# X-Ray and Ultraviolet Flares on AT Microscopii Observed by AstroSat

Alexey A. Kuznetsov Institute of Solar-Terrestrial Physics, Irkutsk, 664033,
Russia  Department of Geography, Irkutsk State University, Irkutsk, 664033,
Russia  Ruslan R. Karakotov  Institute of Solar-Terrestrial Physics, Irkutsk,
664033, Russia  Kalugodu Chandrashekhar Rosseland Centre for Solar Physics,
University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway  Institute of
Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo,
Norway  Dipankar Banerjee Aryabhatta Research Institute of Observational
Sciences (ARIES), Manora Peak, Nainital-263 002, India  Indian Institute of
Astrophysics, Sarjapur Main Road, 2nd Block, Bangalore, Karnataka 560034,
India  Center of Excellence in Space Science, IISER Kolkata, Kolkata 741246,
India

###### Abstract

We present observations of the active M-dwarf binary AT Mic (dM4.5e+dM4.5e)
obtained with the orbital observatory AstroSat. During 20 ks of observations,
in the far ultraviolet ($130-180$ nm) and soft X-ray ($0.3-7$ keV) spectral
ranges, we detected both quiescent emission and at least five flares on
different components of the binary. The X-ray flares were typically longer
than and delayed (by $5-6$ min) with respect to their ultraviolet
counterparts, in agreement with the Neupert effect. Using X-ray spectral fits,
we have estimated the parameters of the emitting plasma. The results indicate
the presence of a hot multi-thermal corona with the average temperatures in
the range of $\sim 7-15$ MK and the emission measure of $\sim(2.9-4.5)\times
10^{52}$ $\textrm{cm}^{-3}$; both the temperature and the emission measure
increased during the flares. The estimated abundance of heavy elements in the
corona of AT Mic is considerably lower than at the Sun ($\sim 0.18-0.34$ of
the solar photospheric value); the coronal abundance increased during the
flares due to chromospheric evaporation. The detected flares had the energies
of $\sim 10^{31}-10^{32}$ erg; the energy-duration relations indicate the
presence of magnetic fields stronger than in typical solar flares.

stars: coronae — stars: flare — stars: late type — X-rays: stars —
ultraviolet: stars — stars: individual: AT Mic

††journal: Research in Astronomy and Astrophysics

##  1 Introduction

Many dwarf stars, including the Sun, demonstrate signatures of magnetic
activity, such as starspots, hot coronae, and flares (Gershberg, 2005). Cool
red dwarfs of dMe spectral type are usually much more active than the Sun,
which is manifested in stronger magnetic fields, hotter and denser coronae
with a persistent presence of nonthermal electrons, and more frequent and
powerful flares (Haisch et al., 1991; Güdel, 2002, 2004; Reiners, 2012);
nevertheless, the physical mechanisms responsible for the coronal heating and
flares are believed to be qualitatively similar to the solar ones.

Observations in the soft X-ray range provide an opportunity to study the
thermal plasma in the stellar coronae and determine its parameters, such as
density, temperature, emission measure, and chemical composition – both in the
quiescent state and during flares (Güdel, 2004). On the other hand, optical
and UV emissions of flares are produced in deeper layers of stellar
atmospheres (the chromosphere and transition region), in response to heating
of these layers by nonthermal electron beams (Benz & Güdel, 2010); the optical
continuum is responsible for the most part of the radiated flare energy
(Kretzschmar, 2011). Simultaneous observations in different spectral ranges
(e.g., soft X-rays and UV) are of special interest, because they allow one to
study the processes at different layers of a stellar atmosphere and, in
particular, investigate correlations between thermal and nonthermal processes.
While the Sun is continuously observed by many instruments providing a broad
spectral coverage (from radio to $\gamma$-rays), multiwavelength observations
of flares on other stars are much less common. Thus expanding the dataset of
such observations (both for the same or for different targets) is highly
important, because it improves the reliability of the derived physical models,
as well as allows one to study long-term variations of the stellar active
phenomena, including activity cycles.

In this work, we investigate the well-known active M-dwarf binary AT Mic using
observations with the orbital observatory AstroSat; manifestations of stellar
activity were detected in X-ray and UV spectral ranges. We analyze the
characteristics of the coronal plasma in the quiescent and flaring states; we
also investigate the relationship between the X-ray and UV flares. We compare
the obtained results with earlier observations of AT Mic and other red dwarfs,
as well as with observations and models of solar flares.

##  2 Observations

###  2.1 Target

AT Mic is a visual binary consisting of two almost identical red dwarfs of
spectral type dM4.5e (Joy & Abt, 1974), at a distance of 9.86 pc (Gaia
Collaboration, 2020). The binary is sufficiently wide, with a semi-major axis
of $\sim 31$ au and an orbital period of about 209 years (Malkov et al.,
2012), so that interaction between the components is negligible; i.e., in
terms of magnetic activity, they can be considered as two separate single
stars. AT Mic is believed to be a member of the $\beta$ Pictoris association,
with an age of $\sim 25$ Myr (Messina et al., 2017). The rotation periods of
the components A and B are of 1.19 and 0.78 days, respectively (Messina et
al., 2016, 2017); the bolometric luminosities of the components A and B have
been estimated as $1.3\times 10^{32}$ and $1.2\times 10^{32}$ erg
$\textrm{s}^{-1}$ (0.034 and 0.031 $L_{\sun}$), respectively (Messina et al.,
2017). Both components are known to be magnetically active (e.g., Gershberg et
al., 1999).

Due to its proximity and high activity level, AT Mic has been a target of many
observations in different spectral ranges. Powerful optical flares with
energies of up to $\sim 4\times 10^{33}$ erg were reported by Kunkel (1970);
Nelson et al. (1986); García-Alvarez et al. (2002), etc. Pallavicini et al.
(1990); Raassen et al. (2003); Robrade & Schmitt (2005), etc. observed AT Mic
in the soft X-ray range and detected quiescent emission of hot coronal plasma
with a luminosity of $\sim 2\times 10^{29}$ erg $\textrm{s}^{-1}$, as well as
a number of flares with energies of up to $\sim 1.3\times 10^{33}$ erg. Linsky
et al. (1982); Elgaroy et al. (1988); Monsignori Fossi et al. (1995), etc.
detected quiescent chromospheric emission and flares in the UV range, while
Mitra-Kraev et al. (2005) investigated correlations between X-ray and UV
flares. The durations of the detected flares varied from less than one minute
up to about one hour, with the above mentioned energies corresponding to the
longest and most powerful flares.

###  2.2 Observations with AstroSat

We observed AT Mic with the instruments onboard the AstroSat satellite (Singh
et al., 2014; Agrawal, 2017), on 2018 October 3-4. The primary instrument was
the Soft X-ray Telescope (SXT) – an X-ray telescope with focusing mirrors that
provides X-ray imaging and spectroscopy in the nominal energy range of $0.3-8$
keV with the energy channel width of 0.01 keV (Singh et al., 2016, 2017). The
SXT operated in the photon counting mode; the total exposure time was 20 ks. A
half of that time was also covered by high-resolution imaging observations
with the Ultra-Violet Imaging Telescope (UVIT) (Tandon et al., 2017a, b) in
the far ultraviolet channel (FUV, $130-180$ nm), in the photon counting mode;
the F148W filter with the $125-175$ nm bandpass was used. The target was
detected by both of these instruments, thus providing simultaneous
observations in the two spectral ranges for $\sim 10$ ks.

Simultaneously, AT Mic was observed with two other X-ray detectors: the Large
Area X-ray Proportional Counter (LAXPC) (Yadav et al., 2016; Agrawal et al.,
2017) in the $3-100$ keV energy range, and the Cadmium Zinc Telluride Imager
(CZTI) (Bhalerao et al., 2017) in the $25-150$ keV energy range. However, no
reliable signal of stellar origin was detected by these instruments, due to
either insufficient sensitivity (for the CZTI, given that the X-ray flux
decreases rapidly with energy) or a high and rapidly varying instrumental
background (for the LAXPC); we do not analyze these observations here.

Multiwavelength observations (including the soft X-ray and UV spectral ranges)
of AT Mic and other active red dwarfs have been performed earlier with the
XMM-Newton observatory (e.g., Mitra-Kraev et al., 2005; Tsang et al., 2012;
Perdelwitz et al., 2018). In comparison with the XMM-Newton European Photon
Imaging Camera (EPIC) (Strüder et al., 2001; Turner et al., 2001), the
AstroSat SXT has a lower sensitivity to the soft X-rays, which requires longer
accumulation times or time bins to obtain a reliable signal from the same
source. On the other hand, in comparison with the XMM-Newton Optical Monitor
(OM) (Mason et al., 2001), the AstroSat UVIT has considerably better
sensitivity and angular resolution in the far UV range, which allows one to
study the morphology and light curves of UV sources with much finer details.

Figure 1: UV (a) and X-ray (b) images of AT Mic from the AstroSat UVIT FUV and
SXT observations on 2018 October 3-4, for the entire observation intervals.
The color bars are in units of counts $\textrm{s}^{-1}$ $\textrm{pixel}^{-1}$.
The blue or white circles show the extraction regions for light curves and
spectra.

##  3 Results

###  3.1 Images

Figure 1 demonstrates the images of AT Mic obtained with the AstroSat UVIT FUV
and SXT, integrated over the entire duration of the observations. Figure 1a
shows a fragment of the UVIT field of view; the binary components are
partially resolved with the component A (the northern one) being slightly
brighter. Figure 1b shows the full SXT field of view (photons in the energy
range of $0.3-7$ keV were selected, because at higher energies the signal
might be contaminated by instrumental noise); the bright spots at the corners
of the detector matrix are the internal calibration sources. The X-ray photons
are scattered over a relatively wide area, so that the binary components are
not resolved; nevertheless, the X-ray centroid position coincides with the AT
Mic position with an accuracy of $\sim 1.5^{\prime}$, and there are no other
candidate X-ray sources in this region of the sky.

The circles in Figure 1 show the regions used to extract the UV and X-ray
light curves and X-ray spectra. For the UV emission, we mainly consider the
total flux from both components of the binary, within a radius of
$4.2^{\prime\prime}$. Since the components are resolved only partially, we
cannot separate the fluxes from them completely; the partial fluxes from the
individual binary components (from the regions shown by white dashed circles
with a diameter of $1.5^{\prime\prime}$, corresponding to the overall FWHM of
the UVIT FUV) are analyzed only qualitatively – to identify the component
where a flare occurred. For the total X-ray flux, we use the extraction region
with a radius of $16^{\prime}$, which contains more than 96.5% of the source
photons (according to the point spread function presented in the AstroSat
Handbook111http://www.iucaa.in/~astrosat/AstroSat_handbook.pdf).

Figure 2: X-ray (top) and UV (bottom) light curves of AT Mic from the AstroSat
SXT and UVIT FUV observations on 2018 October 3-4, with 300 s time bins. The
error bars correspond to the $1\sigma$ level. The blue dashed lines represent
the estimated quiescent (non-flaring) background fluxes. The AstroSat orbit
numbers are shown at the tops of the panels, with the supposed flaring or (for
X-rays) quiescent-only time intervals indicated by red or blue colors,
respectively.

###  3.2 Light Curves

####  3.2.1 Light curves: overview

Figure 2 demonstrates the total (i.e., combining the fluxes from both
components of the binary) X-ray and UV light curves of AT Mic, with the time
bin size of 300 s. Due to periodic occultations of the target by the Earth,
the light curves are not continuous but consist of a number of shorter time
intervals (orbits); due to stricter visibility constraints, the UVIT FUV
observing intervals are shorter than those for the SXT, and the UVIT
observations ceased after the first eight orbits. For the X-ray light curve,
photons in the energy range of $0.3-7$ keV were selected and the instrumental
background provided by the SXT
team222https://www.tifr.res.in/~astrosat_sxt/dataanalysis.html was subtracted;
for the UV observations, the instrumental background is negligible.

Table 1: Parameters of the flares detected on AT Mic: sources (i.e.,
components of the binary where the flares occurred), decay times in the X-ray
($\tau_{\mathrm{X}}$) and UV ($\tau_{\mathrm{UV}}$) ranges, delays of the
X-ray flares with respect to the corresponding UV flares ($\Delta
t_{\mathrm{X}-\mathrm{UV}}$), peak luminosities in the X-ray range
($L_{\mathrm{X}}^{\max}$) and in the optical continuum
($L_{\mathrm{cont}}^{\max}$), emitted energies in the X-ray range
($E_{\mathrm{X}}$) and in the optical continuum ($E_{\mathrm{cont}}$), and
estimated (following the scaling laws by Namekata et al., 2017) sizes of the
flaring regions ($L$) and magnetic field strengths in these regions ($B$).

Flare | Source |  $\tau_{\mathrm{X}}$, |  $\tau_{\mathrm{UV}}$, |  $\Delta t_{\mathrm{X}-\mathrm{UV}}$, |  $L_{\mathrm{X}}^{\max}$, |  $L_{\mathrm{cont}}^{\max}$, |  $E_{\mathrm{X}}$, |  $E_{\mathrm{cont}}$, |  $L$, |  $B$,
---|---|---|---|---|---|---|---|---|---|---
|  | min | min | min |  $10^{29}$ erg $\textrm{s}^{-1}$ |  $10^{29}$ erg $\textrm{s}^{-1}$ |  $10^{31}$ erg |  $10^{31}$ erg |  $10^{9}$ cm | G
F1 | B | $7.88{\pm}7.57$ | $3.67{\pm}1.44$ | $4.87{\pm}1.72$ | $0.46_{-0.19}^{+0.21}$ | $0.92_{-0.62}^{+1.19}$ | $2.19_{-0.68}^{+0.77}$ | $3.03_{-1.94}^{+3.50}$ | $4.46_{-1.48}^{+1.48}$ | $101.1_{-33.6}^{+58.0}$
F2 | B | $\cdots$ | $2.78{\pm}1.15$ | $5.21{\pm}1.72$ | $\cdots$ | $1.19_{-0.77}^{+1.43}$ | $\cdots$ | $2.20_{-1.41}^{+2.56}$ | $3.75_{-1.28}^{+1.27}$ | $112.0_{-37.9}^{+67.7}$
F3 | B | $7.45{\pm}5.90$ | $6.54{\pm}2.68$ | $0.57{\pm}1.72$ | $0.64_{-0.21}^{+0.23}$ | $1.35_{-0.87}^{+1.58}$ | $4.14_{-0.93}^{+0.99}$ | $6.71_{-4.10}^{+6.89}$ | $6.59_{-2.17}^{+2.12}$ | $83.8_{-27.4}^{+48.7}$
F4 | A, B | $10.62{\pm}3.97$ | $\cdots$ | $\gtrsim(5.61{\pm}1.72)$ | $1.05_{-0.26}^{+0.31}$ | $1.27_{-0.84}^{+1.60}$ | $8.71_{-1.40}^{+1.68}$ | $>5.27_{-3.27}^{+5.64}$ | $\cdots$ | $\cdots$
F5 | A | $9.31{\pm}7.00$ | $4.30{\pm}0.85$ | $5.07{\pm}1.72$ | $0.73_{-0.22}^{+0.26}$ | $2.69_{-1.65}^{+2.81}$ | $3.77_{-0.88}^{+1.05}$ | $\gtrsim 6.81_{-4.12}^{+6.82}$ | $\gtrsim 5.59_{-1.34}^{+1.31}$ | $\gtrsim 108.0_{-27.5}^{+33.6}$

Note. — The peak luminosities ($L_{\mathrm{X}}^{\max}$ and
$L_{\mathrm{cont}}^{\max}$) and emitted energies ($E_{\mathrm{X}}$ and
$E_{\mathrm{cont}}$) of the flares were estimated using Equations (7–11), as
described in Section 4.3.1.

Identifying the flaring and non-flaring (quiescent) time intervals in our
observations is not straightforward, because of the above mentioned gaps in
the light curves, and also because of a high activity level: AT Mic spends in
a flaring state $\sim 25\%$ of time, according to Messina et al. (2016), or
even more than $50\%$ of time, according to Kunkel (1970). We determined the
quiescent background levels by iterative fitting the light curves with linear
functions and removing the data points that exceeded these fits by more than
$1\sigma$; this procedure effectively provides a linear fit to the lower
envelope of a light curve. The X-ray quiescent background tends to increase
with time – probably, reflecting the stellar rotation and/or evolution of
active regions; the UV quiescent background also demonstrates a weak increase
with time.

We consider the time intervals where the UV and/or X-ray fluxes exceeded the
respective quiescent background levels by more than $3\sigma$ as candidate
flares. We have identified five such flaring events scattered over four
AstroSat orbits (namely, orbits #16300, #16302, #16306, and #16307; see the
next Section for details). In addition, we have selected in the X-ray light
curve two time intervals with the lowest flux (namely, orbits #16303 and
#16308), which we consider as a “quiescent state”, although these intervals
could still contain weaker unresolved flares.

Figure 3: X-ray and UV light curves for the selected time intervals (cf.
Figure 2) where flaring activity was detected. For the UV emission, both the
total flux from the AT Mic system and the fluxes corresponding to its
individual components are shown. The fluxes are in counts $\textrm{s}^{-1}$;
the time bins are 180 s and 100 s for the X-ray and UV light curves,
respectively. The error bars correspond to the $1\sigma$ level. The flare IDs
used in the text are shown next to the red arrows. The vertical dotted lines
show the flare start/end times used in the analysis, while the continuous
magenta curves represent the exponential fits (1) to the light curves at the
flare decay phases.

####  3.2.2 Light curves of flares

We show in Figure 3 enlarged fragments of the light curves for the time
intervals containing flares. Together with the total (unresolved) X-ray and UV
light curves of AT Mic, we show the UV light curves corresponding to the
individual components of the binary. The time bins are reduced (in comparison
to Figure 2) to 180 s for the X-rays and 100 s for the UV emission. The basic
characteristics of the detected flares are summarized in Table 1. In
particular, the $e$-folding decay times of the flares $\tau_{\mathrm{X}}$ and
$\tau_{\mathrm{UV}}$ (which we use to characterize the flare durations) are
estimated by least-squares fitting the flare decay phases in the total light
curves shown in Figure 3 with exponential functions in the form

$I(t)=I_{\mathrm{bg}}(t)+A\exp\left(-\frac{t-t_{\mathrm{peak}}}{\tau}\right),\qquad
t\geq t_{\mathrm{peak}},$ (1)

where $I(t)$ is the flux in the considered spectral band, $I_{\mathrm{bg}}(t)$
is the estimated quiescent background flux, and $t_{\mathrm{peak}}$ is the
flare peak time. The delays between the X-ray and UV flares $\Delta
t_{\mathrm{X}-\mathrm{UV}}$ are defined as delays between the respective flare
peaks; the uncertainty in estimating the delays $\sigma_{\mathrm{X-UV}}$ is
estimated as $\sigma_{\mathrm{X-UV}}^{2}=(\Delta t_{\mathrm{X}}/2)^{2}+(\Delta
t_{\mathrm{UV}}/2)^{2}$, where $\Delta t_{\mathrm{X}}$ and $\Delta
t_{\mathrm{UV}}$ are the time bins of the X-ray and UV light curves,
respectively.

In the total UV light curve in Figure 3a, one can see two well-defined flares,
peaked at around 09:07 and 09:19 UT, both with “classical” flare profiles
consisting of a sharp rise and a slower exponential decay. Comparison with the
light curves of the individual binary components indicates that both flares
occurred on the component B. The flares are relatively short – with durations
of just a few minutes. In the X-ray light curve, one can see a flare (again,
with a “classical” profile) peaked at around 09:12 UT, which likely
corresponds to the UV flare F1; however, the X-ray flare is longer than (with
the characteristic decay time $\tau_{\mathrm{X}}\simeq 2\tau_{\mathrm{UV}}$)
and delayed by $\sim 5$ min with respect to its UV counterpart. Later, at
around 09:24 UT, there is a barely noticeable X-ray peak – possibly, a
counterpart of the UV flare F2. We cannot determine reliably the decay time of
this supposed X-ray flare; however, like in the previous event, the X-ray peak
is delayed with respect to the UV flare peak by $\sim 5$ min.

In the total light curves in Figure 3b, one can see a flare (F3) that peaked
at around 12:24 UT, nearly simultaneously in the X-ray and UV ranges; the UV
flare occurred on the component B. In contrast to the previous two flares, the
UV flare F3 has a more complicated profile – likely, a result of overlapping
of several partially resolved flaring events. The X-ray flare F3 has a nearly
triangular shape with comparable rise and decay times. The delay between the
X-ray and UV peaks is almost absent, and the flare durations in both spectral
ranges are similar ($\tau_{\mathrm{X}}\simeq\tau_{\mathrm{UV}}$).

The time interval shown in Figure 3c contains the largest and longest X-ray
flare (F4) among the detected ones, with a “classical” flare profile, peaked
at around 18:54 UT. Interpretation of the UV light curves is less
straightforward: at the beginning of the time interval, one can see a UV peak
– likely, a tail of a powerful flare occurred on the component A; if this UV
flare indeed corresponds to the X-ray flare F4, the delay between the X-ray
and UV flares is at least of $5-6$ min. Later, at around 18:53 UT, there is a
weaker UV flare on the component B, which, however, is not pronounced in the
total UV light curve. Because of a complicated time profile, we cannot
estimate reliably the duration of the UV flare. The profile of the X-ray flare
is also most likely a result of overlapping of two flares occurred on
different components of the binary.

Finally, the time interval shown in Figure 3d contains another well-defined
X-ray flare (F5) and its UV counterpart, both with “classical” flare profiles,
peaked at around 20:42 and 20:37 UT, respectively; the UV flare occurred on
the component A. The UV flare was observed only partially; nevertheless, we
can estimate its characteristic decay time. The X-ray flare is longer than
(with $\tau_{\mathrm{X}}\simeq 2\tau_{\mathrm{UV}}$) and delayed by $\sim 5$
min with respect to the corresponding UV flare.

###  3.3 X-Ray Spectral Analysis

We analyzed the SXT X-ray spectra in the energy range of $0.3-7$ keV using the
OSPEX package (Tolbert & Schwartz, 2020) and the SXT instrumental background
spectrum and response files provided by the SXT team2. Model X-ray spectra
were fitted to the observations using the Markov Chain Monte Carlo (MCMC)
approach; the MCMC sampling implementation by Anfinogentov et al. (2021) was
used. Among several spectral models (see the examples and discussion in
Appendix A), the best agreement with the observations was achieved using the
model multi_therm_gauss that describes optically thin bremsstrahlung radiation
from multi-thermal plasma with a Gaussian dependence of the differential
emission measure (DEM) on the logarithm of the temperature ($T$):

$\mathrm{DEM}(T)=\mathrm{DEM}_{0}\exp\left[-\frac{(\log T-\log
T_{0})^{2}}{2\sigma_{T}^{2}}\right],$ (2)

with $\mathrm{DEM}_{0}$, $T_{0}$, and $\sigma_{T}$ being the parameters of the
Gaussian. The corresponding total emission measure (EM) and average plasma
temperature $(\left<T\right>)$ are given by the formulae:

$\mathrm{EM}=\left(\sqrt{2\pi}\ln
10\right)\mathrm{DEM}_{0}T_{0}\sigma_{T}\exp\left(\frac{1}{2}\sigma_{T}^{2}\ln^{2}10\right),$
(3) $\left<T\right>=T_{0}\exp\left(\frac{3}{2}\sigma_{T}^{2}\ln^{2}10\right).$
(4)

The spectral model depended also on the abundance of heavy elements $Z$,
relative to the solar abundance; the ratios between the elements were fixed to
the solar values.

Figure 4: Top: X-ray spectrum of AT Mic from the AstroSat SXT observations on
2018 October 3-4, averaged over the entire interval of observations. At higher
energies, the original spectrum was rebinned over $2-65$ channels ($0.02-0.65$
keV). The error bars correspond to the $1\sigma$ level. The solid red line
represents a model spectral fit with the multi-thermal plasma emission model
given by Equation (2). Bottom: normalized residuals of the model spectral fit,
in units of the $1\sigma$ uncertainties.

To account for the interstellar absorption, we used the model by Morrison &
McCammon (1983). The absorption column density was fixed to the value of
$N_{\mathrm{H}}=3\times 10^{19}$ $\textrm{cm}^{-2}$ that was estimated using
the optical extinction of $A_{V}=0.017$ mag reported by Malkov et al. (2012)
and the empirical relation of $N_{\mathrm{H}}=1.79\times 10^{21}A_{V}$
$\textrm{cm}^{-2}$ $\textrm{mag}^{-1}$ by Predehl & Schmitt (1995). The effect
of the interstellar absorption was found to be minor, and considering the
absorption column density as a free parameter has not significantly affected
the obtained results.

Table 2: Parameters of the X-ray spectral fits for the selected time intervals: emission measures (EM), average temperatures ($\left<T\right>$), relative widths of the DEM distribution ($\sigma_{T}$), and abundances of heavy elements ($Z$). | EM, |  $\left<T\right>$, |  $\sigma_{T}$, |  $Z$,
---|---|---|---|---
|  $10^{52}$ $\textrm{cm}^{-3}$ | keV | $\log(\mathrm{keV})$ | $Z_{\sun}$
Total | $3.54_{-0.11}^{+0.12}$ | $0.728_{-0.020}^{+0.028}$ | $0.168_{-0.016}^{+0.021}$ | $0.192_{-0.014}^{+0.021}$
Quiescent | $2.92_{-0.29}^{+0.29}$ | $0.637_{-0.033}^{+0.053}$ | $0.131_{-0.047}^{+0.050}$ | $0.176_{-0.031}^{+0.070}$
Flare F1 | $3.33_{-0.65}^{+0.60}$ | $0.680_{-0.054}^{+0.169}$ | $0.117_{-0.058}^{+0.122}$ | $0.185_{-0.047}^{+0.192}$
Flare F3 | $3.21_{-0.53}^{+0.45}$ | $1.028_{-0.100}^{+0.464}$ | $0.238_{-0.060}^{+0.100}$ | $0.338_{-0.062}^{+0.282}$
Flare F4 | $4.42_{-0.43}^{+0.66}$ | $1.199_{-0.159}^{+1.335}$ | $0.384_{-0.074}^{+0.300}$ | $0.273_{-0.056}^{+0.156}$
Flare F5 | $3.45_{-0.47}^{+0.61}$ | $0.842_{-0.078}^{+0.417}$ | $0.214_{-0.054}^{+0.167}$ | $0.313_{-0.074}^{+0.205}$

We performed the spectral fitting of the SXT spectra in several time
intervals, including all reliably detected X-ray flares (i.e., the flares F1
and F3-F5, with the used start/end times of the flaring intervals shown by
vertical dotted lines in the X-ray light curves in Figure 3) and the
“quiescent” state (defined as a combination of two AstroSat orbits with the
lowest X-ray flux, i.e. orbits #16303 and #16308), as well as for the entire
(total) duration of the observations. An example of the SXT X-ray spectrum of
AT Mic, together with the best-fit spectral model, is shown in Figure 4 (we
note that, for illustration purposes, the spectrum in Figure 4 was rebinned to
reduce the number of points at high energies, while the spectral analysis was
performed using the original spectral resolution). The obtained best-fit
parameters of the emitting plasma are summarized in Table 2 and demonstrated
in Figure 5.

##  4 Discussion

###  4.1 Light Curves

####  4.1.1 Neupert effect

As can be seen in Figure 3 and Table 1, light curves of flares F1 and F5 (and,
possibly, flare F2) demonstrate the so-called Neupert effect (Neupert, 1968),
when the soft X-ray flares are longer than and delayed with respect to the
corresponding UV flares; the delays ($\sim 5$ min) are similar in all three
flares. The major UV flare F4 (on AT Mic A) was observed only partially;
nevertheless, the light curves indicate a delay of at least $5-6$ min between
the X-ray and UV peaks, in agreement with the Neupert effect. In the
“standard” flare model (e.g., Benz & Güdel, 2010), this effect occurs because
the optical or UV emissions represent a direct (and immediate) response of the
chromosphere to heating by nonthermal electrons, while the soft X-rays are
produced by heated plasma evaporated from the chromosphere to the corona, with
the emission intensity proportional to the cumulative (time-integrated)
nonthermal energy input.

On the other hand, the flare F3 demonstrates no significant delay between the
X-ray and UV peaks, and the flare durations in both spectral ranges are
similar, i.e., the Neupert effect is not pronounced. Probably, this is caused
by a complicated (with several separate peaks, as indicated by the UV light
curve) dynamics of energy release in this flare, when the
chromospheric/coronal responses to separate acts of particle acceleration are
mixed together.

The Neupert effect is often (but not always) observed in solar and stellar
flares (e.g., Benz & Güdel, 2010). Mitra-Kraev et al. (2005), using soft X-ray
and UV observations with XMM-Newton, detected the Neupert effect in flares on
several red dwarfs, including AT Mic, although the reported X-ray-to-UV flare
delays on AT Mic ($\sim 17$ min) were longer than in our observations. Most
likely, this difference is caused by the selection effect: due to a higher
sensitivity and hence shorter time bins of the AstroSat UVIT (in comparison
with the XMM-Newton OM), the flares detected in the UV range in this study
were much shorter and weaker than those reported by Mitra-Kraev et al. (2005),
and had respectively shorter delays between the X-ray and UV peaks.

####  4.1.2 Activity levels of the binary components

In total, in the UV range (where the binary components were partially
resolved) we detected four flares on the component B and one or two (if we
count here the partially observed flare F4) flares on the component A, i.e.,
the component B was considerably more active. A similar conclusion follows
indirectly from the spatially resolved observations of AT Mic in the microwave
range reported by Kundu et al. (1987): in that work, flaring activity was
detected on both components of the binary, with the southern component (AT Mic
B) demonstrating a stronger variability and higher microwave fluxes, although
individual flares could not be identified due to short duration of the
observations and insufficient time resolution. If confirmed, a higher magnetic
activity of AT Mic B is most likely related to the faster rotation of this
component, which results in a more efficient dynamo action (e.g., Brun &
Browning, 2017). On the other hand, we note that the number of detected flares
in our study was too small to make a statistically significant conclusion.

Figure 5: X-ray spectral fit parameters: average plasma temperatures (a) and
abundances (b) vs. emission measures in the corona of AT Mic for different
time intervals. The error bars correspond to the $1\sigma$ level. The dashed
lines in panels (a) and (b) represent model fits given by Equations (5) and
(6), respectively.

###  4.2 X-Ray Spectral Fits

####  4.2.1 Coronal temperatures and emission measures

Figure 5a shows the results of the X-ray spectral analysis – the emission
measures and average plasma temperatures for different time intervals (we note
that these parameters are actually either summed or averaged over both
components of the binary). In the supposedly quiescent state, the emission
measure and average temperature are of $\sim 2.9\times 10^{52}$
$\textrm{cm}^{-3}$ and $\sim 7.4$ MK, respectively. During flares, both the
emission measure and average temperature increase considerably, while the
time-averaged parameters for the entire duration of the observations are
intermediate between the quiescent and flaring values.

Since we analyze the total emission spectra and do not separate the flaring
and non-flaring spectral components, the obtained plasma temperatures during
flares actually represent weighted averages of the temperatures in the
quiescent coronae and in the flaring regions, which can be expressed as

$\left<T\right>=\frac{T_{\mathrm{q}}\mathrm{EM}_{\mathrm{q}}+T_{\mathrm{flare}}(\mathrm{EM}-\mathrm{EM}_{\mathrm{q}})}{\mathrm{EM}},$
(5)

where $T_{\mathrm{q}}$ and $\mathrm{EM}_{\mathrm{q}}$ are respectively the
temperature and emission measure in the quiescent state, and
$T_{\mathrm{flare}}$ is the plasma temperature in a flaring region. We have
fitted Equation (5) to the observations assuming that the temperatures
$T_{\mathrm{flare}}$ in all flaring regions are approximately the same (which
is a very crude assumption) and excluding the “total” data point; the best
agreement has been achieved for $T_{\mathrm{flare}}$ of about $31.8\pm 20.0$
MK. Similar temperatures ($\sim 7-8$ MK and $\sim 28-34$ MK, respectively) of
the quiescent and flaring plasma components in the coronae of AT Mic were
reported earlier in the papers of Raassen et al. (2003) and Robrade & Schmitt
(2005), where these components were resolved spectrally.

####  4.2.2 Coronal abundances

Figure 5b shows the emission measures and coronal abundances of heavy elements
for different time intervals. In the supposedly quiescent state, the coronal
abundance takes its lowest value of about 0.18 of the solar photospheric
abundance. The photospheric abundance for AT Mic is not exactly known;
however, assuming it to be similar to that for other members of the $\beta$
Pictoris association ($\sim 1.12$ of the solar one for $\beta$ Pic itself,
according to Gray et al., 2006), we conclude that the corona of AT Mic is
considerably depleted in heavy elements in comparison to the photosphere.

As can be seen from Figure 5b, the coronal abundance tends to increase during
flares. Most likely, this increase is caused by the chromospheric evaporation:
during flares, the material from lower atmospheric layers is heated and
expands upward into the coronal flaring loops, thus enriching the corona with
heavy elements (we remind that in this study the measured abundances during
flares actually represent weighted averages of the abundances in the quiescent
coronae and in the flaring regions). The time-averaged coronal abundance
($\sim 0.19$ of the solar photospheric abundance) is intermediate between the
quiescent and flaring values, and is consistent with the coronal abundances
for AT Mic reported by Robrade & Schmitt (2005). An increase of the coronal
abundance during flares has been observed earlier on M dwarfs (e.g., Favata et
al., 2000; Liefke et al., 2010), RS CVn binaries (e.g. Pandey & Singh, 2012),
and other active stars (e.g, Güdel et al., 2001).

Similarly to Equation (5), the average coronal abundance during flares
(affected by the chromospheric evaporation) can be expressed in the form

$\left<Z\right>=\frac{Z_{\mathrm{q}}\mathrm{EM}_{\mathrm{q}}+Z_{\mathrm{chromo}}(\mathrm{EM}-\mathrm{EM}_{\mathrm{q}})}{\mathrm{EM}},$
(6)

where $Z_{\mathrm{q}}$ and $Z_{\mathrm{chromo}}$ are the coronal abundance in
the quiescent state and the chromospheric abundance, respectively. We have
fitted Equation (6) to the observations (excluding the “total” data point);
the best agreement has been achieved for the chromospheric abundance
$Z_{\mathrm{chromo}}$ of about $0.53\pm 0.32$ of the solar photospheric
abundance. We note that the obtained value of $Z_{\mathrm{chromo}}$ should be
considered as an effective one, because the used model does not account for
the dynamics of the chromospheric evaporation process as well as for the
physical processes responsible for the underabundance of heavy elements in the
corona.

###  4.3 Flare Energies

####  4.3.1 Energy estimations

We estimate the total radiated energy of a stellar flare $E^{\mathrm{flare}}$
as

$E^{\mathrm{flare}}=\sum\limits_{t}L^{\mathrm{flare}}(t)\Delta t,$ (7)

where $L^{\mathrm{flare}}(t)$ is the time-dependent flare luminosity in the
considered spectral band (see below) and $\Delta t$ is the width of the time
bin. The summation was performed over the time intervals bounded by vertical
dotted lines in the total light curves in Figure 3. The flare luminosity in
the X-ray range is given by (see Mitra-Kraev et al., 2005; Kuznetsov &
Kolotkov, 2021)

$L^{\mathrm{flare}}_{\mathrm{X}}(t)=\frac{\left<L_{\mathrm{X}}\right>}{\left<I_{\mathrm{X}}\right>}\left[I_{\mathrm{X}}(t)-I_{\mathrm{X}}^{\mathrm{bg}}(t)\right],$
(8)

where $I_{\mathrm{X}}(t)$ is the total X-ray light curve (counts
$\textrm{s}^{-1}$), $I_{\mathrm{X}}^{\mathrm{bg}}(t)$ is the corresponding
quiescent background X-ray flux, $\left<I_{\mathrm{X}}\right>$ is the average
total X-ray flux in the selected time interval, and
$\left<L_{\mathrm{X}}\right>$ is the average total X-ray luminosity in the
selected time interval. The latter quantity is estimated using a spectral fit:

$\left<L_{\mathrm{X}}\right>=2\pi
d^{2}\int\limits_{E_{\min}}^{E_{\max}}F(E)E\,\mathrm{d}E,$ (9)

where $d$ is the distance to the target, $F(E)$ is the model X-ray spectral
flux density, and the flux in the spectral range from $E_{\min}$ to $E_{\max}$
is considered ($0.3-7$ keV in this work); this formula represents the energy
flux from an optically thin source into the upper hemisphere. The peak X-ray
luminosities $L_{\mathrm{X}}^{\max}$ of the flares detected on AT Mic
(computed using the spectral fits described in Section 3.3) are presented in
Table 1.

The flare luminosity in the AstroSat FUV spectral band is given by

$L^{\mathrm{flare}}_{\mathrm{FUV}}(t)=\pi
d^{2}G\left[I_{\mathrm{FUV}}(t)-I_{\mathrm{FUV}}^{\mathrm{bg}}(t)\right],$
(10)

where $I_{\mathrm{FUV}}(t)$ is the total UV light curve (counts
$\textrm{s}^{-1}$), $I_{\mathrm{FUV}}^{\mathrm{bg}}(t)$ is the corresponding
quiescent background UV flux, and $G$ is the count rate to flux conversion
factor which equals $1.545\times 10^{-12}$ erg $\textrm{count}^{-1}$
$\textrm{cm}^{-2}$ for the UVIT FUV instrument with the F148W
filter333https://uvit.iiap.res.in/Instrument/Filters; this formula represents
the energy flux from an optically thick flat source into the upper hemisphere.
While the AstroSat SXT spectral range covers most of the thermal X-ray
radiation from stellar flares, the AstroSat UVIT FUV spectral band contains
only a small fraction of a flare radiation. Following Brasseur et al. (2019)
and Fleming et al. (2022), we assume that the UV radiation of a flare can be
described as a blackbody radiation of hot flare ribbons, and estimate the
bolometric flare luminosity $L_{\mathrm{cont}}^{\mathrm{flare}}$ by
extrapolating the luminosity in the FUV spectral band (10) to the entire
optical continuum:

$L_{\mathrm{cont}}^{\mathrm{flare}}=L_{\mathrm{FUV}}^{\mathrm{flare}}\frac{\int\limits_{0}^{\infty}B(\lambda,T_{\mathrm{eff}})\,\mathrm{d}\lambda}{\int\limits_{\lambda_{1}}^{\lambda_{2}}B(\lambda,T_{\mathrm{eff}})\,\mathrm{d}\lambda},$
(11)

where $B(\lambda,T)$ is the Planck function, $T_{\mathrm{eff}}$ is the
effective temperature of the flare ribbons, and the wavelength range in the
denominator corresponds to the bandpass of the AstroSat UVIT FUV F148W filter
($125-175$ nm). We use $T_{\mathrm{eff}}=10\,000$ K as the typical effective
temperature of the UV-emitting flare ribbons (Kowalski et al., 2013), with
possible variations in the range of $9\,000-12\,000$ K. The extrapolation (11)
is very sensitive to the adopted temperature $T_{\mathrm{eff}}$, so that the
uncertainty in this value is the main source of uncertainties in the estimated
bolometric luminosities and radiated energies of stellar flares. The peak
estimated bolometric luminosities $L_{\mathrm{cont}}^{\max}$ of the flares
detected on AT Mic are presented in Table 1.

We note, however, that the bolometric luminosity estimation (11) is
approximate, because, in addition to a blackbody component, the UV emission of
flares can contain a significant contribution of line emission and/or Balmer
continuum. As demonstrated by Kowalski et al. (2019), in the near ultraviolet
range ($\gtrsim 250$ nm) the blackbody model may underestimate the flare flux
by a factor of about two; at shorter wavelengths (including the AstroSat UVIT
FUV spectral band), the contribution of non-blackbody components has not been
determined yet. Thus, a more accurate FUV-to-bolometric conversion would
require spectroscopic observations.

The estimated radiated energies of the detected flares in the soft X-ray range
and in the optical continuum are presented in Table 1. For the flare F4, only
the late part was observed in the UV range; therefore, the radiated energy of
this flare in the optical continuum was likely considerably (up to several
times) higher than the value shown in Table 1. Also, because the decay phase
of the UV flare F5 was observed only partially, the radiated energy of this
flare in the optical continuum shown in Table 1 is likely underestimated by
$\sim 30$% (assuming an exponential decay); this difference, however, is
smaller than the uncertainties caused by other factors.

####  4.3.2 Flare energy partition

As follows from Table 1, the radiated energies of the detected flares were of
$\sim 10^{31}-10^{32}$ erg, i.e., these flares were comparable to the
strongest known solar flares (e.g. Shibata & Yokoyama, 2002; Emslie et al.,
2005), but far less powerful than the strongest flares observed on AT Mic
before (Pallavicini et al., 1990; García-Alvarez et al., 2002). For the three
flares (F1, F3, and F5), where the radiated energies both in the X-ray range
and in the optical continuum are known with a sufficient accuracy, we can
compare the flare energy outputs in these spectral channels: the optical
continuum dominated, with $E_{\mathrm{cont}}/E_{\mathrm{X}}\sim 1.4-1.8$, and
was responsible for $\sim 60-65\%$ of the total radiated flare energy. This
energy partition is consistent with that in solar flares, where the white-
light continuum is responsible, on average, for $\sim 70$% of the total
radiated flare energies (Kretzschmar, 2011). Similar relations between the
optical and X-ray flare emissions on other stars were reported, e.g., by
Guarcello et al. (2019); Schmitt et al. (2019); Kuznetsov & Kolotkov (2021).

Similarity of the flare energy partitions obtained in this and other works
confirms that the above-described approach to estimate the optical continuum
luminosity is justified, i.e. a) the choice of the effective temperature of
flare ribbons to be $T_{\mathrm{eff}}=10\,000$ K is adequate, and b)
contribution of non-blackbody components in the FUV spectral band is minor.

###  4.4 Active Region Parameters

To estimate the parameters of the active regions on AT Mic, we use the
theoretical scaling laws derived (for a magnetic reconnection model) by
Maehara et al. (2015) and Namekata et al. (2017):

$\tau\propto E^{1/3}B^{-5/3},\qquad\tau\propto E^{-1/2}L^{5/2},$ (12)

where $\tau$ is the flare duration, $E$ is the released flare energy, $B$ is
the characteristic magnetic field strength in the flaring region, and $L$ is
the length scale of the flaring region; the scaling coefficients were
determined from observations of solar flares. For consistency with the results
of Namekata et al. (2017), we characterize a flare with the radiated energy in
the optical continuum (assuming $E\simeq E_{\mathrm{cont}}$) and the
optical/UV decay timescale (assuming $\tau\simeq\tau_{\mathrm{UV}}$);
therefore we consider four flares (F1-F3 and F5) where these parameters were
reliably determined. The estimated parameters of the corresponding flaring
regions are presented in Table 1. The flaring regions on AT Mic had typical
sizes of about $35\,000-70\,000$ km and typical magnetic field strengths of
about $80-120$ G (we note that the used scaling laws provide an average
magnetic field strength in the flaring volume in the solar/stellar corona,
while the field strength at the photospheric level can be much higher).

Figure 6: UV/optical flare decay times vs. the optical continuum flare
energies for the flares on the Sun (from Namekata et al., 2017, shown by empty
blue circles) and AT Mic (obtained in this work, shown by filled red circles).
The dashed and dotted lines represent the theoretical scaling laws by Namekata
et al. (2017). The error bars (shown for the stellar flares only) correspond
to the $1\sigma$ level.

In Figure 6, we compare the radiated energies and decay times of the flares
detected on AT Mic in this study with the respective parameters of the solar
flares (of the GOES classes $\textrm{M1.0}-\textrm{X2.8}$) reported by
Namekata et al. (2017); we also overplot theoretical isolines of
characteristic magnetic field strength or flaring region size predicted by the
the scaling laws (12) (cf. similar plots for flares on other stars in the
papers of Namekata et al., 2017, 2018; Brasseur et al., 2019; Tu et al., 2020,
2021; Ramsay et al., 2021, etc.). The flaring region sizes on AT Mic seem to
be comparable to or slightly larger than those for the largest solar flares.
On the other hand, the magnetic field strengths in the flaring regions on AT
Mic are considerably (by a factor of $\sim 1.5-2$) higher than the typical
values in the solar flaring regions. A similar conclusion (i.e., that the
magnetic fields in stellar flaring regions are typically stronger than in
solar ones) was made earlier by Namekata et al. (2017, 2018) for the stellar
flares observed with Kepler in the short cadence (1 min) mode and by Tu et al.
(2020, 2021) for the stellar flares observed with TESS.

The question is open whether the above mentioned differences between the solar
and stellar flares are qualitative or quantitative, i.e., whether flares
similar to the described here flares on AT Mic can occur on the Sun, albeit
rarely. A possible close solar analog of the stellar events was the X9.3 class
solar flare on 2017 September 6 that, despite of its high energetics ($\sim
10^{31}$ erg), was relatively short and compact; notably, an anomalously
strong magnetic field (up to $\sim 4000$ G in the low corona) was detected in
that flare (Anfinogentov et al., 2019). Such rare solar flares with extremely
strong magnetic fields deserve further study, because they may bridge the gap
between “ordinary” solar flares and stellar superflares.

##  5 Summary and conclusions

We observed the active M-dwarf binary AT Mic with the orbital observatory
AstroSat. The target was detected by the SXT telescope in the soft X-ray range
($0.3-7$ keV) and by the UVIT telescope in the far ultraviolet range
($130-180$ nm), with $\sim 10$ ks of simultaneous observations in the two
spectral ranges. The main results can be summarized as follows:

  1. 1.

In both the X-ray and UV spectral ranges, we detected quiescent emission and a
number of flares. Using the spatially resolved UV observations, we have for
the first time identified reliably the components of the binary where the
flares occurred: two flares on AT Mic A and four flares on AT Mic B.

  2. 2.

The X-ray flares were typically longer than (by a factor of $\sim 2$) and
delayed after (by $\sim 5-6$ min) their UV counterparts, demonstrating the
Neupert effect.

  3. 3.

The X-ray-emitting coronal plasma has been found to be best described by a
multi-temperature distribution. In the quiescent state, the emission measure
was of $\sim 2.9\times 10^{52}$ $\textrm{cm}^{-3}$ and the average temperature
was of $\sim 7$ MK. During flares, both the emission measure and average
temperature increased (up to $\sim 4.5\times 10^{52}$ $\textrm{cm}^{-3}$ and
$\sim 15$ MK, respectively), corresponding to the plasma temperature in the
flaring regions of $\sim 32$ MK.

  4. 4.

The abundance of heavy elements in the corona of AT Mic has been found to be
much lower than at the Sun ($\sim 0.18$ $Z_{\sun}$ in the quiescent state).
During flares, the coronal abundance increased (up to $\sim 0.34$ $Z_{\sun}$),
due to chromospheric evaporation.

  5. 5.

The detected flares had the radiated energies of $\sim 10^{31}-10^{32}$ erg.
The optical continuum emission dominated and was responsible for $\sim
60-65\%$ of the total radiated flare energy.

  6. 6.

The estimated sizes of flaring regions on AT Mic ($\sim 35\,000-70\,000$ km)
are comparable to or slightly larger than those for the largest solar flares.
On the other hand, the estimated magnetic field strengths in the flaring
regions on AT Mic ($\sim 80-120$ G) are $\sim 1.5-2$ times higher than those
in typical solar flares.

This work was supported by the BRICS Multilateral Research and Development
Projects-2016 (DST/MRCK/BRICS/PilotCall1/Superflares/2017), the project
“Superflares on stars and the Sun”, the Russian Foundation for Basic Research
under grant 17-52-80064, and the Ministry of Science and Higher Education of
the Russian Federation. K.C. is supported by the Research Council of Norway
through its Centres of Excellence scheme (project number 262622). This
research is based on the results obtained from the AstroSat mission of the
Indian Space Research Organisation (ISRO), archived at the Indian Space
Science Data Centre (ISSDC). This work has used the UVIT data processed by the
payload operations centre at IIA; the UVIT was built in collaboration between
IIA, IUCAA, TIFR, ISRO, and CSA. This work has used the data from the Soft
X-ray Telescope (SXT) developed at TIFR, Mumbai, and the SXT POC at TIFR is
thanked for verifying and releasing the data via the ISSDC data archive and
providing the necessary software tools.

##  Appendix A Comparison of different X-ray spectral models

In order to estimate the parameters of the emitting plasma, we performed
fitting of the observed soft X-ray spectra of AT Mic with several spectral
models using the Markov Chain Monte Carlo (MCMC) approach; the MCMC sampling
implementation by Anfinogentov et al. (2021) was used. In this Section, we
present the results obtained for the SXT spectrum averaged over the entire
(total) duration of the observations, and for the time interval corresponding
to the flare F4 that was the strongest X-ray flare in our observations; the
analysis of other time intervals provided qualitatively similar results. We
have considered three plasma emission models: a) the single-temperature
optically thin thermal model (vth) depending on the emission measure EM,
temperature $T$, and metallicity $Z$; b) the double-temperature optically thin
thermal model (2vth) depending on the emission measures $\textrm{EM}_{1}$ and
$\textrm{EM}_{2}$ of two plasma components, the temperatures $T_{1}$ and
$T_{2}$ of the respective plasma components, and metallicity $Z$; c) the
multi-temperature optically thin thermal model with a Gaussian dependence of
the differential emission measure (DEM) on the logarithm of the temperature as
described by Equations (2–4) (multi_therm_gauss), depending on the total
emission measure EM, the average plasma temperature $\left<T\right>$, the
width of the DEM distribution $\sigma_{T}$, and metallicity $Z$. Figures 7–9
demonstrate the results of the MCMC analysis: the posterior probability
distributions for the above mentioned spectral models and time intervals; the
best-fit model parameters (i.e., the most probable values of the parameters
that also correspond to the minimum values of the $\chi^{2}$ statistics) are
shown as well. Figure 10 compares the spectral fits obtained using different
spectral models.

Figure 7: Results of the MCMC analysis of the AstroSat SXT X-ray spectra of AT
Mic using the single-temperature optically thin thermal model (vth). The
posterior probability distributions are shown, with grey-scale 2D plots
demonstrating the joint posterior probability distributions for different
combinations of the model parameters (darker areas correspond to higher
probability), and histograms demonstrating the marginal posterior probability
distributions of the individual parameters. Two time intervals are considered:
(a) the total duration of the observations, and (b) flare F4. The most
probable values of the model parameters with the $1\sigma$ (68%) confidence
intervals are shown in the panels as well.

Figure 8: Same as in Figure 7, for the double-temperature optically thin
thermal model (2vth).

Figure 9: Same as in Figures 7–8, for the optically thin thermal model with a
Gaussian DEM distribution (multi_therm_gauss).

Figure 10: Top panels: X-ray spectra of AT Mic obtained with the AstroSat SXT
on 2018 October 3-4, for the entire interval of observations (a) and for the
flare F4 (b). At higher energies, the original spectra are rebinned over
$2-65$ channels ($0.02-0.65$ keV). The error bars correspond to the $1\sigma$
level. The solid lines represent the best spectral fits with three different
plasma emission models obtained using the MCMC technique (see Figures 7–9 for
the best-fit model parameters). Bottom panels: normalized residuals of the
model spectral fits for the considered plasma emission models, in units of the
$1\sigma$ uncertainties; the respective values of the $\chi^{2}$ statistic are
shown as well.

One can see in Figure 10 that, in comparison with the single-temperature
model, the double-temperature model provides better fits to the observations
at high energies ($\gtrsim 2$ keV) and also noticeably lower overall
$\chi^{2}$ values. The secondary plasma component (i.e., the component with
the higher temperature) comprises a significant part of the emitting plasma,
with the $\textrm{EM}_{2}/\textrm{EM}_{1}$ ratio varying from 0.12 for the
total duration of the observations up to 0.27 during the flares. These results
indicate the presence of at least two plasma components with different
temperatures. On the other hand, the temperature of the secondary component
$T_{2}$ in the double-temperature model remains unconstrained, when the values
in a very broad range have comparable posterior probabilities (see Figure 8)
and provide equally good spectral fits; therefore the double-temperature
model, while providing useful insights, cannot be used for a reliable
quantitative analysis. The uncertainty in determining the secondary component
temperature can indicate that this secondary component itself has a
complicated composition which cannot be described by a single temperature.

The multi-temperature model with a Gaussian DEM distribution is intermediate
(in terms of the number of parameters) between the single-temperature and
double-temperature models. It is reduced to a single-temperature model when
the width parameter $\sigma_{T}$ approaches zero, while can account for
contributions of multiple plasma components with temperatures in a broad range
around the peak temperature for larger values of $\sigma_{T}$. We have found
that the parameters of this model are well constrained by the observations
(see Figure 9), while the quality of spectral fits (in terms of $\chi^{2}$) is
noticeably better than that for the single-temperature model and comparable to
(or only slightly worse than) that for the double-temperature model (see
Figure 10). Therefore we conclude that, among the considered models, the
multi-temperature spectral model multi_therm_gauss is the most suitable one to
analyze the AstroSat SXT observations of AT Mic.

The presence of multi-thermal plasma in the coronae of red dwarfs, including
AT Mic, has been reported in earlier studies as well. E.g., Robrade & Schmitt
(2005), using the XMM-Newton observations, obtained for AT Mic the DEM
distribution with a peak at $T_{0}=7$ MK and FWHM of about 6 MK, which
corresponds to $\sigma_{T}\simeq 0.15$ in Equation (2); these estimations are
consistent with our results for the total duration of the observations (cf.
Table 2).

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# Benchmarking News Recommendation in the Era of Green AI

Qijiong Liu  PolyU, Hong Kong<EMAIL_ADDRESS>,  Jieming Zhu  Huawei Noah’s
Ark Lab, China<EMAIL_ADDRESS>,  Quanyu Dai  Huawei Noah’s Ark Lab, China
<EMAIL_ADDRESS>and  Xiao-Ming Wu  PolyU, Hong Kong xiao-
<EMAIL_ADDRESS>
(2024)

###### Abstract.

Over recent years, news recommender systems have gained significant attention
in both academia and industry, emphasizing the need for a standardized
benchmark to evaluate and compare the performance of these systems.
Concurrently, Green AI advocates for reducing the energy consumption and
environmental impact of machine learning. To address these concerns, we
introduce the first Green AI benchmarking framework for news recommendation,
known as GreenRec111GreenRec has been published as part of the  Legommenders
benchmark, which is a modular framework for recommender systems. The source
code and data for GreenRec can be found at
https://github.com/Jyonn/Legommenders., and propose a metric for assessing the
tradeoff between recommendation accuracy and efficiency. Our benchmark
encompasses 30 base models and their variants, covering traditional end-to-end
training paradigms as well as our proposed efficient only-encode-once (OLEO)
paradigm. Through experiments consuming 2000 GPU hours, we observe that the
OLEO paradigm achieves competitive accuracy compared to state-of-the-art end-
to-end paradigms and delivers up to a 2992% improvement in sustainability
metrics.

††journalyear: 2024††copyright: acmlicensed††conference: Companion Proceedings
of the ACM Web Conference 2024; May 13–17, 2024; Singapore,
Singapore††booktitle: Companion Proceedings of the ACM Web Conference 2024
(WWW ’24 Companion), May 13–17, 2024, Singapore, Singapore††doi:
10.1145/3589335.3651472††isbn: 979-8-4007-0172-6/24/05††ccs: Information
systems Recommender systems††ccs: Information systems Data mining

##  1\. Introduction

News recommender systems have become a crucial tool in the digital age,
helping users discover relevant news articles and stay informed amidst the
ever-increasing number of sources available. To integrate news content
knowledge into recommender systems, content encoders are employed to capture
semantic news representations. Various approaches have been explored in these
efforts, including simple content encoders represented by CNN (Kim, 2014) and
Attention-based (Vaswani et al., 2017) models (An et al., 2019; Wu et al.,
2019a, c; Li et al., 2022), as well as emerging content encoders based on
pretrained language models (Zhang et al., 2021; Liu et al., 2022).

Despite the success achieved by these studies, there is still a notable
absence of standardized benchmarks and uniform evaluation protocols for news
recommendation. Consequently, even when common datasets like MIND (Wu et al.,
2020) are employed for evaluation, existing studies often use their own data
partitions and apply unique preprocessing steps. The absence of uniformity in
data preprocessing methods leads to non-reproducible and often conflicting
experimental outcomes across different studies, and the use of non-standard
data preprocessing techniques makes it challenging to compare and evaluate
results between papers.

Meanwhile, the environmental impact has also begun to draw attention from the
machine learning community, as training large-scale networks leads to a huge
increase of carbon emission (Spillo et al., 2023). Therefore, a series of
studies (Wilson et al., 2020; Przybyła and Shardlow, 2022) explore ways to
reduce energy consumption in line with Green AI principles (Schwartz et al.,
2020).

Figure 1.  Two training paradigms for news recommendation.

In light of this, we establish the first Green AI Benchmark for News
Recommendation, called GreenRec, and introduce a sustainability metric, namely
unit conversion rate of carbon emission, to strike a balance between
recommendation quality and efficiency. Specifically, we selected six base
models and considered five different variants for each model. In total, we
evaluated the recommendation accuracy and environmental impact across a total
of 30 baselines. This evaluation was carried out under two distinct training
paradigms: the conventional end-to-end training paradigm, where the content
encoder and other recommender components are jointly trained, and our proposed
only-encode-once (OLEO) training paradigm, where the content encoder and other
components are trained in a decoupled manner. Our evaluation is conducted
through hundreds of experiments within a standardized framework using the most
widely used news recommendation datasets, MIND-small and MIND-large (Wu et
al., 2020). The experiments reveal that the conventional end-to-end paradigm
encounters efficiency challenges, while our OLEO-based paradigm is much more
eco-friendly. Moreover, the OLEO-based model variants maintain competitive
performance with the state-of-the-art end-to-end PLM-NR variants (Wu et al.,
2021), and achieve up to 2992% improvement in our sustainability metric.

##  2\. News Recommendation

###  2.1. Basics of News Recommender Systems

News recommender systems are devised to predict the click probability of a
user over a piece of given news article. Typically, a general news recommender
system consists of three main components: content encoder, history encoder,
and interaction module. As depicted in Figure 1 (a), the recommender accepts a
news-user pair as input and yields the click probability. The content encoder
is responsible for capturing the semantic meaning and contextual information
of the news articles, while the history encoder processes the news history
vectors, capturing the preferences, interests, and browsing patterns of users.
Finally, the interaction module facilitates the interaction between the
candidate news vector and user vector to calculate the click probability for
the given news-user pair.

###  2.2. Training Paradigms and Complexity

Traditional models (Wu et al., 2019b, a, c, 2021) typically follow such end-
to-end training paradigm, as displayed in Figure 1 (a), where the three
components are are trained together, guided by click-through data.

However, this traditional approach has shown limitations, particularly in
terms of efficiency. A significant issue is the repetitive work done by the
content encoder due to the repeated encoding of the same news articles, a
consequence of their frequent interaction with various users. For instance, if
there are $N$ news articles, $M$ users, and $K$ instances of user-news
interactions, with an average historical sequence of $L$ interactions per
user, the content encoder ends up processing $M\times L$ articles. The overall
time required for training can be roughly calculated as $O(M\times L\times
t_{c}+K\times(t_{u}+t_{i}))$, highlighting a particularly heavy load when
$M\times L$ significantly exceeds either $N$ or $K$, especially with advanced
content encoders (Zhang et al., 2021; Wu et al., 2021) that have a much higher
time complexity compared to other modules. For example, in the MIND dataset
scenario, a single news article is encoded on average about 1818 times in one
epoch of training, indicating a substantial amount of redundancy.

To address these inefficiencies, we draw inspiration from a new training
approach known as the only-encode-once paradigm, as depicted in Figure 1 (b).
This approach involves initially pretraining the content encoder using the
news content in a self-supervised manner. After this phase, the content
vectors are extracted and stored, allowing the history encoder and interaction
module to be trained separately with much quicker access to the news
representations via a lookup table. The pretraining phase for the content
encoder has a time complexity of $O(N\times t_{c})$, considered a fixed cost
across various models. Meanwhile, the training of the recommendation system
itself becomes significantly more efficient, with a time complexity of
$O(K\times(t_{u}+t_{i}))$, marking a drastic reduction from the traditional
method.

Usage | TorchRec | DeepCTR | DeepRec | RecBole | FuxiCTR | BARS | Ours
---|---|---|---|---|---|---|---
Data Preprocessing | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓
Content-aware CTR | $\times$ | $\times$ | $\times$ | – | – | – | ✓
NewsRec Methods | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | ✓
Decoupled Training | $\times$ | $\times$ | $\times$ | – | – | – | ✓
End-to-end Training | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | ✓
Green AI Evaluation | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | ✓

Table 1. Comparison to exisiting recommendation benchmarks (✓ — – — $\times$
means totally — partially — not met, respectively). “Partially met” represents
incomplete availability.

###  2.3. Adapting CTR Models to both Paradigms

While the prevailing news recommendation models adhere to a matching-based
approach with simple dot product as the interaction module, preserving all
positive samples and conducting negative sampling (including real or fake
negatives) and trained as a classification task, there are still some studies
(Zhang et al., 2021; Liu et al., 2022) that have validated the effectiveness
of ranking-based CTR methods in news recommendation systems. In these
approaches, all samples are retained throughout training, and the click
probability is directly produced as a regression task. These CTR techniques
incorporate intricate feature interaction networks, which can be utilized in
the interaction module. When integrated into the content encoder, either
through the end-to-end training paradigm or by initializing with pretrained
news representations in the OLEO training paradigm, they gain the content-
aware abilities.

###  2.4. Proposed GreenRec Benchmark

Here, we summarize 6 representative methods and 5 variants used in our
GreenRec benchmark:

Base models. We select three representative news recommenders (i.e., NAML (Wu
et al., 2019a), LSTUR (An et al., 2019), and NRMS (Wu et al., 2019c)) and
three widely used CTR methods (i.e., BST (Chen et al., 2019), DCN (Wang et
al., 2017), and DIN (Zhou et al., 2018))

ID-based variants.222We use green, yellow, and red text to represent OLEO-
based or content-free (ID-based) training methods, end-to-end training
variants with simple content encoders and end-to-end training variants with
pretrained language models. We remove the content encoder from the news
recommenders and replace it with a randomly initialized embedding lookup
table. CTR methods are inherently ID-based.

Text-based variants. We remove the news embedding lookup table of the CTR
methods and replace it with a content sequence pooling layer. News
recommenders are inherently text-based.

PLM-NR variants. As proposed by PLM-NR (Wu et al., 2021), we replace the
content encoders of the text-based variants with pretrained language models
such as BERT (Devlin et al., 2018).

PREC variants. As proposed by PREC (Liu et al., 2022), we employ the OLEO
training paradigm which first pretrains the content encoder and then replace
the content encoders of the text-based variants with the informative news
embedding lookup table.

BERT-OLEO variants. Unlike the PREC variants which requires the pretraining
phase, here we directly use the pretrained BERT model to extract and cache the
news representations, and construct the informative lookup table.

##  3\. Implementation and Evaluation

In this section, we first compare our GreenRec with other benchmarking
studies. Then, we outline our evaluation procedures, including quality-based
assessments and our proposed sustainability metric. Finally, we report and
discuss our benchmarking results.

###  3.1. Comparison with Previous Benchmarks

In recent years, the issues of non-reproducibility and unfair comparisons have
garnered increasing attention within the recommendation community. A series of
studies (Ivchenko et al., 2022; Shen, 2017; Zhang et al., 2019; Zhao et al.,
2022; Zhu et al., 2021, 2022) have conducted comprehensive experiments and
analyses, advocating for a unified benchmark construction. As shown in Table
1, we compare our news recommendation benchmark GreenRec with these existing
efforts. It is evident that these studies primarily target in the general
recommendation domain, particularly emphasizing aspects such as CTR prediction
and collaborative filtering. Nevertheless, a standardized benchmarking
pipeline tailored to the news recommendation domain and the environmental
evaluation remains conspicuously absent. Hence, our GreenRec is the first
attempt on benchmarking the news recommenders in the era of Green AI.

###  3.2. Dataset and Data Splitting

|  $\\#$ News |  $\\#$ Users |  $\\#$ Interactions |  $\\#$ Samples | Density
---|---|---|---|---|---
MIND-small | 65,238 | 94,057 | 347,727 | 8,381,093 | 0.1366%
MIND-large | 104,151 | 750,434 | 3,958,501 | 95,447,571 | 0.1221%

Table 2.  Dataset statistics. Density is defined as the ratio of #
interactions to # all possible interactions.

Dataset | MIND-small | MIND-large
---|---|---
Method | Matching | CTR | Matching | CTR
NAML | LSTUR | NRMS | BST | DCN | DIN | NAML | LSTUR | NRMS | BST | DCN | DIN
ID-based | AUC | 50.13 | 51.04 | 54.84 | 50.09 | 53.92 | 55.95 | 52.98 | 54.98 | 57.59 | 52.10 | 57.41 | 57.36
MRR | 23.01 | 22.90 | 26.53 | 22.13 | 25.18 | 25.88 | 24.52 | 25.99 | 27.41 | 24.81 | 26.76 | 26.70
N@5 | 22.35 | 22.31 | 26.34 | 21.59 | 24.43 | 25.95 | 24.12 | 25.64 | 27.05 | 24.63 | 26.90 | 26.84
CO2E$\downarrow$ | 19 | 20 | 28 | 38 | 60 | 84 | 294 | 353 | 471 | 555 | 926 | 1294
ApC | 0.68 | 5.20 | 17.29 | 0.24 | 6.53 | 7.08 | 1.01 | 1.41 | 1.61 | 0.38 | 0.80 | 0.57
Text-based (End-to-end) | AUC | 60.14 | 61.27 | 62.21 | 60.51 | 62.63 | 62.90 | 63.03 | 63.89 | 64.12 | 63.28 | 63.88 | 64.02
MRR | 28.93 | 29.64 | 30.19 | 28.59 | 29.73 | 30.06 | 30.40 | 31.24 | 31.77 | 30.73 | 31.65 | 31.98
N@5 | 29.33 | 30.28 | 31.10 | 29.09 | 30.52 | 30.65 | 31.82 | 32.15 | 32.64 | 31.95 | 32.40 | 33.00
CO2E$\downarrow$ | 42 | 58 | 62 | 53 | 63 | 90 | 648 | 892 | 1010 | 1212 | 972 | 1386
ApC | 24.14 | 19.43 | 19.69 | 19.83 | 20.05 | 14.33 | 2.01 | 1.56 | 1.40 | 1.09 | 1.43 | 1.01
PLM-NR (End-to-end) | AUC | 62.06 | 63.64 | 62.53 | 64.40 | 63.32 | 63.26 | 65.19 | 65.73 | 65.57 | 66.03 | 65.42 | 65.31
MRR | 31.66 | 31.74 | 30.74 | 32.21 | 32.00 | 31.83 | 32.74 | 33.18 | 32.94 | 33.40 | 32.85 | 32.68
N@5 | 32.25 | 32.72 | 31.31 | 33.34 | 32.58 | 32.40 | 33.77 | 34.26 | 34.13 | 34.70 | 33.99 | 33.70
CO2E$\downarrow$ | 178 | 202 | 252 | 505 | 1,752 | 1,839 | 2,527 | 3,032 | 4,043 | 8,086 | 27,036 | 28,329
ApC | 6.78 | 6.75 | 4.97 | 2.85 | 0.76 | 0.72 | 0.60 | 0.52 | 0.39 | 0.20 | 0.06 | 0.05
BERT (OLEO) | AUC | 60.62 | 61.09 | 60.94 | 60.81 | 62.65 | 62.40 | 63.02 | 63.62 | 63.40 | 62.94 | 64.29 | 63.75
MRR | 29.31 | 29.26 | 29.31 | 29.04 | 30.92 | 30.75 | 31.23 | 31.59 | 31.38 | 30.56 | 32.60 | 31.58
N@5 | 29.71 | 29.60 | 29.65 | 29.38 | 31.37 | 32.44 | 31.79 | 32.30 | 32.16 | 31.83 | 33.63 | 32.43
CO2E$\downarrow$ | 22 | 23 | 33 | 38 | 62 | 86 | 353 | 404 | 505 | 640 | 956 | 956
ApC | 48.27 | 48.22 | 33.15 | 28.45 | 20.40 | 14.41 | 3.69 | 3.37 | 2.65 | 2.02 | 1.49 | 1.44
PREC (OLEO) | AUC | 62.95 | 62.16 | 62.95 | 62.43 | 64.57 | 63.12 | 64.78 | 64.88 | 64.34 | 65.33 | 65.44 | 64.53
MRR | 31.26 | 31.00 | 31.18 | 30.42 | 32.60 | 31.28 | 32.64 | 32.94 | 32.93 | 33.29 | 33.04 | 32.72
N@5 | 32.01 | 31.79 | 32.10 | 30.94 | 33.48 | 32.01 | 33.66 | 34.00 | 33.95 | 34.35 | 34.03 | 33.58
CO2E$\downarrow$ | 22 | 23 | 33 | 38 | 62 | 86 | 353 | 404 | 505 | 640 | 956 | 956
ApC | 58.86 | 52.87 | 39.24 | 32.71 | 23.50 | 15.25 | 4.19 | 3.68 | 2.84 | 2.40 | 1.61 | 1.52
ApC Imp. (%) | 768% | 683% | 690% | 1048% | 2992% | 2018% | 598% | 608% | 628% | 1100% | 2583% | 2940%

Table 3. Comparison of variants of different recommenders. “ApC Imp”
represents the environmental sustainability growth rate of PREC variants
compared to the SOTA PLM-NR variants. We bold the best results and underline
the second-best results.

In this work, we mainly use two versions of the most prevalent news
recommendation dataset: MIND-small and MIND-large (Wu et al., 2020). Table 2
summarizes the data statistics information.

Due to the fact that the MIND-small dataset only provides training and
validation sets, many studies have failed to specify their exact partitioning
during training, and in some cases, they have directly reported results on the
validation set, which leads to an unfair comparison among different models.
Furthermore, the MIND-large dataset only offers online testing, which is not
conducive to offline environment assessment. To address these issues, we have
restructured both datasets by splitting the validation sets of both datasets
in a 1:1 ratio to create new validation and testing sets. The scripts can be
found in our released repository.

###  3.3. Evaluation Metrics

We employ three widely-used metrics for accuracy evaluation, including AUC,
MRR, nDCG@5 (Wu et al., 2020). Moreover, we also introduce one Green AI
metrics: Carbon Emission (Lacoste et al., 2019) (CO2E) and AUC per Carbon
Emission (ApC), to evaluate the sustainability and energy utilization of model
$\Psi$. $CO_{2}E$ is computed by:

(1) $CO_{2}E=p\times t\times c,$

where $p$ is the power consumption differ by hardware types, $t$ is the
hardware running time, and $c$ is carbon efficiency differ by power provider.
ApC measures the unit conversion rate of carbon emissions on AUC, defined as:

(2) $ApC=\frac{AUC-50}{CO_{2}E}\times 100.$

Training Details. The Adam optimizer is employed for optimization. We consider
various learning rates from the set $\\{1e-5,2e-5,5e-5,1e-4,2e-4,5e-4\\}$ and
batch sizes from the set
$\\{64,128,256,500,1000,5000\\}$. The embedding dimensions for all base models
and their variants are fixed to 64. For the OLEO training paradigm which uses
cached news vectors for initialization, we keep the pretrained embeddings
fixed and use learnable transformation matrices for dimension projection.
Experimental results are averaged over five runs, and all methods were trained
using Nvidia GeForce RTX 3090 with 24GB memory, which has a power consumption
of 350W. The carbon efficiency in our experimental region (anonymous for
review) is 722g CO2-eq/kWh.

###  3.4. Findings

The comparative results of various models are summarized in Table 3, from
which we derive the following observations.

ID- vs. Modality-based Recommender. Among the five variants, the ID-based
variants exhibit the worst performance, showing the significance of news
content comprehension in news recommenders. The findings in recent study (Yuan
et al., 2023) are in line with ours.

Enhancement of PLMs in the end-to-end training paradigm. The PLM-NR variants
consistently outperforms the ID-based and Text-based ones, benefiting from the
augmented understanding of news content offered by pretrained knowledge.
However, they grapple with an efficiency issue, resulting in significantly
higher carbon emissions compared to other variants.

Enhancement of PLMs in the OLEO training paradigm. The BERT variants maintain
an environmentally sustainable level of efficiency. Nonetheless, there is a
deficiency in the ability of general language models to fully grasp news
content, resulting in a notable decline in accuracy compared to the PLM-NR
variants. However, PREC variants achieve comparable performance to PLM-NR ones
while significantly reducing carbon emissions, which represents the prime case
of the tradeoff between accuracy and efficiency.

##  4\. Conclusion

We have established the first standardized Green AI benchmark for news
recommendation. Through extensive experiments over 30 base models and their
variants, we conclude that the OLEO training paradigm successfully strikes a
balance between accuracy and efficiency. We encourage other researchers to
explore the OLEO paradigm and make contributions to environmental
conservation.

## Acknowledgement

Qijiong Liu would like to thank Dr. Guanliang Chen and Mr. Haoxiang Shi for
their insightful input during the brainstorming process of our paper.
Additionally, the authors would like to thank the anonymous reviewers for
their valuable feedback.

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