Reconnection Fluxes in Eruptive and Confined Flares and Implications for Superflares on the Sun

During solar flares, huge amounts of energy are released over a course of tens of minutes (Fletcher et al. 2011). The energy is stored in stressed coronal magnetic fields and released via magnetic reconnection (Priest & Forbes 2002). While a flare can occur together with a coronal mass ejection (CME), flares without CMEs or CMEs without flares are also frequently observed. Yashiro et al. (2005) studied the association rate of flares and CMEs. In their study, they found an association rate of 20% for small (C-class) flares, which steeply increases with increasing flare strength. About 50% of the M-class flares are associated with a CME, while the percentage increases up to >90% for X-class flares. Finally, all flares ≳X5 are associated with CMEs.

The widely accepted model for the physical processes in eruptive two-ribbon flares is the CSHKP model, based on the works by Carmichael (1964), Sturrock (1966), Hirayama (1974), and Kopp & Pneuman (1976). A rising filament leads to the formation of a current sheet below it, and, due to some instabilities, magnetic reconnection sets in. Within this framework and its extension to three dimensions, many of the observed flare features can be successfully explained (cf. review by Janvier et al. 2015). The flare ribbon evolution gives indirect evidence of the magnetic reconnection process and can be observed at Hα, (E)UV, and hard X-ray (HXR) wavelengths (cf. reviews by Fletcher et al. 2011; Holman 2016; Benz 2017). The flare ribbons mark the chromospheric footpoints of the newly reconnected magnetic field and are caused by energetic particles transported downward along the field lines, in particular by accelerated electron beams (for reviews of the underlying reconnection process, see, e.g., Priest & Forbes 2002; Shibata & Magara 2011).

The reconnection process itself takes place in the corona and is in general not accessible to direct observations. Therefore, we have to rely on other means to get insight into the associated energy release processes. Forbes & Priest (1984) showed that in 2D, the reconnection rate in a flare is directly proportional to the reconnection electric field in the corona, E₀, and can be derived from observed quantities as

$$\begin{eqnarray}&&{E}_{0}={B}_{n}{V}_{R},\end{eqnarray} \tag{ 1 }$$

where B_n is the component of the photospheric magnetic field normal to the surface and V_R is the separation velocity of the flare ribbons perpendicular to the polarity inversion line. Forbes & Lin (2000) generalized Equation (1) to three dimensions to overcome the limitations of the 2D magnetic field configuration required in Equation (1). They considered the magnetic flux, φ, of one polarity swept by the flare ribbons:

$$\begin{eqnarray}&&\varphi ={\iint }_{A}{\boldsymbol{B}}\cdot d{\boldsymbol{a}}.\end{eqnarray} \tag{ 2 }$$

By taking the time derivative of Equation (2), one obtains an expression for the rate of change in the reconnection magnetic flux over time in the form

$$\begin{eqnarray}&&\dot{\varphi }={\int }_{C}({\boldsymbol{B}}\times {{\boldsymbol{V}}}_{R})\cdot d{\boldsymbol{l}}={\oint }_{C}{{\boldsymbol{E}}}_{0}\cdot d{\boldsymbol{l}},\end{eqnarray} \tag{ 3 }$$

where ${{\boldsymbol{E}}}_{0}$ is the electric field along a separator line, ${\boldsymbol{B}}$ is the magnetic field vector measured in the photosphere, and C is the closed curve surrounding the newly closed area A. A separator line is a field line connecting a pair of magnetic neutral points. Due to line tying, in Equation (3), the term $\partial {\boldsymbol{B}}/\partial t$ is neglected. Equation (3) gives the voltage drop along the separator line and corresponds to the rate of open flux converted to closed flux (Forbes & Lin 2000).

This method was used in several case studies to derive magnetic reconnection rates in flares (e.g., Qiu & Yurchyshyn 2005; Miklenic et al. 2007, 2009; Veronig & Polanec 2015). Qiu & Yurchyshyn (2005) showed that the speed of the associated CME correlates with the amount of flux processed during magnetic reconnection. They also noted that the amount of flux in opposite-polarity regions involved in the reconnection should equal each other, and that this balance is never perfectly obtained due to measurement uncertainties. Thus, they argued that a ratio of positive and negative magnetic flux in the range [0.5, 2] is a reasonable range to identify flux balance. Veronig & Polanec (2015) found a correlation between the total reconnection flux and the peak soft X-ray (SXR) flux of c = 0.78 using data of 27 eruptive flares collected from four different studies. In addition, it was found that $\dot{\varphi }(t)$ resembles the flare HXR time profile and the SXR time derivative, both proxies of the energy release rate in the flare (Miklenic et al. 2009; Veronig & Polanec 2015).

This empirical relationship between the HXR (and microwave) flux produced by flare-accelerated electrons and the time derivative of the SXR flux was termed the "Neupert effect" by Hudson (1991), based on its first recognition in Neupert (1968). Therafter, it has been established in several observational studies (e.g., Dennis & Zarro 1993; Veronig et al. 2002, 2005). The HXR flux in solar flares is due to nonthermal bremsstrahlung from electrons that are accelerated during the energy release process by magnetic reconnection in the corona and precipitate downward along the newly reconnected (closed) field lines. Most of the nonthermal HXR emission is produced when the electrons reach the chromosphere, due to the steep gradient in the column density, emitting nonthermal bremsstrahlung when scattering off the ions of the ambient plasma (Brown 1971, 1973). Thus, the HXR flux is an instantaneous response to this energy input by flare-accelerated electrons, which carry a large fraction of the total energy released during a flare (e.g., Hudson 1991; Dennis et al. 2003). The increase of the SXR flux during a flare is due to the response of the chromosphere and corona to the heating by collisions of the high-energy flare electrons with the thermal electrons of the ambient plasma. The strong heating of the chromosphere causes the upper chromospheric layers to convect into the corona in a process called "chromospheric evaporation" (Neupert 1968; Fisher et al. 1985). This process increases the density and temperature in the flare loops, which results in a continuous increase of the SXR emission during the flare impulsive phase. Thus, the SXR flux profile is an indicator of the cumulated flare energy (ignoring cooling effects to first order), whereas the HXRs are a proxy of the instantaneous flare energy release rate (Veronig et al. 2005).

Recently, several statistical studies of flare reconnection fluxes and their relation to the flare energy in terms of the GOES SXR peak flux became available. Toriumi et al. (2017) studied all flare events of GOES class ≥M5.0 that occurred in the period 2010 May to 2016 April and within 45° from the center of the solar disk, a total number of 51 events. They found a low correlation between the GOES peak flux and the total magnetic flux swept by flare ribbons derived from Solar Dynamics Observatory (SDO) AIA 1600 Å data, c = 0.37 in log–log space. Kazachenko et al. (2017) analyzed more than 3000 flares (GOES class C1.0 and larger) that occurred between 2010 May and 2016 April and within 45° from the disk center, also using SDO AIA 1600 Å data. They found a Spearman ranking correlation coefficient of 0.66 between the peak SXR flux and the magnetic flux swept by the flare ribbons. In both studies, the largest flare in the data set was of GOES class X5.4.

In the present study, we perform a similar analysis but with the following important differences. (1) Our data set comprises a large range from B3 to X17, i.e., covering almost four orders of magnitude in GOES class. (2) We use full-disk Hα filtergrams for the analysis of the flare-associated ribbons and corresponding estimation of the reconnection fluxes. (3) We study the relationship between the reconnection flux and the flare GOES class separately for confined and eruptive flares. (4) We discuss the implications of our findings with respect to the largest flares that can be expected from the present day's Sun and their relation to stellar superflares on solar-like stars recently discovered by the Kepler satellite (Maehara et al. 2012).

In this study, we use high-cadence full-disk Hα filtergrams and line-of-sight (LOS) magnetograms to calculate the magnetic reconnection fluxes and rates of a homogeneous data set of 51 confined and eruptive flares distributed over four orders in GOES class (cf. Table 1). High-cadence Hα filtergrams are provided by Kanzelhöhe Observatory for Solar and Environmental Research (KSO; http://kso.ac.at). We selected the events based on the flares observed by KSO.³

For our data set, we aimed for a broad distribution over the flare classes and to include eruptive as well as confined flares of different classes. We limited the selection to events within 45° of the center of the solar disk in order to reduce uncertainties due to projection effects. Between 2000 and 2015, KSO observed a total of 4357 flares, of which 15 were of Hα importance class 3 or 4. All of them occurred close enough to the center of the solar disk and therefore are selected for our study. Then, we selected an appropriate number of well-observed smaller flares, beginning with class 2 flares. Finally, we selected a number of suitable flares of classes 1 and subflares (S), beginning in 2014 and going backward. While compiling the data set, we put emphasis on including large confined flares while maintaining a good distribution among all flare classes. The resulting data set contains a total of 51 flares distributed over all flare classes (cf. Tables 1 and 2). Note that in an accompanying paper, the same data set was used to study the flare ribbon characteristics (initial ribbon distance, separation, and speed) and the reconnection electric field (Hinterreiter et al. 2018).

The Hα filtergrams for two of the flares were provided by other observatories, allowing us to include the strongest flares in solar cycle 23 that occurred close to the disk center. For the X17 flare on 2003 October 28, we use data from the Udaipur Solar Observatory (USO), and for the X10 flare on 2003 October 29, we use data from the Improved Solar Observing Optical Network (ISOON). KSO observations for the X17 flare on 2003 October 28 have large data gaps during the impulsive phase and are therefore not suitable for our analysis, while the X10 flare on 2003 October 29 occurred at KSO night.

For each event, our analysis is based on a time series of Hα filtergrams starting 5 minutes prior to the nominal flare start time and ending 5 minutes after the nominal end time. The respective times can be found in Table 2 and are taken from the list of observed flares from KSO. For the event on 2003 October 29, the times provided by NOAA's National Geophysical Data Center (NGDC)⁴ are used.

The observations at KSO are performed with a refractor with an aperture number of d/f = 100/2000. The filter is a Lyot bandpass filter centered on the Hα spectral line with a full width at half maximum (FWHM) of 0.07 nm. An interference filter with a FWHM of 10 nm is placed in the light path for thermal protection (Pötzi et al. 2015). Since 2000, three different CCD cameras have been used at KSO. Beginning in 2000, regular observations were carried out with a 1k × 1k  8 bit CCD with a spatial resolution of 22. The cadence was one image per minute (Otruba 1999). The CCD was replaced with a 10 bit CCD with the same number of pixels in mid-2005. The observing cadence stayed the same (Otruba & Pötzi 2003). Since 2008, the observations have been carried out with a 2048 × 2048 pixel 12 bit CCD with a spatial resolution of approximately 1'' pixel^–1 and an increased observing cadence of 6 s (Pötzi et al. 2015).

The USO high-resolution Hα filtergrams are obtained by a 15 cm aperture f/15 telescope and a 12 bit CCD. The images have a cadence of approximately 30 s. Comparison and coalignment with KSO data, which partially covered this event, resulted in a plate scale of ∼06. The ISOON data are obtained by a 12 bit CCD with a plate scale of ∼1'' and a cadence of 1 minute (Neidig et al. 1998).

The Hα data set is complemented by either 96 m full-disk LOS magnetograms from the Michelson Doppler Imager aboard the Solar and Heliospheric Observatory (SOHO/MDI) or 720 s full-disk LOS magnetograms from the Helioseismic and Magnetic Imager aboard the SDO (SDO/HMI) for flares after 2010 May 1. The MDI magnetograms are recorded with a CCD with 1024 × 1024 pixels and have a spatial resolution of 4'' (Scherrer et al. 1995). The HMI provides 4096 × 4096 pixel LOS magnetograms with a spatial resolution of about 1'' (Schou et al. 2012). We use the 720 s LOS magnetograms from HMI because of the better signal-to-noise ratio compared to the 45 s LOS magnetograms (Couvidat et al. 2016). For each event, we selected the latest magnetogram available before the start of the flare as listed in Table 2.

The CME association for the flares under study was determined using the SOHO/LASCO CME catalog.⁵ If there were CMEs with back-extrapolated onset times within 1 hr of the flare start time, then these events were considered as candidates for eruptive flares. In addition, we verified the CME association of the flares under study by visual comparison of LASCO-C2 observations to the flare observations, demanding that the CME position angle coincide with the quadrant of the flare location on the solar disk. For each eruptive flare, we use the linear speed of the associated CME from the catalog. The SOHO/LASCO CME catalog does not list an entry for the M1.2/1N flare on 2011 October 1. Therefore, we use the speed determined with STEREO-B in Temmer et al. (2017). The GOES class, and therefore the peak GOES 1–8 Å SXR flux (F_SXR), was taken from the flare reports from NGDC.⁶ The F_SXR is used as an indicator of the flare energy.

This section is divided into two parts. In Section 3.1, we describe the preprocessing to obtain a homogeneous data set, which can be analyzed by our flare detection algorithm. In Section 3.2, we explain how we derived the magnetic reconnection quantities for the flares under study, illustrated on two sample events.

3.1. Preprocessing of Hα Filtergrams

The use of Hα filtergrams from different telescopes and CCDs makes a normalization of the data necessary. We apply a zero-mean and whitening transformation described in Pötzi et al. (2015). We first normalize the intensity of each image using

$$\begin{eqnarray}&&{f}_{i,n}=\displaystyle \frac{{f}_{i}-\mu }{\sigma },\end{eqnarray} \tag{ 4 }$$

where f_i,n is the normalized intensity; f_i is the original intensity of the ith pixel of the image;μ is the mean value of the intensity of all pixels on the solar disk, defined as

$$\begin{eqnarray}&&\mu =\displaystyle \frac{1}{N}\displaystyle \sum _{i}^{N}{f}_{i};\end{eqnarray} \tag{ 5 }$$

and σ is the corresponding standard deviation, defined as

$$\begin{eqnarray}&&\sigma =\sqrt{\displaystyle \frac{1}{N-1}\displaystyle \sum _{i}^{N}{({f}_{i}-\mu )}^{2}},\end{eqnarray} \tag{ 6 }$$

where N is the number of pixels on the solar disk. This means that the normalized intensity is given in units of the standard deviation of the solar disk pixels.

The area covered by the flare ribbons is small compared to the area of the solar disk and thus has no significant impact on the mean value μ. After normalization, a median filter is applied to eliminate large-scale intensity variations such as the center-to-limb variation and the effect of terrestrial clouds. This results in the normalized intensity values of the quiet Sun being close to zero. All features darker than the quiet Sun show negative values, while brighter features have positive values of the normalized intensity.

All images are rotated to solar north and differentially rotated to the time of the first image of the Hα image sequence used to analyze the individual flare events. For each event, a subregion containing the flare ribbons is selected. We coalign the Hα images with the first image of the time series using cross-correlation techniques to compute the offsets and shift the images accordingly. The SOHO/MDI and SDO/HMI LOS magnetograms are coregistered to the plate scale of the Hα images and then coaligned with the first Hα filtergram of each event-based image sequence using the corresponding MDI or HMI continuum images, respectively.

3.2. Analysis of Reconnection Rates and Fluxes

In each Hα filtergram of the observation series, we detect those pixels that belong to the flare ribbons. We define all pixels as flare pixels whose normalized intensity is ≥5.5; i.e., the pixel intensity lies 5.5σ above the mean value of the solar disk pixel intensities. The normalization allows us to use the same threshold for all events. The threshold is found by visual inspection of the flare pixel tracking method based on different thresholds, in comparison with the flare ribbon area observed in the Hα filtergrams. Within a range of [4.5, 6.5] in normalized intensity, qualitatively similar detection results are obtained. Therefore, we use a value of 5.5 for the normalized intensity as a threshold for flare pixel detection and values of 4.5 and 6.5 to assign a lower and upper uncertainty bound, respectively.

Figures 1 and 2 illustrate the detection of flare pixels during the eruptive M1.1/2N flare on 2011 November 9 (event #25) and the confined C8.7/2N flare on 2014 May 10 (event #43), respectively. The left column shows the newly detected flare pixels between the image shown and the previous one (recorded 6 s earlier), while the middle column shows the accumulated ribbon area up to the time of the image recorded. The right column shows the accumulated flare area on top of a pre-flare HMI LOS magnetogram. Areas colored red and blue correspond to flare ribbons populating regions of negative and positive polarity, respectively. With time, the accumulated ribbon area grows, with the largest growth happening during the impulsive phase of the flare and slowing down in the later phases of the flare. This is displayed in Figures 3(b) and 4(b), showing the growth rates of the ribbon area during the two sample events.

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For each time step, the magnetic flux of the newly brightened flare pixels is calculated. A pixel is considered a newly brightened flare pixel belonging to a certain magnetic polarity if (a) the normalized intensity of the pixel exceeds a threshold of 5.5, (b) this intensity threshold has not been exceeded in any of the previous Hα filtergrams, and (c) the absolute value of the LOS magnetic flux density is above the noise level. The noise level used is 20 G in the case of the MDI magnetograms (Scherrer et al. 1995). For the HMI 720 s LOS magnetograms, the photon noise is 3 G at the disk center (Couvidat et al. 2016). A noise level of 10 G is used to account for the increase of noise toward the limb.

The magnetic flux in the newly brightened flare pixels is then used to evaluate the reconnection flux. First, we calculate the difference in the reconnection flux between the time step t_k and t_k−1 as

$$\begin{eqnarray}&&{\rm{\Delta }}\varphi ({t}_{k})=\displaystyle \sum _{i}{a}_{i}({t}_{k}){B}_{n}({a}_{i}),\end{eqnarray} \tag{ 7 }$$

where a_i(t_k) is the area of the flare pixels that newly brightened between time step t_k−1 and t_k; ${B}_{n}({a}_{i})$ is the component of the magnetic field normal to the surface in the newly brightened area; and B_n is estimated by multiplying the LOS magnetic flux density with $1/\cos (u)$, where u is the angular distance of the centroid of all flare pixels to the center of the solar disk. Likewise, the calculated flare area is corrected for projection effects by multiplying with $1/\cos (u)$. The calculation of Δφ(t_k) is done separately for the positive and negative polarity domains. From this sequence, we obtain the cumulated reconnection flux up to time t_k as

$$\begin{eqnarray}&&\varphi ({t}_{k})=\displaystyle \sum _{j\leqslant k}{\rm{\Delta }}\varphi ({t}_{j}).\end{eqnarray} \tag{ 8 }$$

In Equation (8), the reconnection flux $\varphi ({t}_{k})$ is derived as the sum of all fluxes in the flare areas that brightened up until time t_k. The time series is smoothed with a 3 minute time window. The reconnection rate, i.e., the change rate of the magnetic reconnection flux at each time step, is then calculated as (cf. Veronig & Polanec 2015)

$$\begin{eqnarray}&&\dot{\varphi }({t}_{k})=\displaystyle \frac{{\rm{\Delta }}\varphi ({t}_{k})}{({t}_{k}-{t}_{k-1})}.\end{eqnarray} \tag{ 9 }$$

Figures 3 and 4 show the time evolution of all the parameters calculated, along with the GOES 1–8 Å flux and its time derivative for sample events #25 and #43, respectively. Figures 3(a) and 4(a) show the reconnection flux φ(t) separately for positive and negative magnetic flux areas (thick lines), with the shaded regions indicating the uncertainty range obtained by the flare detection thresholds of [4.5, 6.5]. The reconnection flux increases with time while showing small differences in positive and negative flux. Figures 3(b) and 4(b) show the corresponding growth rate of the flare ribbon areas. Note that the ribbon areas covering opposite-polarity regions do not necessarily grow homogeneously, as is the case in, e.g., event #25. Figures 3(c) and 4(c) show the mean magnetic flux density in the newly brightened flare areas. Figures 3(d) and 4(d) show the evolution of the reconnection rate $\dot{\varphi }(t)$.

We define the total flare reconnection flux φ_FL as the mean of the absolute values of the reconnection fluxes in both polarity regions at the end of the time series, i.e.,

$$\begin{eqnarray}&&{\varphi }_{\mathrm{FL}}=\displaystyle \frac{| {\varphi }_{+}| +| {\varphi }_{-}| }{2},\end{eqnarray} \tag{ 10 }$$

where φ₊ and φ₋ are the cumulated magnetic flux in the positive and negative polarity regions, respectively. Accordingly, the peak reconnection rate is calculated as

$$\begin{eqnarray}&&{\dot{\varphi }}_{\mathrm{FL}}=\displaystyle \frac{| {\dot{\varphi }}_{+}| +| {\dot{\varphi }}_{-}| }{2},\end{eqnarray} \tag{ 11 }$$

where ${\dot{\varphi }}_{+}$ and ${\dot{\varphi }}_{-}$ are the peaks of the reconnection rate within positive and negative magnetic polarity, respectively. The uncertainties of these quantities due to a particular choice of threshold were estimated by performing the analysis described above based on intensity thresholds [4.5, 6.5]. We find that these uncertainties are about 20%–30%. The effects of these uncertainties in the alignment of the images was estimated by artificially misaligning the Hα images with respect to the magnetograms by 1–2 pixels in both, either positive or negative, x- and y-direction and running the calculations for the misaligned images with a fixed flare detection threshold of 5.5. We find that the uncertainties in the reconnection flux due to inaccurate alignment are about 10%. In total, we therefore estimate the maximum uncertainties in the derived reconnection fluxes to be 30%–40%.

In order to compare the flare reconnection flux to the total magnetic flux contained in the source active region (AR), we selected a subregion containing the whole AR. This box was chosen to be as small as possible around the AR to minimize the contribution of magnetic flux from areas outside the source AR. We used the same pre-flare LOS magnetogram that was used for the calculation of the flare reconnection fluxes and calculated the flux in the subregion selected to provide an estimate of the total magnetic flux contained in the flare-hosting AR. Three of our flares did not originate from ARs (events #1, #4, and #36). In these cases, we used the same subregion that was used in the analysis of the flare reconnection rates. The flux within each polarity was calculated separately, and, analogously to Equation (10), we defined a total active region flux φ_AR as the mean of the absolute values of the magnetic flux of both polarity regions. The errors in the calculation of the magnetic flux in the AR that causes the flare are estimated to be about 5%. They mostly arise due to the selection of the box around the AR from where the flux is derived, as it may either include parts of quiet Sun fluxes around the AR or miss some flux from the periphery of the AR. In both cases, these contributions are small, as they cover only regions with small magnetic flux densities, whereas most of the AR flux stems from the umbra and penumbra of the main sunspots.

The partition of the AR flux involved in the flare reconnection process was estimated as

$$\begin{eqnarray}&&r=\displaystyle \frac{{\varphi }_{\mathrm{FL}}}{{\varphi }_{\mathrm{AR}}}.\end{eqnarray} \tag{ 12 }$$

Combining the relative error bounds of 30% for φ_FL and 5% for φ_AR, we find a maximum estimate of the relative error on r of about 35%.

In Table 3, we list the reconnection parameters derived for all the flare events under study. The reconnection fluxes φ_FL derived for our sample range over more than two orders of magnitude, with a minimum of φ_FL = 1.7 × 10²⁰ Mx for event #50 and a maximum of φ_FL = 2.5 × 10²² Mx for event #7, while F_SXR covers a range of four orders of magnitude from B3 to X17 (cf. Table 3 and Figure 6). The peak reconnection rates ${\dot{\varphi }}_{\mathrm{FL}}$ are also distributed over two orders of magnitude ranging from ${\dot{\varphi }}_{\mathrm{FL}}=5.2\times {10}^{17}\,\mathrm{Mx}\,{{\rm{s}}}^{-1}$ in the case of event #50 to ${\dot{\varphi }}_{\mathrm{FL}}=3.4\times {10}^{19}\,\mathrm{Mx}\,{{\rm{s}}}^{-1}$ in the case of event #8.

Table 3.  Flare Reconnection Fluxes φ, Reconnection Rates $\dot{\varphi }$, and Peak of GOES 1–8 Å SXR Flux Derivate ${\dot{F}}_{\mathrm{SXR}}$

Event #	φ+	φ−	φFL	${\dot{\varphi }}_{+}$	${\dot{\varphi }}_{-}$	${\dot{\varphi }}_{\mathrm{FL}}$	${\dot{F}}_{\mathrm{SXR}}$
	(1021 Mx)	(1021 Mx)	(1021 Mx)	(1019 Mx s−1)	(1019 Mx s−1)	(1019 Mx s−1)	(10−8 W m2 s−1)
1	1.32	−1.37	1.34	0.421	−0.400	0.410	3.940
2	7.68	−12.9	10.3	0.543	−0.737	0.640	40.80
3	11.8	−12.5	12.1	0.923	−0.600	0.761	4.680
4	2.27	−3.68	2.97	0.127	−0.152	0.139	0.696
5	15.8	−11.1	13.4	1.56	−1.51	1.53	138.0
6	15.6	−12.2	13.9	0.625	−0.922	0.773	2.910
7	29.0	−21.5	25.2	3.94	−2.86	3.40	508.0
8	27.2	−19.4	23.3	4.58	−2.30	3.44	302.0
9	6.18	−8.24	7.21	0.307	−0.377	0.342	4.290
10	4.74	−6.95	5.84	0.641	−1.89	1.27	29.70
11	13.1	−6.28	9.69	2.39	−1.50	1.94	209.0
12	5.92	−3.35	4.63	1.71	−0.980	1.34	66.00
13	8.56	−12.4	10.5	2.27	−3.84	3.05	37.00
14	8.10	−7.24	7.67	1.24	−0.537	0.888	4.650
15	17.5	−22.4	19.9	1.14	−0.658	0.899	45.60
16	2.51	−4.24	3.37	0.744	−0.760	0.752	8.300
17	12.9	−9.19	11.0	1.68	−1.73	1.70	20.10
18	10.7	−12.0	11.3	3.34	−3.16	3.25	62.10
19	4.28	−4.08	4.18	0.554	−0.342	0.448	5.830
20	3.50	−2.52	3.01	0.548	−0.358	0.453	2.310
21	1.59	−6.39	3.99	0.232	−1.01	0.621	1.550
22	0.617	−0.676	0.646	0.101	−0.097	0.099	0.516
23	1.18	−1.44	1.31	0.439	−0.731	0.585	5.650
24	1.94	−2.37	2.15	0.175	−0.148	0.161	1.320
25	2.16	−2.85	2.50	0.169	−0.343	0.256	1.220
26	4.69	−6.01	5.35	0.561	−0.587	0.574	4.670
27	2.72	−1.52	2.12	0.319	−0.188	0.253	5.350
28	1.10	−1.25	1.17	0.241	−0.218	0.229	4.390
29	2.35	−5.68	4.01	0.426	−0.804	0.615	3.750
30	2.84	−2.48	2.66	0.370	−0.411	0.390	10.40
31	0.765	−0.463	0.614	0.188	−0.176	0.182	1.240
32	0.286	−0.183	0.234	0.125	−0.035	0.080	0.310
33	0.267	−0.973	0.620	0.095	−0.206	0.151	0.161
34	0.371	−0.297	0.334	0.143	−0.143	0.143	0.194
35	1.36	−0.602	0.981	0.424	−0.207	0.315	0.446
36	0.784	−0.700	0.742	0.181	−0.111	0.146	1.160
37	0.332	−0.153	0.242	0.144	−0.035	0.089	0.429
38	1.55	−0.888	1.22	0.195	−0.110	0.152	0.309
39	1.61	−0.872	1.24	0.573	−0.320	0.446	1.460
40	3.65	−1.82	2.73	0.894	−0.562	0.728	4.350
41	0.760	−0.445	0.603	0.069	−0.056	0.062	0.194
42	2.44	−2.25	2.34	0.298	−0.340	0.319	0.580
43	2.38	−2.21	2.29	0.339	−0.457	0.398	2.390
44	0.912	−1.04	0.976	0.114	−0.209	0.161	0.271
45	0.406	−0.673	0.539	0.119	−0.136	0.127	0.097
46	0.831	−0.112	0.471	0.146	−0.028	0.087	0.068
47	0.202	−0.366	0.284	0.047	−0.110	0.078	0.285
48	9.97	−14.0	12.0	1.74	−2.38	2.06	24.90
49	7.48	−3.05	5.26	0.844	−0.419	0.631	2.350
50	0.137	−0.201	0.169	0.058	−0.046	0.052	0.158
51	7.71	−7.26	7.48	0.580	−0.790	0.685	39.90

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Figure 5 shows the negative versus positive magnetic flux reconnected during each of the events analyzed. In most events, the reconnected magnetic flux in the two polarities resides near the black line indicating r_pn = 1, indicating perfect flux balance in the opposite polarities. The dashed lines represent the lines where r_pn is either 0.5 or 2. For the majority of events (82%), we find ratios of ${r}_{\mathrm{pn}}=| {\varphi }_{+}/{\varphi }_{-}|$ within a range of 0.5 and 2. Considering the uncertainties in the measurements, this is a good flux balance. Six events show a ratio r_pn larger than 2, while three events exhibit r_pn smaller than 0.5.

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Figure 6 shows the total reconnection flux, φ_FL, as a function of the peak of the GOES 1–8 Å SXR flux, F_SXR, indicating an excellent correlation with a Pearson correlation coefficient of c = 0.92, derived in log–log space. This is also true for the subsets of confined and eruptive flares, with the corresponding fit parameters showing no significant differences within their given uncertainties. For the whole set of events, we find values of a = 0.580 and d = 24.21 for the regression line $\mathrm{log}(y)=a\,\mathrm{log}(x)+d$ (see first column in Table 4). The coefficient of determination for our regression to the data (black line in Figure 6) is given by c² = 0.85. The coefficient of determination provides us with a measure of how well the regression line can account for the variation of the data. In the case of the relation φ_FL versus F_SXR, 85% of the total variation of the flare reconnection fluxes can be accounted for by the regression model, confirming a high applicability of the regression model.

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Table 4.  Fit Parameters and Correlation Coefficients Corresponding to the Scatter Plots in Figures 6–9

x	FSXR		${\dot{F}}_{\mathrm{SXR}}$	AFL		${\bar{| B| }}_{\mathrm{FL}}$
y	φFL	${\dot{\varphi }}_{\mathrm{FL}}$	${\dot{\varphi }}_{\mathrm{FL}}$	φFL	FSXR	φFL	FSXR
a	0.580 ± 0.034	0.457 ± 0.038	0.457 ± 0.032	1.207 ± 0.071	1.845 ± 0.137	1.709 ± 0.245	2.284 ± 0.444
acon	0.602 ± 0.052	0.484 ± 0.045	0.467 ± 0.041	1.259 ± 0.082	1.778 ± 0.170	1.959 ± 0.305	2.404 ± 0.553
aer	0.579 ± 0.050	0.577 ± 0.060	0.501 ± 0.048	1.705 ± 0.144	2.525 ± 0.365	1.833 ± 0.170	2.925 ± 0.312
d	24.21 ± 0.17	20.82 ± 0.19	22.03 ± 0.24	10.23 ± 0.66	−21.92 ± 1.28	17.23 ± 0.60	−10.41 ± 1.09
dcon	24.34 ± 0.27	21.05 ± 0.23	22.16 ± 0.32	9.82 ± 0.74	−21.28 ± 1.55	16.42 ± 0.76	−11.07 ± 1.38
der	24.17 ± 0.22	21.20 ± 0.27	22.26 ± 0.34	5.36 ± 1.37	−28.49 ± 3.49	17.27 ± 0.41	−11.35 ± 0.75
c	0.92(−0.05/0.03)	0.86(−0.09/0.06)	0.90(−0.07/0.04)	0.93(−0.05/0.03)	0.89(−0.08/0.05)	0.71(−0.17/0.12)	0.59(−0.21/0.15)
ccon	0.90(−0.09/0.05)	0.89(−0.11/0.06)	0.90(−0.10/0.05)	0.94(−0.06/0.03)	0.89(−0.13/0.07)	0.76(−0.07/0.03)	0.62(−0.08/0.04)
cer	0.94(−0.09/0.04)	0.92(−0.12/0.05)	0.93(−0.11/0.04)	0.95(−0.09/0.04)	0.86(−0.16/0.07)	0.93(−0.29/0.14)	0.92(−0.39/0.22)

Note.  The fit parameters and correlation coefficients are calculated in log–log space using $\mathrm{log}(y)=a\mathrm{log}(x)+d$ for all events, as well as separately for the subsets of confined and eruptive events.

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Figure 7(a) shows ${\dot{\varphi }}_{\mathrm{FL}}$ as a function of the peak of the time derivative of the SXR flux, ${\dot{F}}_{\mathrm{SXR}}$. These quantities also show a very high correlation with c = 0.90. We find values for the fit parameters of a = 0.456 and d = 22.03 (see third column in Table 4), with no significant differences in the fit parameters when considering confined and eruptive flares separately. Figure 7(b) shows that ${\dot{\varphi }}_{\mathrm{FL}}$ is also strongly correlated with the SXR peak flux, F_SXR (c = 0.86). There is some trend that for a given GOES flare class (F_SXR), confined flares reveal higher peak reconnection rates ${\dot{\varphi }}_{\mathrm{FL}}$ than eruptive flares.

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Figures 8(a) and (b) show φ_FL as a function of the flare area A_FL and the mean magnetic flux density ${\bar{| B| }}_{\mathrm{FL}}$ in the flare ribbons, respectively. We find very high correlation coefficients for both eruptive and confined flares (c ≈ 0.9) but a difference in the regression lines. For a given reconnection flux φ_FL, confined flares involve a higher mean magnetic flux density ${\bar{| B| }}_{\mathrm{FL}}$ and a smaller area as compared to eruptive flares. The effect is most pronounced in the magnetic field underlying the flare ribbons, which is about a factor of 2 larger in the case of confined flares than in eruptive events, quite constant over the whole distribution. (Note that the flare area A_FL and the mean magnetic flux density ${\bar{| B| }}_{\mathrm{FL}}$ in the flare ribbons themselves are only very weakly correlated, c = 0.34 (−0.26/+0.21).)

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Figures 9(a) and (b) show the GOES SXR peak flux F_SXR as a function of A_FL and ${\bar{| B| }}_{\mathrm{FL}}$, respectively, and reveals distinct correlations, but in the case of F_SXR versus ${\bar{| B| }}_{\mathrm{FL}}$, the correlation coefficient is significantly higher for eruptive (c ≈ 0.9) than for confined (c ≈ 0.6) flares. For a certain mean magnetic flux density ${\bar{| B| }}_{\mathrm{FL}}$, eruptive flares yield a higher F_SXR than confined flares. While there exists a distinct correlation between the GOES peak flux and the flare area, it is worth mentioning that eruptive flares of high GOES class seem to involve a similar range of areas, and the increase of F_SXR with the reconnection flux is mostly due to higher magnetic flux densities involved in these cases.

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In Table 4, we list the correlation coefficients and the fit parameters obtained from the regression (linear model applied in log–log space) for the different relations plotted in Figures 6–9. We applied significance tests to all of the correlations using Steiger's z test. All of the correlations in Table 4 are significant on the 99.99% level (p = 0.0001). In addition, we also list the 95% confidence range on our correlation coefficients based on Fisher's transformation.

Figure 10 shows the flare reconnection flux φ_FL against the total flux φ_AR of the source AR that produces the flare. The ARs in our study host magnetic fluxes between 1.9 × 10²¹ and 8.3 × 10²² Mx, whereas the flare reconnection fluxes range from 1.7 × 10²⁰ to 2.5 × 10²² Mx. From the figure, it is seen that small events (i.e., small flare reconnection fluxes) can result from a large variety of AR fluxes, whereas the largest events require ARs with a high magnetic flux content.

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Figure 11 shows the ratio r of the flare reconnection flux and the AR flux as a function of F_SXR. We find a minimum of r ≈ 0.03, meaning that only 3% of the AR magnetic flux is involved in the flare. In contrast, we find a maximum value of r = 0.46; i.e., almost half of the AR flux was involved in the eruptive 3B/X3.8 flare on 2005 January 17 (event #15). Figure 11 shows that in small events (i.e., class B and C), the AR magnetic flux involved can range from a few percent up to 30%, whereas in flares ≥M1 (except for the 2N/X2.0 flare on 2014 October 26), at least 10% of the AR flux was involved. For flares ≳X4, more than ≈30% of the AR flux was involved in the flare reconnection. Also note that in these largest events, the total flux contained in the source AR is considerably higher than that in smaller flares (cf. Figure 10).

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Figure 12 shows the dependency of the CME speed on the flare reconnection flux. We find that for higher φ_FL, the speed of the associated CME tends to be higher. The CMEs in our study have speeds ranging between v_CME = 398 and v_CME = 2547 km s⁻¹. We find a high correlation with a correlation coefficient of c_CME = 0.84 (−0.22/+0.10) in linear space.

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We analyzed the magnetic reconnection rates and fluxes of a set of 51 flares covering 19 eruptive and 32 confined events. Our main focus was to derive reconnection parameters over a large range in flare energy and study the differences in confined and eruptive flares. In addition, we were interested in whether the results obtained allowed us to draw estimates of the largest flares that may occur on the Sun. Our study delivered the following main results.

• 1.  
  We find a very high correlation of the peak GOES SXR flux, F_SXR, with the flare reconnection flux, φ_FL, of c = 0.92 (−0.05/+0.03) in log–log space. This value also implies that 85% of the data can be explained by the regression model. There is no difference for confined or eruptive flares; both lie close to the same regression line. While F_SXR covers a range of over four orders of magnitude, we find a range of two orders of magnitude for φ_FL.
• 2.  
  We also find a very high correlation between the peak of the GOES SXR time derivative ${\dot{F}}_{\mathrm{SXR}}$ and the peak reconnection rate ${\dot{\varphi }}_{\mathrm{FL}}$ with c = 0.90 (−0.10/+0.05). The fit parameters are significantly different between confined and eruptive flares.
• 3.  
  We find that confined and eruptive flares significantly differ only regarding the ribbon area and the mean magnetic flux density swept by the ribbons. In the largest events, the flare areas reach values up to about 10¹⁰ km², and the mean photospheric magnetic flux density underlying the flare ribbons has values from ≈100 to 800 G. For a given GOES class, the mean magnetic flux density in the flare ribbons is larger for confined than for eruptive events, on average, by a factor of 2. Correspondingly, for a given reconnection flux, we find smaller flare ribbon areas in confined flares. These findings are consistent with the tendency of confined flares to occur closer to the flux-weighted center of ARs (Wang & Zhang 2007; Cheng et al. 2011; Baumgartner et al. 2017). where the mean magnetic flux density swept by the flare ribbons is expected to be larger.
• 4.  
  We find that the fraction of the AR magnetic flux that is involved in the flare reconnection process ranges between 3% and 46%. It increases with the GOES class, amounting to at least 10% of the AR magnetic flux in flares ≥M1. For the largest flares (≳X4), we find that at least 30% of the AR flux is involved.
• 5.  
  For eruptive flares, we find a high correlation of c = 0.84 (−0.22/+0.10) between the flare reconnection flux φ_FL and the speed of the associated CME, in agreement with the correlation reported by Qiu & Yurchyshyn (2005) of c = 0.89.

In the following, we place our main findings, as listed above, in the context of earlier studies within the research field before we discuss their relevance in terms of the largest flares that may occur on the Sun. Our study reveals a higher correlation between F_SXR and φ_FL (c = 0.92) compared to the correlation found by Veronig & Polanec (2015) with c = 0.78. The reason for the higher correlation presented here is most likely the use of a homogeneous data set and the application of the same method to all events in order to derive the relevant physical quantities, in contrast to that earlier study, in which the results for 27 events from four different studies were combined. Recent statistical studies were published by Toriumi et al. (2017) and Kazachenko et al. (2017). In contrast to these studies, which analyze flares >M5.0 and >C1.0, respectively, and the largest event included is of class X5.4, we use a set of flare events covering a substantially wider range of flare classes, ranging from class B3.1 to X17. Another difference is that in our study, we use Hα filtergrams, whereas Toriumi et al. (2017) and Kazachenko et al. (2017) used SDO AIA 1600 Å images for the analysis of flare ribbons. Toriumi et al. (2017) found a correlation between φ_FL and F_SXR of c = 0.37, while Kazachenko et al. (2017) found a Spearman ranking correlation coefficient of 0.66. The substantially higher correlation found in our study (c ≃ 0.9) is most likely due to the larger range of flares included. Our data set spans four orders of flare class, whereas, e.g., the study of Toriumi et al. (2017) spans just one order of magnitude. If there is some intrinsic correlation between two data sets, which may be affected by measurement uncertainties and noise, then the larger the base range of the values included, the better this intrinsic correlation can be recovered from the data, resulting in a higher correlation coefficient.

Toriumi et al. (2017) found a linear regression between F_SXR and φ_FL that is less steep than what we find in our study, which we also attribute to the different data range. Kazachenko et al. (2017) fitted a power law in the form of y = d x^a to their data set, using x = φ_FL and y = F_SXR and finding a = 1.53. We find a similar power-law index of a = 1.47 ± 0.09 when using the same notation (cf. Figure 6 and Table 4.). Kazachenko et al. (2017) speculated about the existence of a good correlation between the peak reconnection rate and the peak HXR flux. In our study, using the time derivative of the GOES SXR flux as an approximation for the HXR time profile, we were able to prove this strong dependency (c ≃ 0.9).

Our results show a very tight correlation between the total flare reconnection flux and the GOES SXR peak flux, c = 0.92, over four orders of magnitude in flare class and two orders in the involved flare reconnection fluxes, with a typical scatter of about 0.3 orders of magnitude (cf. Figure 6). The linear regression model (in log–log space) can account for as much as 85% of the variation of the data. These findings allow us to quite accurately specify the relation between the two quantities, which in the following can also be used to extrapolate the relation toward the largest flares that may occur on the present day's Sun, depending on the total magnetic flux contained in the source AR. These considerations are interesting in their implications for solar activity but are also very important in terms of estimating the strongest space weather events that may affect Earth. In addition, such extrapolation that is well grounded by observed solar quantities also allows us to place the strongest flares expected from the present day's Sun in context to "superflares" on solar-like stars that have been recently discovered in Kepler data (Maehara et al. 2012; Shibayama et al. 2013). The estimates of the energies of these stellar superflares are up to 10³⁵–10³⁶ erg, making them a factor of 100–10,000 times larger than the biggest solar flares observed so far.

In the present study, we find that in the largest solar events observed, say GOES classes ≳X4, between 30% and 50% of the magnetic flux of the source AR is involved in the flare reconnection process. These numbers are in accordance with the recent studies by Kazachenko et al. (2017) and Toriumi et al. (2017). The largest fluxes measured for ARs associated with major flare activity range from several times 10²² Mx up to a few times 10²³ Mx (e.g., Zhang et al. 2010; Chen et al. 2011; Yang et al. 2017). For instance, AR 12192 (covered in our study) was the largest AR on the Sun in 24 yr, with an area of 2750 μhem. It hosted a maximum photospheric vertical magnetic flux of ∼2 × 10²³ Mx on 2014 October 27 (Sun et al. 2015) and was the source of a large number of confined X-class flares (see, e.g., Thalmann et al. 2015). This AR was even bigger than the famous AR 10486 that was the source of the strongest "Halloween" events, including the X17 and X10 flares of 2003 October 28 and 29, which are covered in our study. AR 10486 also produced the strongest SXR flare that was recorded in the GOES era, the X28+ event on 2003 November 4, during which the GOES fluxes were saturated for a few minutes. However, as this event occurred on the solar limb, magnetic reconnection fluxes cannot be derived for it. The X17 flare of 2003 October 28 (included in our study) occurred when AR 10486 was close to disk center. It was the fourth-strongest flare recorded by the GOES satellites (see, e.g., Tsurutani et al. 2005).

In principle, of course, it is the free magnetic energy stored in the corona of magnetically complex ARs and released during a flare via magnetic reconnection that is the most relevant and direct physical quantity describing the process. However, to calculate the energy in flares and CMEs from observations is a difficult task, and the uncertainties are an order of magnitude (e.g., Emslie et al. 2005, 2012; Veronig et al. 2005). Estimates of the magnetic energy of an AR and, even more specifically, the free magnetic energy available to power flare/CME events are not directly accessible, as we cannot reliably measure the coronal magnetic field. Therefore, such estimates are usually based on advanced three-dimensional coronal magnetic field models, using the vector magnetic field measured in the photosphere. However, the uncertainties of these estimates are again up to an order of magnitude, depending on the input data (e.g., Thalmann et al. 2008), model approach (e.g., De Rosa et al. 2009), and possibly other factors (e.g., DeRosa et al. 2015).

The big advantage in our study is that we relate the flare energy release to the magnetic reconnection fluxes derived from direct photospheric and chromospheric observations. In addition, the errors in the derived quantities are within ≈30% (see the present study and Qiu & Yurchyshyn 2005). The distinct correlation obtained between the GOES SXR peak flux (a robust indicator of flare energy) and the flare reconnection flux over four orders of magnitude in GOES class, together with the finding that in the largest events up to ≈50% of the total AR flux is involved in the flare reconnection, allows us to estimate the size of the largest flares that may occur on the present-day Sun.

From the occurrence rates of stellar superflares observed on solar-like stars, Maehara et al. (2012) derived that on the Sun, superflares with energies of 10³⁴ erg may occur once in 800 yr and flares with 10³⁵ erg once in 5000 yr. Shibata et al. (2013) estimated from order-of-magnitude considerations of solar dynamo theory that ARs on the Sun hosting a magnetic flux of 2 × 10²³ Mx can be produced within one solar cycle period and may be able to power flares with energies up to 10³⁴ erg. Note that the value of 2 × 10²³ Mx is actually confirmed from observations of the largest and most active solar ARs (e.g., Chen et al. 2011; Sun et al. 2015; Yang et al. 2017).

Shibata et al. (2013) also estimated that a superflare with an energy of 10³⁵ erg would require the hosting AR to carry a magnetic flux of some 10²⁴ Mx, which would take about 40 yr to be generated by the solar dynamo. Aulanier et al. (2013) derived the maximum energy that could be released by a solar flare using a dimensionless MHD model and scaling it by the size of the largest AR and the highest flux densities observed in sunspots, assuming that in large flares 30% of the AR flux is involved in the magnetic reconnection process. Their estimate is that a flare with an energy up to 6 × 10³³ erg could be produced, which they note would be about 10 times larger in energy than the X17 event from 2003 October 28.

In our study, we found that in the largest solar flares, up to 50% of the AR magnetic flux is involved in the flare reconnection process. In addition, we established a very tight correlation between the flare reconnection flux, φ_FL, and the peak of the GOES 1–8 Å SXR flux, F_SXR, with c = 0.92 (in log–log space). For the set of events under study, we find values of a = 0.580 and d = 24.21 for the regression line, $\mathrm{log}({\varphi }_{\mathrm{FL}})=a\,\mathrm{log}({F}_{\mathrm{SXR}})+d$ (see first column in Table 4; and Figure 6). Now, we want to use these findings to make a maximum estimate, i.e., an estimate of the largest flares that might be produced by the present day's Sun, based on the extreme values determined from the range of observed data for flare reconnection and AR fluxes.

In Figure 13, we replot this relation and the regression line for an extrapolation range up to energies corresponding to an X1000 flare. In addition, we plot the 95% confidence interval and the prediction interval for individual data. Assuming the maximum percentage of 50% of the magnetic flux contained in the AR contributing to the flare reconnection process, we find that for an AR with a total flux of 2 × 10²³ Mx —a value that is in accordance with the largest AR fluxes that have been measured (Zhang et al. 2010; Sun et al. 2015)—a flare of GOES class X80 could be powered (with confidence bounds in the range X40 to X200).

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Note that in Figure 13, we have also plotted a second x-axis, where we converted the GOES peak flux to bolometric flare energy. We use the scaling results from Kretzschmar (2011), who applied superposed epoch analysis on SOHO VIRGO Sun-as-a-star measurements to derive the bolometric flare energy as function of GOES class. The relation is described by a power law, $\mathrm{log}({E}_{\mathrm{bol}})=a\,\mathrm{log}({F}_{\mathrm{SXR}})+d$, with a = 0.79 ± 0.10 and d = 34.5 ± 0.5. Note that the extreme events studied in Emslie et al. (2012) also well follow that relation (cf. Figure 8 in Warmuth & Mann 2016). Based on this relation, the bolometric energy of a flare of GOES class X80 is about 7 × 10³² erg. Redoing the fit in Figure 13 of reconnection fluxes as a function of bolometric flare energy, we find $\mathrm{log}({\varphi }_{\mathrm{FL}})=a\,\mathrm{log}({E}_{\mathrm{bol}})+d$, with a = 0.73 ± 0.04 and d = −1.1 ± 0.1.

The largest AR ever observed on the Sun was in 1947 April, with a size of approximately 6000 μhem (Taylor 1989). Schrijver et al. (2012) estimated that the magnetic flux of this AR might have been as large as 6 × 10²³ Mx. Such an AR could produce a flare of about class X500 (with confidence bounds in the range of X200 to X1000), corresponding to a bolometric energy of about 3 × 10³³ erg. These estimates are about an order of magnitude larger than the largest flares that have been reported during the GOES era, and they lie on the lower end of the energies of stellar superflares reported by Maehara et al. (2012). Our data are in line with previous estimates from dynamo theory and MHD modeling (Aulanier et al. 2013; Shibata et al. 2013) and indicate that the present day's Sun may be capable of producing a superflare and related space weather events that are at least an order of magnitude stronger than have been observed so far on the Sun.

This study was supported by the Austrian Science Fund (FWF): P27292-N20. We thank Dr. Bhuwan Joshi from the Physical Research Laboratory (PRL) for providing the USO Hα filtergrams and Dr. Chang Liu from the NJIT Space Weather Research Lab for the NSO Hα filtergrams. HMI data are courtesy of NASA/SDO and the HMI science teams. SOHO is a project of international cooperation between ESA and NASA.