfiguration of the magnetic structure in the AR, particle acceleration and mass motions. Large SFs are well known to correlate strongly with CMEs, which are the eruptions of magnetized plasma from the corona towards the heliosphere. Often, during their eruption and propagation, SFs and CMEs form shock waves that are known to accelerate particles. The solar energetic particles [6] consists mostly of protons, electrons and smaller fraction of heavy ions that gyrate along the heliospheric magnetic field lines.

The above agents of solar activity are known to have an impact in the heliosphere, on the planetary magnetospheres and atmospheres, technological devices, both in space and ground based, and are also considered a health risk for humans (https://www.esa.int/ESA_Multimedia/Images/2018/11/What_is_space_weather, accessed on 31 July 2024). This short-scale influence (from minutes to a month) of the Sun is termed ‘space weather’ (SW) [7,8,9] and nowadays is a subject of intense research. The different representations of solar activity have a distinct SW signature, see [10] and the references therein (https://www.esa.int/ESA_Multimedia/Videos/2018/11/What_is_space_weather, accessed on 31 July 2024). Namely, the EM emission from SFs is impacting mostly the ionosphere and the radio transmissions [11], the interplanetary (IP) counterparts of CMEs (or ICMEs) and their accompanied IP shocks wave are the primary cause for geomagnetic storms (GSs) and can also cause power blackouts [12], the solar energetic protons (SEPs) constitute a radiation hazard for astronauts [13], whereas the solar energetic electrons (SEEs) can damage the spacecraft corpus and systems [14]. All these phenomena are known to follow the solar cycle (SC) [15], defined as the (roughly 11-year) variation of the sunspot number (SN), and thus bound to the magnetic nature of solar activity.

Still, the estimation of the magnetic fields of solar eruptions is impeded by the lack of direct observations in the corona and IP space [16]. With the launch of the Solar Dynamics Observatory (SDO) spacecraft, photospheric magnetic maps (line-of-sight magnetic flux and vector magnetic field data) are provided with 1 arc second spatial resolution and 45 s cadence by the Helioseismic and Magnetic Imager (HMI), [17]. Based on the line-of-sight and and vector magnetograms, there are a number of methods developed for performing magnetic field extrapolations in the corona, starting with potential [16,18] to non-linear force-free solutions [19,20]. The structure of the IP magnetic field (IMF) is often approximated as a spiral, termed the Parker spiral [21], where the 2D shape (ecliptic plane projection) is a function of the solar wind speed. Later modifications, e.g., Fisk-type IMF [22], were also proposed. The propagation and merging of multiple ICMEs can, however, severely disturb the quiet-time, well-ordered IMF spiral [23].

Disturbances in the heliosphere (plasma and magnetic fields) are generated by the interactions and shock formation between fast and slow solar wind streams and by the transport and merging of ICMEs (modeled by, for example, https://www.spaceweatherlive.com/en/solar-activity/wsa-enlil.html, accessed on 31 July 2024). The most important requirement for the subsequent generation of disturbances in the planetary magnetosphere is the opposite (with respect to the planetary configuration) magnetic field orientation of the impacting plasma structure. The process that takes place is similar to the reconnection responsible for the generation of SFs. Thus, the embedded magnetic fields in the CMEs and their orientations and rotations in the IP space are crucial for the generation of disturbances in the planetary magnetospheres and a subject of ongoing research, e.g., [24,25,26] and the references therein.

The geomagnetic disturbances (together with the accompanying atmospheric effects, i.e., the polar lights, https://www.swpc.noaa.gov/content/aurora-tutorial, accessed on 31 July 2024) are the terrestrial aspect of these phenomena, and the term GS is used to describe the global decrease in the (horizontal) ground-based magnetic field [27]. Numerous parameters have been introduced to quantify the disturbance as listed in https://www.ncei.noaa.gov/products/geomagnetic-indices (accessed on 31 July 2024). For the purpose of the study here, we selected the disturbance storm time index (Dst), which is the hourly average of the magnetic field (given in negative nT) available since 1957 by the World Data Center for Geomagnetism—Kyoto, https://wdc.kugi.kyoto-u.ac.jp/dstdir/index.html (accessed on 31 July 2024). The values are derived from a network of near-equatorial geomagnetic observatories that measures the intensity of the globally symmetrical equatorial electrojet (the ‘ring current’). The latter ionospheric structure is an eastern flowing current created after the impact of magnetic ejecta (e.g., ICME) at the daytime magnetosphere and the subsequent magnetic reconnection between field lines; see, for example, [28]. A south-directed component of the ICME is a well-known precondition for the initiation of the process leading to a GS [29]. Thus, an important observational and/or numerical task is the accurate knowledge of the direction of the embedded magnetic field at the ICME front or/and flanks [30].

The problem of the correct identification of the ICME magnetic field direction is rooted in the possibility of the overall rotation and deflection of the CMEs during their propagation through the IP space; see the review by [31] and the relevant listed literature. The most probable reasons are considered the longitudinal deflection towards the equator due to (polar) coronal holes, clockwise filament rotation during the rise phase when originating at positive helicity source regions and vice versa, and CME−CME interaction in the heliosphere.

As noted by [31], the amount of CME rotation cannot be observed but is instead estimated based on comparison between the magnetic field orientation of pre-eruptive phenomena (e.g., polarity inversion line (PIL) of the source region or filament observations) and the ejecta at 1 AU (by the fitting of a 3D model to the in situ data).

At the photospheric end, one could evaluate the magnetic field properties of ARs also with the aid of HMI observations and their data products, although many models start from coronal structures [32]. Moreover, the importance of the interaction between the photospheric and heliospheric magnetic fields was shown early on, e.g., [33]. At the other end, i.e., 1 AU/ahead of Earth, one can sample the magnetic fields at a single point in the ICME structure. Caution needs to be applied to interpretations based on the single-point sampling of large ejecta or solar wind structures. By ensuring that a given IP structure leads to a GS, one could focus on the photospheric magnetic field structure of those events and search for tendencies in their properties. We point out that the IP transport is not accounted for by this approach, which is adopted also in the present study.

Thus, the main aim of the presented study is to investigate the parameters of ARs (e.g., the (orientation of) photospheric magnetic fields, current systems and energy density properties) leading to GSs, which we term geoeffective ARs. The significance of this work with respect to the previous research is to investigate in detail the link between the available magnetic field parameters and the parameters of GSs, SFs, and CMEs.

2. Data and Event Sample

For this study, we use all Space-weather HMI Active Region Patch (SHARP) products [34] that provide estimations of magnetic fields and fluxes, currents, helicity, and twist. The parameters are based on data from the SDO/HMI instrument. The database provides information about multiple parameters, calculated with a 12 min cadence, based on the automatic recognition of ARs, http://jsoc.stanford.edu/doc/data/hmi/sharp/sharp.htm (accessed on 31 July 2024).

The 16 SHARP parameters used in our study are as follows:

• USFLUX: Total unsigned flux [Mx];
• MEANGAM: Mean inclination angle, $\gamma$ [degrees];
• MEANGBT: Mean value of the total field gradient [G/Mm];
• MEANGBZ: Mean value of the vertical field gradient [G/Mm];
• MEANGBH: Mean value of the horizontal field gradient [G/Mm];
• MEANJZD: Mean vertical current density [mA/m²];
• TOTUSJZ: Total unsigned vertical current [A];
• MEANALP: Mean twist parameter, $\alpha$ [1/Mm];
• MEANJZH: Mean current helicity [G²/m];
• TOTUSJH: Total unsigned current helicity [G²/m];
• ABSNJZH: Absolute value of the net current helicity [G²/m];
• SAVNCPP: Sum of the absolute value of the net currents [A];
• MEANPOT: Mean photospheric excess magnetic energy density [Ergs/cm³];
• TOTPOT: Total photospheric magnetic energy density [Ergs/cm³];
• MEANSHR: Mean shear angle for B_total [degrees];
• R_VALUE: Unsigned flux, R [35] [Mx].

The details are described in [34].

As the aim of our analyses is to investigate the magnetic properties of geo-effective ARs, we start with a pre-selection of all GSs in SC24 (2009–2019). In order to improve the statistics, we extend the event list by including GSs with a Dst index below −50 nT in the current SC as well. Weaker than this threshold, GSs are not driven by fast solar wind structures [36] and thus are not considered SW effective. Moreover, the solar origin driver of weak GSs is very difficult to identify.

We use the Dst values as reported in the final and provisional Kyoto lists by mid-2023, https://wdc.kugi.kyoto-u.ac.jp/dst_final/index.html (accessed on 31 July 2024) and https://wdc.kugi.kyoto-u.ac.jp/dst_provisional/index.html (accessed on 31 July 2024), leading to the compilation of an initial list of 125 events. The next step is the identification of the solar origin of the GSs, following the procedure described in [37]. Firstly, the GS association of the ICME is completed using the online catalogs provided by https://izw1.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm (accessed on 31 July 2024) [38,39] together with its parent CME as reported by the Coordinated Data Analyses workshop (CDAW) database, https://cdaw.gsfc.nasa.gov/CME_list/ (accessed on 31 July 2024) [40] using data from the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric COronagraph (LASCO) instrument, where possible. From the SOHO/LASCO CDAW reports, we adopt the CME projected (linear) speed and the angular width (AW). After completing the analysis of the original list of 125 GSs, we could finally identify the CME-origin for 84 cases.

Then, we continue with the identification of the CME-associated SF, using the information provided in the Geostationary Operational Environmental Satellite (GOES) reports https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/ (accessed on 31 July 2024) and also https://solarmonitor.org/ (accessed on 31 July 2024). In addition to the timing of the SF, we collect the SF class, location on the solar disc, and number of AR, if reported. In the final step, the parent AR (mostly related to the SF) is selected and is used as the link to the SHARP data. After the association procedure and the check with SHARP data availability, the final number of events dropped to 64 as provided below,

Table 1. Event list based on GSs detected since 2009 with an identified solar origin. Dst index is in nT; time in UT; SF class, timing (onset, peak and end times), location and AR are from the GOES reports; CME information is from the CDAW database; speed in km s⁻¹; d: double; h: hour; m: multiple; u: uncertain; v: visual. SR types are given at the day of the SF/CME and in the case of any changes on the following day, the type is shown in parentheses.

No.	GS			SR	CME		SF
	yyyy-mm-dd	h	Dst	Type	Day/Onset	Speed	AW	Onset/Peak/End	Class	Location	AR
1	2010-08-04	2	−74	$\alpha$	01/13:42	850	360	07:55/08:26/09:35	C3.2	N20E36	11092
2	2011-03-11	6	−83	$\beta \gamma \delta$	07/20:00 u	2125	360	19:43/20:12/20:58	M3.7	N31W53	11164
3	2011-08-06	4	−115	$\beta \gamma$ ($\beta \gamma \delta$)	04/04:12	1315	360	03:41/03:57/04:04	M9.3	N19W36	11261
4	2011-09-10	5	−75	$\beta \gamma$ ($\beta \gamma \delta$)	06/23:06 u	575	360	22:12/22:20/22:24	X2.1	N14W18	11283
5	2011-09-26	24	−118	$\beta \gamma$ ($\beta \gamma \delta$)	24/12:48	1915	360	12:33/13:20/14:10	M7.1	N10E56	11302
6	2011-09-28	7	−68	$\beta \gamma$ ($\beta \gamma \delta$)	24/19:36 u	972	360	19:09/19:21/19:41	M3.0	N12E42	11302
7	2011-10-25	2	−147	$\alpha$ (no)	22/10:24	1005	360	10:00/11:10/13:09	M1.3	N25W77	11314
8	2012-01-23	6	−71	$\beta$	19/14:36	1120	360	13:44/16:05/17:50	M3.2	N32E22	11402
9	2012-01-25	11	−75	$\beta$	23/04:00	2175	360	03:38/03:59/04:34	M8.7	N28W21	11402
10	2012-02-27	20	−57	$\alpha$ ($\beta$)	25/15:12 u	1039	97	14:20/15:00/15:15	B5.9	N09E68 v	11424
11	2012-03-04	2	−50	no	02/18:00 u	710	206	17:29/17:46/18:07	M3.3	N16E83	11429
12	2012-03-07	10	−88	$\beta \gamma$ ($\beta \gamma \delta$)	04/11:00 d	1306	360	10:29/10:52/12:16	M2.0	N19E61	11429
13	2012-03-09	9	−145	$\beta \gamma \delta$	07/00:24	2684	360	00:02/00:24/00:40	X5.4	N17E27	11429
14	2012-03-12	17	−64	$\beta \gamma \delta$	10/18:00	1296	360	17:15/17:44/18:30	M8.4	N17W24	11429
15	2012-03-15	21	−88	$\beta \gamma$	13/17:36	1884	360	17:12/17:41/18:25	M7.9	N17W66	11429
16	2012-04-13	5	−60	no	09/12:36 u	921	360	12:12/12:44/13:08	C3.9	N20W65	11451
17	2012-06-17	14	−86	$\beta \gamma \delta$	14/14:12 u	987	360	12:52/14:35/15:56	M1.9	S17E06	11504
18	2012-07-09	13	−78	$\beta \gamma \delta$	06/23:24 u	1828	360	23:01/23:08/23:14	X1.1	S13W59	11515
19	2012-07-15	17	−139	$\beta \gamma \delta$	12/16:48	885	360	15:37/16:49/17:30	X1.4	S15W01	11520
20	2012-09-03	11	−69	$\alpha$	31/20:00 u	1442	360	19:45/20:43/21:51	C8.4	S19E42	11562
21	2012-09-05	6	−64	$\beta \gamma$	02/04:00	538	360	01:50/01:58/02:10	C2.9	N03W05	11560
22	2012-10-01	5	−122	$\beta$	28/00:12	947	360	23:36/23:57/00:34	C3.7	N06W34	11577
23	2012-10-13	8	−90	no	09/00:48 u	692	122	23:56/01:06/02:01	C2.0	S26E86	11589
24	2013-03-01	11	−55	$\beta \gamma$	27/04:00 u	622	138	03:25/03:32/03:39	B8.3	S19W05	11682
25	2013-03-17	21	−132	$\alpha$	15/07:12	1063	360	05:46/06:58/08:35	X1.1	N11E12	11692
26	2013-03-29	17	−59	no ($\alpha$)	23/12:24 u	663	177	12:15/12:22/12:27	B6.8	N17E87 u	11704
27	2013-05-18	5	−61	$\beta \gamma \delta$	15/01:48 m	1366	360	01:25/01:48/01:58	X1.2	N12E64	11748
28	2013-05-19	15	−51	$\beta \gamma \delta$	17/09:12	1345	360	08:43/08:57/09:19	M3.2	N12E57	11748
29	2013-05-25	7	−59	$\beta$	22/13:26	1466	360	13:08/13:32/14:08	M5.0	N14W87	11745
30	2013-07-06	19	−87	no ($\beta$)	03/07:24 u	807	267	07:00/07:08/07:18	M1.5	S11E82	11787
31	2013-10-02	8	−72	$\beta \gamma$	29/22:12	1179	360	21:43/23:39/01:03	C1.2	N10W43	11850 v
32	2013-10-30	24	−54	$\beta \gamma \delta$	28/02:24	695	360	01:41/02:03/02:12	X1.0	N04W66	11875
33	2014-02-19	9	−119	$\beta \gamma$	16/10:00	634	360	09:20/09:26/09:29	M1.1	S11E01	11977
34	2014-02-27	24	−97	$\alpha$	25/01:26	2147	360	00:39/00:49/01:03	X4.9	S12E82	11990
35	2014-11-10	18	−65	$\beta \gamma \delta$	07/18:08 u	795	293	16:53/17:26/17:34	X1.6	N15E33	12205
36	2014-12-22	6	−71	$\beta \gamma \delta$	17/05:00 u	587	360	04:25/04:51/05:20	M8.7	S20E09	12242
37	2014-12-23	23	−57	$\beta \gamma \delta$	19/01:05 u	1195	360	21:41/21:58/21:45	M6.9	S11E15	12242
38	2014-12-24	23	−53	$\beta \gamma \delta$	20/01:26 u	830	257	00:11/00:28/00:55	X1.8	S21W24	12242
39	2014-12-26	2	−57	$\beta \gamma \delta$	21/12:12 u	669	360	11:24/12:17/12:57	M1.0	S14W25	12241
40	2015-03-17	23	−234	$\beta \gamma \delta$	15/01:48	719	360	01:15/02:13/03:20	C9.1	S22W25	12297
41	2015-06-23	5	−198	$\beta \gamma \delta$	21/02:36 m	1366	360	01:02/01:42/02:00	M2.0	N12E16	12371
42	2015-06-25	17	−81	$\beta \gamma \delta$	22/18:36 d	1209	360	17:39/18:23/18:51	M6.5	N12W08	12371
43	2015-06-26	18	−51	$\beta \gamma$	25/08:36 u	1627	360	08:02/08:16/09:05	M7.9	N09W42	12371
44	2015-08-16	8	−98	$\beta$	12/14:48 u	647	204	14:26/15:26/16:47	B7.0	S27W27	12399 v
45	2015-08-23	9	−57	$\beta \gamma$ ($\beta \gamma \delta$)	22/07:12 u	547	360	06:39/06:49/06:59	M1.2	S15E13	12403
46	2015-09-20	16	−81	$\beta \gamma$	18/05:00	823	131	04:22/06:31/07:20	C2.6	S21W10	12415
47	2015-10-18	10	−56	$\beta$ ($\beta \gamma$)	14/00:24 u	770	79	23:34/23:40/23:44	B6.4	S06E76	12434
48	2015-11-03	13	−51	$\beta \gamma \delta$ ($\beta \gamma$)	01/12:00 m	751	114	12:03/12:06/12:10	C1.3	N07E30	12443
49	2015-11-07	7	−87	$\beta \delta$	04/14:48	578	360	13:31/13:52/14:13	M3.7	N09W04	12443
50	2015-11-10	14	−56	$\beta$	09/13:26 u	1041	273	12:49/13:12/13:28	M3.9	S11E41	12449
51	2015-12-14	20	−55	$\beta$	11/04:36 u	628	84	04:22/04:47/05:15	C1.4	S15E52	12468
52	2015-12-20	23	−166	$\beta$	16/09:36	579	360	08:34/09:03/09:23	C6.6	S13W04	12468
53	2016-02-01	9	−53	$\beta$ ($\beta \gamma$)	28/22:12 u	684	71	21:48/21:57/22:02	C3.3	N09W50	12488
54	2016-02-16	20	−65	$\beta \gamma$ ($\beta \gamma \delta$)	11/21:18 u	719	360	20:18/21:03/21:28	C8.9	N09W08	12497
55	2017-04-22	17	−51	no ($\beta \gamma$)	18/19:48	926	360	19:21/20:10/20:49	C5.5	N14E77	12651
56	2017-07-16	16	−72	$\beta$	14/01:26	1200	360	01:07/02:09/03:24	M2.4	S06W29	12665
57	2017-09-08	2	−122	$\beta \gamma \delta$	06/12:24	1571	360	11:53/12:02/12:10	X9.3	S08W33	12673
58	2021-05-12	15	−61	$\beta$ ($\beta \gamma$)	09/12:00	266	284	13:38/13:58/14:09	C4.0	N15E51	12822
59	2021-10-12	15	−65	$\beta \gamma$	09/07:12	712	360	06:19/06:38/06:53	M1.6	N17E09	12882
60	2022-02-03	11	−66	$\beta$	29/23:36	530	360	22:32/23:32/00:32	M1.1	N17E11 v	12936 v
61	2022-02-10	20	−60	$\beta$	06/14:00	334	360	12:52/13:41/14:41	C3.1	S20W07	12939
62	2022-04-14	22	−81	no	11/05:48	940	360	04:59/05:21/05:58	C1.6	S18E11	12987 v
63	2023-02-27	13	−132	$\beta$	25/19:24	1170	360	20:03/20:30/21:29	M3.7	N23W43	13229 v
64	2023-04-24	7	−213	$\beta$	21/18:12	1284	360	17:44/18:12/18:44	M1.7	S22W11	13283 u

.

The SF class is defined as the peak value of the soft X-ray (SXR) flux, in Wm⁻², with the so-called X-class being the most energetic eruptive phenomena, with SXR flux above 10⁻⁴ Wm⁻², whereas the M, C, B, A-classes are 10 times smaller than the previous. At the day of SF occurrence, we also check the NOAA reports and collect the solar region (SR) types based on the so-called $\alpha$-$\beta$-$\gamma$ (or Mount Wilson sunspot magnetic) classification, https://www.spaceweather.com/glossary/magneticclasses.html (accessed on 31 July 2024).

The results from Table 1 show a wide distribution of the Dst index, with mean (median) values of −86 (−72) nT, respectively. The values are very similar compared to the overall distribution of GSs in the last two SCs [37], reporting −86 (−69) nT. The CMEs identified as the GS-origin have values for the projected speed of ∼750 (620) km s⁻¹, and are predominantly halo, with 51/64 cases with 360 degrees for the AW. The CMEs in our list are much slower than those reported by [37], ∼1000 (870) km s⁻¹. In contrast, the CME-related SFs in Table 1 have larger mean/median SXR flux of M6.9 (M1.6) compared to M1.5 (M1.4) in [37].

The resulted SR types are as follows: 6 $\alpha$, 16 $\beta$, 1 $\beta \delta$, 15 $\beta \gamma$, 19 $\beta \gamma \delta$, and 7 cases had no reported SR type. We note that the used identification for limb events is partially reliable, as the classification changes from one day to the next. In our list, eight events have a reported longitude larger than 80 degrees. In addition, since the reports are conducted at midday, they give more accurate information for the previous day. This is why we also collect the SR reports on the day following the SF. Any changes in the SR type are listed in parentheses in Table 1. The updated SR results are mostly consistent, providing 5 $\alpha$, 15 $\beta$, 1 $\beta \delta$, 13 $\beta \gamma$, 25 $\beta \gamma \delta$, and 5 cases had no reported type.

3. Results

3.1. Timing Estimation

The temporal evolution of the SHARP parameters is explored for all events in our list, Table 1, with an example shown in Figure 1 for the event on 1 August 2010. Daily overviews are generated for all events. The flare timings are over-plotted with different colors, for the start (green), peak (red) and end (blue) times, respectively. Some of the parameters have redundant trends, though we decided to keep all 16 SHARP parameters while performing the correlation analysis.

By inspecting the temporal behavior of all events in the sample (not provided), we notice no consistent trends in the daily trends and especially around the time of the SF. Moreover, the change of the different SHARP parameters is usually within a rather narrow range.

Several time markers can be considered while selecting a representative value of each SHARP parameter, namely, the following:

• An exact value taken just prior to the SF start;
• Averaged value during the rise phase of the SF (onset-to-peak);
• Averaged value during the entire SF duration (onset-to-end);
• Averaged value during the decline phase of the SF (peak-to-end).

The statistical correlations were performed using all four values of the SHARP parameters, leading to consistent results (explicitly shown at https://astro.bas.bg/project-sun/, accessed on 31 July 2024). In this work, we present the results for the first estimation only, namely, based on the SHARP values prior to the SF onset.

3.2. Correlations

The results are organized in terms of linear (Pearson) and non-linear (rank or Spearman) correlation coefficients. The event size (n) is the same (64) for all pairs and one could easily calculate the standard error for a given correlation coefficient (r), as $\sqrt{(1-r^2)/(n-2)}$, proposed by [41]. For the two extreme cases, we obtain 0.01 ± 0.13 and 0.99 ± 0.01, which demonstrates the statistical validity of the obtained correlations.

The matrix of the Spearman correlations is shown in Figure 2 for the entire sample, whereas the Pearson correlations are organized in Appendix A, Figure A1. By comparing the two matrices, one can deduce that overall, the values for the Spearman correlations are larger compared to the Pearson ones, however, not statistically significant. The larger values are shown in darker color with the exact value present in the respective cell. The lowest correlation coefficients are obtained between the SHARP parameters and the Dst index of the GSs (first column in both matrices). The correlations with the SF class are stronger than those obtained with the CME speed and AW. The flare rise time and duration do not correlate with the SHARP parameters.

The total unsigned magnetic flux (USFLUX) has the strongest correlation coefficients (well above 0.8–0.9) with the other summed values, namely, for the current, current density and energy density. Also, USFLUX correlates strongly with the net current helicity, net currents, R-value, and SF class.

In contrast, all components of the field gradients are well inter-correlated but are poorly related to the other SHARP and solar parameters, with the exception of the horizontal gradient (MEANGBH) responding well to the mean shear angle (MEANSHR), the other components of the field gradient, and the inclination angle (MEANGAM). Interestingly, the components of the field gradient do not correlate well with the remaining SHARP and solar parameters. Similarly, the mean twist parameter (MEANAPL) correlates well only with the mean current helicity (MEANJZH).

The inclination angle (MEANGAM), however, has large correlation coefficients with the shear angle (MEANSHR), the excess energy density (MEANPOT), and the horizontal gradient (MEANGBH). The remaining SHARP parameters from the list (total/net current, current helicities and magnetic energy densities) show strong inter-correlations.

In addition, we present the correlation matrices for two sub-sets, namely, for the strong (with Dst index ≤ −100 nT) and weak GSs (with Dst index from ≤−50 to −100 nT). The results are shown in Figure 3 for the Spearman correlations and in Figure A2 for the Pearson correlations. The correlation matrices are optimized for the sub-set of parameters with moderate-to-strong correlations. The strong GSs are associated with halo CMEs only; thus, the AW parameter will be dropped. Apart from the flare rise and duration, we drop also MEANGBT, MEANGBZ, MEANJZD, MEANALP, MEANJZH. The matrices with the complete set of parameters are available online, https://astro.bas.bg/project-sun/ (accessed on 31 July 2024). After comparing the results in Figure 3, as expected, we obtain stronger correlations for nearly all pairs for the case of stronger GSs. Moreover, for the majority of the correlations between the SHARP parameters, the differences between the strong and weak GS samples are statistically significant.

3.3. Scatter Plots

The distribution (linear scatter plots) of the SHARP parameters vs. the Dst index are explicitly shown in Figure 4, except for the R-value due to a lack of correlation in that case (close to 0). Overall, the points tend to cluster at lower values of the Dst (i.e., upper part of the scatter plots).

Similar sets of scatter plots are prepared for the correlations with the SF class and CME speed, available as supplementary materials and also online, https://astro.bas.bg/project-sun/ (accessed on 31 July 2024). The correlations between the SHARP parameters and the SF class show clustering of the values at the C and M classes with some outliers; however, this could be an artifact of the chosen linear scale (used for consistency in all cases). The strongest correlations (e.g., with the total values of the unsigned flux, vertical current, and magnetic energy density) show only few isolated outliers. On the other hand, the correlations with the CME speed show large scatter for most of the correlations, with occasional clustering of the data points (i.e., with MEANJZD, MEANAPL, and MEANJZH).

While inspecting Figure 4 for MEANGBT, MEANGBZ, MEANJZD, MEANAPL, and ABSNJZH, one notices notable outliers. In order to quantify the effect of the outliers (usually at very large values of the selected SHARP parameter), we calculate the Spearman correlation coefficients and their uncertainty after their removal:

• Dst vs. MEANGBT: $-0.16\pm 0.13$ ($-0.17\pm 0.13$);
• Dst vs. MEANGBZ: $-0.22\pm 0.12$ ($-0.24\pm 0.12$);
• Dst vs. MEANJZD: $-0.22\pm 0.12$ ($-0.16\pm 0.13$);
• Dst vs. MEANAPL: $0.02\pm 0.13$ ($0.06\pm 0.13$);
• Dst vs. ABSNJZH: $-0.17\pm 0.13$ ($-0.22\pm 0.12$),

where the values over the original sample are given in parentheses. There is only a small difference between the correlation coefficients of the reduced and original samples, and these are not statistically significant (e.g., there is a large uncertainty of up to 13%). Thus, no significant improvement in the correlations with the GSs is to be expected after the removal of notable outliers.

4. Discussion

Based on the obtained correlations, several of the SHARP parameters are not very promising markers of statistical associations and could well be dropped in larger studies in order to save resources, namely, the components of the field gradient (MEANGBT, MEANGBZ, and MEANGBH), the vertical current density, twist, and current helicity (MEANJZD, MEANAPL and MEANJZH, respectively). In contrast, the parameters for the total flux, current, current helicity, magnetic energy density, and shear angle show moderate-to-strong correlations also with the SF class and the CME parameters but not with the Dst index.

The low correlations between the SHARP parameters and the Dst index of the GSs can be interpreted twofold. On one side, the lack of correlation can be explained as a lack of causation between the AR magnetic field properties and the resultant Dst index of the GSs. Namely, the AR generates the eruption only, and under suitable coronal conditions, the resultant CME can escape into the IP space. Thus, an ejecta is geoeffective when a combination of suitable conditions are present in the heliosphere (and unrelated to the distribution of the surface magnetic fields): specific direction of propagation (i.e., Earth-directed/halo CMEs) with strong southward-directed magnetic fields. Finally, the early precursors of geo-effective eruptions need to be sought in the correct identification of the magnetic properties of the ejecta and/or its tracking its orientation through the heliosphere.

The majority of the ARs in our list are classified as the $\beta \gamma \delta$ type (∼40% or 25/64), $\beta \gamma$ and $\beta \delta$ (14/64), which is evidence of their magnetic field complexity. This is consistent with the trends of complex magnetic configurations leading to solar eruptive events [42,43]. Also, complex ARs (like $\beta \gamma \delta$) have more than one PIL, and the main direction of the magnetic field of the ejecta will depend on at which PIL the flare/CME is originating.

Thus, an alternative interpretation of our findings can be put forward, namely, the correlation is lost due to the subsequent rotation or deflection of the eruptions in the solar corona [44,45] and/or in the heliosphere, at least for some of the cases. These effects would mask any trends of the underlying magnetic structure of the parent ARs. Namely, some of the GSs may originate from initially unfavorable magnetic field conditions and, vice versa, initially southward magnetic field configurations can be lost in the IP space.

The small event size in our case (64 ARs with SHARP data and accompanied GSs) is also insufficient to highlight the trends, if any. Moreover, our analysis is based on photospheric magnetic fields with no subsequent tracking of the resultant ICMEs. In this way, the conditions in the IP space turn out to be a crucial factor for the geomagnetic potential of the IP ejecta, whereas the AR configuration can be explored for solar eruption forecasting.

In order to differentiate between the two scenarios, one needs to deduce the magnetic field configurations of CMEs in the corona and IP space, which is the missing piece of information between the remotely observed photospheric and in situ detected magnetic fields. With the lack of multiple spacecraft from the sun to Earth, the improvement in CME modeling seems to be the only solution at present [26].

Alternatively, we expect closer association between the SHARP parameters and SFs because there is some direct causal connection (i.e., large flares are only possible if there is large amount of free energy and if the AR is highly non-potential). This is why previous studies have focused on the properties of SFs (e.g., confinement or not [46,47]).

In summary, there are many uncertainties involved in the relationship between the SHARP parameters of the ARs and the geomagnetic effect of the CMEs they produce: most important are the changes close to the Sun (like CME deflection/rotation) and in the IP space (change in ICME speed due to interaction with ambient solar wind flow, erosion of the ICME magnetic field due to interaction with IMF, etc.). These aspects deserve further investigation. When a comprehensive list of (I)CME deflections is available, the above analyses could be performed using such event groups. In this way, the effect of (I)CME deflection/rotation on the correlations between AR properties and the geomagnetic impact (Dst) can be quantitatively tested.

5. Conclusions

This study focuses on the exploration of the statistical relationship between a set of magnetic field parameters of ARs (from SDO/HMI SHARP database) with the properties of solar eruptions and GSs. A search for the parent ARs of GSs during SC24 leads to a final list of 64 events. The main findings from the statistical analyses can be summarized as follows:

• The mean (median) value of the Dst index of our sample of GSs is −86 (−72) nT, which is similar to the respective value over the last two SCs −86 (−69) nT [37].
• The GS-associated CMEs are slower with the mean (median) projected speed of ∼750 (620) km s⁻¹, compared to the ∼1000 (870) km s⁻¹ values reported by [37] over SC23+24.
• The GS-associated SFs have larger mean SXR flux of M6.9 compared to M1.5 reported by [37] over SC23+24, although the median value is nearly the same.
• Selected SHARP (MEANGBT, MEANGBZ, MEANJZD, MEANALP, and MEANJZH) and solar (flare rise and duration) parameters show weak or negative statistical correlations with the other SHARP or solar parameters, apart from a few strong inter-correlations.
• The remaining SHARP parameters (USFLUX, MEANGAM, MEANGBH, TOTUSJZ, TOTUSJH, ABSNJZH, SAVNCPP, MEANPOT, TOTPOT, and MEANSHR) show moderate-to-strong correlations with the SF class (but not to the rise and duration times) and to a degree also with the CME speed and AW, whereas no correlation is found with the Dst index of the GSs. The latter correlation trend is improved slightly when considering strong GSs (with Dst ≤ −100 nT).
• The weak correlations with the GSs are not improved after the removal of outliers from the event samples.

In the current analyses, we started with the list of GSs and deduced their solar origin, in terms of CMEs, SFs, and ARs. The opposite direction, starting with a comprehensive list of ARs, summarizing their SHARP parameters and exploring the resultant GSs, goes beyond the scope of this work.

The closer association between the SHARP parameters and the geoeffective SFs obtained in the present study has been previously reported but for the research topic of confined vs. eruptive SFs [48], and thus for a different event sample. Alternative (to SHARP) photospheric magnetic field parameters for flare eruption are also proposed [49]. Nevertheless, the SHARP parameters seem to be more promising for exploring the photospheric link to SFs and/or CMEs, despite the large scatter present. The semi-automatic numerical procedures developed in this work (https://github.com/MohamedNedal/sharp_analysis, accessed on 31 July 2024) are currently being optimized in order to be applied to a much larger sample of SFs detected since SC24. The investigation of the AR configurations for confined and eruptive SFs, based on the SHARP parameters, is under way and will be reported elsewhere.