# Asymmetric Hard X-ray Radiation of Two Ribbons in a Thermal-Dominated
C-Class Flare

G.L.Guanglu Shi0000-0001-7397-455X  L.Li Feng0000-0003-4655-6939  J.Jun
Chen0000-0003-3060-0480  B.L.Beili Ying0000-0001-8402-9748  S.T.Shuting
Li0000-0003-2694-2875  Q.Qiao Li0000-0001-7540-9335  H.Hui
Li0000-0003-1078-3021  Y.Ying Li0000-0002-8258-4892  K.F.Kaifan
Ji0000-0001-8950-3875  Y.Yu Huang0000-0002-0937-7221  Y.P.Youping
Li0000-0001-5529-3769  J.W.Jingwei Li  J.Jie Zhao0000-0003-3160-4379  L.Lei
Lu0000-0002-3032-6066  J.C.Jianchao Xue0000-0003-4829-9067  P.Ping Zhang
D.C.Dechao Song0000-0003-0057-6766  Z.Y.Zhengyuan Tian0000-0002-2158-0249
Y.N.Yingna Su0000-0001-9647-2149  Q.M.Qingmin Zhang0000-0003-4078-2265
Y.Y.Yunyi Ge  J.H.Jiahui Shan0009-0001-4778-5162  Y.Yue
Zhou0000-0002-3341-0845  J.Jun Tian0000-0002-1068-4835  G.Gen Li  X.F.Xiaofeng
Liu0000-0002-3657-3172  Z.C.Zhichen Jing0000-0002-8401-9301  S.J.Shijun Lei
W.Q.Weiqun Gan0000-0001-9979-4178  Key Laboratory of Dark Matter and Space
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing
210023, China  School of Astronomy and Space Science, University of Science
and Technology of China, Hefei 230026, China  Yunnan Observatories, Chinese
Academy of Sciences, Kunming 650216, China  University of Chinese Academy of
Sciences, Nanjing 211135, China

###### Abstract

The asymmetry in hard X-ray (HXR) emission at the footpoints (FPs) of flare
loops is a ubiquitous feature closely associated with nonthermal electron
transport. In this study, we analyze the asymmetric HXR radiation at two flare
ribbons which is thermal-dominated during a long-duration C4.4 flare that
occurred on March 20, 2023, combining multi-view and multi-waveband
observations from the Advanced Space-based Solar Observatory (ASO-S), Solar
Orbiter (SolO), and Solar Dynamics Observatory (SDO) spacecraft. We find that
the H i Lyman-alpha (Ly$\alpha$) emission captures similar features to the He
ii $\lambda$304 emission in both light curve and spatio-temporal evolution of
a pair of conjugate flare ribbons. The spectra and imaging analysis of the HXR
emission, detected by Spectrometer Telescope for Imaging X-rays (STIX) in 4-18
keV, reveal that the two-ribbon flare radiation is thermal dominated by over
95%, and the radiation source mainly concentrates on the northern ribbon,
leading to an asymmetric distribution. To understand the underlying reasons
for the HXR radiation asymmetry, we extrapolate the magnetic field within the
active region using the nonlinear force-free field (NLFFF) model. For 78% of
the magnetic field lines starting from the northern flare ribbon, their
lengths from the loop-tops (LTs) to the northern FPs are shorter than those to
the southern FPs. For 62% of the field lines, their magnetic field strengths
at the southern FPs exceed those at the northern FPs. In addition, considering
the larger density, $\approx 1.0\times 10^{10}\ {\rm cm^{-3}}$, of the low-
lying flare loops ($<32\ {\rm Mm}$), we find that the shorter path from the LT
to the northern FP enables more electrons to reach the northern FP more easily
after collisions with the surrounding plasma. Therefore, in this thermal-
dominated C-class flare, the asymmetric location of the flare LT relative to
its two FPs plays a dominant role in the HXR radiation asymmetry, while such
asymmetry is also slightly influenced by the magnetic mirror effect resulting
in larger HXR radiation at the FPs with weaker magnetic strength. Our study
enriches the understanding of particle transport processes during solar
flares.

###### keywords:

Flares, Energetic Particles; Heating, in Flares; Active Regions, Magnetic
Fields; Spectrum, X-Ray

##  1 Introduction

Solar flares are known to accelerate particles and heat plasma, producing hard
X-ray (HXR) bursts and gamma-ray bursts (Hudson and Ryan, 1995; Holman et al.,
2011). To investigate the underlying physical processes of plasma heating,
particle acceleration, and magnetic reconnection, spectra and imaging analysis
of the HXR emission during flares serve as crucial methods (Masuda et al.,
1994; Liu, Chen, and Petrosian, 2013; Su et al., 2013; Krucker and Battaglia,
2014; Li et al., 2022b). The enhancement of X-ray fluxes mainly originates
from the thermal emission that heats the plasma to a high temperature and
nonthermal bremsstrahlung emission associated with the energy release of
energetic particles (Brown, 1971; Fletcher et al., 2011; Lin, 2011; Raymond et
al., 2012). HXR sources are often observed at the footpoints (FPs), loop-top
(LT) and above the LT of flare loops, which have been extensively studied
using instruments such as the Yohkoh (Ogawara et al., 1992) and the Reuven
Ramaty High-Energy Solar Spectroscopic Imager (RHESSI, Lin et al., 2002).

In observations, the HXR sources located at the FPs of solar flares typically
present asymmetry, which can be classified into two main types: S-type (Sakao
type, Sakao, 1994) and N-type (non-Sakao type). These asymmetric phenomena are
generally believed to be associated with the transport processes of nonthermal
electrons in the flare loop. The S-type asymmetry of the HXR sources is often
explained by the magnetic mirror effect (e.g., Sakao, 1994; Kundu et al.,
1995; Li et al., 1997; Aschwanden et al., 1999; Alexander and Metcalf, 2002;
Ding et al., 2003; Siarkowski and Falewicz, 2004; Falewicz, Siarkowski, and
Berlicki, 2006; Silva et al., 2020; Naus et al., 2022; Qiu et al., 2023). In
this scenario, the brighter HXR FP is located in a region where the strength
of the photospheric magnetic field is weak. The magnetic mirror effect plays a
role in guiding and trapping nonthermal electrons, leading them to concentrate
and emit more X-rays at one FP than the other. The N-type asymmetry is
featured as the brighter FP of the HXR emission corresponds to the region with
a stronger magnetic field, which can be interpreted as the reconnection site
generated by interactions with other flare loops being closer to that FP
(e.g., Asai et al., 2002; Goff et al., 2004; Falewicz and Siarkowski, 2007;
Joshi et al., 2017). The magnetic reconnection reduces the effect of magnetic
field convergence, allowing numerous electrons to precipitate at the brighter
FP.

The Advanced Space-based Solar Observatory (ASO-S, Gan et al., 2023), launched
in Oct. 2022, is the first comprehensive solar space observatory in China. The
scientific objectives of ASO-S are focused on “1M2B” (Gan et al., 2019),
namely the magnetic fields and two types of violent eruptions on the sun –
solar flares and coronal mass ejections (CMEs). There are three coordinated
payloads on board the ASO-S, the Full-disk vector MagnetoGraph (FMG, Deng et
al., 2019; Su et al., 2019), the Lyman-alpha (Ly$\alpha$) Solar Telescope
(LST, Li et al., 2019; Chen et al., 2019; Feng et al., 2019), and the Hard
X-ray Imager (HXI, Zhang et al., 2019; Su et al., 2019). Three payloads can be
used to investigate the relationships among solar flares, CMEs, and magnetic
fields. The LST payload consists of three instruments: the Solar Disk Imager
(SDI), the Solar Corona Imager (SCI), and the White-light Solar Telescope
(WST). These instruments enable simultaneous dual-waveband observations from
the solar disk to the low corona, focusing on the studies of flare, prominence
and CME eruptions.

In this work, we analyze the asymmetric HXR sources in a two-ribbon flare
dominated by over 95% thermal radiation during the very long rise phase of
about two hours in a long-duration event (LDE). We further explain this
phenomenon by combining the results of the nonlinear force-free field (NLFFF)
extrapolation. Section 2 provides an overview of the LDE observations. Section
3 presents our analysis and results: (1) STIX HXR spectra and imaging
analysis; (2) comparisons between H i Ly$\alpha$ and He ii 304 Å emissions;
(3) the configuration of the magnetic field extrapolated by the NLFFF model.
Our conclusions and discussion are given in Section 4.

##  2 Overview of Observations

The two-ribbon flare (SOL2023-03-20T15:34) studied in this paper was produced
by the eruption of a hot channel and filament system in the active region NOAA
AR 13258. This event was observed by various instruments, including the SDI
instrument of the LST payload on board the ASO-S, Spectrometer Telescope for
Imaging X-rays (STIX, Krucker et al., 2020) on board the Solar Orbiter (SolO,
Müller et al., 2020), the Atmospheric Imaging Assembly (AIA, Lemen et al.,
2012) on board the Solar Dynamics Observatory (SDO, Pesnell, Thompson, and
Chamberlin, 2012), the Geostationary Operational Environmental Satellite
(GOES), and the Chinese H$\alpha$ Solar Explorer (CHASE, Li et al., 2022). The
SolO was located at a longitude separation of 18.4$\,{}^{\circ}$ from Earth
and had a heliocentric distance of 0.51 AU. Multi-view and multi-waveband
observations provide detailed insights into the dynamics of the flare and
enable a more comprehensive understanding of the associated particle
behaviors.

This event is a GOES C4.4 flare that started at 13:30 UT and peaked at 15:34
UT on March 20, 2023, shown in Figure 1a, which is a long-duration event (LDE)
lasted for an impressive duration of 11 hours. The curve of the time
derivative (purple line) presented in Panel a is derived from the GOES data
(Thomas, Starr, and Crannell, 1985). The light curves of HXR emissions at
photon energies of 4-10 keV (green line) and 10-18 keV (magenta line),
detected by STIX, are shown in Panel b. Panel c displays the light curves of
AIA He ii 304 Å (black line), AIA 94 Å (cyan line), and SDI H i Ly$\alpha$
(blue line), obtained by integrating over the entire flare region. All of
these light curves display a significant enhancement during the flare. This
event is classified as a relatively small C-class flare, only low-energy
photons (4-18 keV) were detected by STIX at a distance of about 0.51 AU.
Additionally, the peak time of the SXR emission, marked by a red dashed line,
is close to that of the HXR emission. It implies that the energy released
during this event is probably not dominated by nonthermal electrons (further
evidence is presented in Section 3.1). Unfortunately, due to the instrument
being in the test status, the SDI only has available observations starting
from 13:57 UT during this period. Despite this limitation, it is still
possible to observe a good temporal correlation between the HXR emissions and
the light curves of H i Ly$\alpha$ and He ii 304 Å, implying that they might
have similar radiation origins. In the flare rising phase, Ly$\alpha$ and 304
Å radiation were from flare ribbons. However, clear distinctions are evident
between the HXR and 94 Å.

Figure 2 presents the flare-related structures observed by multiple
instruments during this LDE. Panels a and b clearly show the associated
filament and hot channel observed by CHASE H$\alpha$ and AIA 94 Å,
respectively. As the filament rotates and rapidly rises, it subsequently
develops into a CME accompanied by the formation of an elongated current sheet
(CS), a series of blobs, and supra-arcade downflows (SADs). Simultaneous
observations from AIA He ii 304 Å and SDI H i Ly$\alpha$ capture the spatio-
temporal evolution of a pair of conjugate flare ribbons, as shown in Panels c
and d, presenting a good consistency with each other. During the flare rising
phase, the two ribbons rapidly separate towards the northern and southern
directions, respectively. The flare ribbons can also be observed in the
H$\alpha$ images. There is no significant brightening in the AIA 1600 Å and
1700 Å images, while brightening in these two passbands is generally believed
to be associated with the motion of nonthermal electrons in the flare loops.
These phenomena indicate that the flare ribbons are mainly dominated by
thermal emission, and formed in the middle-to-upper chromosphere and
transition region.

##  3 Analysis and Results

###  3.1 HXR Spectra and Imaging Analysis

To determine the nonthermal/thermal nature of the two-ribbon flare and clarify
the origin of the HXR emission, we conduct an analysis of both the spectra and
imaging of the HXR detected by STIX during the flare rising phase. Figure 3
and Figure 4 present the results for the selected time intervals marked by the
pink and blue shadows in Figure 1, respectively.

First, we use a double thermal model that describes optically thin thermal
bremsstrahlung radiation to fit the observed HXR spectra. Figure 3 presents
the spatially integrated count spectra (black solid lines) detected by STIX
for various time intervals from 2 to 4 minutes, after subtracting the pre-
flare background (black dashed lines) from 13:20 to 13:22 UT. The chosen time
intervals are to ensure sufficient count rates in 4 to 18 keV. Considering the
extremely long rising phase of about 2 hours for this flare, the temperature
may not have significant change in 2 to 4 minutes. Blue lines in each panel
represent the optimal fitting curves. Free parameters of the double thermal
functions, including electron temperature (T) and emission measure (EM), are
indicated in each panel. The residual distribution and the coefficient chi-
square ($\chi^{2}$) quantitatively evaluate the level of consistency between
the fitting function and the HXR spectra. We also attempted to use a standard
combination of thermal and nonthermal power-law functions to fit the HXR
spectra. It turns out that their $\chi^{2}$ values are at least twice as large
as those in the double-thermal fittings. The thick-target spectral indices are
about 8 to 10 during the flare rising phase, and the ratios of integrated
nonthermal to thermal count fluxes are less than 5%. Therefore, based on these
two different fitting models, the spectral fitting analysis demonstrates that
the two-ribbon flare radiation is thermal dominated by over 95%. Panel a
presents the spectral fitting results at 13:51 UT of the sub-peak preceding
the main peak of the HXR light curves, which corresponds to the filament
eruption. In Panels b-d, it can be seen that during the rising phase, the
weighted mean temperature range of the flare is from 6.83 MK (14:21 UT) to
7.76 MK (15:30 UT).

Then, we reconstruct the HXR maps detected by STIX and superpose them on AIA
He ii 304 Å (left column) and SDI H i Ly$\alpha$ (right column) images, as
shown in Figure 4. Panel c additionally presents the composite image combining
AIA 304 Å (red) and AIA 94 Å (cyan) at 14:58 UT. To generate these images,
visibilities are computed by subcollimators labeled from 3 to 10, with an
integration time of 6 minutes centered on the observation time of AIA, and
applied to the MEM_GE algorithm (Massa et al., 2020) for the thermal sources
in the 4-18 keV energy range, resulting in an angular resolution of $\approx
14.6^{\prime\prime}$. The co-alignment of the STIX images was done with the
Full Sun Imager (FSI) 304 Å images observed by the Extreme Ultraviolet Imager
(EUI, Rochus et al., 2020) on board the SolO. Subsequently, we reprojected the
STIX images from the SolO view to Earth view, assuming that all photons
originate from almost the same altitude, i.e., the middle-to-upper
chromosphere or transition region. The reason for selecting a 6-minute
integration time is that it can obtain the HXR images more consistent with the
flare ribbons observed in AIA 304 Å and SDI Ly$\alpha$ compared to the
4-minute images during the initial stage of the flare, and they have similar
imaging results near the peak time of the GOES flux. There were no SDI
Ly$\alpha$ observations before 13:57 UT, and the parallel sections of the
flare ribbons formed after 14:00 UT. Therefore, STIX imaging results at 13:51
UT are not presented in Figure 4. The gold contours in each panel indicate
45%-90% of the maximum HXR intensity, with a step of 15%. The HXR radiation
mainly originates from the flare FPs and presents an asymmetric distribution,
primarily concentrated along the parallel section of the northern ribbon. As
the flare evolves towards the peak time of the SXR flux, a weak HXR source
begins to appear at the southern FP (not shown in Figure 4). The white
contours in each panel represent 55% of the maximum intensity of the AIA He ii
304 Å. From comparisons, it is evident that the He ii 304 Å and H i Ly$\alpha$
emissions present a good spatial consistency in the evolution of the flare
FPs, consistent with the study of Li et al. (2022a).

Note that the HXR sources are predominantly from the flare ribbon instead of
the projection of the higher coronal source. From the light curves in Figure
1, the STIX light curve has more similarity to that of AIA 304 Å than AIA 94
Å. Moreover, if we compare the morphology details of the STIX HXR source with
that of the flare ribbon observed in AIA 304 Å and that of flare loops
observed in AIA 94 Å, we find that the HXR source resembles the northern
ribbon more, especially at the upper-left end in Figure 4a and c.

The spectra and imaging analysis further support the conclusion that the HXR
emission from the flare FPs is dominated by the collision of thermal electrons
injected downward from magnetic reconnection with the surrounding plasma in
the dense flare loop. Furthermore, both the emissions of He ii 304 Å and H i
Ly$\alpha$ have similar radiation features produced by the thermal process
that occurred in the two ribbons of the flare.

###  3.2 H i Ly$\alpha$ and He ii 304 Å Emissions

To quantitatively investigate the relationship between the radiation
intensities of He ii 304 Å and H i Ly$\alpha$, we conduct pixel-by-pixel
comparisons in the two-ribbon regions and calculate their Pearson correlation
coefficients (CCs).

Aligning the SDI images with the AIA using the method developed by Cai et al.
(2022) is crucial to ensure that the calculated radiation comes from the same
flare region, enabling accurate point-to-point comparison of radiation
intensities between He ii 304 Å and H i Ly$\alpha$. We then uniformly sample
points within the white contour (representing 55% of the 304 Å intensity)
shown in Figure 4 and extract their corresponding radiation intensities on a
pixel-by-pixel basis. Figure 5 presents scatter diagrams of the intensity
comparisons under logarithmic axes between He ii 304 Å and H i Ly$\alpha$ in
the southern (left column) and northern (right column) ribbon regions from
14:23 UT to 15:28 UT. One can see that the H i Ly$\alpha$ radiation has
moderate intensity correlations with He ii 304 Å, while the CCs of the
southern ribbon (0.60-0.71) are greater than that of the northern ribbon
(0.44-0.60). The calculated difference in CCs between the two ribbons may be
attributed to the distinct environmental conditions in each region. Meanwhile,
as the flare ribbons evolve, there is a gradual increase in the correlation
between H i Ly$\alpha$ and He ii 304 Å emissions, which may be closely
associated with the heating process in the flare.

###  3.3 NLFFF Extrapolation

To understand the asymmetric distribution of the HXR emission and the
morphology of the two ribbons, we conduct the NLFFF extrapolation based on the
optimization method (Wiegelmann and Neukirch, 2003) in the flare region. The
structure of the magnetic fields is presented in Figure 6.

The Space-Weather HMI Active Region Patches (SHARP, Bobra et al., 2014) map,
derived from the Helioseismic and Magnetic Imager (HMI, Hoeksema et al., 2014)
on board the SDO, is used as the boundary condition for the NLFFF model. The
180-degree ambiguity is corrected, and the map is projected onto the
cylindrical equal-area (CEA) coordinate. Figure 6a presents the $B_{\rm z}$
component of the SHARP map at 14:58 UT with a pixel scale of 0.36 Mm. The gold
contour represents 30% of the maximum HXR intensity projected from the
Helioprojective-Cartesian (HPC) coordinate in Figure 4c and d to the CEA
coordinate, and red dots are uniformly sampled within it as the start points
for tracing magnetic field lines (green lines). The dark green lines represent
magnetic field lines, where the magnetic field strengths at the southern FPs
are larger than those at the northern FPs. In Panel c, the distribution of
traced field lines is displayed along with the ribbon contours of AIA He ii
304 Å (55%, red lines) and HXR (30%, gold lines) on the HMI Line-of-Sight
(LoS) magnetogram. The blue rectangle represents the Field-of-View (FoV) of
the SHARP map shown in Panel a. One can see that the configuration of the
magnetic field follows a horn-like shape, featuring a convergence field rooted
in the southern region with negative fluxes and a divergent distribution in
the northern region with positive fluxes.

Based on the extrapolated magnetic field, we calculate the squashing factor Q
(Titov, Hornig, and Démoulin, 2002) to quantify the magnetic connectivity
using the FastQSL code developed by Zhang et al. (2022). Figure 6b presents
the distribution of the signed log Q, ${\rm slog}\,Q={\rm sgn}(B_{\rm
z})\cdot{\rm log}\,Q$, at the photosphere. The magnetic field lines
originating from the red dots marked in the high-Q region (red) in the
northern region are all connected to the high-Q region (blue) in the southern
region. To gain insights into the three-dimensional structure of the magnetic
field, particularly the quasi-separatrix layer (QSL), we calculate the Q
within the 3D box region. Panel d shows its distribution on a cross-section
along the dashed line in Panel b and perpendicular to the XOY plane. From the
QSL map, we can see the positions of the LT and FPs (F1, F2) of the flare
loop. The LT is located at a height of $\approx 32\ {\rm Mm}$ above the
photosphere, while F1 and F2 are rooted in the northern and southern ribbons,
respectively. One can see that the distance from the flare LT to the two FPs
is asymmetric, indicating that the length from the LT to F1 is shorter than
that to F2. Such magnetic field configuration suggests that for the flare
loops at the eastern side, the energy release of particles is located closer
to F1.

In addition, we conduct a statistical analysis on the relationship between the
distance from LT to FPs, magnetic field strength $B$, and HXR intensity $I$
for each traced field line, as shown in Figure 7. In Panel a, we calculate the
ratio of the de-projected length $L_{\rm S}/L_{\rm N}$ from the LT to the
northern FT $L_{\rm N}$ and the southern FT $L_{\rm S}$, as well as the ratio
of the distance $D_{\rm S}/D_{\rm N}$ from the projected points of the LT onto
the XOY plane to the two FPs, respectively. The subscript ‘S’ denotes the
southern FP, while ‘N’ denotes the northern FP. We find that 78% of the traced
magnetic field lines have $L_{\rm S}>L_{\rm N}$, while 22% of the remains have
$L_{\rm S}<L_{\rm N}$. Similarly, 79% of magnetic field lines have $D_{\rm
S}>D_{\rm N}$, whereas 21% have $D_{\rm S}<D_{\rm N}$. The statistical
relationship quantitatively demonstrates that the position of the flare LT is
asymmetric. We then compare the relationship between the de-projected length
ratio $L_{\rm S}/L_{\rm N}$ from LT to FPs and the ratio of the magnetic field
strength $B_{\rm S}/B_{\rm N}$ at FPs, which is presented in Panel b. Based on
the distribution of $B_{\rm S}/B_{\rm N}$, there is a slight difference in the
magnetic field strength between the northern FPs and the southern FPs (62% of
magnetic field lines have $B_{\rm S}>B_{\rm N}$ at their FPs). The comparisons
reveal that the asymmetry of the LT position is mainly attributed to the horn-
shaped magnetic field configuration and is slightly influenced by the magnetic
field strength at the FPs.

Furthermore, we compare the ratio of the HXR intensity $I_{\rm N}/I_{\rm S}$
at the FPs with the magnetic field strength $B_{\rm S}/B_{\rm N}$ and the loop
length $L_{\rm S}/L_{\rm N}$, as shown in Figure 7c and d. Due to the uniform
sampling of the northern FP for each magnetic field line within the contour of
30% maximum HXR intensity, the HXR intensity ratios between the northern and
southern FPs are always greater than 1, i.e., $I_{\rm N}>I_{\rm S}$.
Similarly, one can see that there is a small difference in the magnetic field
strength between the northern FP (38% field lines of $B_{\rm S}<B_{\rm N}$)
and the southern FP (62% field lines of $B_{\rm S}>B_{\rm N}$), while 78% of
LTs are closer to the northern FP, $L_{\rm S}>L_{\rm N}$. Therefore, we
conclude that the asymmetric distribution of the HXR radiation is mainly
attributed to the asymmetry of the flare LT, and is also slightly influenced
by the magnetic mirror effect.

##  4 Conclusions and Discussions

In this work, we investigate the asymmetry of the HXR radiation at two ribbons
in a C4.4 flare by combining multi-view and multi-waveband observations from
the ASO-S, SDO, and SolO spacecraft. The LDE observed on March 20, 2023, was
caused by the eruption of a filament system, accompanied by a CME and an
elongated CS. The light curves of both the SXR and HXR emissions present a
consistent peak time, with no brightening observed in the 1600 Å and 1700 Å
passbands, implying that thermal electrons dominate this event. The light
curves of HXR, SDI H i Ly$\alpha$ and AIA He ii 304 Å during the flare rising
phase exhibit a consistent trend, indicating a common radiation origin
primarily from flare ribbons formed in the middle-to-upper chromosphere and
transition region.

Thanks to the 24-hour uninterrupted full-disk observations from Earth’s view
provided by the SDI on board the ASO-S, we can study the spatio-temporal
features of the two ribbons in H i Ly$\alpha$ waveband. These observations,
along with those in the He ii 304 Å, reveal similar evolution of the two
ribbons, presenting rapid separation towards the northern and southern
directions. The pixel-by-pixel comparisons between the SDI and AIA images
further quantitatively demonstrate the moderate correlation between H i
Ly$\alpha$ and He ii 304 Å. Meanwhile, their emissions may be closely
associated with the heating process in the flare.

The spectral fitting of the HXR emission detected by STIX further confirms
that the flare mainly releases energy through the process of thermal bremss-
trahlung emission, implying that the radiations in both He ii 304 Å and H i
Ly$\alpha$ are produced by a thermal process. Additionally, the MEM_GE
algorithm is applied to reconstruct the HXR maps observed by STIX. We find
that the HXR radiation presents an asymmetric distribution, with the majority
of the emission concentrated at the northern ribbon.

Using the method of differential emission measure (DEM, Cheung et al., 2015;
Su et al., 2018), we estimate the electron density $n_{\rm e}$ inside the
flare loops. The total emission measure EM and the average electron number
density are deduced via,

$\displaystyle{\rm EM}$ $\displaystyle=$ $\displaystyle\int_{T_{\rm
min}}^{T_{\rm max}}{{\rm DEM}(T)dT},$ (1) $\displaystyle n_{\rm e}$
$\displaystyle=$ $\displaystyle\sqrt{\frac{\rm EM}{l}}\ ({\rm cm}^{-3}).$ (2)

where $l$ represents the effective depth along LoS. We further assume that the
flare loops have similar extents in depth and width, and we estimate $l$ to be
$\approx 2.3\times 10^{8}\ {\rm cm}$ by measuring the loop width observed by
AIA 94 Å. The value of EM can be directly derived from the DEM result.
Therefore, we determine the density $n_{\rm e}$ is $\approx 1.0\times 10^{10}\
{\rm cm^{-3}}$, indicating that the flare loop is relatively dense.

By combining the NLFFF extrapolation with observations, we explore the
magnetic configuration and physical parameters within this active region. This
approach allows us to understand the magnetic field structure and derive
important physical properties within the two ribbons. The characteristic loop
length $L$, derived from the traced field lines, is $\approx 5.9\times 10^{9}\
{\rm cm}$. Based on the magnetic topology, we further demonstrate that the
asymmetric HXR emission is produced by the asymmetric position of the flare LT
and the magnetic mirror effect. The statistical parameters of the extrapolated
field lines indicate that the de-projected length from the LT to the northern
FP is shorter than that to the southern FP, and the magnetic field strength at
the southern FP is stronger than that at the northern FP, which promotes
thermal electrons to collide with the plasma inside the dense flare loop and
easily reach the northern ribbon. At the same time, considering the physical
conditions such as the lower height, $\approx 32\ {\rm Mm}$, of the LT above
the photosphere, as well as the denser plasma inside the flare loops, $\approx
1.0\times 10^{10}\ {\rm cm^{-3}}$, more thermal electrons are more easily able
to reach the northern FP during the collision process with the surrounding
plasma, resulting in a stronger HXR emission compared to the southern FP.

Our work provides a novel approach for investigating the asymmetric HXR
radiation in the two-ribbon flare dominated by over 95% thermal radiation.
This approach involves combining the NLFFF extrapolation with observations to
understand the magnetic field structure and physical properties within the
flare region. Unfortunately, due to no obvious HXR emissions above $\approx
18$ keV in this flare, the HXI on board the ASO-S did not receive sufficient
counts for data analysis. Future research endeavors will statistically analyze
the asymmetric events of the HXR emission at FPs using the HXR data observed
by the HXI and combine them with the unique H i Ly$\alpha$ waveband full-disk
observations from the SDI to conduct more detailed studies of the asymmetric
HXR radiation.

We sincerely thank the anonymous referee for providing valuable suggestions
that helped us improve the quality of the manuscript. We thank Shangbin Yang
and Zhentong Li for their helpful discussions on the NLFFF model and STIX data
processing. The authors thank the teams of SolO/STIX, SDO, GOES, CHASE for
their open-data use policy. The ASO-S mission is supported by the Strategic
Priority Research Program on Space Science, Chinese Academy of Sciences. SolO
is a space mission of international collaboration between ESA and NASA,
operated by ESA. The STIX instrument is an international collaboration between
Switzerland, Poland, France, Czech Republic, Germany, Austria, Ireland, and
Italy. SDO is a mission of NASA’s Living with a Star (LWS) Program. The CHASE
mission is supported by China National Space Administration.

G.L. Shi wrote the main manuscript, analyzed the data, and generated figures.
L. Feng discovered the asymmetric HXR radiation event, conceived the study,
and revised the manuscript. J. Chen, B.L. Ying, S.T. Li, and Q. Li discussed
results and provided helpful suggestions on this work. W.Q. Gan is PI of the
ASO-S. H. Li and L. Feng are PI and Co-PI of the LST, respectively. K.F. Ji
provided an alignment code for the AIA and SDI images. Y. Li, Y. Huang, Y.P.
Li, J.W. Li, J. Zhao, L. Lu, J.C. Xue, P. Zhang, D.C. Song, Z.Y. Tian, Y.N.
Su, Q.M. Zhang, Y.Y. Ge, J.H. Shan, Y. Zhou, J. Tian, G. Li, X.F. Liu, Z.C.
Jing, and S.J. Lei contributed to the in-orbit testing, pipeline, and release
of LST data. All authors reviewed the manuscript.

This work is supported by the National Key R&D Program of China
2022YFF-0503003 (2022YFF0503000), Strategic Priority Research Program of the
Chinese Academy of Sciences, Grant No. XDB0560000, NSFC (grant Nos. 11973012,
11921003, 12103090, 12203102, 12233012, 12373115), the mobility program
(M-0068) of the Sino-German Science Center.

The ASO-S data before Apr. 1, 2023 are currently being tested and not publicly
available, but can be obtained from the corresponding author with reasonable
request. The ASO-S data after Apr. 1, 2023 are publicly available at
http://aso-s.pmo.ac.cn/sodc/dataArchive.jsp. The AIA&HMI data are downloaded
from the Joint Science Operations Center (JSOC) at http://jsoc.stanford.edu.
The STIX data are publicly available at
https://datacenter.stix.i4ds.net/view/list/fits. The GOES data are obtained
from the National Oceanic and Atmospheric Administration (NOAA) at
https://www.ngdc.noaa.gov/. The CHASE data are accessible through the solar
science data center of Nanjing university at
https://ssdc.nju.edu.cn/NdchaseSatellite.

The authors declare no competing interests.

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Figure 1: Light curves from multiple wavebands for the long-duration event
(LDE) on March 20, 2023. (a) GOES SXR light curve ranging from 1.0-8.0 Å along
with its time derivative (purple line). (b) STIX HXR light curves at 4-10 keV
(green line) and 10-18 keV (magenta line). (c) Integrated light curves of AIA
He ii 304 Å (black line), AIA 94 Å (cyan line) and SDI H i Ly$\alpha$ (blue
line) in the flare region. Pink and blue shadows represent the integration
times for HXR spectra and imaging analysis shown in Figure 3 and Figure 4,
respectively. The red vertical line marks the SXR peak time at 15:34 UT.

Figure 2: An overview of the observations of the LDE. (a) A long filament
before the flare onset observed in H$\alpha$ by CHASE. (b) Eruption of the hot
channel observed in the AIA base-difference image in the 94 Å passband. (c)
and (d) Separation of the two ribbons captured in AIA He ii 304 Å (c) and SDI
H i Ly$\alpha$ (d) towards the northern and southern directions.

Figure 3: HXR spectral fitting for the times marked by the pink shadows in
Figure 1 using a double thermal model. The fitting parameters, including
electron temperature (T), emission measure (EM), and chi-square ($\chi^{2}$),
are displayed in each panel. Black solid lines represent the count rate of the
HXR emissions detected by STIX after subtraction of the pre-flare background
(dashed lines), while blue lines represent the optimal fitting curves.

Figure 4: Evolution of two ribbons in the AIA He ii 304 Å (left column) and
SDI H i Ly$\alpha$ (right column) observations for the times selected by the
blue shadows in Figure 1. Panel c presents the composite image of AIA 304 Å
(red) and 94 Å (cyan). The overlaid gold contours represent HXR maps of STIX
reconstructed by the MEM_GE algorithm at 4-18 keV, using levels at 45%-90% of
the maximum intensity with a step of 15% in each panel. The white contour
indicates 55% of the maximum intensity of He ii 304 Å.

Figure 5: Scatter diagrams of the pixel-by-pixel comparisons between the AIA
He ii 304 Å (horizontal axis) and SDI H i Ly$\alpha$ (vertical axis)
intensities within regions of the southern ribbon (left column) and the
northern ribbon (right column) at different times. Correlation coefficients
(CCs) are calculated in each panel.

Figure 6: Magnetic configuration in the two-ribbon region. (a) HMI $B_{z}$
component of NOAA AR 13258 in the CEA coordinate applied for the NLFFF
extrapolation, with a linear saturating at 300 G. Green field lines root at
the red dots within the gold contour that represents the 30% level of the
maximum intensity of HXR. Dark green lines indicate a stronger magnetic field
in the southern FP compared to the northern FP. (b) Signed log Q map, ${\rm
slog}\,Q={\rm sgn}(B_{\rm z})\cdot{\rm log}\,Q$, on the NLFFF photospheric
boundary. (c) HMI line-of-sight (LOS) magnetogram overlaid the red contour
(55% of the maximum intensity of He ii 304 Å) outlining the flare ribbons; the
blue rectangle indicates the field-of-view (FoV) of the SHARP map in Panel a.
(d) Log Q map, with its axes along the dashed line and Z direction in Panel b,
respectively. F1 and F2 denote footpoints (FPs) of the flare loop, while LT
represents the flare loop-top.

Figure 7: (a) Scatter diagram of the ratios between the de-projected length
$L_{\rm S}/L_{\rm N}$ and the projected length $D_{\rm S}/D_{\rm N}$ from the
LT to the FPs for each extrapolated field line. $L$ represents the integrated
length from the LT to the FPs along each field line, while $D$ represents the
distance between the projected point of the LT onto the XOY plane and the FPs.
(b) Comparisons between the ratios of the integrated length $L_{\rm S}/L_{\rm
N}$ from the LT to the FPs and the magnetic field strength $B_{\rm S}/B_{\rm
N}$ at the FPs. Comparisons of the ratios of the HXR intensity $I_{\rm
N}/I_{\rm S}$ with magnetic field strength $B_{\rm S}/B_{\rm N}$ at FPs (c)
and length $L_{\rm S}/L_{\rm N}$ from the LT to the FPs (d). $B$ and $I$
represent the magnetic field strength and the HXR radiation at the FPs,
respectively. The subscript ‘S’ denotes the southern FP, while ‘N’ denotes the
northern FP. The value after the letter ‘S’ (‘N’) in the corners indicates the
percentage of the magnetic field lines where the physical quantity at the
southern FP is larger (smaller) than that at the northern FP.