# Properties and Energetics of Magnetic Reconnection: I. Evolution of Flare
Ribbons

J. Qiu  J. Cheng  Department of Physics, Montana State University, Bozeman,
MT, 59717, USA (email<EMAIL_ADDRESS> CAS Key Laboratory of Planetary
Sciences, Shanghai Astronomical Observatory, Chinese Academy of Sciences,
Shanghai 200030, China

###### keywords:

Sun: flares – Sun: UV radiation – Sun: X-rays – Magnetic Reconnection

##  1 INTRODUCTION

sec:intro

Whereas flare energy release is governed by fast magnetic reconnection, of
order 10 - 10000 V m-1 in terms of the reconnection electric field (see
Hinterreiter et al., 2018, and references therein), it is not clear what
mechanism governs the efficiency of conversion of this energy into non-thermal
electrons, plasma heat, or bulk kinetic energy. In the effort to answer this
question, past observational studies have explored the temporal and/or spatial
correlation between hard X-ray (HXR) and/or microwave emissions and
reconnection rate in solar flares, following the early attempt by Poletto and
Kopp (1986). Flare HXR and microwave emissions are produced by non-thermal
electrons interacting with plasmas and magnetic field (Benz, 2017), and the
reconnection rate has been frequently inferred from imaging observations of
the flare emission in the lower atmosphere, using the recipe provided by
Forbes and Priest (1984). The rate of magnetic reconnection is characterized
by the reconnection electric field $E=v_{in}B_{in}$, where $B_{in}$ is the
magnetic field brought into the reconnection current sheet in the corona with
the inflow speed $v_{in}$. Lacking direct measurements of magnetic field in
the corona, $E$ can be estimated by $E\approx v_{l}B_{l}$, $v_{l}$ being the
apparent motion speed of flare ribbons or kernels in the lower atmosphere, and
$B_{l}$ the magnetic field there (Forbes and Priest, 1984; Poletto and Kopp,
1986). The path integral of this electric field along the current sheet yields
the total flux change rate $\dot{\psi}$, which, in practice, is equated by the
time rate of the magnetic flux $\psi(t)$ swept up by newly brightened flare
ribbons $\psi(t)=\int B_{l}dA_{l}$ (Fletcher and Hudson, 2001; Qiu et al.,
2004; Saba, Gaeng, and Tarbell, 2006; Miklenic et al., 2007; Kazachenko et
al., 2017). In the following text, we will refer to $\dot{\psi}$ as the global
or total reconnection rate, and the reconnection electric field $E$ as the
local or mean reconnection rate.

When inferring $E$ from the lower atmosphere observations, $B_{l}$ is usually
measured as the vertical or longitudinal magnetic field in the photosphere,
with a few exceptions that sometimes extrapolate the field to the chromosphere
(e.g. Qiu et al., 2007). The apparent motion speed $v_{l}$ is measured in a
variety of ways, either as the mean speed $v_{l}\approx v_{\perp}$ of the
perpendicular expansion of flare ribbon fronts or leading edges observed in
optical or UV wavelengths (Poletto and Kopp, 1986; Qiu et al., 2004; Asai et
al., 2004; Xu et al., 2004; Isobe, Takasaki, and Shibata, 2005; Jing et al.,
2005; Saba, Gaeng, and Tarbell, 2006; Temmer et al., 2007; Miklenic et al.,
2007; Jing, Chae, and Wang, 2008; Liu and Wang, 2009; Qiu et al., 2010, 2017;
Wang et al., 2017b; Hinterreiter et al., 2018), or as the proper motion speed
$v_{l}\approx v_{k}$ of the brightest or prominent kernels observed in
infrared, optical, UV, or hard X-ray wavelengths, regardless of the direction
of the motion (Qiu et al., 2002; Krucker, Hurford, and Lin, 2003; Fletcher,
Pollock, and Potts, 2004; Krucker, Fivian, and Lin, 2005; Lee, Gary, and Choe,
2006; Liu et al., 2009; Yang et al., 2011; Inglis and Gilbert, 2013). The
interpretation of $v_{l}$ measured in different ways much depends on the
magnetic configuration presumed or invoked for the given cases in the study
(see the discussion in Fletcher, 2009). These past studies have shown, with
varying degrees of success, that HXR (or microwave) emissions are temporally,
and sometimes spatially, correlated with the global or local reconnection
rate. On the other hand, these studies did not verify a one-to-one coincidence
between significant HXR emission and enhanced reconnection rate, however it is
measured (e.g. see the discussion in Fletcher and Hudson, 2002; Miklenic et
al., 2007; Inglis and Gilbert, 2013; Qiu, 2021). In particular, a recent case
study by Naus et al. (2021), using high-resolution observations of flare
ribbons by the Interface Region Imaging Spectrograph (IRIS: De Pontieu et al.,
2014), has characterized in great detail the bursty nature of flare
reconnection. The analysis has identified locations (of size 600 - 1200 km) on
flare ribbons, where the width of the newly brightened ribbon is enhanced, and
EUV emissions at these locations are correlated with the $\geq$25 keV HXR
lightcurve. The study has also revealed enhanced ribbon front width at other
locations a few minutes before the onset of the HXR emission. The ribbon front
width may be translated into the local reconnection rate, and the findings by
Naus et al. (2021) therefore suggest that the production of non-thermal
electrons is strongly connected with, yet not solely dependent on, the locally
enhanced reconnection rate.

The mean or local reconnection rate is inferred with a 2D approximation
following the proposal by Forbes and Priest (1984). The extension to a 2.5D
configuration of the reconnection current sheet would require the
consideration of the third dimension, the direction of the inferred electric
field, along which the magnetic field component, or the guide field $B_{g}$,
does not vanish. The presence of an appropriate guide field may play an
important role in energizing electrons (e.g. Holman, 1985; Litvinenko, 1996).
A recent development of new computational models has produced power-law
distributions of electrons in reconnection current layers with a modest guide
field $B_{g}/B_{in}\leq 1$ (Arnold et al., 2021). In flare observations,
direct measurements of the magnetic field vector in the reconnection current
sheet in the corona have been hard and rare (Chen et al., 2020), posing
difficulties to test theoretical models. On the other hand, it has been widely
recognized that flare brightening often starts near the polarity inversion
line (PIL) of the photospheric magnetic field, forming flare loops much
inclined toward the PIL, or strongly sheared. As flare arcades form at higher
altitude with two ribbons moving away from the PIL, flare loops become less
sheared. Such strong-to-weak shear evolution is most evident in eruptive two-
ribbon flares, such as the SOL2000-07-14 X5.7 flare, or the Bastille Day flare
(Aschwanden and Alexander, 2001; Qiu et al., 2010). It indicates that flare
reconnection likely starts with a strong guide field in the early phase, and
reconnection then proceeds at higher altitudes with the ever weakening guide
field. Using high-resolution 3D MHD simulations, Dahlin et al. (2021) have
reproduced such strong-to-weak shear evolution observed in flare ribbons or
loops (e.g. Qiu et al., 2017, and references therein), and confirmed its
association with the variation of the guide field in the reconnection current
sheet that cannot be directly measured in observations. The verification with
high-resolution numerical models provides the crucial bridge between
reconnection properties in the coronal current sheet and measurements with
observations of flare ribbons.

In the past decade, magnetic shear has been measured in a number of studies
(Su et al., 2006; Ji et al., 2006; Su, Golub, and Van Ballegooijen, 2007; Yang
et al., 2009; Liu et al., 2009; Qiu et al., 2010; Cheng, Kerr, and Qiu, 2012;
Inglis and Gilbert, 2013; Qiu et al., 2017; Sharykin et al., 2018; Zimovets,
Sharykin, and Gan, 2020), but its relation with flare energetics is not yet
elucidated. In this study, we examine the relationship between flare
energetics and reconnection properties inferred from flare ribbon
observations, taking into account the shear evolution during the flare. The
study is attempted to explore the following questions: Upon reconnection, what
happens first, particle acceleration or direct heating, or do they occur
simultaneously? Does magnetic shear, apart from the reconnection rate, affect
heating or electron acceleration? To answer these questions, we analyze six
flares that exhibit coherent two ribbons and have $\geq 25$keV HXR emissions.
These flares were well observed by the Atmospheric Imaging Assembly (AIA:
Lemen et al., 2012) and Helioseismic and Magnetic Imager (HMI: Schou et al.,
2012) on board the Solar Dynamics Observatories (SDO: Pesnell, Thompson, and
Chamberlin, 2012) and the Ramaty High Energy Solar Spectroscopic Imager
(RHESSI: Lin et al., 2002) from the flare onset throughout the impulsive
phase. In the next section, we will provide an overview of the selected
flares. With these observations, in Section 3, we measure the evolution of the
mean shear using the method developed in Qiu (2009) and Qiu et al. (2010), and
analyze flare thermal and non-thermal properties using the X-ray spectral
analysis. In the last section, results will be summarized, discussed, and
compared with prior research.

##  2 Overview of Observations: Eruptive Flares and Confined Flares

sec:overview In this article, we present the analysis of six flares listed in
Table tab:info. The sample includes three eruptive flares accompanied by
coronal mass ejections (CMEs), and three confined flares without evident
association with large-scale eruptions like filament eruptions or CMEs. These
flares are selected based on their geometry and the availability of the RHESSI
X-ray observations. We have inspected $\approx$ 400 flares from the flare
ribbon database by Kazachenko et al. (2017), together with the relevant CME
and X-ray observations, and selected the six events listed in Table tab:info
for the preliminary experiment. These flares have a relatively simple
morphology, all exhibiting prominent and nearly coherent two ribbons aligned
along the polarity inversion line (PIL) of the photospheric magnetic field. It
is therefore justifiable to infer physical parameters with respect to an
approximate 2.5-dimensional configuration (e.g. Qiu et al., 2010, 2017). To
examine flare energetics in the early phase of the flare evolution, we select
events observed by RHESSI from the start of the flare and throughout the
impulsive phase, with a relatively clean background. The flares in Table
tab:info have significant HXR emissions at photon energies larger than 20 keV,
which are usually produced by non-thermal electrons. With these observations,
spectral analysis can be conducted to provide diagnostics of thermal and non-
thermal properties of the flares. The stringent selection criterion leads to
the small sample and also sets the limit on what we can conclude from this
study.

Table 1.: List of eventstab:info

| Start timea | Mag.a | NOAA positiona | CME | Shear index and energetics properties
---|---|---|---|---|---
|  |  |  |  | $\rho^{b}$ | $\langle\mathcal{R}\rangle(\mathcal{F}_{p})^{c}$ |  $\langle\gamma\rangle$ ($\mathcal{F}_{p})^{c}$ | $\langle\mathcal{R}\rangle(T_{p})^{d}$ | $\langle{\rm T_{p}}\rangle~{}{\rm[MK]}^{d}$
1 | 2014-08-25T14:46 | M2.0 | 12146 N06W39 | yes | -0.87 | $0.6\pm 0.1$ | $4.2\pm 0.5$ | $0.6\pm 0.2$ | $18.2\pm 0.6$
2 | 2014-12-18T21:41 | M6.9 | 12241 S11E10 | yes | -0.65 | $0.6\pm 0.2$ | $5.6\pm 0.7$ | $2.4\pm 0.8$ | $20.0\pm 2.2$
3 | 2013-08-12T10:21 | M1.5 | 11817 S21E17 | yes | -0.29 | $2.1\pm 0.4$ | $5.7\pm 0.4$ | $2.1\pm 0.8$ | $21.7\pm 0.8$
4 | 2015-01-29T05:15 | C8.2 | 12268 S13W03 | no | -0.89 | $1.7\pm 0.4$ | $6.1\pm 0.5$ | $2.5\pm 0.8$ | $26.2\pm 4.0$
5 | 2014-05-10T06:51 | C8.7 | 12056 N03E27 | no | -0.79 | $2.4\pm 0.2$ | $4.3\pm 0.1$ | $4.4\pm 0.8$ | $21.4\pm 5.2$
6 | 2014-12-17T14:56 | C9.8 | 12242 S18E00 | no | -0.86 | $2.2\pm 0.2$ | $5.7\pm 0.4$ | $2.2\pm 0.4$ | $23.3\pm 1.6$

$a$: Flare information provided by the Solar Monitor
https://solarmonitor.org/; the flare magnitude and start time are based on
GOES data.
$b$: Coefficient of the linear cross correlation between the $25-50$ keV HXR
counts rate $\mathcal{F}_{hxr}$ and the shear index $\mathcal{R}$ during the
rise of the HXR emission.
$c$: The mean and standard deviation of the shear index $\mathcal{R}$ measured
from flare ribbons and the mean and standard deviation of the power-law index
$\gamma$ of the non-thermal HXR photon spectrum, derived during the time
intervals when $\mathcal{F}_{hxr}$ is more than 70% of its peak value.
$d$: The mean and standard deviation of the shear index $\mathcal{R}$ and of
the plasma temperature during three time intervals around the peak plasma
temperature.

Figure 1.: Overview of the SOL2014-08-25 eruptive flare. (a) SXR (GOES) and
its time derivative, HXR (RHESSI), and UV (AIA) light curves, and reconnection
rate $\dot{\psi}$. (b) Evolution of flare ribbon fronts superimposed on a pre-
flare longitudinal magnetogram by HMI. Contour levels indicate the magnetic
flux density at $\pm$400, and 800 Mx cm-2. Orange symbols outline the PIL. (c)
Snapshots of flare ribbon evolution in UV 1600 Å by AIA, superimposed with HXR
images at 25 - 50 keV from RHESSI. Contour levels indicate 40%, 50%, 60%, 70%,
80%, and 90% of the maximum intensity of each HXR image. (d) Snapshots of
flare loops in EUV 131 Å by AIA, superimposed with HXR images at 12 - 25 keV
from RHESSI. Contour levels indicate 60%, 70%, 80%, and 90% of the maximum
intensity of each HXR image.fig:overview˙140825

Figure fig:overview_140825 gives an overview of the evolution of the
SOL2014-08-25 M2.0 eruptive flare. The ultraviolet (UV 1600 Å, AIA) and soft
X-ray (1-8 Å, GOES) emissions start to rise about 10 minutes before the rapid
rise of the 25-50 keV HXR emission (in units of counts per second, RHESSI),
hereafter denoted as $\mathcal{F}_{hxr}$ (Figure fig:overview_140825a). At the
flare onset, the global reconnection rate, or the flux change rate
$\dot{\psi}$, also rises rapidly. The flux change rate is measured by summing
up the longitudinal magnetic flux enclosed in newly brightened flare ribbons
per unit time (see Qiu et al., 2010, for the discussion of the measurement
method and uncertainties). Evolution of the newly brightened flare ribbon
fronts is presented in Figure fig:overview_140825b, with the convention that
cold colors indicate the earlier times, whereas warm colors indicate later
times. The flare ribbon fronts are derived from the time sequence of the UV
1600 Å images obtained by AIA, shown in Figure fig:overview_140825c. Two flare
ribbons are aligned with the PIL, which is outlined by orange symbols. Flare
ribbons in magnetic fields of opposite polarities map the conjugate feet of
reconnection formed flare loops, as confirmed in AIA 131 Å images (Figure
fig:overview_140825d) that exhibit flare loops of 10 MK plasmas connecting the
two ribbons. From the morphological evolution of the flare, it is apparent
that earlier formed flare loops, connecting the violet-blue patches of the two
ribbons, are more sheared with respect to the PIL than later formed loops
connecting the green-orange ribbon patches. Such a pattern of the strong-to-
weak shear evolution has been widely reported in observations of eruptive two-
ribbon flares (e.g. Su, Golub, and Van Ballegooijen, 2007; Yang et al., 2009,
and references therein), and also demonstrated in magnetohydrodynamic
simulations (e.g. Aulanier, Janvier, and Schmieder, 2012; Dahlin et al.,
2021). Finally, HXR maps have been obtained using the Pixon method at two
energies, 25 - 50 keV and 12 - 25 keV, and are superimposed with the AIA
images in Figure fig:overview_140825c and Figure fig:overview_140825d,
respectively. Despite the coarse resolution of the HXR maps, it is shown that
25 - 50 keV HXR emission tracks the UV emission on the two ribbons, whereas 12
- 25 keV HXRs are likely from the loop connecting the ribbons, and the strong-
to-weak shear evolution is evident from the morphology of HXR sources.

Figure 2.: Overview of the SOL2015-01-29 confined flare. (a) SXR, HXR, and UV
light curves, and reconnection rate $\dot{\psi}$. (b) Evolution of flare
ribbon fronts superimposed on a pre-flare longitudinal magnetogram. Orange
symbols outline the PIL. (c) Snapshots of flare ribbon evolution in UV 1600 Å
by AIA, superimposed with HXR images at 12 - 25 keV obtained by RHESSI.
Contour levels indicate 40%, 50%, 60%, 70%, 80%, and 90% of the maximum
intensity of each HXR image. (d) Snapshots of flare loops in EUV 131 Å by AIA,
superimposed with HXR images at 6 - 12 keV obtained by RHESSI, and contour
levels indicate 60%, 70%, 80%, and 90% of the maximum intensity of each HXR
image.fig:overview˙150129

Figure fig:overview_150129 gives an overview of the SOL2015-01-29 C8.2
confined flare, which evolves much faster without an apparent lead time of the
enhanced UV emission (from flare ribbons) ahead of the rapid rise of the $\geq
25$ keV HXR emission. This confined flare exhibits more than two ribbons; here
we focus on the most energetic part of the flare that form two major ribbons
next to the PIL in the west of Figure fig:overview_150129b. As shown in Figure
fig:overview_150129c and fig:overview_150129d, these two ribbons are conjugate
feet of flare loops, where HXR emissions are concentrated. The connectivity
between these two ribbons is also confirmed in the non-linear-force-free
(NLFF) extrapolation by Zhong et al. (2019). The ribbon in the negative
magnetic field to the east of the major ribbons appears to be connected with a
remote brightening in a different active region not shown in this figure,
forming long loops overlying the loop systems of the two major ribbons, as
also demonstrated in Zhong et al. (2019). The overlying long loops are visible
in the EUV and X-ray images in Figure fig:overview_150129c and d after 5:20
UT. It is apparent that the flare loops connecting the two major ribbons near
the PIL are strongly sheared at the onset of the flare; then both ribbons
spread westward with different speeds, illustrating the strong-to-weak shear
variation during the flare evolution; on the other hand, the extent of the
ribbon expansion in the direction perpendicular to the PIL is less significant
compared with the eruptive flare.

Figure fig:overview_eruptive shows the evolution of the other two eruptive
flares SOL2014-12-18 M6.9 and SOL2013-08-12 M1.5, and Figure
fig:overview_confined shows the evolution of the other two confined flares
SOL2014-05-10 C8.7 and SOL2014-12-17 C9.8. For eruptive flares, we observe a
5-10 min lead time of enhanced UV and soft X-ray emission before the rapid
rise of the $\geq 25$ keV HXR emission $\mathcal{F}_{hxr}$, whereas the
confined flares evolve on a much shorter timescale, with a less than 2 min lag
of $\mathcal{F}_{hxr}$ with respect to the rise of the soft X-ray and UV
emissions. In these events, because of the close proximity of the two ribbons
and the limited spatial resolution and dynamic range of the HXR maps, we
cannot distinguish whether the $\geq 25$ keV HXR is emitted at the flare
footpoints or from the flare loop tops; nevertheless, significant HXR
emissions appear to concentrate at the major flare ribbons or loops enclosed
in the orange boxes in each figure.

Observations shown in these overview figures reveal the following interesting
facts. First, emission in the UV 1600 Å passband, and the inferred flux change
rate, $\dot{\psi}$, exhibit multiple spikes, indicative of multiple episodes
of energy release. It is also noted that flare UV emission and $\dot{\psi}$
start to rise before the rise of significant $\geq 25$ keV HXR emissions.
Particularly in the eruptive flares in this study, $\dot{\psi}$ has several
spikes before $\mathcal{F}_{hxr}$, suggesting episodes of energy release that
do not produce significant non-thermal emission. This has been observed in a
number of other flares, such as those reported by Warren and Warshall (2001)
and more recently by Naus et al. (2021) and Qiu (2021). Second, all these
flares, eruptive or confined, exhibit the strong-to-weak shear evolution when
we consider the connectivity between the major pair of conjugate ribbons. We
note that the initial large enhancement of the flux change rate $\dot{\psi}$
is primarily contributed by the fast spreading of flare ribbons along the PIL,
when the shear also decreases rapidly. In a 2.5D approximation, the local
reconnection rate, characterized by the mean reconnection electric field
$\langle E\rangle=V_{\perp}B$ (e.g. Forbes and Priest, 1984), is small despite
the large $\dot{\psi}$ in the early phase of the flare.

Figure 3.: Overview of the other two eruptive flares. (a) SXR, HXR, and UV
light curves, and flux change rate $\dot{\psi}$ for the SOL2014-12-18 flare.
(b) Evolution of flare ribbon fronts superimposed on a pre-flare longitudinal
magnetogram. Orange symbols outline the PIL. Overlaid in red contours is the
HXR maps in 25-50 keV at the peak of the emission, with the contour levels at
40%, 50%, 60%, 70%, 80%, and 90% of the maximum intensity. The orange box
encloses the parts of the ribbons where shear index is measured. (c-d) Same as
(a-b) but for the SOL2013-08-12 flare.fig:overview˙eruptive

Figure 4.: Same as Figure fig:overview_eruptive, but for the confined flares
SOL2014-05-10 (a-b) and SOL2014-12-17 (c-d). fig:overview˙confined

In this article, we discuss the energetic behavior along with the different
patterns of reconnection reflected in the evolution of flare ribbons,
following the previous study by Qiu et al. (2010). We track the geometric
evolution of conjugate flare ribbons to infer the shear of post-reconnection
flare loops. Flare energetics, namely plasma heating and electron
acceleration, will be learned from spectroscopic analysis of RHESSI (and GOES)
X-ray observations. We compare flare energetics with the evolution of the mean
magnetic shear during the progress of flare reconnection, particularly during
the rise of the flare. For consistency in the following text, we define the
rise of the flare as the rise of the flare soft X-ray emission in the GOES 1-8
Å channel. The impulsive phase of the flare, typically characterized by flare
HXR emissions, often coincides with the rise of the flare (Fletcher et al.,
2011).

It is also noted that, in this study, we focus on these most energetic parts
of the flare ribbons that exhibit continuous and coherent apparent motions.
The SOL2014-12-18 flare was studied by Wang et al. (2017a) and Joshi et al.
(2017), both suggesting that the ribbon sections at the two ends outside the
orange box in Figure fig:overview_eruptiveb are likely the feet of a flux
rope, whereas the major ribbons enclosed inside the box are formed by tether-
cutting reconnection below the flux rope following a standard picture (Moore
et al., 2001). Assuming the connectivity of the two ends, the evolution
pattern shown in Figure fig:overview_eruptiveb suggests that they are moving
apart, consistent with the flux rope expanding outward. With the expansion,
the length of field lines and the magnetic shear would grow, and such pattern
has been revealed in recent MHD simulations (Aulanier and Dudík, 2019; Jiang
et al., 2021a; Dahlin et al., 2021). Similarly, the evolution of the active
region hosting the SOL2013-08-12 flare has been thoroughly studied by Liu et
al. (2016), suggesting a low-lying flux rope being disturbed and erupting,
with two-ribbons below the rope from tether-cutting reconnection. Again, the
two ends of the two ribbons outside the box well represent the feet of a flux
rope identified by Wang et al. (2021, in preparation) from combined coronal
dimming and vertical current analysis. This study focuses on flare energetics,
so we do not analyze the two ends of the ribbons reflecting the flux rope
signatures. Each of the other two confined flares also exhibit more than two
ribbons; we focus on the major ribbons enclosed in the box, where HXR
emissions appear to concentrate. In the subsequent analysis, we measure the
shear index $\mathcal{R}$ and reconnection rate $\dot{\psi}$ only on these
major ribbons that are close to and aligned with the PIL.

##  3 Evolution of Reconnection Properties and Flare Energetics

sec:evo

###  3.1 Methodology

ssec:method

The spatial evolution of flare ribbon brightening may be translated to
magnetic shear of reconnecting field lines. Lacking direct measurements of
magnetic field in the corona during the flare, it has not been possible to
determine the 3D magnetic field participating in magnetic reconnection in the
current sheet. Conventional and regular magnetic field measurements have been
provided in the photosphere, at which the reconnection formed flare loops are
anchored; therefore, properties of magnetic reconnection in the corona may be
inferred by tracking the flare ribbon evolution across the magnetic field in
the lower atmosphere.

The six flares selected in this study display two conjugate ribbons aligned
along the PIL, as well as globally organized motion patterns; these allow us
to approximate the flare geometry to a 2.5D configuration, with the presumed
macroscopic reconnection current sheet along the PIL, or the direction of the
elongation of the flare ribbons, which we consider as the guide direction.
Using the method by Qiu (2009) and Qiu et al. (2010, 2017), we measure
reconnection properties following the evolution of newly brightened flare
ribbons. In this study, UV 1600 Å images by AIA have been used to analyze
flare ribbons. Newly brightened flare ribbon pixels are identified if the
pixel brightness stays $N$ times greater than the median brightness of the
pre-flare quiescent regions for 10 consecutive time frames, or 4 minutes.
Based on statistics of flare ribbon brightness in the UV 1600 Å passband, we
choose $N$ to be in the range of 4 to 6, which effectively distinguishes flare
brightness from plages. The requirement for the pixel to stay bright for a few
minutes is based on the statistics of heating and cooling timescales at the
footpoints of reconnection formed flare loops, and it helps to minimize
effects such as saturation or brief brightening due to the projection effect
of bright ejecta in the corona. The methodology and uncertainties are
discussed in Naus et al. (2021, and references therein). We then project the
positions of newly brightened ribbon pixels in the direction along the curved
PIL that is smoothed by a low-degree polynomial function, and measure the
time-dependent mean parallel distance $\langle d_{||}\rangle(t)$ of newly
brightened flare ribbons. We also measure the mean distance of the ribbon
fronts perpendicular to the PIL, by $\langle
d_{\perp}\rangle(t)=A(t)/l_{||}(t)$, where $A(t)$ is the area covered between
the PIL and newly brightened ribbon fronts, and $l_{||}(t)$ the total length
of the newly brightened ribbon projected along the PIL. Measurements are made
for ribbons in the positive and negative magnetic fields separately.
Uncertainties are estimated by using varying thresholds to determine newly
brightened ribbon pixels.

We then infer the time dependent reconnection geometry in two-ribbon flares.
In particular, we define the shear index $\mathcal{R}\equiv|\Delta\langle
d_{||}\rangle/\sum{\langle d_{\perp}\rangle}|,$ the difference and sum derived
with the measurements of the positive and negative ribbons. The shear index
may be related with the ratio of the reconnection guide field to the
reconnection outflow field $\mathcal{R}\sim B_{g}/B_{o}$ (Qiu et al., 2017).
We note that the exact mapping of the current sheet structure to the ribbon
evolution is non-trivial, and much depends on the dynamic evolution of the
post-reconnection magnetic field in a truly 3D manner; on the other hand, with
a 2.5D approximation, $\mathcal{R}$ provides a qualitative proxy of the
variation of the guide field during the flare reconnection (Dahlin et al.,
2021). Qualitatively, a large $\mathcal{R}$ is indicative of a relatively
strong guide field, which often decreases during the rise of the flare. Such
measurements of the shear variation from the ribbon geometry have been made
previously on a few two-ribbon flares, and the inferred shear evolution
pattern is found to be consistent with the measurements of the inclination of
observed post-reconnection flare loops with respect to the extrapolated PIL in
the corona (Qiu et al., 2017). In this study, we measure the shear index
exclusively with the UV 1600 Å observations of flare ribbons, and do not
extend the analysis to flare loops. The cadence of the measurements is 24 s.

Readers are reminded that, first, the method only returns the average shear,
by assuming the connectivity of newly brightened ribbon patches in opposite
polarities. Second, flare ribbon brightening usually starts with a few bright
kernels adjacent to the PIL, and in a few minutes, the ribbon starts to form
connecting the bright kernels. This is the case with several flares analyzed
here, and the measurements only apply when a continuous section of the ribbon
has properly formed and exhibits a coherent motion. Finally, we track the
newly brightened ribbons, defined by Qiu et al. (2010); it is different from
tracking the brightest kernels in optical, UV, or HXR emissions (Qiu et al.,
2002; Krucker, Hurford, and Lin, 2003; Fletcher, Pollock, and Potts, 2004; Lee
and Gary, 2008; Yang et al., 2009; Inglis and Gilbert, 2013). On the other
hand, Figures 1-4 suggest that $>$25 keV HXR emissions tend to be coincident
with newly brightened ribbons. Therefore, in the following analysis, we track
the evolution of the two major conjugate ribbons and examine how it is related
to flare energetics reflected in flare X-ray emissions.

For each flare, we collect HXR observations by RHESSI, and employ the Object
Spectral Executive (OSPEX) from the Solar SoftWare (SSW) to model the X-ray
photon spectra (Freeland and Handy, 1998, 2012). Each spectrum, with the
integration of 20 s, is fitted to the model with an isothermal component and a
broken power-law component, with the OSPEX fitting procedure ${\rm
vth+bpow+drm\\_mod}$. The photon energy range for the fitting is determined
based on the attenuator status and the signal to noise level. For the six
flares in this study, the lower limit of the photon energy is at 6 keV, and
the upper limit varies from about 15 keV to up to 50 keV at the peak of the
HXR emission. During these flares, the background X-ray emission is low and
mostly flat; we select the background from the pre- or post- flare period.
Spectral fitting is conducted with data obtained with a single detector; we
have also experimented fitting with data from two or more well-performing
detectors, typically detector 8 or 9, which return consistent fitting results.
These flares are moderate, with their magnitude ranging between C8.0 and M7.0,
so the pile-up effect is not significant, and there is only trivial difference
between the fitting results with and without pile-up correction. For each
flare, fitting starts from the peak time of the flare HXR emission, and
proceeds to earlier or later times. For each interval, when necessary, the
initial guesses have been further adjusted to randomize the residual pattern
to the maximal extent. Finally, we discard fitting results for time intervals
with $\chi^{2}\geq 3$.

From the spectral fitting, we derive the time evolution of the power-law index
$\gamma$ of the photon spectrum, the low-energy cutoff of the power-law
distribution $E_{c}$, and the temperature and emission measure of thermal
plasmas. In these flares, $E_{c}$ is found to be around 15 keV; therefore,
$\geq 25$keV HXRs are produced by non-thermal electrons. Additionally, we also
derive the temperature and emission measure of flare plasmas using the GOES
two-channel X-ray observations, to be compared with the flare parameters
obtained from RHESSI observations. The flares selected for this study were
observed by RHESSI from the onset throughout the rise phase, so that the
evolution of the flare temperature and non-thermal spectral index can be
studied in comparison with reconnection properties inferred from flare ribbon
evolution. On the other hand, given the uncertainties associated with the
electron low-energy cutoff, the isothermal assumption of the fitting model,
and lack of exact knowledge of whether the non-thermal emission is from thick-
target or thin-target, in this study, we do not calculate thermal or non-
thermal energies using the fitting parameters (see discussions in Aschwanden
et al., 2016; Aschwanden, Kontar, and Jeffrey, 2019). Energies of individual
flares will be estimated in a separate study, taking advantage of the UV
Footpoint Calorimeter (UFC) method (Qiu, Liu, and Longcope, 2012; Liu et al.,
2013; Zhu, Qiu, and Longcope, 2018; Qiu, 2021), and the model of Thin Flux
Tubes (TFTs) heated by slow magnetosonic shocks (Longcope, Qiu, and Brewer,
2016). These methods have been developed to model multi-loop heating in
observed flare events, and are free from the isothermal assumption.

###  3.2 Eruptive Flares

ssec:eruptive

We examine the time evolution of reconnection properties and flare energetics
in eruptive flares (Figure fig:eruptive) and confined flares (Figure
fig:confined). For the SOL2014-08-25 event (Figure fig:eruptivea), during the
first 12 minutes from around 14:48 UT to 15:00 UT, $\mathcal{R}$ varies from
2.0 to 0.6, which reflects the strong-to-weak shear evolution of the post-
reconnection arcade. Note that the rapid elongation of the brightening in the
early phase of the flare leads to a large $\dot{\psi}$; the mean reconnection
electric field, on the other hand, is more significant when the perpendicular
motion dominates later in the flare progress. From 14:52 UT, the non-thermal
HXR emission $\mathcal{F}_{hxr}$ gradually grows as the shear decreases, and
the photon spectrum exhibits the well-known soft-hard-soft behavior with the
power-law spectral index $\gamma$ roughly anti-correlated with the HXR count
rates. $\mathcal{F}_{hxr}$ starts to rise rapidly at 15:00 UT when the mean
magnetic shear has dropped to less than 1, and peaks at $\mathcal{R}\approx
0.6$. At this time, there is a significant non-thermal component in the flare
HXR photon spectrum from 15 to 40 keV, with the hardest spectrum
$\gamma\approx 4.0$.

Overall, from the flare onset to the peak of $\mathcal{F}_{hxr}$, the non-
thermal photon spectrum gradually hardens as the shear $\mathcal{R}$
decreases. In the following 7 minutes, whereas the mean shear stays low,
$\mathcal{F}_{hxr}$ starts to diminish and $\gamma$ increases, as reconnection
is diminishing. These observations suggest that the combination of a strong
reconnection rate and relatively low shear are in favor of producing non-
thermal electrons in this event.

It is worth noting that, before 14:50 UT, prior to the significant enhancement
of the $>25$ keV HXRs, spectroscopic analysis reveals the presence of a hot
plasma component of temperature $T_{e}\approx 18$ MK with a low emission
measure $EM\approx 8\times 10^{46}$ cm-3, coincident with the spike in the
$\dot{\psi}$ profile at the start of the flare. The rise of the plasma
temperature prior to significant non-thermal emission in this event is also
confirmed with GOES data. Such a hot onset has been reported in recent studies
(e.g. Hudson et al., 2021). Note that in this event, at the onset, both the
temperature and emission measure grow, different from Hudson et al. (2021)
where the temperature is nearly constant at 10 - 15 MK. In the first few
minutes of the flare, the rise of $T_{e}$ along with the rise of $\dot{\psi}$
is an indication of continuous and enhanced heating. EUV and HXR images before
14:50 UT suggest that this high temperature emission may come from sheared
loops (Figure fig:overview_140825d).

In the same manner, we have analyzed the other two eruptive flares, the
SOL2014-12-18 M6.9 flare, and the SOL2013-08-12 M1.5 flare. Both flares
exhibit a slow rise of the UV emission starting 5-10 min before the rapid rise
of $\mathcal{F}_{hxr}$, when the mean shear $\mathcal{R}$ has decreased
substantially. Evolution of the SOL2014-12-18 M6.9 flare follows a very
similar pattern to that of the SOL2014-08-25 flare, with the mean shear
variation from $\mathcal{R}\approx 2.5$ at the onset of the flare to
$\mathcal{R}<1$ in 10 minutes, when $\mathcal{F}_{hxr}$ starts to rise
rapidly. The last event, the SOL2013-08-12 M1.5 flare, exhibits strong shear
throughout the flare, which varies from 2.5 to 1.7 at the rise of
$\mathcal{F}_{hxr}$. In all three flares, prior to the rapid rise of
$\mathcal{F}_{hxr}$, high temperature ($T_{e}\leq 20$ MK), but not super-hot,
plasmas are produced, and the plasma temperature and emission measure derived
from RHESSI observations are generally consistent with those derived using the
GOES two-channel observations.

Figure 5.: Evolution of the eruptive flares SOL2014-08-25 (a), SOL2014-12-18
(b), and SOL2013-08-12 (c). Top: evolution of the mean shear index
$\mathcal{R}$ (black) and the reconnection rate $\dot{\psi}$ (red) measured in
the two major ribbons (or ribbon sections). Purple arrows indicate the onset
times of eruptions observed in EUV images obtained by AIA (see Figure
fig:eruption). Middle: time evolution of the HXR count rates at $25-50$ keV
$\mathcal{F}_{hxr}$ (black) and the power-law index $\gamma$ of the non-
thermal photon spectrum (red symbols), and the $\chi^{2}$ of the spectral
fitting (blue plus symbols). Bottom: temperature (red) and emission measure
(blue) of the isothermal component derived from RHESSI (symbols) and GOES
(lines). Also shown are the HXR count rates at $12-25$ keV (black). Vertical
bars in properties derived from RHESSI spectral analysis indicate the
1$--\sigma$ uncertainty of the fitting parameters. fig:eruptive

Furthermore, in eruptive flares, the eruption can significantly change the
magnetic configuration. We therefore examine the evolution of the mean shear,
as well as flare energetics, with respect to the timing of the onset of the
eruption in the three eruptive flares, identified from high-cadence high-
resolution observations of coronal structures in AIA EUV images. Figure
fig:eruption shows EUV images (panels a), and the ratio images, which are the
same images normalized to the pre-flare base image (panels b), of the active-
region corona during the flare. Erupting coronal structures can be tracked in
the time-distance diagrams constructed using ratio images along the slits
shown in panels a and b. Arrows in panels c indicate the identified times of
the eruption onset, which are also marked by purple arrows in Figure
fig:eruptive. For the first two flares, the onset of the eruption occurs in
the early phase of flare reconnection, when $\mathcal{R}$ starts to decrease,
and before the perpendicular expansion of flare ribbons. Significant HXR
emission occurs several minutes after the eruption onset, when the mean shear
has decreased substantially. Whereas in the third event, the observed onset of
the eruption occurs in the phase of ribbon expansion, a few minutes after the
rise of $\mathcal{F}_{hxr}$ when the shear has already decreased. The relative
timing of the shear evolution with respect to the eruption onset is different
in these three flares, which may be related to the configuration of overlying
fields. On the other hand, the timing of significant HXRs seems to be more
sensitive to the shear decrease than to the eruption onset.

Figure 6.: Snapshots of coronal structures observed in (a) AIA EUV images, (b)
the ratio images, and (c) the time-distance diagram along the slit in panels
b, for the three eruptive flares SOL2014-08-25 (top), SOL2014-12-18 (middle),
and SOL2013-08-12 (bottom). Arrows in panels c1-c3 indicate the times when
coronal structures are observed to erupt.fig:eruption

###  3.3 Confined Flares

ssec:confined

Analyses of the shear evolution and X-ray energetics are also conducted with
the confined flares (Figure fig:confined). The SOL2015-01-29 C8.9 flare
(Figure fig:confineda) is fast evolving, exhibiting HXR emissions in photon
energy $\geq$25 keV nearly coincident with the enhanced UV emission. During
the rise of $\mathcal{F}_{hxr}$, the inferred magnetic shear decreases rapidly
from $\mathcal{R}\approx 3.0$ to $\mathcal{R}\approx 1.5$. Spectroscopic
analysis reveals the presence of a weak non-thermal component with a rather
soft photon spectrum, $\gamma\approx 5.0-6.5$. Throughout the flare evolution,
the non-thermal photon spectrum is gradually softening. Notably, at the onset
of the flare when the shear index is large $\mathcal{R}\approx 3.0$, the X-ray
spectrum is dominated by a super-hot component, characterized by a mean
temperature over 25 MK and tenuous emission measure $3\times 10^{47}$ cm-3.
The plasma temperature subsequently decreases as the flare progresses in the
following 10 minutes. Different from the eruptive flares, analysis with the
GOES observations does not yield the high temperature component at the onset
of the flare, perhaps because of the low sensitivity of GOES detectors to
$>20$ MK plasmas (Hannah et al., 2011).

The properties of the other two confined flares are presented in Figure
fig:confinedb and fig:confinedc, respectively. The lead time between the flare
onset and production of significant non-thermal HXR emission is very short,
within a minute. Although all confined flares also exhibit the strong-to-weak
shear evolution, the mean shear of confined flares is larger than that of
eruptive flares in this sample. The mean shear of the SOL2014-05-10 event
varies from 4.5 at the onset to 2.5 at the peak of the HXR, and the HXR photon
spectral index $\gamma$ varies between 4.0 and 4.5. For the SOL2014-12-17
event, the shear varies sharply from more than 5.0 at the onset to 2.0 at the
HXR peak, when the HXR spectral index varies between 6.5 and 5.0. The two
flares also exhibit a hot plasma component during the rise of the HXR
emission, with the peak temperature up to 25 MK. This is a prominent
difference from eruptive flares in this study. On the other hand, we caution
that, for the SOL2014-05-10 flare, the presence of this hot component is
brief, and there are large uncertainties in the fitting results. These
uncertainties are possibly related to the choices of the initial guess or
fitting model, such as the low-energy cutoff and the isothermal assumption,
which can affect the results derived from the non-linear inversion method.

Figure 7.: Same as Figure fig:eruptive, but for the confined flares
SOL2015-01-29 (a), SOL2014-05-10 (b), and SOL2014-12-17 (c). For the
SOL2014-05-10 flare, we take the mean of the fitting results from two
different detectors.fig:confined

###  3.4 Evolution of Magnetic Shear and Flare Energetics

ssec:all

Comparison between Figures fig:eruptive and fig:confined suggests differences
in the evolution of flare energetics between eruptive and confined flares
studied in this sample. For the eruptive flares, there appears a long, of up
to 10 minutes, warm-up phase before the onset of impulsive and significant
non-thermal HXR emission. During this warm-up phase, as reconnection proceeds,
the mean shear decreases, X-ray and UV emissions ramp up gradually, and the
temperature and emission measure of X-ray emitting plasmas also grow slowly.
These signatures indicate gradual energy release at a low level, with the
lower atmosphere being heated by either thermal conduction or small amounts of
non-thermal flux. Significant HXR and UV emissions take place afterwards, with
a much enhanced rate of energy release, in particular non-thermal energy
release, per unit reconnection flux. It is also noted that, in this limited
sample, the progress of the shear evolution and flare energetics does not seem
to depend on when the eruption takes place. The confined flares, on the other
hand, evolve on shorter timescales, and significant HXR and UV emissions, or
qualitatively the energy release rate, tracks the reconnection rate more
closely from the start of the flare.

In spite of these differences, in both groups of flares, the mean shear
decreases as the flare proceeds. We further probe whether, and how, non-
thermal and/or thermal properties of the flare are related to the shear
evolution. Figure fig:allevent illustrates the flare HXR emission
$\mathcal{F}_{hxr}$ with respect to the shear variation during the progress of
flare reconnection. In each panel, $\mathcal{F}_{hxr}$ is plotted against the
shear index $\mathcal{R}$ in asterisk symbols. The color code indicates the
time evolution from the rise (violet-blue) to the peak (cyan-green) and then
to the decay (orange-red) of $\mathcal{F}_{hxr}$. For each event, only time
intervals with $\mathcal{F}_{hxr}$ above 20% of its peak are plotted.

From these plots, it is immediately evident that, in most of the events, there
is nearly an anti-correlation between $\mathcal{F}_{hxr}$ and $\mathcal{R}$
during the rise of the HXR emission; this is just the representation that the
shear decreases as the HXR rises, as demonstrated in Figures fig:eruptive and
fig:confined. The $R-\mathcal{F}_{hxr}$ pairs from the onset to the peak of
$\mathcal{F}_{hxr}$ in most events can be well fitted to a straight line, as
indicated by the dashed lines. The coefficient $\rho$ of the linear cross-
correlation between these two parameters is provided in Table tab:info, which
ranges between $-0.60$ and $-0.90$ in the five events. Given that the number
of time intervals for the correlation analysis is rather small, between 5 and
10, the presented anti-correlation should be taken as a conservative result.

The analysis is not extended to the decay of the HXR emission, because
$\mathcal{R}$ stays low and does not vary much after the peak of the HXR
emission; on the other hand, the reconnection rate $\dot{\psi}$ starts to
decrease. These observations suggest that production of non-thermal HXRs
should be related with the combination of the reconnection rate $\dot{\psi}$
and the shear index $\mathcal{R}$, although it is unclear in what way.

The evolution of the non-thermal spectral index $\gamma$ with respect to the
HXR flux $\mathcal{F}_{hxr}$ generally follows the well-known soft-hard-soft
pattern, with the hardest spectrum around the peak of $\mathcal{F}_{hxr}$ (and
also the lowest shear) for each flare. A correlation analysis between $\gamma$
and $\mathcal{R}$, however, returns only an insignificant correlation
coefficient; therefore, the quantitative relation between these two parameters
is still remote from this limited sample study. We may also compare the
$\gamma-\mathcal{R}$ relation between different events. Here, for each event,
we derive $\langle\gamma\rangle$ and $\langle\mathcal{R}\rangle$ averaged over
the time intervals when $\mathcal{F}_{hxr}$ is above 70% of its peak. The mean
and deviation of $\gamma$ and $\mathcal{R}$ are provided in Table tab:info.
From this small sample, we do not observe any meaningful relation between
$\langle\mathcal{R}\rangle$ and $\langle\gamma\rangle$ across different
flares.

Apart from non-thermal properties, we also examine the plasma thermal
properties. For each flare, the mean temperature and mean shear index averaged
over three time intervals around the peak temperature are presented in Table
tab:info. It is noted that, pending some uncertainties in the fitting
procedure, the confined flares exhibit a hot plasma component at the start of
the flare when the shear is high, with the temperature up to 25 MK, whereas
none of the eruptive flares have produced hot plasmas beyond 20 MK. Confined
flares in general have a larger shear index than eruptive flares in this
sample. Beyond these observations, we find no further quantitative relation
between plasma temperatures and shear indices.

Figure 8.: HXR 25-50 keV count rates $\mathcal{F}_{hxr}$ (normalized to its
peak) against the shear index $\mathcal{R}$ for erutpive flares (top) and
confined flares (bottom). Here the color indicates the time evolution from the
rise (violet-blue) to the peak (cyan-green) and then the decay (yellow-red) of
the HXRs. Only time intervals when $\mathcal{F}_{hxr}$ is above 20% of its
peak are plotted.fig:allevent

##  4 Discussion

sec:discussion

To understand the results from this study and their implications, we discuss
assumptions underlying the measurements, the similarities and differences of
these results in comparison with earlier studies, and how our studies may be
further improved in the future.

###  4.1 Measurements of Shear and Inference of Reconnection Guide Field

To measure the shear, this study uses an approximate approach that projects
the apparent motion of newly brightened ribbon fronts along (parallel with)
and across (perpendicular to) the curved PIL. The approach in this experiment
applies to a relatively simple configuration characterized by a single major
PIL separating nearly bipolar magnetic fields, which can be approximated to a
2.5D geometry, with the guiding direction along the PIL. The key to establish
the shear is connectivity. In this study (and also in Qiu et al., 2010), the
connectivity is assumed between newly brightened ribbon fronts, and is
qualitatively confirmed by post-flare loops observed in EUV images and/or maps
of the thick-target HXR emission. Using a different method, Qiu et al. (2017)
also measured the shear as the angle between the top of a set of post-
reconnection flare loops outlined in EUV images and the PIL of the magnetic
field extrapolated to the height of the flare loops, and showed that the
general pattern of shear variation is consistent with that measured from flare
ribbons. Again, we emphasize that the measurements in this article are
approximate and return the average shear. Qiu (2009) applied a more refined
flare ribbon analysis to the SOL2004-11-07 X-2.0 flare, by considering the
connectivity between multiple patches of flare ribbons in both polarities; a
reconnection sequence analysis was conducted to derive dynamically evolving
connectivity between eight ribbon patches in the positive magnetic field and
six patches in the negative field. The more involved approach has provided a
more comprehensive description of the connectivity, yet the pattern of the
shear evolution is similar: as the flare progresses, the shear decreases. In
some other studies, the shear was measured with a simpler method, as the angle
of a straight line connecting two prominent and conjugate footpoints
identified in either H$\alpha$ and UV/EUV images (Su et al., 2006; Ji et al.,
2006; Su, Golub, and Van Ballegooijen, 2007) or HXR maps (Yang et al., 2009;
Inglis and Gilbert, 2013) with respect to the PIL also approximated as a
straight line. However the shear is measured, the strong-to-weak shear
evolution is found for the majority of flare events reported in the
literature; for example, Su, Golub, and Van Ballegooijen (2007) measured the
shear from conjugate UV footpoints at two times during a flare, and found the
strong-to-weak shear change in 86% of the 50 M- and X- class flares. Such
shear evolution is often accompanied by the two-phase motion pattern of flare
ribbon fronts or kernels, with the ribbon brightenings first elongating along
the PIL, followed by the apparent perpendicular expansion of the two ribbons
(Qiu et al., 2017, and references therein). The shear index $\mathcal{R}$
defined and measured in the selected samples in this study exhibits a behavior
consistent with that reported in the literature, and such evolution pattern
reflects the sequence of magnetic reconnection driven in the magnetic
configuration that builds up free magnetic energy with strong magnetic shear
near the PIL (Dahlin et al., 2021).

On the other hand, we recognize that although the strong-to-weak shear
evolution is commonly observed and/or measured, it is not universal. A small
number of measurable events do exhibit different patterns of shear evolution
(Su, Golub, and Van Ballegooijen, 2007; Yang et al., 2009; Cheng, Kerr, and
Qiu, 2012). A lot many flare events occur in regions of complicated magnetic
configuration characterized by complex-shaped PILs, for which it is not always
feasible to apply a simplified approach to measure, or even define, the shear
(Bogachev et al., 2005; Grigis and Benz, 2005). Furthermore, published
methods, including the one used in this study, measure the shear assuming the
connectivity between two sources. In different studies, these two sources are
selected in different ways. In this article, we measure the average positions
of newly brightened ribbons in the central or core region, and the mean shear
derived for this core region tends to follow the strong-to-weak evolution. It
is noted that, in some eruptive flares, if the connectivity is established
between the far ends of the two ribbons, which may indicate the feet of an
erupting flux rope, the shear appears to increase, as also shown in numerical
simulations (Aulanier and Dudík, 2019; Dahlin et al., 2021). Many other
studies assume connectivity between two kernels of strong emissions on the two
sides of the PIL, and estimate the magnetic shear tracking this specific
connectivity. During the flare, a large number of flare loops, of order a few
hundred, are produced. Improved measurement of the shear requires a more
refined connectivity analysis applied to high-resolution observations, such as
by Fletcher (2009) and Qiu (2009), and examine the tempo-spatial variations of
magnetic shear in contrast to the average shear measured in prior and present
studies.

Next, shear measured from the morphological evolution of flare ribbons or
kernels reflects topology of reconnection in the corona. However, establishing
the mapping of the coronal magnetic field down to the ribbon is not trivial.
Approximating the coronal magnetic field with a 2.5D configuration,
$\mathcal{R}$ may be related to the ratio of the reconnection guide field to
the outflow field $\mathcal{R}\sim B_{g}/B_{o}$. We emphasize that the value
of $B_{g}/B_{o}$ inferred in this way should not be taken on face value,
although the trend of the evolution is evident, and is also broadly consistent
with the $B_{g}/B_{in}$ evolution derived using high-resolution MHD
simulations that do provide the mapping of the coronal magnetic field to the
ribbons (Dahlin et al., 2021). In our future effort, observational
measurements of the shear and inference of the guide field $B_{g}/B_{o}$ will
also be explored together with microwave observations when available (Gary et
al., 2018; Chen et al., 2020), and be complemented with magnetic field
modeling guided by observed flare loop geometry. Ultimately, the guide field
relative to the inflow magnetic field $B_{in}$ at the reconnection current
sheet could be estimated incorporating advanced and high-resolution numerical
models of flare reconnection (e.g. Jiang et al., 2021b; Dahlin et al., 2021).

###  4.2 Reconnection Properties and Flare Eenergetics

In this article, the preliminary study of the sample suggests that a
significant production of non-thermal electrons may take place a few minutes
after the onset of the flare, when the inferred mean shear is decreasing.
Previous studies have reported delayed HXR emission with respect to the UV or
optical emission. To cite a few prominent examples, Warren and Warshall (2001)
collected nine M-class flares observed with very high cadence (2-3 s) and from
the beginning of the flare by the Transition Region and Coronal Explorer
(TRACE: Handy et al., 1999), the Hard X-ray Telescope (HXT; Kosugi et al.,
1991) on board Yohkoh, and/or the Burst And Transient Source Experiment on
board the Compton Gamma-Ray Observatory (BATSE/CGRO: Schwartz et al., 1992),
and all events exhibit evident delay of the onset of the HXR emission with
respect to the UV emission by 1 – 10 minutes. In the SOL2006-12-06 X6.5 flare
analyzed in Krucker et al. (2011), the onset of $\geq 25$ keV HXRs lags the
flare SXR emission by as long as 10 minutes. These studies did not analyze the
shear evolution using UV or optical observations. In eruptive flares in the
present study, HXR emission starts to rise rapidly when the shear index has
decreased to $\mathcal{R}\leq 2$. Previously, Qiu et al. (2010) analyzed the
SOL2000-07-14 X5.7 flare (the Bastille-day flare, also see Aschwanden and
Alexander, 2001) with the same method that decomposes the motion of flare UV
kernels in the directions along and across the PIL, and suggested that
significant non-thermal emission occurs when shear is modest. Similarly, Su et
al. (2006) measured the shear of the conjugate EUV footpoints of the
SOL2003-10-28 X17 flare, and showed that the shear angle, defined as the angle
of the footpoint line with respect to the vertical of the PIL, decreased from
75∘ (equivalent to $\mathcal{R}\approx 3.7$) two minutes before the onset of
the $\geq 150$ keV HXR emission to 55∘ ($\mathcal{R}\approx 1.4$) when $\geq
150$ keV HXR emission rises. Ji et al. (2006) measured the shear tracking
H$\alpha$ emission centroids using the same method as Su et al. (2006), and
found that the shear starts to decrease, $\mathcal{R}\leq 1$, at the onset of
the $\geq$25 keV HXR emission of the SOL2004-11-01 M1.1 flare. If
$\mathcal{R}$ is translated to the relative guide field $B_{g}/B_{o}$, these
observations would support recent findings from the numerical modeling that
efficient production of non-thermal electrons occurs with a modest guide field
$B_{g}/B_{in}\approx 1$ (Arnold et al., 2021).

On the other hand, a number of other studies have measured shear by tracking
the HXR foot-points, and showed that, although most events exhibit the strong-
to-weak shear evolution, non-thermal HXRs can be produced in the early phase
when the shear angle is as large as 60 - 70∘, or equivalently
$\mathcal{R}\approx 1.7-2.7$ (Yang et al., 2009; Cheng, Kerr, and Qiu, 2012;
Inglis and Gilbert, 2013; Sharykin et al., 2018). Furthermore, in all flares
in the present paper and in previous studies, shear remains low as the HXR
emission diminishes. These observations suggest that shear is not the only
parameter related to HXR emissions.

Previous studies have extensively explored the connection between reconnection
rate and production of non-thermal emissions (see Section 1). In particular,
Qiu et al. (2010) showed that $\geq 20$keV HXR light curve correlates more
strongly with the flux change rate taking into account only the perpendicular
motion $\dot{\psi}_{\perp}\approx\int B_{l}v_{\perp}dl$ than with the total
flux change rate $\dot{\psi}$. For the events in this study, we have observed
a large flux change rate $\dot{\psi}$ prior to the significant increase of
HXRs; since in these events the strong-to-weak shear evolution is coincident
with the transition from parallel to perpendicular motion of the ribbons,
$\dot{\psi}_{\perp}$ would be much reduced from $\dot{\psi}$ prior to the HXR
emission and therefore is better correlated with $\mathcal{F}_{hxr}$ than
$\dot{\psi}$, similar to that shown in Qiu et al. (2010). Qiu et al. (2017)
have measured shear evolution as well as the mean parallel and perpendicular
motion of flare ribbons; it is suggestive from the properties listed in Table
1 of that study, that flares or episodes of flares with significant HXR
emissions tend to exhibit large perpendicular motion $v_{\perp}$ in strong
magnetic fields $B_{l}\geq 500$ G. These observations indicate that the
reconnection rate in terms of $\dot{\psi}_{\perp}$ or the reconnection
electric field $\langle E\rangle\approx v_{\perp}B_{l}$ is important, though
not always sufficient, for the production of non-thermal emissions (e.g. Naus
et al., 2021).

Finally, although strong-to-weak shear evolution is observed in confined
flares as well, the energetic behavior appears to be different. HXR emission
occurs when the shear is strong $\mathcal{R}\approx 2-3$, and a high-
temperature (up to $25$ MK), low density plasma component is produced at the
onset of the confined flares in this sample. Super-hot emissions have been
studied in a number of flares, a good sample having been presented by Caspi,
Krucker, and Lin (2014). It remains to be investigated what kind of flares,
confined or eruptive, tend to produce hot and super-hot plasma emissions, and
what role magnetic shear plays in this regime (Dahlin, Drake, and Swisdak,
2015; Warmuth and Mann, 2020). It is also noted that the shear measurement is
based on a 2.5D approximation, and the direction of the PIL is assumed to be
the direction of the (macroscopic) electric field in the reconnection current
sheet in the corona. This same assumption has been adopted for the confined
flare in this study, which presents rather well defined two ribbons along the
PIL, although many confined flares are envisioned as (semi-)circular ribbon
flares developed around a null point and circular fan-shaped quasi-separatrix
layers (QSLs, see Masson et al., 2009, and references thereafter). It warrants
further research how to locate the reconnection current sheet and determine
the reconnection rate $\langle E\rangle$ and guide field in a truly 3D
configuration.

From available observations and measurements, it is evident that the
production of non-thermal electrons is not singularly or even primarily
dependent on one parameter. The disparity presented in prior and present
observations is partly due to large differences in the spatio-temporal
resolutions, coverage in time and space domains, observing wavelengths, and
analysis methods. On the other hand, it is anticipated that in different
flares and different magnetic configurations, the governing mechanisms for
flare energetics, for example, the particle acceleration mechanism, can be
different as well. How, and which, key parameters collectively control
particle acceleration and generation of the power-law energy spectrum remains
to be clarified from both theoretical investigation and improved observational
analysis that can provide measurements of temporally and spatially resolved
properties of flare reconnection and energetics.

##  5 Summary

This article presents an experiment that infers the mean magnetic shear from
the evolution of flare ribbons observed in the lower atmosphere, and examines
properties of flare energy release during the progress of magnetic
reconnection. The sample includes three eruptive flares and three confined
flares ranging from C8.0 - M7.0 class. All these flares exhibit well-defined
two ribbons aligned with a relatively simple PIL. We define the shear index
$\mathcal{R}$ as the ratio of the mean parallel distance between newly
brightened conjugate flare ribbons projected along the PIL to their mean
distance in the direction perpendicular to the PIL. All these flares have been
observed by RHESSI from the onset of the flare throughout the rise phase. At
the peak time, these flares have non-thermal HXRs at photon energies above 25
keV. Spectral analysis provides flare non-thermal properties such as the
power-law slope of the photon spectrum, as well as the thermal properties
including the plasma temperature. Our analysis yields the following results.

  * •

In the six events in this study, $\mathcal{R}$ varies from more than 3 at the
onset of the flare to below 1 at the peak of the HXR emission, confirming the
widely reported strong-to-weak shear variation during the progress of flare
reconnection. The mean shear does not vary much after the peak of the HXR
emission. On average, confined flares exhibit stronger shear.

  * •

In most of the events, there is an indication of anti-correlation between the
$\geq 25$ keV HXR count rates $\mathcal{F}_{hxr}$ and the shear index
$\mathcal{R}$ during the rise of the HXR emission. In eruptive flares in this
sample, the UV emission and global reconnection rate $\dot{\psi}$ lead the
significant and impulsive HXR emission by up to 10 minutes, suggesting the
presence of a gradual warm-up phase when the efficiency of (non-thermal)
energy release is low. Significant non-thermal emission occurs later when the
shear is modest, $\mathcal{R}\leq 2$. In this limited sample, the production
of significant non-thermal emissions appears more sensitive to the shear
decrease than the timing of the eruption onset.

  * •

In all flares, we observe the temperature rise in the early phase when the
flare ribbons rapidly spread along its length. RHESSI X-ray spectral analysis
reveals a high-temperature component (up to 25 MK) at the onset of the
confined flares, lasting for up to one minute. This high-temperature component
is not observed in the eruptive flares, although the eruptive flares all have
higher magnitude than the confined flares in this sample.

These observations bear some indications of the role magnetic shear possibly
plays in the production of non-thermal electrons and hot plasmas during the
progress of flare reconnection and in different magnetic configurations,
namely in eruptive versus confined flares. Improved diagnostics of flare
energetics combined with modeling will help with the progress towards
elucidating physical mechanisms underlying these results.

#### Acknowledgments

This work was started from the discussion with Dr. Paul Cassak, and its
completion was motivated by the Solar Flare Energy Release (SolFER)
collaboration and conversation with Dr. James Drake. We thank the anonymous
referee for insightful suggestions and the editor (Cristina H. Mandrini) for
editing the manuscript. We thank Ms. Lilly Bralts-Kelly and Heather Mei for
helping prepare observations during the Research Experiences for
Undergraduates (REU) program at Montana State University. J.C. is funded by
the B-type Strategic Priority Program of the Chinese Academy of Sciences,
Grant No. XDB41000000, NSFC grants 11673048. SDO is a mission of NASA’s Living
With a Star Program. The authors also thank the RHESSI Mission Archive
https://hesperia.gsfc.nasa.gov/rhessi_extras/flare_images/hsi_flare_image_archive.html
for the data support.

## Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

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