11institutetext: School of Earth and Space Sciences, Peking University,
Beijing, 100871, People’s Republic of China 22institutetext: National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101,
People’s Republic of China
22email<EMAIL_ADDRESS>33institutetext: School of Astronomy and Space
Science, University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China 44institutetext: State Key Laboratory of Solar Activity and
Space Weather, Beijing 100190, China 55institutetext: Max Planck Institute for
Solar System Research, Göttingen D-37077, Germany

# Magnetic helicity evolution during active region emergence and subsequent
flare productivity

Zheng Sun 11 Ting Li 223344 Quan Wang 2233 Shangbin Yang 2233 Mei Zhang 2233
Yajie Chen 55

###### Abstract

Aims. Solar active regions (ARs), which are formed by flux emergence, serve as
the primary sources of solar eruptions. However, the specific physical
mechanism that governs the emergence process and its relationship with flare
productivity remains to be thoroughly understood.

Methods. We examined 136 emerging ARs, focusing on the evolution of their
magnetic helicity and magnetic energy during the emergence phase. Based on the
relation between helicity accumulation and magnetic flux evolution, we
categorized the samples and investigated their flare productivity.

Results. The emerging ARs we studied can be categorized into three types,
Type-I, Type-II, and Type-III, and they account for 52.2%, 25%, and 22.8% of
the total number in our sample, respectively. Type-I ARs exhibit a synchronous
increase in both the magnetic flux and magnetic helicity, while the magnetic
helicity in Type-II ARs displays a lag in increasing behind the magnetic flux.
Type-III ARs show obvious helicity injections of opposite signs.
Significantly, 90% of the flare-productive ARs (flare index $\geq$ 6) were
identified as Type-I ARs, suggesting that this type of AR has a higher
potential to become flare productive. In contrast, Type-II and Type-III ARs
exhibited a low and moderate likelihood of becoming active, respectively. Our
statistical analysis also revealed that Type-I ARs accumulate more magnetic
helicity and energy, far beyond what is found in Type-II and Type-III ARs.
Moreover, we observed that flare-productive ARs consistently accumulate a
significant amount of helicity and energy during their emergence phase.

Conclusions. These findings provide valuable insight into the flux emergence
phenomena, offering promising possibilities for early-stage predictions of
solar eruptions.

###### Key Words.:

magnetic helicity - flux emergence - flares

##  1 Introduction

Solar active regions (ARs) encompass all the observable occurrences that
result from the expansion of the Sun’s magnetic field, stretching from the
photosphere to the corona, which become evident through emissions across a
broad spectrum of wavelengths (van Driel-Gesztelyi & Green 2015; Toriumi &
Wang 2019). Due to their strong magnetic field and complicated magnetic
configuration, ARs are the principal source of a broad range of solar
activities, ranging from small-scale brightenings and jets (Archontis et al.
2010; Chen et al. 2019; Duan et al. 2022; Sun et al. 2023) to large-scale
flares and coronal mass ejections (CMEs) (Li & Zhang 2015; Janvier et al.
2016; Sun et al. 2022). Active regions are formed through the process of flux
emergence from the convection zone in the Sun (Cheung et al. 2010; Zhang & Low
2001; Fan 2021). The initial stage of creating a simple bipolar AR involves
the emergence of an $\Omega$-shaped flux tube. The interaction between the
axial magnetic field of the tube and the photosphere leads to the emergence of
two magnetic polarities within the AR. As the flux tube continues to emerge,
the two main polarities gradually separate, giving rise to the appearance of
small magnetic polarities between them (Cheung & Isobe 2014). Despite numerous
simulations having been conducted to study the process of AR emergence (Fan &
Fang 2014; Fournier et al. 2017), the specific mechanisms of the emergence
process and the correlation with subsequent flare and CME productivity remain
subjects of ongoing discussions.

There are various parameters that can be utilized to characterize the
properties of ARs (Zhang 2001; Chintzoglou et al. 2019; Li et al. 2022).
Welsch et al. (2009) classified these parameters into categories of extensive
type and intensive type. Extensive-type parameters generally scale with the
size of the AR, such as the magnetic flux $\Phi$ and magnetic energy $E$. On
the other hand, intensive-type parameters are normalized quantities, for
example, the reconnection flux divided by the total flux $\Phi_{r}/\Phi_{t}$
and free energy divided by the total energy $E_{f}/E_{t}$. The extensive-type
parameters usually correlate with flares, while intensive-type parameters are
associated with CMEs (Sun et al. 2015; Kazachenko et al. 2022). Several
studies have demonstrated that the distribution of some parameters (e.g.,
magnetic shear, net current) near the polarity inversion line (PIL) can
provide valuable insights into the productivity of solar eruptions (Dalmasse
et al. 2015; Kontogiannis et al. 2019). However, during the emergence of ARs,
the PIL structure may not be unambiguously identified (Stein & Nordlund 2012;
Toriumi et al. 2014). Consequently, to investigate the properties of emerging
ARs, it becomes necessary to consider parameters calculated over the whole
region of ARs. Theoretical studies simulating the magnetic flux tube emergence
have suggested that a higher initial twist of the magnetic tube may result in
a higher flux emergence rate $d(\Phi)/dt$ (Magara 2001; Murray et al. 2006; Fu
& Welsch 2016). Abramenko et al. (2017) measured the flux emergence rate for
36 ARs and found that the relationship between $d(\Phi)/dt$ and the peak
unsigned flux $\Phi_{p}$ could be described by a power-law index of 0.69 $\pm$
0.10 for the entire sample of ARs. Kutsenko et al. (2021) performed a
statistical analysis and found a significant correlation between flare
productivity and flux emergence rate, which offers valuable information for
predicting flare productivity during the early phase of ARs.

In our study, we investigate the properties of emerging ARs by employing two
key parameters: magnetic helicity and magnetic energy. Magnetic helicity
serves as a measure of the net linking and the twisting of magnetic field
lines within a given volume (Berger 1999; Pevtsov et al. 2014; Valori et al.
2016). It is important to note that magnetic helicity is only gauge invariant
under the condition that the normal component $B_{n}$ of the magnetic field
vanishes on the bounding surface (Woltjer 1958; Berger 1999). However, in the
solar atmosphere, this condition is not satisfied due to the presence of a
strong vertical magnetic component perpendicular to the solar surface. To
address this issue, the concept of relative magnetic helicity is introduced
(Berger & Field 1984; Yang et al. 2013, 2018). Relative magnetic helicity is
defined as the difference between the total magnetic helicity and the magnetic
helicity of a reference field. This quantity maintains gauge invariance even
when the boundary condition does not match, making it an effective
characterization of helicity in the solar atmosphere. For the sake of
simplicity, we refer to relative magnetic helicity as ”magnetic helicity”
throughout this paper. Regarding magnetic energy, it serves as a fundamental
parameter that quantifies the amount of energy stored within magnetic fields
(Démoulin & Berger 2003; Trujillo Bueno et al. 2004).

Various studies have demonstrated the relationship between magnetic helicity
and solar eruptions (Zhang & Flyer 2008; Jing et al. 2015; Park et al. 2021;
Wang et al. 2023). LaBonte et al. (2007) conducted a statistical analysis of
48 X-flaring regions and 345 non-X-flaring regions, revealing that a peak
helicity flux threshold of $6\times 10^{36}$ Mx2s-1 is required to produce an
X-class flare. Park et al. (2010) performed a statistical study of 378 ARs and
found a strong correlation between helicity accumulation and flare
productivity. They also observed a distinct difference in the helicity
injection rate between flaring and non-flaring ARs. Korsós et al. (2020) and
Soós et al. (2022) observed differences in the identified periodicities of
magnetic helicity between flaring ARs associated with large M- and X-class
flares compared to ARs associated with smaller B- and C-class flares. When
characterizing CMEs, the use of intensive-type parameters is generally
considered more appropriate (Sun et al. 2015; Toriumi & Takasao 2017). Pariat
et al. (2017) proposed the ratio of magnetic helicity of the current-carrying
magnetic field to the total relative helicity $H_{j}/H_{r}$ as a useful
indicator for CME eruptions. Numerous subsequent observational cases have
supported this proposition (Moraitis et al. 2019; Thalmann et al. 2019; Gupta
et al. 2021). Among them, Gupta et al. (2021) examined ten ARs and found that
$H_{j}/H_{r}$ effectively distinguishes between CME-productive and CME-poor
ARs. However, Duan et al. (2023) conducted a statistical analysis of 45 M- and
X-class flares from 30 different ARs and found no systematic differences in
the value of $H_{j}/H_{r}$ between confined and eruptive flares. The ratio of
free magnetic energy to potential energy $E_{f}/E_{p}$ and normalized current-
carrying helicity $H_{j}/\Phi^{2}$ instead exhibited the highest
discriminative ability between confined and eruptive flares.

Numerous simulations and observations have investigated the transport of
helicity from the solar interior to the atmosphere during flux emergence
(Pevtsov et al. 2003; Yang et al. 2009; Liu et al. 2014; Prior & MacTaggart
2019; Wang et al. 2021). However, there is a lack of large-sample statistical
analysis focusing on the helicity evolution during AR emergence. Moreover,
there are only a few statistical investigations examining the relationship
between emerging ARs and subsequent eruptions (Kutsenko et al. 2021; Liokati
et al. 2022). Our work aims to examine the evolution of helicity in emerging
ARs and subsequent AR flare productivity. We analyzed 136 samples that we
divided into three categories based on the evolution of magnetic helicity and
magnetic flux and found the differences in flare productivity among them. This
paper is organized as follows. Section 2 and Section 3 describe the dataset
and analysis methods used in our study, respectively. In Section 4, we divide
the samples into three distinct categories according to the evolution of
magnetic helicity and magnetic flux. Section 5 presents our statistical
results in detail. Finally, we discuss and summarize the major results in
Section 6.

##  2 Dataset

The data used in our study were obtained from the Helioseismic and Magnetic
Imager (HMI; Scherrer et al. 2012) on board the Solar Dynamics Observatory
(SDO), which provides magnetograms of the entire solar disk with a spatial
resolution of 0.5′′ pixel -1. For our analysis, we mainly used the
Spaceweather HMI Active Region Patch (SHARP) data (Bobra et al. 2014), which
offers the advantage of automated identification and tracking of AR data. The
SHARP data also comprises Lambert cylindrical equal-area (CEA) projections of
the magnetic field vector, enabling the conversion of the components from
[$B_{x}$, $B_{y}$, $B_{z}$] to the spherical heliographic components
[$B_{\phi}$, $B_{\theta}$, $B_{r}$] with a cadence of 720s (Sun 2013), which
can be used to calculate the magnetic helicity and magnetic energy.

In total, we selected 136 emerging ARs according to the dataset provided in
Kutsenko et al. (2021). In the study conducted by Kutsenko et al. (2021), a
total of 243 emerging ARs between 2010 May and 2017 December 31 were examined.
The starting and ending times of the emergence phase were automatically
determined using a two-segment piecewise continuous linear fitting method
applied to the unsigned flux curves (Kutsenko et al. 2019). The selection
criteria for these samples are as follows: (i) clear identification of the
starting and ending times of the emergence phase and (ii) ensuring that the
ARs remain within the central meridian distance of less than 60∘ throughout
the entire process. When we used SHARP to access these samples, in some cases
the initial stages of emergence for some ARs were not detected by SHARP. We
evaluated the ratio between the data-covering interval provided by SHARP and
the overall emergence interval and considered that samples with a ratio above
approximately 90% can be regarded as possessing nearly complete temporal
coverage. Given that there are seven samples with a ratio between 87% and 90%,
we manually set the threshold as 87% in order to include seven more samples
and develop a more robust analysis. Consequently, based on the additional
criterion we introduced, namely (iii) SHARP data has over 87% time range of
the emergence process. In this way, we selected 136 samples in total: 61
flaring ARs and 75 non-flaring ARs (shown in Table LABEL:chartable).

##  3 Methods

We computed unsigned magnetic flux, magnetic helicity, magnetic energy and
flare index for the selected 136 samples within their respective emergence
time intervals:

For unsigned magnetic flux $\Phi$, we performed a summation of the absolute
magnetic flux density in pixels on the radial magnetic field component $B_{r}$
provided by SHARP. Only pixels with magnetic flux density values exceeding 18
Mx cm-2 were included in the calculation, corresponding to three times the
noise level of the HMI magnetogram (Liu et al. 2012). We used the peak value
(normally at the final time step) as the peak unsigned magnetic flux
$\Phi_{p}$.

We employed a helicity flux method to calculate the magnetic helicity $H$
(Berger 1999). The helicity flux equation, Equation (1), is shown below:

$\left.\frac{dH}{dt}\right|_{S}=2\int_{S}\left(\mathbf{A}_{P}\cdot\mathbf{B}_{t}\right)V_{\perp
n}dS-2\int_{S}\left(\mathbf{A}_{P}\cdot\mathbf{V}_{\perp t}\right)B_{n}dS.$
(1)

In the equation, $\mathbf{A_{p}}$ represents the magnetic vector potential,
while $B_{n}$ and $\mathbf{B_{t}}$ denote the normal and tangential magnetic
field, respectively. Similarly, $V_{n}$ and $\mathbf{V_{t}}$ respectively
indicate the normal and tangential velocity. Typically, the integral surface
$\mathbf{S}$ for the helicity flux calculation should be a closed hexahedron
situated in the corona, with the photosphere serving as the bottom boundary.
However, since the contribution of helicity is primarily provided by the
photosphere, we considered the integral surface $\mathbf{S}$ to be the
photosphere itself (Pevtsov et al. 2014). The first term on the right-hand
side of the equation is associated with $V_{n}$ and is referred to as the
”emergence term.” This term reflects the helicity contributed by the emergence
of magnetic structures from the convection zone. The second term on the right-
hand side is associated with $\mathbf{V_{t}}$ and is known as the ”shear
term.” This term reflects the helicity contributed by the shearing motion of
magnetic structures in the photosphere.

To calculate the velocity vector on the photosphere, we used the differential
affine velocity estimator for vector magnetograms (DAVE4VM; Schuck 2008)
method. We used an apodization window size of 19 pixels following the
suggestion by Schuck (2008). In this method, the achieved velocity undergoes
an additional adjustment to account for the exclusion of any irrelevant field-
aligned plasma flow (Liu & Schuck 2012; Wang et al. 2022). This correction is
achieved using the following equation:

$\mathbf{V}_{\perp}=\mathbf{V}-\frac{\mathbf{V}\cdot\mathbf{B}}{B^{2}}\mathbf{B}.$
(2)

Here, $\mathbf{V}_{\perp}$ represents the velocity perpendicular to the
magnetic field lines, while $\mathbf{V}$ corresponds to the velocity obtained
through the application of the DAVE4VM. The corrected velocity
$\mathbf{V}_{\perp}$ serves as the crucial component for calculating the
helicity flux. Liu & Schuck (2012) and Liu et al. (2014) also used DAVE4VM to
calculate the helicity flux in emerging ARs. They used Monte Carlo methods to
estimate the numerical errors when calculating the helicity flux, and the
results are considered to be within the margin of errors. Thus, in this paper
we regard the calculation as reliable.

Since we could calculate $dH/dt$ for each time step, we integrated $dH/dt$
over the entire duration of emergence. This integration allowed us to obtain
the accumulated change in helicity, denoted as $\Delta H$:

$\Delta H=\int_{t_{0}}^{t}{\frac{dH}{dt}}dt.$ (3)

To evaluate the eruptive potential of ARs based solely on their structural
complexity rather than their area, it is valuable to examine the helicity
normalized by the square of the magnetic flux (Toriumi & Park 2022), denoted
as $\Delta H$/$\Phi_{p}^{2}$.

We employed the energy flux method, equation (4),

$\left.\frac{dE}{dt}\right|_{S}=\frac{1}{4\pi}\int_{S}B_{t}^{2}V_{\perp
n}dS-\frac{1}{4\pi}\int_{S}\left(\mathbf{B}_{t}\cdot\mathbf{V}_{\perp
t}\right)B_{n}dS,$ (4)

which is similar to the helicity flux method, in order to calculate magnetic
energy $E$. . Once we obtained the energy flux dE/dt for each time step, we
integrated these values to obtain the accumulated energy, denoted as $\Delta
E$:

$\Delta E=\int_{t_{0}}^{t}{\frac{dE}{dt}}dt.$ (5)

Flare index (FI) was introduced by Abramenko (2005) to assess the flare
productivity of an AR, which provides a quantitative measure of the AR’s
ability for flaring. The equation to calculate the FI is presented below:

$\mathrm{FI}=\left(100S^{(\mathrm{X})}+10S^{(\mathrm{M})}+1.0S^{(\mathrm{C})}+0.1S^{(\mathrm{B})}\right)/\tau.$
(6)

Here, $S^{(j)}=\sum_{i=1}^{N_{j}}I_{i}^{j}$ represents the summation of the
GOES peak intensities $I_{i}^{j}$ for a specific flare class (X, M, C, B),
where $N_{j}$ denotes the number of flares within that class. In the above
equation, $\tau$ signifies the total duration of the AR observation in days,
indicating that this parameter is normalized by time. The FI data of the ARs
are obtained from online dataset111http://solar.dev.argh.team. It should be
noted that the parameters $\Phi$, $H$, and $E$ are calculated during
emergence, while FI includes the entire period of an AR until we could no
longer observe it.

##  4 Classification of active regions

Once we had calculated the parameters outlined in Section 3, namely, the
unsigned magnetic flux, helicity, and energy, we could construct the
corresponding curves during the emergence phase. From the 136 samples, we
found that almost all the unsigned magnetic flux $\Phi$ curves exhibit a
monotonically increasing trend. This outcome is expected since the magnetic
flux naturally increases as the AR emerges. In contrast, the accumulated
magnetic helicity $\Delta H$ curves manifested different characteristics.
Based on the $\Delta H$ and $\Phi$ curves, we categorized the samples into
three distinct groups. Figure 1 illustrates three representative examples for
each category. It is worth mentioning that the intensity-normalized helicity
represented by the orange curves refers to the normalization of helicity
values into the range of (0, 1) rather than the previously mentioned
normalized helicity $\Delta H$/$\Phi_{p}^{2}$.

The Type-I ARs (the first row in Figure 1) exhibited a simultaneous growth in
the unsigned magnetic flux $\Phi$ and accumulated magnetic helicity $\Delta
H$. The absolute value of the Pearson correlation coefficient between them
exceeds 0.9. This high correlation indicates that the helicity steadily
increases with unsigned flux, and it can be inferred that the helicity
injection is mainly dominated by a single sign. For Type-II ARs, the helicity
curves exhibit a lag behind the $\Phi$ curve during the initial phase of
emergence. As depicted in the middle row in Figure 1, the helicity curves
demonstrate a slow initial growth followed by a rapid increase. As a result,
the absolute value of the correlation coefficient between them is not more
than 0.9. It is important to note that the second example of Type-II ARs
displays a consistent helicity decrease. This is because this AR is dominated
by a negative helicity. We also calculated the ratio between the lag period
and the entire period for each Type-II AR, and the results showed that they
exhibit a 50% lag phase on average. In this way, the missing data (up to 13%
time period) of some samples would not affect the classification for Type-II
ARs. Type-III ARs display a significant injection of opposite helicity,
resulting in a clear reversal of the helicity curve. Type-I and Type-II ARs
may also exhibit slight opposite helicity injections in addition to their
dominant helicity sign. However, they are relatively slight in contrast to the
total helicity accumulation. To classify an AR as a Type-III, positive and
negative signs of helicity must both be considered to constitute at least 30%
of the total unsigned helicity. Based on the criterion mentioned above, there
are 71 Type-I ARs, 34 Type-II ARs, and 31 Type-III ARs, accounting for 52.2%,
25%, and 22.8% of the total sample, respectively.

Figure 2 presents an example of $B_{r}$ magnetograms of AR 11620 corresponding
to Type-I ARs, which provides a visual depiction of the entire process of AR
emergence. During the emergence of the AR, a typical scenario involves the
presence of a pair of positive and negative magnetic poles. As the AR emerges,
the magnetic flux associated with both poles gradually increases, and the
poles start to separate from each other. In the area where the poles meet, the
PIL structures develop and are characterized by a significant magnetic field
gradient and strong shearing motions. The clockwise rotation of the magnetic
footpoints at the poles is also observed. This rotation contributes to the
shearing term of the helicity injection within the AR. As the emergence
process continues, the magnetic field becomes progressively more complicated.
Apart from the two main magnetic poles, numerous smaller magnetic poles are
also formed. The interaction of opposite polarities leads to ubiquitous
magnetic cancellation. Figure 3 depicts the temporal evolution of the
calculated parameters corresponding to Figure 2. In the top row, panel (a), of
Fig. 3, we observed that the unsigned flux $\Phi$ and accumulated energy
$\Delta E$ exhibited a monotonic increase over time. Panel (b) displays the
time evolution of helicity flux $dH/dt$, while panel (c) presents the
accumulated helicity $\Delta H$ obtained by integrating $dH/dt$. Notably, we
can observe the strong correlation between the $\Delta H$ and $\Phi$ curves, a
characteristic associated with Type-I ARs. Moreover, we observed that the
shear term contributes to the majority of the helicity.

Figure 4 presents another example of AR 11768, classified as a Type-II AR, and
illustrates its emergence from the quiet region. Through these magnetograms,
we could observe a similar emergence process with Type-I ARs: a bipole
magnetic configuration with a PIL structure in the middle. We could also
observe the main pole rotation and the emerging smaller magnetic poles. As a
result, it is hard to distinguish Type-I and Type-II ARs solely based on the
magnetogram. Figure 5 displays the temporal evolution of the calculated
parameters for this AR. We observed a monotonic increase in the $\Phi$, while
the $\Delta H$ shows a lag behind $\Phi$ by about 30 hours. Moreover, helicity
does not begin to increase rapidly until around 60 hours after the start of
emergence. We found that the when the helicity is not accumulated prominently,
the energy accumulates slowly, indicating a small amount of energy injection
during the initial phase of emergence for Type-II ARs. When examining the
magnetograms from the early phase of emergence (i.e., helicity accumulation is
small), we could see a clear increase in magnetic flux (see Figure 4 and
Figure 5(a)). Consequently, the minimal helicity injection can be attributed
to the relatively diminished velocity field during the initial phase of
emergence.

Figure 6 shows another example of AR 12521, and its temporal evolution of the
calculated parameters is shown in Figure 7. This example is a Type-III AR
characterized by a distinct reversal in the helicity curve. This implies that
the helicity injection is primarily driven by positive helicity in the initial
stage followed by a transition to negative helicity dominance. From Figure 6,
we could not get conclusive evidence substantiating helicity reversal. The
emergence process exhibits similarities with that of the other two types of
ARs, rendering their differentiation based solely on magnetograms a challenge.
However, the spatial area and the time interval during emergence are
relatively smaller than the other two types. Importantly, discerning the
source position of helicity reversal proved to be intricate due to the gauge-
dependent nature of helicity flux density, which lacks a distinctly defined
physical interpretation (Pariat et al. 2005; Liu et al. 2023). We observed
that the energy curve also displays alternating positive and negative
phenomena, though the trend is different from the helicity. This phenomenon
may be attributed to magnetic cancellations occurring between opposite
polarities. Notably, among all the cases, the shear terms (represented by the
red curves) contribute significantly to the helicity, as opposed to the
emerging terms (represented by the green curves). This indicates that the
helicity injection is mainly caused by shearing motions rather than emerging
twisted structures, which aligns with previous observations (Liu et al. 2014;
Vemareddy 2015; Liokati et al. 2022).

##  5 Statistical results

Figure 8 displays the scatter plots on various parameters for the three types
of ARs. Panel (a) shows the distribution of accumulated helicity $\Delta H$.
It is evident that samples with markedly larger $\Delta H$ values (above
$3\times 10^{42}$ Mx2) mainly belong to Type-I ARs. Furthermore, the $\Delta
H$ values for Type-I ARs are significantly larger than those of the other two
types. The mean $\Delta H$ for Type-I ARs is 1.81$\times 10^{42}$ Mx2,
approximately three times larger than that of Type-II ARs and about six times
larger than that of Type-III ARs. Panel (b) presents the distribution of
accumulated energy $\Delta E$. Notably, samples with significantly larger
$\Delta E$ values (above $5\times 10^{32}$ erg) are predominantly associated
with Type-I ARs. Additionally, the $\Delta E$ values for Type-I ARs are also
larger than those of the other two types. The mean $\Delta E$ for Type-I ARs
is 1.51$\times 10^{32}$ erg, which is approximately twice as large as that of
Type-II ARs and Type-III ARs. Panel (c) shows the distribution of normalized
helicity. This quantity allowed us to assess the structural complexity of the
ARs rather than focusing solely on their area (Démoulin & Pariat 2009). It is
evident that Type-III ARs exhibit the lowest normalized helicity compared to
the other two types of ARs. In panel (d) the distribution of emergence time
for the three types of ARs is presented. This parameter indicates the interval
from the beginning of emergence to the end of the increase of the magnetic
flux calculated by Kutsenko et al. (2019), as mentioned in Section 2. The
analysis reveals that Type-II ARs exhibit a slightly longer mean emergence
time compared to Type-I ARs. However, the ARs with a long emergence time,
above 100 hours, are almost Type-I ARs. Notably, Type-III ARs have the
shortest mean emergence time. This observation could be attributed to the fact
that Type-III ARs typically have the smallest spatial range, as is evident
from panels (a) and (b). Panels (e) and (f) depict the distribution of
helicity injection rate and the energy injection rate, respectively. Both
panels highlight that Type-I ARs exhibit a higher injection rate, which is
similar to the result in panels (a) and (b). Based on the above statistical
analyses, we could infer substantial differences among the three types of ARs.
Moreover, $\Delta H$ and $\Delta E$ emerge as good indicators for Type-I ARs,
while $\Delta H$/$\Phi_{p}^{2}$ can be used to distinguish Type-III ARs.

Figure 9 presents scatter plots related to the flare index and other
parameters. Notably, panel (a) of this figure reveals that the vast majority
(90%) of ARs with a flare index greater than six belong to Type-I ARs. In
contrast, only one sample (10%) falls into the category of Type-III. In other
words, Type-I ARs are the most likely candidates for becoming highly flare-
productive ARs. Moreover, it is noteworthy that these highly flare-productive
ARs consistently exhibit substantial helicity accumulation, with values
exceeding 2.2$\times 10^{42}\ {Mx}^{2}$. Furthermore, there are several Type-
III ARs with a flare index above four, which indicates that Type-III ARs
possess a moderate likelihood of becoming flare-productive ARs. In contrast,
Type-II ARs demonstrate a notably limited propensity to develop into flare-
productive regions. In panel (b), a flare index trend similar to that in panel
(a) can be seen. However, we observed that the normalized helicity $\Delta
H$/$\Phi_{p}^{2}$ does not exhibit a strong correlation with the flare index.
It appears that the flare index may not be closely associated with normalized
helicity. Panel(c) illustrates the $\Delta E$-$\Delta H$ diagram. A quasi-
linear relationship with a Pearson coefficient of 0.8 can be observed between
helicity and energy accumulation, which is consistent with previous
observations (Tziotziou et al. 2012; Liokati et al. 2022). Using the least-
squares best logarithmic fits with a Kolmogorov-Smirnov significance level of
about 0.8, the relationship between energy and helicity satisfies the
following equation:

$\Delta H=6.46\times 10^{11}\ \Delta E^{0.94}.$ (7)

Notably, samples with a high flare index (red and orange scatter points) tend
to concentrate in the upper-right corner of the diagram, indicating that
flare-productive ARs exhibit a larger helicity and energy accumulation.
However, non-flaring ARs (indicated by deep blue scatter points with FI=0) can
also be found in the upper-right corner, suggesting that even with significant
helicity and energy accumulation, certain ARs may remain inactive. Moderately
active ARs (marked as green and light blue scatter points) can be observed in
the lower-left corner, indicating that ARs with a relatively smaller helicity
and energy injection can still exhibit moderate flare productivity. In
contrast to the $\Delta E$-$\Delta H$ diagram with a random time duration in
Tziotziou et al. (2012), we strictly defined the starting and ending time of
the emergence. In this way, the helicity and energy could reflect the exact
value accumulated during the emergence of each AR. Moreover, we used data from
SDO/HMI, which are widely used nowadays, to develop the helicity and energy
calculation, thus providing a supplement to and validation of their work.

##  6 Summary and discussion

In this work, we selected 136 samples of emerging ARs and calculated their
parameters of magnetic flux, helicity, and energy accumulation during
emergence. Through analysis of the distribution of the parameters and their
relationship with the flare index, we obtained the following important
results:

(i) According to the time evolution of magnetic helicity and unsigned magnetic
flux, we classified the emerging ARs into three categories. Type-I ARs exhibit
a continuous increase in helicity during emergence closely synchronized with
the changes in magnetic flux, with a correlation coefficient above 0.9. In
Type-II ARs, the helicity shows minimal growth during the initial phase of
emergence followed by a rapid increase after a certain period, with a
correlation coefficient below 0.9 compared to the magnetic flux. Type-III ARs
display evident injection of opposite helicity, where the accumulated value of
helicity with a specific sign constitutes at least 30% of the total
accumulated unsigned helicity.

(ii) The three types of ARs exhibit notable differences in terms of flare
index, magnetic flux, helicity, normalized helicity, and energy. The most
prominent distinction lies in the flare index. We observed that 90% of highly
flare-productive ARs ($FI\geq 6$) belong to Type-I ARs, suggesting that Type-I
ARs are the most likely candidates for achieving a high level of flare
productivity. In contrast, Type-II ARs show a very low likelihood of becoming
flare productive, while Type-III ARs still maintain a moderate probability of
becoming flare productive. Moreover, the $\Delta H$ and $\Delta E$ values for
Type-I ARs are predominantly larger than those of the other two types, and
significantly Type-III ARs have the lowest $\Delta H$/$\Phi_{p}^{2}$ value.

(iii) A highly flare-productive AR is certain to accumulate a significant
amount of helicity and energy during its emergence phase. However, despite
accumulating substantial energy during emergence, some ARs may remain as non-
flaring. We also found that there is a quasi-linear relationship between
helicity and energy accumulation, which is in accordance with previous studies
(Tziotziou et al. 2012; Liokati et al. 2022).

Our findings have two significant implications. Firstly, it provides valuable
insights into the physical mechanisms of flux emergence from the perspectives
of magnetic helicity and magnetic energy evolution. It also enhances our
understanding of the transport of magnetic helicity from the solar interior to
the solar atmosphere. Secondly, it helps establish a potential relationship
between magnetic parameters during emergence and subsequent flare activities.
Being able to identify whether an AR is flare productive or not when it
emerges offers the possibility of early-stage predictions for solar eruptions.

The most distinct characteristic of Type-II ARs is their lag between the
helicity and the unsigned flux. They constitute 25% of the total number of
emerging ARs, indicating that the phenomenon of delayed helicity injection is
widespread. This raises the question of why such a delay in helicity
accumulation leads to a flare-poor nature. There are two possible
explanations. The first is that the coherency of the emerging flux tube is
weak in Type-II ARs. At the initial stage of the emergence, because of the
weak coherency of the flux tube, the magnetic helicity can be dispersed due to
the convection flows at the photosphere, and thus there is only a small
increase in the magnetic helicity. However, for Type-I ARs, which may have a
strong coherency, the initial magnetic helicity is not dispersed due to the
convection flows at the photosphere, and thus it accumulates from the
beginning. In conclusion, the difference in the relations of magnetic helicity
with magnetic flux for Type-I and Type-II ARs may reflect the coherency of the
emerging magnetic flux tubes. The flux tubes with a strong coherency in Type-I
ARs tend to produce more flares compared to those with a weak coherency in
Type-II ARs. The second explanation is the lack or minimal injection of
helicity during the initial phase of emergence. Previous studies as well as
ours have shown that helicity injection is primarily driven by shear motions
in the photosphere and sub-photosphere (Liu et al. 2014; Liokati et al. 2022).
The absence of helicity injection in the early stages of emergence suggests
the absence of significant shear motions at the onset of emergence. Toriumi et
al. (2023) performed numerical simulations of the emergence of three types of
magnetic flux tubes: non-twisted, weakly twisted, and strongly twisted. They
placed the three magnetic flux tubes in the convection zone and observed their
emerging process and helicity injection upward, respectively. Their results
revealed that in the case of non-twisted flux tubes, the onset of helicity
injection is delayed compared to the other two cases (see their Figure 2). The
total helicity accumulation for the non-twisted case is also significantly
less than the other two cases. Additionally, their model predicts that ARs
formed by non-twisted flux tubes are hard to produce above M-Class flares. The
scenario of the non-twisted case appears plausible when applied to Type-II ARs
in our work. During the initial phase of emergence, the lack of prominent
shear motions results in minimal helicity injection. A short time later, the
footpoint motions induced by convective turbulence leads to the injection of
helicity. These ARs formed by a non-twisted flux tube will have a relatively
small helicity accumulation, and it will be difficult for them to be flare
productive.

Type-III ARs demonstrate a distinctive characteristic of successive injections
of opposite helicity signs. They constitute 22.8% (31 out of 136) of the
samples, but only one Type-III case can develop into an AR with a flare index
greater than six. Zhang et al. (2006) proposed the concept of an upper bound
on the total magnetic helicity that a force-free field can contain. Exceeding
this upper bound would initiate a non-equilibrium situation, such as CMEs. In
this scenario, the continuous injection of opposite helicity can effectively
remove a portion of the accumulated helicity, thus inhibiting CMEs. To support
this idea, Vemareddy & Démoulin (2017) and Vemareddy (2021, 2022) conducted
detailed case studies of several emerging ARs. They found that the helicity
flux changed sign during the evolution of these cases and that the magnetic
flux ropes and CMEs are absent. Though they are CME-poor, these cases can be
associated with numerous C-class and sub-C-class flaring activities. They
concluded that the injection of opposite helicity causes the relaxation of the
sheared field through magnetic reconnection, resulting in small-scale flares,
but it is difficult to form a large-scale flux rope and a large flare. Their
investigations might explain why Type-III ARs have a moderate probability of
becoming flare productive. Moreover, the injection of opposite magnetic
helicity results in a smaller total helicity accumulation (see Fig. 8(d)),
which is another contributing factor to the inhibition of large flares. There
are indeed some studies showing that opposite helicity injection can cause a
large flare (Park et al. 2012; Jing et al. 2015); however, the detailed
triggering mechanism between opposite helicity injection and flares is
debated. These results may explain why four out of our 31 Type-III ARs can
have a flare index exceeding four.

Through our study, we conducted a large-sample analysis of the relationship
between parameters of emerging active regions and subsequent flare eruptions.
However, several limitations must be acknowledged in our approach. Firstly, we
did not consider the surrounding conditions of ARs during their emergence. In
scenarios where an AR emerges in the presence of a pre-existing neighboring
AR, the magnetic field structure can become more complicated, potentially
leading to a higher probability of flare production (Toriumi et al. 2017).
Thus, we focused solely on calculating the parameters of the AR within its
emergence region. Secondly, we did not conduct a detailed analysis of how the
energy and helicity accumulations trigger and contribute to flare eruptions.
Our investigation only focused on a general examination of the relationship
between the calculated parameters and the flare index. In future, we would
like to investigate the long-term helicity evolution of ARs and their
following solar eruptions in order to establish the relationship between AR
helicity evolution and flare/CME productivity. Moreover, we will likely
conduct some simulations focusing on the eruption potential of emerging ARs,
which can provide possibilities for early-stage predictions of solar
eruptions.

Figure 1: Unsigned magnetic flux $\Phi$ (blacks curve) and accumulated
magnetic helicity $\Delta H$ (orange curves) evolutions for nine examples. The
top, middle, and bottom rows represent the Type-I, Type-II, and Type-III ARs,
respectively. The decreasing helicity indicates a negative helicity injection.
The correlation coefficients between the two curves are marked in the upper-
left corner of each panel.  Figure 2:  Selected HMI images of the normal
component, $B_{n}$ , of the photospheric field of the Type-I AR 11620 showing
the emergence process. The length of the horizontal white line corresponds to
100 arcsec.  Figure 3: Time profiles of the magnetic flux, helicity, and
energy for the Type-I AR 11620. Panel (a): Time evolution of the unsigned
magnetic flux $\Phi$ (black) and accumulated energy $\Delta E$ (blue). Panel
(b): Time profile of the helicity flux, $d(H)/dt$ (black). The red and green
curves represent the shear and emergence terms, respectively. Panel (c): Time
profiles of accumulated helicity $\Delta H$. The red and green curves indicate
the helicity of the emergence term and shear term, respectively.  Figure 4:
Same as Fig. 2 but for the Type-II AR 11768.  Figure 5: Same as Fig. 3 but for
the Type-II AR 11768.  Figure 6: Same as Fig. 2 but for the Type-III AR 12521.
Figure 7: Same as Fig. 3 but for the Type-III AR 12521.  Figure 8: Scatter
plots of various parameters for the three types of ARs. The horizontal axes
represent the peak unsigned magnetic flux $\Phi_{p}$, while the vertical axes
display the (a) accumulated helicity $\Delta H$, (b) accumulated energy
$\Delta E$, (c) normalized helicity $\Delta H/\Phi_{p}^{2}$ , (d) emergence
time $t$, (e) helicity injection rate $\Delta H/t$, and (f) energy injection
rate $\Delta E/t$. The mean values of the parameters for the three types of
ARs are listed at the top of each panel.  Figure 9: Scatter plots of the flare
index versus the (a) accumulated helicity $\Delta H$, (b) normalized helicity
$\Delta H/\Phi_{p}^{2}$, and (c) $\Delta H$-$\Delta E$ diagram. The color of
the scatters in panel (c) indicate the value of the flare index. The black
straight line represents the result of the least-squares best logarithmic fits
between $\Delta E$ and $\Delta H$.

###### Acknowledgements.

We thank Dr. Jingxiu Wang and Dr. Shin Toriumi for fruitful suggestions. This
work is supported by the Strategic Priority Research Program of the Chinese
Academy of Sciences (Grant No. XDB0560000 and XDB41000000), the National Key
R&D Program of China (2019YFA0405000) and the National Natural Science
Foundations of China (11973056, 12222306, and 12273060).

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##  Appendix A Calculated parameters of the dataset

Table 1: Emerging AR samples and their corresponding parameters. NOAA Number | Emergence Time | $\Delta H$ | $\Delta E$ | $\Phi_{p}$ |  $\Delta H$/$\Phi_{p}^{2}$ | Correlation | Flare Index | Type
---|---|---|---|---|---|---|---|---
| (hour) | $10^{41}(Mx^{2})$ | $10^{31}(erg)$ | $10^{21}Mx$ | $10^{-2}$ |  |  |
11072 | 58.4 | 14.37 | 12.65 | 6.29 | 3.64 | 0.94 | 0.00 | I
11076 | 80.6 | 3.82 | 13.30 | 9.72 | 0.40 | 0.77 | 0.00 | II
11081 | 25.2 | 0.64 | 1.91 | 11.73 | 0.05 | 0.46 | 2.84 | III
11096 | 42.0 | 3.65 | 4.96 | 6.46 | 0.87 | 0.95 | 0.00 | I
11105 | 90.0 | 29.95 | 8.56 | 17.71 | 0.95 | 0.99 | 0.73 | I
11130 | 74.6 | 2.60 | 29.79 | 12.66 | 0.16 | 0.83 | 0.00 | III
11138 | 34.0 | 2.48 | 1.41 | 3.32 | 2.25 | 0.97 | 0.00 | I
11141 | 38.6 | 7.39 | 5.83 | 5.86 | 2.15 | 0.96 | 0.38 | I
11156 | 63.4 | 2.03 | 3.76 | 2.24 | 4.06 | 0.09 | 0.00 | II
11158 | 83.2 | 24.26 | 67.76 | 18.89 | 0.68 | 0.96 | 41.46 | I
11162 | 26.6 | 14.34 | 16.91 | 6.91 | 3.01 | 0.22 | 0.24 | II
11175 | 77.1 | 16.12 | 24.82 | 17.87 | 0.50 | 0.79 | 0.00 | II
11199 | 92.4 | 44.22 | 30.36 | 22.43 | 0.88 | 0.97 | 1.64 | I
11214 | 95.6 | 9.23 | 13.80 | 8.12 | 1.40 | 0.98 | 0.00 | I
11217 | 33.8 | 1.86 | 1.38 | 2.02 | 4.58 | 0.72 | 0.00 | II
11223 | 31.4 | 0.45 | 2.93 | 3.27 | 0.42 | 0.54 | 0.00 | III
11224 | 42.4 | 6.59 | 6.10 | 8.56 | 0.90 | 0.98 | 0.00 | I
11241 | 57.0 | 2.85 | 4.83 | 3.27 | 2.66 | 0.96 | 0.00 | I
11242 | 54.8 | 10.14 | 3.85 | 7.08 | 2.02 | 0.93 | 0.00 | I
11273 | 34.2 | 0.14 | 0.31 | 1.73 | 0.46 | 0.20 | 0.00 | III
11291 | 7.4 | 0.06 | 0.14 | 0.51 | 2.44 | 0.95 | 0.00 | I
11297 | 25.4 | 4.50 | 1.59 | 9.91 | 0.46 | 0.50 | 5.98 | III
11311 | 27.6 | 1.68 | 5.00 | 5.22 | 0.62 | 0.97 | 0.00 | I
11318 | 32.8 | 0.20 | 1.42 | 2.58 | 0.30 | 0.56 | 0.17 | III
11326 | 52.0 | 1.40 | 4.05 | 5.63 | 0.44 | 0.97 | 0.00 | I
11344 | 90.4 | 10.59 | 9.66 | 6.62 | 2.41 | 0.73 | 2.89 | II
11345 | 33.4 | 0.66 | 0.86 | 5.35 | 0.23 | 0.63 | 0.00 | III
11365 | 50.6 | 3.03 | 6.31 | 7.11 | 0.60 | 0.37 | 0.00 | II
11398 | 48.0 | 2.53 | 5.62 | 9.03 | 0.31 | 0.94 | 0.00 | I
11404 | 14.4 | 0.04 | 0.51 | 1.14 | 0.31 | 0.44 | 0.00 | III
11407 | 78.4 | 1.35 | 1.46 | 6.37 | 0.33 | 0.52 | 0.00 | III
11416 | 59.4 | 14.70 | 1.03 | 14.53 | 0.70 | 0.99 | 0.10 | III
11422 | 51.0 | 30.13 | 21.54 | 13.33 | 1.70 | 0.92 | 0.36 | I
11430 | 76.0 | 25.85 | 12.39 | 8.57 | 3.52 | 0.63 | 2.67 | II
11444 | 109.2 | 0.50 | 0.26 | 5.07 | 0.19 | 0.33 | 0.00 | III
11446 | 40.6 | 0.53 | 1.00 | 1.47 | 2.45 | 0.48 | 0.00 | II
11455 | 66.8 | 1.05 | 9.01 | 7.24 | 0.20 | 0.84 | 0.00 | III
11456 | 14.6 | 0.03 | 0.02 | 0.52 | 1.04 | 0.02 | 0.00 | III
11460 | 111.8 | 54.32 | 76.97 | 16.11 | 2.09 | 0.91 | 0.93 | I
11464 | 6.4 | 0.01 | 0.09 | 0.50 | 0.30 | 0.54 | 0.00 | III
11468 | 65.2 | 6.96 | 11.40 | 4.71 | 3.14 | 0.85 | 0.00 | II
11473 | 17.4 | 2.03 | 2.92 | 5.30 | 0.72 | 0.92 | 0.00 | I
11503 | 17.4 | 0.10 | 1.68 | 2.36 | 0.19 | 0.07 | 0.00 | III
11523 | 116.4 | 11.99 | 11.43 | 5.83 | 3.52 | 0.93 | 0.00 | I
11554 | 38.0 | 1.13 | 12.98 | 5.91 | 0.32 | 0.26 | 0.00 | III
11560 | 85.6 | 94.95 | 36.09 | 9.69 | 10.10 | 0.95 | 0.00 | I
11568 | 23.4 | 1.27 | 0.27 | 4.22 | 0.72 | 0.99 | 0.00 | I
11620 | 54.4 | 49.47 | 26.38 | 25.63 | 0.75 | 0.98 | 8.22 | I
11630 | 98.2 | 3.62 | 8.62 | 7.48 | 0.65 | 0.86 | 0.99 | II
11632 | 110.4 | 20.29 | 26.26 | 19.38 | 0.54 | 0.97 | 0.15 | I
11640 | 133.0 | 75.27 | 45.72 | 21.58 | 1.62 | 0.97 | 1.32 | I
11670 | 82.0 | 15.47 | 21.25 | 8.00 | 2.42 | 0.96 | 0.15 | I
11682 | 82.4 | 22.22 | 25.41 | 12.12 | 1.51 | 0.94 | 0.00 | I
11697 | 30.4 | 0.23 | 0.98 | 3.52 | 0.19 | 0.03 | 0.00 | III
11699 | 45.8 | 1.81 | 0.81 | 6.11 | 0.48 | 0.77 | 0.00 | II
11706 | 39.8 | 0.13 | 0.85 | 0.99 | 1.34 | 0.87 | 0.00 | III
11707 | 21.6 | 2.21 | 1.46 | 2.78 | 2.85 | 0.93 | 0.00 | I
11709 | 61.2 | 0.56 | 0.71 | 1.83 | 1.67 | 0.92 | 0.00 | I
11726 | 75.8 | 110.16 | 67.83 | 31.90 | 1.08 | 0.95 | 20.77 | I
11762 | 61.6 | 106.61 | 46.75 | 20.12 | 2.63 | 0.95 | 12.00 | I
11764 | 28.8 | 4.64 | 5.87 | 7.35 | 0.86 | 0.99 | 0.00 | I
11765 | 71.6 | 8.13 | 22.00 | 8.31 | 1.18 | 0.85 | 0.21 | II
11768 | 74.4 | 22.47 | 23.05 | 17.30 | 0.75 | 0.78 | 0.16 | II
11776 | 65.6 | 7.35 | 16.81 | 12.13 | 0.50 | 0.71 | 1.29 | III
11780 | 24.4 | 0.01 | 0.31 | 5.62 | 0.00 | 0.41 | 1.59 | III
11781 | 62.8 | 5.54 | 10.14 | 13.28 | 0.31 | 0.89 | 0.14 | III
11789 | 14.2 | 0.28 | 0.76 | 1.55 | 1.15 | 0.72 | 0.00 | II
11831 | 47.8 | 6.52 | 2.83 | 9.89 | 0.67 | 0.89 | 0.00 | II
11886 | 35.0 | 0.53 | 1.33 | 2.88 | 0.64 | 0.92 | 0.00 | I
11889 | 75.6 | 7.46 | 9.13 | 6.51 | 1.76 | 0.92 | 0.72 | I
11891 | 33.8 | 5.36 | 4.05 | 5.91 | 1.53 | 0.89 | 6.35 | I
11902 | 43.4 | 0.93 | 0.86 | 1.68 | 3.31 | 0.96 | 0.00 | I
11928 | 75.8 | 43.34 | 53.08 | 16.62 | 1.57 | 0.93 | 14.68 | I
11933 | 20.2 | 9.69 | 2.21 | 6.03 | 2.67 | 0.96 | 0.00 | I
11961 | 20.6 | 3.13 | 1.50 | 5.52 | 1.03 | 0.94 | 0.00 | I
11978 | 13.6 | 0.19 | 0.15 | 1.33 | 1.08 | 0.96 | 0.00 | I
11988 | 58.8 | 7.95 | 1.44 | 11.82 | 0.57 | 0.97 | 0.39 | I
11992 | 34.8 | 3.61 | 1.35 | 2.19 | 7.51 | 0.98 | 0.00 | I
11995 | 44.8 | 2.87 | 3.67 | 2.06 | 6.76 | 0.98 | 0.00 | I
11999 | 18.6 | 0.23 | 0.84 | 1.00 | 2.25 | 0.78 | 0.00 | II
12006 | 64.4 | 26.74 | 17.83 | 14.44 | 1.28 | 0.98 | 3.33 | I
12018 | 77.6 | 1.73 | 6.79 | 2.37 | 3.07 | 0.12 | 0.00 | III
12036 | 87.2 | 93.49 | 69.64 | 15.93 | 3.69 | 0.94 | 12.94 | I
12037 | 65.0 | 10.81 | 16.78 | 5.81 | 3.32 | 0.94 | 2.80 | I
12048 | 53.6 | 4.70 | 3.25 | 9.22 | 0.55 | 0.96 | 0.85 | I
12051 | 55.2 | 37.10 | 20.62 | 14.90 | 1.67 | 0.96 | 11.90 | I
12063 | 44.0 | 4.86 | 5.92 | 3.76 | 3.43 | 0.77 | 0.70 | II
12085 | 79.4 | 51.27 | 111.36 | 22.89 | 0.98 | 0.78 | 11.02 | III
12089 | 135.2 | 33.38 | 41.53 | 24.64 | 0.55 | 0.99 | 2.49 | I
12091 | 21.6 | 1.45 | 0.82 | 2.60 | 2.15 | 0.86 | 0.00 | II
12126 | 82.0 | 1.12 | 2.26 | 2.35 | 2.03 | 0.87 | 1.28 | II
12129 | 11.4 | 0.48 | 0.97 | 1.63 | 1.83 | 0.89 | 0.00 | II
12193 | 91.0 | 5.12 | 23.03 | 8.71 | 0.67 | 0.86 | 0.66 | II
12198 | 10.4 | 0.31 | 0.26 | 1.04 | 2.88 | 0.97 | 0.00 | I
12203 | 49.0 | 15.21 | 14.71 | 8.56 | 2.07 | 0.98 | 0.59 | I
12219 | 109.0 | 26.57 | 49.36 | 18.26 | 0.80 | 0.84 | 1.80 | II
12223 | 33.2 | 0.46 | 1.01 | 1.74 | 1.51 | 0.95 | 3.12 | I
12226 | 66.3 | 3.75 | 0.43 | 9.77 | 0.39 | 0.80 | 1.00 | II
12228 | 17.2 | 0.55 | 0.50 | 0.86 | 7.42 | 0.98 | 0.00 | I
12229 | 15.2 | 0.67 | 0.27 | 0.58 | 19.80 | 0.97 | 0.00 | I
12230 | 84.6 | 1.40 | 43.03 | 6.36 | 0.35 | 0.31 | 3.80 | III
12231 | 18.6 | 1.20 | 1.49 | 1.45 | 5.70 | 0.73 | 1.54 | II
12234 | 64.0 | 14.70 | 16.31 | 5.21 | 5.41 | 0.98 | 1.20 | I
12257 | 81.2 | 21.95 | 67.38 | 20.02 | 0.55 | 0.94 | 23.79 | I
12265 | 38.8 | 0.01 | 1.75 | 1.46 | 0.06 | 0.57 | 0.00 | III
12266 | 42.6 | 24.28 | 19.91 | 7.73 | 4.07 | 0.90 | 0.00 | I
12271 | 121.8 | 44.39 | 36.07 | 16.31 | 1.67 | 0.98 | 0.77 | I
12275 | 47.6 | 1.55 | 19.14 | 12.45 | 0.10 | 0.69 | 0.26 | II
12291 | 16.6 | 0.23 | 0.04 | 0.82 | 3.35 | 0.98 | 0.00 | I
12294 | 30.4 | 1.98 | 4.00 | 5.80 | 0.59 | 0.91 | 1.93 | I
12309 | 7.2 | 0.09 | 0.36 | 0.83 | 1.25 | 0.98 | 1.41 | I
12315 | 29.2 | 0.50 | 3.90 | 4.04 | 0.31 | 0.12 | 0.00 | II
12332 | 28.6 | 0.07 | 0.50 | 1.99 | 0.17 | 0.66 | 0.38 | III
12353 | 68.0 | 0.08 | 6.16 | 5.66 | 0.02 | 0.45 | 0.63 | III
12380 | 16.0 | 0.24 | 0.05 | 0.82 | 3.53 | 0.98 | 0.00 | I
12388 | 28.8 | 0.02 | 0.30 | 2.83 | 0.02 | 0.67 | 0.45 | III
12414 | 76.0 | 20.62 | 10.54 | 15.29 | 0.88 | 0.53 | 0.32 | II
12424 | 8.8 | 0.33 | 0.34 | 1.69 | 1.17 | 1.00 | 0.00 | I
12440 | 35.6 | 0.20 | 0.92 | 2.80 | 0.25 | 0.58 | 0.16 | III
12453 | 75.8 | 0.59 | 2.15 | 2.02 | 1.46 | 0.22 | 0.00 | II
12475 | 10.0 | 0.01 | 0.28 | 1.02 | 0.07 | 0.89 | 0.00 | III
12500 | 20.6 | 0.47 | 0.20 | 1.70 | 1.63 | 0.87 | 0.26 | II
12503 | 7.0 | 0.07 | 0.31 | 0.80 | 1.10 | 0.98 | 0.00 | I
12509 | 10.0 | 0.21 | 0.85 | 1.76 | 0.69 | 0.90 | 0.00 | I
12511 | 38.6 | 1.73 | 2.00 | 5.49 | 0.57 | 0.79 | 0.15 | II
12514 | 22.2 | 2.23 | 1.61 | 4.43 | 1.14 | 0.97 | 0.00 | I
12521 | 56.6 | 2.04 | 0.13 | 4.69 | 0.93 | 0.76 | 0.89 | III
12528 | 71.4 | 3.26 | 3.82 | 3.39 | 2.83 | 0.95 | 0.00 | I
12543 | 95.8 | 10.15 | 8.71 | 6.47 | 2.42 | 0.93 | 3.04 | I
12548 | 83.0 | 26.25 | 17.92 | 10.82 | 2.24 | 0.89 | 0.16 | II
12550 | 17.4 | 0.70 | 0.34 | 3.73 | 0.50 | 0.88 | 0.00 | II
12557 | 74.4 | 2.11 | 2.20 | 1.42 | 10.41 | 0.75 | 0.00 | II
12558 | 20.6 | 1.69 | 0.65 | 3.06 | 1.80 | 0.95 | 0.00 | I
12607 | 16.0 | 2.73 | 0.25 | 4.65 | 1.26 | 0.94 | 0.00 | I
12619 | 5.2 | 0.18 | 0.10 | 1.14 | 1.39 | 0.93 | 0.00 | I
12632 | 32.8 | 4.16 | 1.07 | 4.15 | 2.41 | 0.93 | 0.00 | I

* The column ”Emergence Time” shows the total time of emergence, which is calculated by the two-segment piecewise continuous linear fitting method applied to the unsigned flux curves (Kutsenko et al. 2019). The columns of ”$\Delta H$” and ”$\Delta E$” indicate the total helicity and energy accumulation during emergence, respectively. The column of ”$\Phi_{p}$” is the peak unsigned magnetic flux during emergence. The ”Correlation” column indicates the Pearson correlation coefficient between the accumulated helicity $\Delta H$ curve and the unsigned flux $\Phi$ curve during emergence.