#  Simultaneous ALMA−Hinode−IRIS observations on footpoint signatures of a
soft X-ray loop-like microflare

Toshifumi Shimizu Institute of Space and Astronautical Science, Japan
Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa
252-5210, Japan  Department of Earth and Planetary Science, The University of
Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan  Masumi Shimojo National
Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588,
Japan  Department of Astronomical Science, SOKENDAI (The Graduate University
for Advanced Studies), 2-21-1, Osawa, Mitaka, Tokyo 181-8588, Japan  Masashi
Abe  Department of Earth and Planetary Science, The University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan  Institute of Space and Astronautical
Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo,
Sagamihara, Kanagawa 252-5210, Japan

(Accepted September 16, 2021)

###### Abstract

Microflares have been considered to be among the major energy input sources to
form active solar corona. To investigate the response of the low atmosphere to
events, we conducted an ALMA observation at 3 mm coordinated with IRIS and
Hinode observations, on March 19, 2017. During the observations, a soft X-ray
loop-type microflare (active-region transient brightening) was captured using
Hinode X-ray telescope in high temporal cadence. A brightening loop footpoint
is located within narrow field of views ALMA, IRIS slit-jaw imager, and Hinode
spectro-polarimeter. Counterparts of the microflare at the footpoint were
detected in Si IV and ALMA images, while the counterparts were less apparent
in C II and Mg II k images. Their impulsive time profiles exhibit the Neupert
effect pertaining to soft X-ray intensity evolution. The magnitude of thermal
energy measured using ALMA was approximately 100 times smaller than that
measured in the corona. These results suggest that impulsive counterparts can
be detected in the transition region and upper chromosphere where the plasma
is thermally heated via impinging non-thermal particles. Our energy evaluation
indicates a deficit of accelerated particles that impinge the footpoints for a
small class of soft X-ray microflares. The footpoint counterparts consist of
several brightening kernels, all of which are located in weak (void) magnetic
areas formed in patchy distribution of strong magnetic flux at the
photospheric level. The kernels provide a conceptual image in which the
transient energy release occurs at multiple locations on the sheaths of
magnetic flux bundles in the corona.

Unified Astronomy Thesaurus concepts: Solar physics[1476], Solar
electromagnetic emission[1490], Solar activity[1475], Solar flares[1496]

††journal: ApJ

##  1 Introduction

The solar corona is formed at more than $10^{6}$ K above the surface
(photosphere) with a temperature of 6,000 K. The corona is highly structured
and has active regions with high energy input that are observed to be bright
and active in soft X-rays and high-temperature extreme ultraviolet (EUV)
lines. Small-class transient reconnection events, that is, microflares (in the
order of $10^{27}$ erg) and nanoflares (in the order of $10^{24}$ erg), have
been considered to be among the major energy input sources to form the active
corona. This is because extremely high temperature plasma ($>8$ MK) is
observed in active regions (Yoshida and Tsuneta, 1996; Teriaca et al., 2012).
Microflares have been predominantly observed as transient brightenings in
active regions (Shimizu et al., 1992) that morphologically show various
brightening coronal structures in soft X-rays (Shimizu et al., 1994).
Simultaneous multiple loop brightenings are more often seen than single loop
brightenings and the loops tend to brighten either from their footpoints
and/or from the the apparent contact point , followed by the brightening of
the entire loops. In such cases, the energy release site is located in the
corona. Certain portion of the energy released in the corona is transported
via accelerated particles and thermal conduction along the magnetic field to
the footpoints, where the chromospheric and transition region cool plasma is
transiently heated. We are yet to understand the partition of the energy; the
amount of energy transferred to the footpoints and significant heating of the
chromosphere. Studies have been conducted on the energy partition in flares
(references in Section 4.3). Observational understanding of the energy
partition in microflares and nanoflares can significantly expand the range of
energy to disucss the energy partition. This helps to understand the energy
partition changes as a function of event energy size.

The energy released by small-scale transient events has been evaluated as
thermal energy via temperature and density diagnostics using soft X-ray or EUV
intensities. This provides frequency distribution in microflare and nanoflare
energy range (Shimizu, 1995; Aschwanden et al., 2000, and references herein).
Hard X-ray observations are also used to evaluate non-thermal energy; however,
they are solely conducted for flares above $5\times 10^{28}$ erg (Crosby,
Aschwanden and Dennis, 1993). The hard X-ray emission originated predominantly
in the accelerated particles that impinge the lower atmosphere at the
footpoints of the magnetic structure of coronal flaring. The Interface Region
Imaging Spectrograph (IRIS)(De Pontieu et al., 2014), launched in 2013, has a
high-resolution used to observe the movement of heat and energy in the
chromosphere and lower portion of the coronal transition region. IRIS has a
spectrograph and slit-jaw imagers to monitor the intensity of some wavelength
bands that contain spectral lines originating from the chromosphere and lower
portion of transition region. Later in the decade following 2010, a new
diagnostic capability for the chromosphere was incorporated when the Atacama
Large millimeter and sub-millimeter Array (ALMA) (ALMA Partnership, 2016)
began solar observations. ALMA can perform interferometric observations of the
Sun at millimeter (mm) wavelengths. Most of the mm emission comes from the
chromosphere (Vernazza et al., 1981). The mm-wavelength emission is a free-
free emission (thermal bremsstrahlung) produced by free electrons scattering
off ions without being captured. The free electrons can be assumed to be in
local thermodynamic equilibrium: thus, the source function is equivalent to
the Plank function. In the mm wavelengths, the Rayleigh–Jeans law is an
approximation to the Plank function that demonstrates a linear relationship
between the emission intensity and the brightness temperature (Kraus, 1986).
This indicates that the radiation at mm wavelengths can be used as a
thermometer to probe the chromospheric temperature. The thermometer provides
acts as a useful tool to detect changes in the chromospheric temperature to
estimate the amount of energy transferred to the chromosphere.

In this study, we present the first example of small-scale transient
brightenings produced in the solar corona (hereafter, referred to as soft
X-ray microflare) and their responses in the chromosphere and lower portion of
coronal transition region. The soft X-ray microflare was captured in high
temporal cadence using Hinode X-ray telescope to observe the evolution of
brightening loop structure in the corona and locations of the brightening loop
footpoints on the solar surface. One footpoint was within the narrow fields of
view of the ALMA, IRIS, and Hinode spectro-polarimeter. The spectro-
polarimeter provides high precision and high spatial resolution maps of
magnetic flux distributed on the photosphere, which are helpful to understand
the magnetic field configurations of the soft X-ray microflare.

This article is organized as follows. Section 2 describes the observations and
data analysis. Section 3 presents the results of the data analysis. Section 4
and Section 5 present the discussion of the results and summary, respectively.

##  2 Observations and Data analysis

###  2.1 Observations

A coordinated observation was conducted among the ALMA, IRIS, and Hinode on
March 19, 2017. The ALMA project, with project code 2016.1.00030.S (PI:
Shimizu), was executed. The Hinode and IRIS operation plan was numbered as
IHOP 327. We selected a tiny active region located in the eastern hemisphere
on the solar disk as the observing region for the coordinated observations.
The region is seen as a compact bright region in the soft X-rays; it exhibits
a magnetic bipolar distribution on photospheric SDO/HMI magnetograms.

The ALMA observation was conducted at 100 GHz (Band 3) from 15:33 to 19:10 UT.
The observation consists of three runs (15:33–16:26 UT, 16:53–17:46 UT, and
18:16–19:10 UT); a soft X-ray microflare occurred during the first run. This
tiny active region is located at ($-495$″, $-40$″) on the heliocentric
coordinate at the beginning of the first run. The antenna layout is the C40-1
configuration, which is the most compact layout in the solar observing mode
with sets of 39 and 7 antennas with diameters 12 m and 7 m, respectively. The
longest baseline is 249 m with a spatial resolution of $5.0\times 3.9\arcsec$.
The common astronomy software applications (CASA Ver 5.4; McMullin et al.,
2007) was used to calibrate and image the data. The CLEAN procedure ’tclean’
was used to synthesize each image (Shimojo et al., 2017). The synthesis was
conducted excluding the visibilities between the two antenna sets (39 and 7
antennas) because appropriate synthesis was not obtained when all the
visibilities among the antennas were used. When the $7-12$ m baselines were
involved in the synthesis, artificial stripes appeared in the synthesized
images. The stripes disappeared when the baselines were removed. We do not
appropriately understand the origins of the stripes; however, the visibility
data of $7-12$ m baselines degraded the image quality. Careful calibration
might solve this issue; however, we removed the baselines in the image
synthesis presented in this study because we do not know the calibration
process for the $7-12$ m baselines. The data were self-calibrated in phase.
The self-calibration process has five steps with different accumulating
periods to obtain the solution from 10 min for the first step to 2 s for the
last step such that the temporal cadence is 2 s in this study. No single dish
(total power) data were acquired to calibrate the absolute brightness
temperature in this observation. Thus, the temporal profiles presented in this
article show the deviation from the averaged brightness temperature in the
observation field-of-view. The increase in temperature brightness for the
event considered can be derived even without absolute temperature information.

The IRIS satellite performed the spectroscopic and slit-jaw imaging
observations during the period. This article presents the results obtained
from the slit-jaw images because the slit positions were not present around
the footpoint of the soft X-ray microflare. The slit-jaw images were acquired
at three channels 1400, 1330, and 2796, each of which covers Si IV 1394/1402 Å
lines ($10^{4.8}$ K), C II 1335 Å lines ($10^{4.2}$ K), and Mg II k line
($10^{4.0}$ K), respectively, at a cadence of 22 s. The pixel size is
$0.34\arcsec$. Each image has a field of view of $60\times 65\arcsec$, but it
moves in the EW direction at each exposure because of the scanning for
spectroscopic measurements. This provides the maximum coverage in the field of
view, at $120\times 65\arcsec$. The level 2 data from the IRIS were used in
this analysis, which were obtained following instrumental calibration
including dark current, flat field, and geometric corrections.

The X-Ray Telescope (XRT) (Golub et al., 2007; Kano et al., 2008) on the
Hinode satellite (Kosugi et al., 2007) repeatedly and continuously acquired
Al-poly filter images every 4 s with occasional exposures of G-band images
(XOB #1B76). The image size is $128\times 128$ pixels with a pixel scale of
$1.031\arcsec$(Shimizu et al., 2007). The standard calibration routine on
Solar SoftWare was used to calibrate the time series of the XRT images.

The Hinode’s Solar Optical Telescope (SOT) (Tsuneta et al., 2008; Suematsu et
al., 2008; Shimizu et al., 2008; Ichimoto et al., 2008) repeatedly and
continuously recorded the full-polarization states of line profiles of two
magnetically sensitive Fe I lines at 630.15 and 630.25 nm using the spectro-
polarimeter (SP, Lites et al., 2013). The fast-mapping mode was used, which
covers a $77\times 80\arcsec$ field of view with an effective pixel size
$0.32\arcsec$. The spectral sampling is 21.549 mÅ pixel-1. The map cadence was
approximately 30 min. We used the SOT/SP level 2 databasefromthe Community
Spectro-polarimetric Analysis Center (CSAC) 111http://www2.hao.ucar.edu/csacat
HAO/NCAR, which are results ofMilne–Eddington inversions by the MERLIN code
with the calibration described in Lites & Ichimoto (2013).

###  2.2 Image Co-alignment and Spatial Distribution Correspondence

The data from the different instruments were carefully investigated to
identify a better method for the co-alignment; we finally achieved better than
$2\arcsec$ in the uncertainty of the co-alignment. IRIS and Hinode data were
mapped on the full Sun images from the Solar Dynamic Observatory (SDO, Pesnell
et al., 2012) by obtaining the maximum correlation between the corresponding
data; A Hinode SP map was mapped on the HMI magnetogram (Scherrer et al.,
2012; Schou et al., 2012) by obtaining the best matching in the spatial
distribution of the magnetic flux. The time series of the Hinode XRT images
were mapped on an AIA 94 Å coronal image to determine the co-alignment
accuracy. The IRIS slit-jaw images were mapped on the AIA 1600 Å chromospheric
image using an image of 2794 Å. For the ALMA data, the coordinates available
for each map were used to co-align to the SDO full-sun images because the
pointing accuracy of the ALMA antennas has been established as more than
$2\arcsec$ (ALMA Partnership, 2016). Nevertheless, the coordinates of the
image provided by the ALMA observatory exhibit a problem when the coordinates
are not appropriately revised using the reference time. Generally, the
coordinates are not revised when there is no pointing data that are derived
from the encoders of the antennas. To avoid this problem, we revised the
coordinate using the reference time, which differs from that mentioned in the
readme file of the data package in the ALMA Archive.

Figure 1 shows the spatial distribution of features in the co-aligned images.
The SP line-of-sight magnetic flux density map (Figure 1(a)) demonstrates a
bipolar flux distribution in the field of view. The areas where the magnetic
flux is concentrated are brighter than their surroundings in the three IRIS
slit-jaw images (Figure 1(c)–(e)). Brighter features in the IRIS images
correspond to small flux concentrations. Diffuse features can be recognized
around the bright features, which may be caused owing to the expansion of
magnetic flux at the chromospheric height. Bright features at flux
concentrations mean that high heating rate is sustained from the middle
chromosphere to a lower portion of the transition region at the magnetic flux
concentrations; the temperature responses of the Mg II, C II, and Si IV
filters are at peak values in the middle chromosphere ($10^{4.0}$ K), upper
chromosphere ($10^{4.2}$ K) and a lower portion of the transition region
($10^{4.8}$ K), respectively. Figure 1(b) shows the corresponding ALMA
brightness temperature map, which is time-averaged over the first run. The
brightness temperature here is the deviation from the temperature averaged
over the field of view. The overall spatial distribution in the ALMA
temperature map corresponds well with those observed in the IRIS chromospheric
maps. However, the ALMA map shows a more diffuse distribution, which may be
because of the lower spatial resolution of the ALMA in this observation.
Figure 1(f) is a co-aligned X-ray image. The bright corona is not observed as
a bipolar structure connecting the flux concentrations to each other, which is
completely different from what is observed in the chromosphere and lower
transition region.

Figure 1: Spatial distribution of time-averaged features visible in (a) SP
line-of-sight magnetic flux density, (b) ALMA brightness temperature, (c) IRIS
slit-jaw Mg II filter, (d) IRIS slit-jaw C II filter, (e) IRIS slit-jaw Si IV
filter, and (f) Hinode XRT Al-poly filter. They are co-aligned to each other
according to the method described in section 2. In (a), the white and black
are positive and negative polarities, respectively. Solar north is upwards and
west is to the right direction. DN is data number units.The boxes show the
field of view of Figures 4 and 5.

##  3 Results

###  3.1 Loop-like Microflare in Soft X-rays

Figure 2 shows the time series of soft X-ray images (with Al-poly filter)
obtained from the Hinode XRT. Six frames were selected from the cadence series
of images at 4 s to show the occurrence of a loop-like microflare, which is
located almost at the center of the images. A single coronal loop became
apparent up to the 4th frame (15:54:41 UT), which was the time when the
intensity was at peak. This loop brightening started from 15:51 UT immediately
after the 1st frame, in which a couple of loop structures had been faintly
visible previously. Another loop structure existed at the right side parallel
to the brightening loop considered; it may have been extended towards the west
direction. This structure showed a temporal evolution similar to that of the
brightening loop. Figure 3 (a) shows the time profile of the soft X-ray
intensity for the area identified with light blue lines in Figure 2. The
vertical dashed lines represent the time at which each frame in Figure 2 was
acquired. The intensity stayed at a constant level until 15:51 UT (1st frame
in Figure 2), followed by a transient increase in the intensity. The intensity
required approximately 3 min to attain its peak at 15:54:30 UT (4th frame in
Figure 2). The increased total intensity of the brightening loop is $5.8\times
10^{3}$ DN s-1, where DN is data number.Itwas derived by integrating the
pixels surrounded by the light blue lines in Figure 2(c). Then, the intensity
gradually decreased and required approximately 10 min to attain the minimum.
This temporal evolution is conventional for the soft X-ray behaviors observed
well in the solar flares and microflares.

Figure 2:  Time series of soft X-ray images (Al-poly filter) acquired by
Hinode X-Ray Telescope. The time sequence is from (a) to (c) and then from (d)
to (f). The field of view is wider than that in Figure 1. Solar north is
upwards and west is to the right direction. The rectangle in (a) shows the
field of view used in Figure 1. The area surrounded by light blue lines in (c)
indicates the pixels where the intensity was integrated for Figure 3(a).
Figure 3: Intensity profiles of (a) the soft X-ray microflare and its
counterparts measured in (b) 100 GHz, (c) Si IV, (d) C II, and (e) Mg II k.
The counterparts were measured at one of the footpoints of the soft X-ray
brightening loop, while the soft X-ray profile is for the entire area of the
brightening loop, as specified in Figure 2. The vertical dash lines determine
the time of the images shown in Figures 2, 4 and 5.

One of the brightening loops, that is, the upper (north) end of the loop, is
located within the observing fields of view of IRIS, ALMA, and Hinode/SP such
that we can investigate the behaviors of the footpoint at different
wavelengths. Figure 3(c) shows the area intensity profile in the Si IV slit-
jaw channel of the IRIS. The Si IV intensity began to increase at 15:52 UT and
peaked at 15:53:25 UT, followed by an immediate decrease of the intensity to
the initial level by 15:55 UT. This transient intensity increase is faster
than the ascending slope in the soft X-ray profile (Figure 3(a)); the
increased Si IV intensity quickly reduced before reaching the peak in soft
X-ray.

Some Si IV images are shown in Figure 4, whose acquired times are identified
by the vertical dash lines in Figure 3(c). The field of view is $13.3\times
11.6\arcsec$, where the loop footpoint is located around the center. As
described in Section 2, a $60\times 65\arcsec$ field was repeatedly moved in
the EW direction at each exposure to sample spectral lines at several
positions in the $120\times 65\arcsec$ field of view. Because of this
operation, observing field of view changed with time, which can be partly
recognized in the 2nd and 3rd frames as the dark area. Four or five bright
kernels, each of which has a size of less than $1\arcsec$, appeared in the 2nd
frame (15:52:41 UT). In the 3rd frame (15:53:25 UT), that is, at the peak
time, the bright kernels showed a slight increase in intensity, location, and
shape. However, we recognized two bright kernels at similar locations. The
frame at the lower right shows the intensity difference in the 3rd frame when
compared with the 1st frame (15:50:51 UT). This clearly provides the location
of brightening features at the footpoint of the soft X-ray microflare. The
bright features may be grouped into two areas centered at (X, Y) = (5.5, 4)
and (8, 6) in arcsec.

Figure 4: Si IV channel images from the IRIS slit-jaw imager for the five
times specified in Figure 3. The 1st frame (a) is before the intensity began
increasing, and the 3rd frame (c) is at the intensity peak. The frame (f) is
obtained from the difference between (a) and (c). The field of view is
$13.3\times 11.6\arcsec$ and its location is shown in Figure 1.  Figure 5:
Difference frames for (a), (b) Si IV, (c) 100 GHz, (e) C II, and (f) Mg II k,
which were obtained by subtracting the background image (identified by the 1st
vertical dash line for each time plot shown in Figure 3). The frames in (b),
(c), (d), and (e) are for the images recorded at peak time. (f) Spatial
distribution of the magnetic flux density derived from the Hinode SP scan in
15:38:01–16:07:44 UT. The red and blue contours indicate the position of Si IV
bright kernels observed in (a) and (b), respectively. The field of view is
same as that of Figure 4.

Figure 3(b) is the temporal evolution of the brightness temperature at 100 GHz
for the region considered, which shows that the counterpart signals are
detected by ALMA at 100 GHz. The ALMA temporal profile of the brightness
temperature is almost same as that in the Si IV channel. The intensity
increase is also visible in the C II channel, as shown in Figure 3(d), but not
in the Mg II k channel (Figure 3(e)). Figures 5 (b), (c), (d), and (e) show
the Si IV, 100 GHz, C II, and Mg II k images, respectively, at the intensity
peak time with the background removed. The background is the frame specified
by the 1st vertical dash line in each time plot in Figure 3. The counterparts
are clearly detected in Si IV and 100 GHz at 15:52–15:53 UT. The spatial
resolution of the ALMA data is at least 10 times lesser than that of the IRIS.
Although the intensity is weak, the counterparts can be observed in the C II
frame. No apparent counterpart is observed in the Mg II k frame.

Figure 5(f) is the spatial distribution of magnetic flux at the photosphere.
Almost all the bright kernels observed in Si IV and C II are located in weak,
void areas surrounded by strong magnetic flux concentrations, as shown by the
contours.

###  3.2 Thermal energy of the soft X-ray microflare

Using the total soft X-ray intensity at the time of its peak intensity, we
estimated the thermal energy content for the soft X-ray microflare. The
thermal energy content $E_{th}$ is

$E_{th}=3n_{e}k_{B}TV,$ (1)

where $n_{e}$ is the electron density, $k_{B}$ is the Boltzmann constant, $T$
is the electron temperature, and $V$ is the volume. In the Yohkoh era, many
studies used a filter ratio method for the temperature and density by assuming
isothermal plasma (e.g. Shimizu, 1995; Shimojo and Shibata, 2000), followed by
more advanced techniques, such as differential emission measure. In this
observation, only Al-Poly filter images were acquired to obtain dynamical
behaviors with high temporal cadence. Thus, we used the method proposed by
Sako (2014) to estimate the order of energy. This method states that the
thermal energy is not sensitive to the temperature of the XRT filter
intensities. The filter response curve $R(T)$ is simplified to be

$R(T)=\frac{I}{\int n_{e}^{2}dV}\approx\frac{I}{n_{e}^{2}V},$ (2)

where $I$ is the measured total soft X-ray intensity. Thus, the thermal energy
content can be described as

$E_{th}=3\sqrt{\frac{I}{R(T)V}}k_{B}TV=3k_{B}\sqrt{\frac{T^{2}}{R(T)}}\sqrt{IV}.$
(3)

The response curve of the Al-poly filter is approximately a power-law
distribution as a function of temperature in $10^{6}-10^{7}$ K (Golub et al.,
2007). If the power-law index is 2, $R(T)$ is proportional to $T^{2}$. Thus,
$E_{th}$ is insensitive to the temperature. The Al-poly filter exhibits a
power-law index approximately equal to 2, that is, it exhibits a very weak
dependence on the temperature, as shown in Figure 6. In our estimation, we
used $1.1\times 10^{38}$ K2 s pixel DN-1 cm-5 for $T^{2}/R(T)$, which is the
average of $4-8$ MK. Transient brightenings in active regions have
conventionally exhibit a temperature of $4-8$ MK (Shimizu, 1995). The
$T^{2}/R(T)$ has an error range of $1.0\times 10^{38}-1.2\times 10^{38}$ in
the energy estimation. The volume of the brightening loop was determined by
measuring the length ($l$ = 27”) and width ($w$=3.7”) of the loop. Assuming
that the depth (the length of line-of-sight) of the loop is equal to the
width, we simplified the volume $V$ as $l\times w^{2}$. The XRT pixel size
(1”) was used for error estimation. This calculation obtained a volume of
$1.4\times 10^{26}$ cm3 with an uncertainty range between $0.75\times 10^{26}$
cm3 and $2.4\times 10^{26}$ cm3. Therefore, the thermal energy content was
estimated to be $2.9\times 10^{26}$ erg with an uncertainty range between
$2.0\times 10^{26}$ erg and $4.0\times 10^{26}$ erg. The thermal energy
produced by the microflare in the corona is larger than the thermal energy
content because the thermal energy content is the amount of the thermal energy
at a single time (peak time) without considering energy losses from the
radiation and thermal conduction during the ascending phase (Shimizu, 1995).

Figure 6:  $T^{2}/R(T)$ as a function of temperature ($T$) for the XRT Al-Poly
filter, where $R(T)$ is the filter response curve.

###  3.3 Thermal energy measured at the chromosphere

The ALMA data can provide an order estimate of the thermal energy supplied to
the chromosphere to which the 100 GHz microwave is sensitive. Here, we assumed
that the ALMA signal is the thermal free-free radiation. As observed from
Figure 3, the ALMA signal was peaked during the ascending phase of the soft
X-ray emission. No polarization was measured using ALMA in this observation;
thus, we cannot ignore gyro-cynchrotron radiation for the transient enhanced
signal at the footpoint in the ALMA data. Nevertheless, we interpreted it as
the signal caused by the thermal plasma heated in the chromosphere by the
electrons that are predominantly impinging the chromosphere.

The thermal energy supplied to the chromosphere is evaluated as the thermal
energy content $E_{ch}$, which is

$E_{ch}=3n_{e}k_{B}\Delta TV,$ (4)

where $\Delta T$ is the excess in electron temperature. (Nindos et al., 2020).
Because the brightness temperature is a reasonable measure of the gas
temperature at an effective formation height in the chromosphere (Loukitcheva
et al., 2015), for the increase in electron temperature, we obtained the
increase in brightness temperature above the background level at the time when
the ALMA time profile was at its peak. The ALMA application (CASA) derived the
flux density defined as the integration of brightness over the antenna beam
angle in the units of Jansky per beam size. Assuming that the beam is
Gaussian, the flux density was converted to brightness temperature, according
to the formula presented in ALMA Cycle 4 Technical Handbook. The background
level is the brightness temperature just before the event, whose time is
identified by the left most dashed line in Figure 3(b). The increased
brightness temperature derived was 545 K.

The electron density was assumed to be in the order of $10^{11}$ cm-3
according to certain numerical modeling efforts. Loukitcheva et al. (2015)
derived that the range of brightness temperature for an active-region magnetic
structure is from 2,945 K to 13,104 K with an average of 6,090 K and root mean
square variation of 1,333 K for the 100 GHz radiation. The 100 GHz (3 mm)
radiation has effective formation height of approximately 1,500 km with a
contributing range of $1,200-2,000$ km depending on the magnetic structures,
where the electron density is approximately $10^{11}$ cm-3.

The volume used in the evaluation was determined by assuming that the area
where the 100 GHz radio emission is in excess during the event was almost same
as the footpoint area of brightenings clearly detected in the Si IV (Figure
4). The upper left frames in Figure 5 indicate that the footpoint area changed
from image to image. For simplicity, we selected $8\arcsec$ for the N-S
direction and $5\arcsec$ for the E-W direction to cover the entire area of
various footpoints $A$ with $\pm 1\arcsec$ for uncertainty evaluation.
Assuming that the extent in the height is comparable to the horizontal size,
the volume $V$ was estimated to be $A^{3/2}$. This might be an overestimation
because the effective height of the 100 GHz radio is 800 km (approximately
$1\arcsec$). However, the transient heating by impinging electrons at the
chromosphere may expand the heated plasma towards the upper layers. With these
parameters, we obtained $(2.2\pm 1.2)\times 10^{24}$ erg as the thermal energy
supplied to the chromosphere.

##  4 Discussions

In this article, we investigated the heating of the footpoints using IRIS and
ALMA when an energy of $2.9(\pm 1.0)\times 10^{26}$ erg was transiently
released in coronal structure that is observed as a single brightening loop
using the Hinode XRT. Counterparts were clearly detected in the Si IV and ALMA
at 100 GHz. They are visible but less apparent in the C II, and it is
difficult to distinguish them in the Mg II k. Their time profiles were
impulsive; the intensities attained their peaks at approximately 1.5 min
before the peak of the soft X-ray intensity was attained. This was followed by
a prompt decrease in intensity in a few minutes. This temporal behavior is
similar to the Neupert effect (Neupert, 1968), which has been observed in
(non-thermal) hard X-rays pertaining to the soft X-ray (thermal) temporal
behavior. Moreover, the exact position of the footpoints was identified with
high spatial resolution maps of the magnetic flux density at the photosphere
from the Hinode SOT/SP with a spatial relation to bright kernels in Si IV.
Almost all the bright kernels are located in weak, void areas surrounded by
strong magnetic flux concentrations.

###  4.1 Height dependence

The Si IV (1400 Å ) filter is dominated by the Si IV 1394/1402 Å lines with
the continuum. The continuum is sensitive to the upper photosphere and low
chromosphere, but the Si IV lines are formed at an equilibrium temperature of
approximately 80,000 K, which corresponds to the temperature in the transition
region (Peter et al., 2014). The C II (1330 Å ) filter is dominated by C II
lines at 133.5 nm (upper chromosphere) with the continuum while the Mg II k
(2796 Å ) filter dominates the Mg II k (chromosphere) and inner wings
(photosphere). The C II and Mg II k lines are formed at similar heights below
the transition region, but the C II lines can be formed at a height higher and
lower than the core of the Mg II k line depending on the quantitative measure
of the materials in the temperature range of 14,000 – 50,000 K. Significant
amounts of materials in this temperature range form the C II lines at a height
higher than that of the Mag II k line core (Rathore and Carlsson, 2015;
Rathore et al., 2015).

Certain studies derived the mean brightness temperatures (with standard
deviation) of the 3 mm ALMA band 7,300 ($\pm 100$) K (White et al., 2017),
7,250 ($\pm 170$) K (Alissandrakis et al., 2017) for the disk center, and
7,250 ($\pm 1,140$) K (da Silva Santos et al., 2018) for radiative
magnetohydrodynamics (MHD) simulation of an enhanced network region. da Silva
Santos et al. (2018) studied the diagnostic potential of combined optical,
ultraviolet, and ALMA observations and showed that the response function to
temperature is at maximum at log $\tau=-5.6$, distributed between log
$\tau=[-6.0,-5.1]$, which is slightly higher or almost same as that of the Mg
II k line core, that is, the maximum at log $\tau=-5.5$, distributed between
log $\tau=[-6.4,-5.1]$, where $\tau$ is optical depthat 500 nm.

From these studies, we can interpret that the order of the mean temperature is
Si IV, C II, 100 GHz, and Mg II k from higher to lower temperatures.
Furthermore, C II, 100 GHz, and Mg II k are distributed in a small temperature
range at the upper chromosphere but below the transition region. Considering
the temperature distribution models of the solar atmosphere as a function of
height, the Mg II k image is located at the lowest height, followed by 100
GHz, C II, and Si IV toward the upper heights. This order of heights, with
particles impinging from the corona to the chromosphere, can explain the
observation at one of the footpoints for the soft X-ray microflare, that is,
more apparent signals were observed at Si IV, 100 GHz, C II, and Mg II k,
respectively.

###  4.2 Thermal energy supplied to the chromosphere

In Section 3.3, the thermal energy supplied to the chromosphere was estimated
on the assumption of thermal free-free radiation. The increased brightness
temperature from the ALMA signal was used for the excess in electron
temperature. This is valid when the optical thickness is unity or larger,
i.e., optically thick, at 100 GHz. The relationship between brightness
temperature and electron temperature can be written as

$T_{b}=T_{e}(1-e^{-\tau_{100}}),$ (5)

where $\tau_{100}$ is the optical thickness at 100 GHz (Kraus, 1986). As the
optical thickness decreases, the brightness temperature becomes smaller than
the electron temperature. For the optical thickness much smaller than the
unity, the brightness temperature can be approxiated by $\tau_{100}T_{e}$.

Alissandrakis et al. (2020) measured the brightness temperature from ALMA
center-to-limb observations at 100 GHz for magnetic bright networks. From the
inversion of this measurement, the electron temperature was derived as a
function of the optical thickness at 100 GHz for magnetic bright networks,
giving $7,383-7,916$ K where the optical thickness is unity at 100 GHz. They
also computed the electron temperature as a function of the optical thickness
using opacity from the model parameters of Model F, characterized as very
bright network element, of the FAL93 (Fontenla et al., 1993) model. The Model
F gives the electron temperature of 9,200 K for the optical thickness of unity
at 100 GHz. These values are only $0-25$ % increase from the mean brightness
temperatures at 100 GHz (Section 4.1) and thus equation (5) provides that the
optical thickness is about unity or higher. With this assessment, we conclude
no big difference for the order estimation of thermal energy supplied to the
chromosphere event if the brightness temperature is used as the electron
temperature. Similar treatment is applied by Nindos et al. (2020, 2021), which
derived the energy of transient brightenings observed in the quiet Sun with
ALMA.

We assumed thermal free-free radiation for the signals detected with ALMA.
Kontar et al. (2018) examined mm and UV radiations from bright flare ribbons
observed at various M- and X-class flares and showed that mm radiation
(including 100 GHz) is consistent with free-free radiation from the plasma of
flare ribbons at temperatures $10^{4}-10^{6}$ K, providing the assumption is
reasonable for the order estimation of a much smaller energy releasing event
examined in this study. However, the plasma may be in a dynamic state due to
the transient response of the flux of impinging particles, which can deviate
largely the mm radiation from what is expected by thermal free-free radiation.
As Morgachev et al. (2020) points out, it is important to consider not only
thermal flare plasma emission but also dynamics of accelerated electrons and
nonequillibrium effects on radiation transfer. Better understanding of these
effects would predict the intensity of the radiation at 100 GHz more
accurately and improve the accuracy of the energy estimation. Such efforts
will enhance the validity of the energy obtained in this study.

###  4.3 Energy partition

The thermal energy supplied to the chromosphere was estimated at $(2.2\pm
1.2)\times 10^{24}$ erg with the 100 GHz measurement. This is only 1% of the
thermal energy observed at the peak time of the soft X-ray brightening loop in
the corona, $(2.9\pm 1.0)\times 10^{26}$ erg. It is only 2% even when the same
amount of energy was transported to the two footpoints of the coronal loop.
Considering the temporal evolution of 100 GHz signals with respect to the soft
X-ray thermal evolution, the thermal energy from the 100 GHz measurement is
created by the particles impinging the dense layers. Thus, this estimated
energy can be regarded as the energy exhibited by non-thermal accelerated
particles required for the order estimation. The energy partition between the
thermal and non-thermal plasmas in solar flares has been an important issue in
the physics of magnetic reconnection and particle acceleration. For example,
Emslie et al. (2004) evaluated the energy budget for two X-class flares/CME
events and showed that the peak energy in the thermal soft X-ray plasma (in
the order of $10^{31}$ erg) is approximately one order of magnitude less than
the energy in the accelerated particles. Saint-Hilaire and Benz (2002) also
evaluated that the thermal energy of the flare kernel (approximately $10^{29}$
erg) was more than an order of magnitude smaller than the electron beam energy
for a smaller (C9.7 class) compact flare. More recent studies reported the
energy partition for more numbers of flares (Stoiser et al., 2007; Emslie et
al., 2012; Inglis and Christe, 2014; Warmuth and Mann, 2016a, b; Aschwanden et
al., 2017). However, they provided contradicting results on energy partition,
particularly for weak flares. For A- and B-class flares, Inglis and Christe
(2014) derived the ratio of nonthermal energy and peak thermal energy at a few
times of $10^{-1}$ for 10 events, whereas Stoiser et al. (2007) obtained
$10^{1}-10^{2}$ from 18 events. Warmuth and Mann (2020) reviewed these studies
and identified uncertainties in deriving the energy partition. Considering
these studies together with the identified uncertainties, they suggested that
the thermal–nonthermal energy partition changes with the flare importance; a
deficit of energetic electrons is observed in weak flares,while the nonthermal
energy is sufficient to account for the thermal component in strong flares.
However, we did not evaluate the energy partition for much smaller events.

Our observation detected one microflare with various instruments to discuss
the energy partition. However, it is only one event. Our result may suggest
that energetic electrons are much less generated when the magnitude of energy
release events decreases to the small energy group of microflares, that is,
$10^{26}$ erg. It is in the order of $10^{-2}$ in the case of the event
examined. Less number of energetic electrons may also mean that the heights
that the energetic electrons can impinge to are not low. Battaglia and Kontar
(2011) showed that the hard X-ray emission at 30 keV is approximately 1,000 km
above the photosphere. Moreover, the energy deposition rate as a function of
height for two different cases of electron cutoff energy shows that the
electrons of $12-20$ keV predominantly release the energy at $2,000-3,000$ km.
These heights correspond to the upper chromosphere or lower transition region
with a density of between $10^{11}$ cm-3 and $10^{12}$ cm-3, where the Si IV
line can be formed when compared to radio at 100 GHz, C II and Mg II k lines.

Energy deposition at the chromosphere by a beam of energetic electrons drives
strong chromospheric evaporation leading to a significantly denser corona and
much brighter emission in the corona. Flare model simulations indicate that
the energy flux of an electron beam required for explosive evaporation is
approximately $2\times 10^{9}$ erg cm-2 s-1 for 10 keV electrons and increases
to $10^{10}$ erg cm-2 s-1 for 20 keV electrons (Reep et al., 2015). Because
two bright kernels with a size of approximately $1\arcsec$ were observed in Si
IV, the area to which electron beams impoinge is approximately $1\times
10^{16}$ cm2. Assuming that 10 s is the duration at which electron
acceleration occurs, the beam energy threshold for turning on explosive
evaporation is estimated to be $2\times 10^{26}$ erg, which is two orders of
magnitude smaller than that of the energy deposition measured at the
chromosphere. Thus, explosive evaporation did not work in this event,
resulting in less amount of the heated plasma supplied to the coronal loop
structures. Considering the temperature response curve of the XRT Al-poly
filter, the magnitude of the observed soft X-ray increase can be expected with
a $1-2$ MK increase of temperature even when less amount of heated plasma is
supplied from the chromosphere. The soft X-ray morphological evaluation
(Figure 2) showed no transient brightening at the loop footpoints. In soft
X-ray microflares, the brightening loops brighten from their footpoints,
followed by the brightening of the entire loop (Shimizu et al., 1994).
However, in this event, the brightening loop gradually brightened from the
apex without brightening at the footpoints, followed by the brightening of the
entire loop.

###  4.4 Magnetic environment at the footpoint and configuration for energy
release

The exact location of the soft X-ray brightening loop was identified by
transient brightenings in high resolution Si IV images. The Si IV brightenings
consist of more than four bright kernels surrounded by diffuse intensity
increase. The bright kernels represent the location of magnetic flux in which
accelerated particles generated in the corona impinged the transition region.
Although the distance of the change is less than $1\arcsec$, the position of
the bright kernels changes with time frame by frame. This suggests that
particle acceleration occurs in the magnetic field lines connecting several
positions at the low atmosphere, and that the magnetic field lines associated
with particle acceleration change with time. Several positions of magnetic
field discontinuity exist in the magnetic structure relating to the microflare
in the corona if the energy release shows magnetic reconnection.

Comparison of the Si IV brightening kernels to the photospheric magnetic flux
map (Figure 5(f)) showed that all the brightening kernels are located in weak
magnetic areas surrounded by strong magnetic flux distribution. This means
that the heated coronal magnetic structures are rooted into the weak magnetic
fields at the photosphere. In such magnetic environment, the magnetic effects
such as mirror effect do not work and thus, they did not cause a deficit of
accelerated particles observed at the footpoint of this event.

This field connectivity is reasonable considering pressure balance; as the gas
pressure is higher in the brightening magnetic bundle than outside, the
pressure balance exhibits lower magnetic pressure in the bundle. Thus, the
magnetic flux density of the brightening loop structure may be lower than that
of the surroundings. When the brightening loop structure is formed with
magnetic reconnection, the field discontinuities for the reconnection may be
located between the magnetic field lines arising from the strong magnetic
islands just beside the Si IV brightening kernels. As the pressure of external
longitudinal magnetic fields changes, unstable current sheets may be formed
preferably around and along twisted magnetic flux ropes, as investigated by
Tsap et al. (2020) and Solov’ev and Kirichek (2021).

##  5 Summary

We investigated the footpoint behaviors of a soft X-ray loop-type microflare,
which was captured during an ALMA campaign coordinated with Hinode and IRIS
instruments. Counterparts at one footpoint of a brightening coronal loop were
detected in Si IV slit-jaw images and ALMA at 100 GHz, while they were less
apparent in the C II and Mg II k images. Their counterparts showed impulsive
temporal profiles, which were at peak during the rising phase of the soft
X-ray intensity, followed by the intensity backing to the pre-brightening
level at the peak time of the soft X-ray intensity. The magnitude of thermal
energy measured with ALMA is approximately 100 times smaller than that
measured in the corona. These results suggest that impulsive counterparts can
be detected in transition region and upper chromosphere at the footooints when
soft X-ray loop-type microflares occur in the corona. The impulsive
counterparts are considered as signals of thermal plasma heated at the upper
chromosphere or transition region by impinging non-thermal particles, although
we should consider the addition of polarization measurements in future. The
energy evaluation indicates a deficit of accelerated particles that impinge
the footpoints of a small class of soft X-ray microflares. The footpoint
counterparts consist of several tiny brightening kernels, all of which are
located in weak and void magnetic areas formed in strong magnetic flux patchy
distribution at the photospheric level. They provide a conceptual image in
which the transient energy release occurs at multiple numbers of discontinuity
formed on the sheaths of magnetic flux bundles in the corona.

To the best of our knowledge, the event presented in this article is a unique
case in which the ALMA, IRIS, and Hinode instruments captured the foopoint
behaviors of a small class of soft X-ray loop-like microflares. To understand
if footpoint behaivors presented in this article are common in microflares,
further observations should be conducted.

This study used the following ALMA data: ADS/JAO.ALMA#2016.1.00030.S. ALMA is
a partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. Hinode is a Japanese
mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and
NASA and STFC (UK) as international partners. It is operated by these agencies
in cooperation with ESA and NSC (Norway). The Hinode/SP level 2 data
(10.5065/D6JH3J8D) are provided by the Community Spectropolarimetric Analysis
Center at HAO/NCAR. IRIS is a NASA small explorer mission developed and
operated by LMSAL with mission operations executed at NASA Ames Research
center and major contributions to downlink communications funded by ESA and
the Norwegian Space Center. This work was partially supported by JSPS KAKENHI
Grant Number 15H05750, 15H05814, and 18H05234.

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