20XX Vol. X No. XX, 000–000

11institutetext: Key laboratory of Space Astronomy and Technology, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101,
China<EMAIL_ADDRESS>
22institutetext: Key laboratory of solar activity, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China
33institutetext: Lab of Web and Mobile Data Management, Renmin University of
China, Beijing 100872, China
44institutetext: Guangxi Key Laboratory for Relativistic Astrophysics, School
of Physical Science and Technology, Guangxi University, Nanning 530004,
Peopleʼs Republic of China
55institutetext: School of Artificial Intelligence of Beijing Normal
University, No.19, Xinjiekouwai St, Haidian District, Beijing, 100875, China
66institutetext: School of Astronomy and Space Science, Nanjing University,
Nanjing 210093, People’s Republic of China
77institutetext: Key Laboratory of Modern Astronomy and Astrophysics (Nanjing
University), Ministry of Education, Nanjing 210093, People’s Republic of China
Received 20XX Month Day; accepted 20XX Month Day

# Magnetic activities and parameters of 43 flare stars in the GWAC archive

Guang-Wei Li (李广伟) 11 Chao Wu (吴潮) 11 Gui-Ping Zhou (周桂萍) 22 Chen Yang (杨晨) 33
Hua-Li Li (黎华丽) 11 Jie Chen (陈洁) 22 Li-Ping Xin (辛立平) 11 Jing Wang (王竞) 44
Hasitieer Haerken (哈斯铁尔·哈尔肯) 5511 Chao-Hong Ma (马超红) 33 Hong-Bo Cai (蔡洪波) 11
Xu-Hui Han (韩旭辉) 11 Lei Huang (黄垒) 11 Xiao-Meng Lu (卢晓猛) 11 Jian-Ying Bai
(白建迎) 11 Xu-Kang Zhang (张旭康) 33 Xin-Li Hao (郝新丽) 33 Xiang-Yu Wang (王祥玉) 6677
Zi-Gao Dai (戴子高) 6677 En-Wei Liang (梁恩维) 44 Xiao-Feng Meng (孟小峰) 33 Jian-Yan
Wei (魏建彦) 11

###### Abstract

In the archive of the Ground Wide Angle Camera (GWAC), we found 43 white light
flares from 43 stars, among which, three are sympathetic or homologous flares,
and one of them also has a quasi-periodic pulsation with a period of $13.0\pm
1.5$ minutes. Among these 43 flare stars, there are 19 new active stars and 41
stars that have available TESS and/or K2 light curves, from which we found 931
stellar flares. We also obtained rotational or orbital periods of 34 GWAC
flare stars, of which 33 are less than 5.4 days, and ephemerides of three
eclipsing binaries from these light curves. Combining with low resolution
spectra from LAMOST and the Xinglong 2.16m telescope, we found that $L_{\rm
H\alpha}/L_{\rm bol}$ are in the saturation region in the rotation-activity
diagram. From the LAMOST medium-resolution spectrum, we found that Star #3
(HAT 178-02667) has double H$\alpha$ emissions which imply it is a binary, and
two components are both active stars. Thirteen stars have flare frequency
distributions (FFDs) from TESS and/or K2 light curves. These FFDs show that
the flares detected by GWAC can occur at a frequency of 0.5 to 9.5 yr-1. The
impact of flares on habitable planets was also studied based on these FFDs,
and flares from some GWAC flare stars may produce enough energetic flares to
destroy ozone layers, but none can trigger prebiotic chemistry on their
habitable planets.

###### keywords:

stars: flare; magnetic reconnection; stars: activity; (stars:) binaries:
eclipsing; stars: low-mass; stars: rotation; (stars:) starspots; astrobiology

##  1 Introduction

Stellar flares are powerful explosions that can occur on stars ranging from
A-type (Balona 2015) to even L-type (Paudel et al. 2020). Solar flares have
been well studied based on space observatories, such as the _Geostationary
Operational Environmental Satellite_ (GOES), _Solar Dynamics Observatory_
(Pesnell et al. 2012), the _the Reuven Ramaty High Energy Solar Spectroscopic
Imager_ (Lin et al. 2002), and the _Interface Region Imaging Spectrograph_ (De
Pontieu et al. 2021), etc. They may release explosive energy via magnetic
reconnection (Zweibel & Yamada 2009) and released by electromagnetic
radiations from radio to $\gamma$-ray (e.g. Bai & Sturrock 1989; Osten et al.
2005), and coronal mass ejections (CMEs) (e.g. Kahler 1992). The stronger the
flare, the more likely it is to produce a CME (Li et al. 2021). Since the Sun
belongs to an ordinary incative star of G2V type (Balona 2015), it is worthy
of investigating stellar flare activities from most kinds of active stars to
understand whether stellar flares may experience similar physics to solar
flares or not.

Statistical studies of stellar flares have been conducted based on many survey
projects. In the space, the Kepler (Borucki et al. 2010) provided photometric
data with high precision, which can be used to study flare activities on stars
across the H-R diagram with homogenous data for the first time (Balona 2015;
Yang & Liu 2019). The Transiting Exoplanet Survey Satellite (TESS; Ricker et
al. 2015) surveys all the sky, covering much wider than Kepler/K2. As a
result, many new flare stars with high photometric precision can be studied
(e.g. Tu et al. 2021; Howard & MacGregor 2022). On the ground, the Next
Generation Transit Survey (Wheatley et al. 2018), ASAS-SN (Shappee et al.
2014), Evryscope (Law et al. 2015), and so on, have achieved fruitful results
on flare study (e.g. Jackman et al. 2021; Rodríguez Martínez et al. 2020;
Howard et al. 2020a).

Rotation is a key parameter to decide the activity of a star, e.g., factor in
inducing stellar flares. Some indicators of stellar activity show the well-
known activity-rotation relationship with a critical period. For stars with
rotation periods smaller than the critical period, the activity is saturated,
otherwise the activity decreases as the rotation period increases. The stellar
activity-rotation relationship has been identified by X-ray (Pizzolato et al.
2003), white light (Raetz et al. 2020), Ca II H & K (Zhang et al. 2020) and
H$\alpha$ (Newton et al. 2017; Yang et al. 2017; Lu et al. 2019).

Pre-main sequence stars often show intense flare activities, which result in
the hot plasma escaping and then angular momentum losses (Colombo et al.
2019). Magnetized stellar winds also can brake stellar rotations (Gallet &
Bouvier 2013). Therefore, with rotation slowing dwon, flare activity decreases
with age (Ilin et al. 2021; Davenport et al. 2019). The same mechanism is also
proposed to occur in a close binary system (Yakut & Eggleton 2005). Magnetic
braking may result in the shrink of the orbit period, and then make both
components in the binary synchronously spin up (Qian et al. 2018), and thus
the more frequent flare activity.

Flare activity may play key roles in affecting habitability of nearby planets
in the way of UV irradiation and CMEs. For M stars, on one hand, M stars can
not produce enough UV photos (Rimmer et al. 2018), so UV radiation from
frequent flares is needed to contribute to the creation of primitive life (Xu
et al. 2018); on the other hand, UV radiation from frequent flares can also
destroy ozone layers and life would not survive (Tilley et al. 2019).
Moreover, CMEs from flares can erode even the whole atmosphere of a habitable
exoplanet (Lammer et al. 2007; Atri & Mogan 2021).

In this paper, we present 43 stellar white light flares in the archive of the
Ground-based Wide Angle Cameras (GWAC). GWAC is one of ground facilities of
the Space-based multi-band astronomical Variable Objects Monitor (SVOM; Wei et
al. 2016), in order to detect the optical transits with a cadence of 15
seconds (Xin et al. 2021; Wang et al. 2020). We searched all light curves
during December 2018 and May 2019 of stars with Gaia G $<15$ mag, and found 43
stellar flares form 43 stars. In Section 2, we will introduce the light curves
we used; In Section 3, we will show three sympathetic or homologous flares and
one quasi-periodic pulsation; In Section 4, four binaries are studied; In
Section 5, we will present the rotation-activity relationship by H$\alpha$
emissions; The impacts of flares on habitable planets are discussed in Section
6; At last, Section 7 is conclusion.

##  2 Light Curves

The GWAC stellar flare candidates between December 2018 and May 2019 were
obtained by the program given by Ma (2019), which tried to find flares by a
wavelet algorithm. We inspected all candidates by eye and found 43 stellar
flares from 43 stars. We checked these stars in SIMBAD
111http://simbad.u-strasbg.fr/Simbad and the International Variable Star Index
222https://www.aavso.org/vsx/ , and found that 19 stars have never been
reported as flare stars or having H$\alpha$ emissions, thus new active stars.
All GWAC flares are listed in Table LABEL:tab:gwacflare. We searched their
light curves from the MAST site 333https://mast.stsci.edu, and found TESS and
K2 light curves for 39 stars. For the stars that have both K2 and TESS light
curves, the TESS light curves were used. For TESS light curves, we noticed
that there are several products for the same sector from different groups, and
if light curves of the Science Processing Operations Center (SPOC; Jenkins et
al. 2016) are available, then use them, otherwise use light curves of TESS-
SPOC (Caldwell et al. 2020). The light curves of simple aperture photometry
(SAP) were used, because pre-search data conditioning (PDC) ones may remove
real variabilities (Vida et al. 2019). We also checked the PDC light curves of
our sample, and found they work as well as SAP ones. Star #3 (HAT 178-02667),
#14 (1RXS J075908.2+171957), #24, and #38 (BX Ari) have no available light
curves in the MAST site. Star # 3 (HAT 178-02667) is not observed by TESS, and
Star #24 is contaminated by a very bright star 13 arcseconds away. As a
result, we obtained light curves of Star #14 (1RXS J075908.2+171957) and #38
(BX Ari) from their Full Frame Images. In sum, 41 of 43 GWAC flare stars have
TESS or K2 light curves. The TESS sectors and K2 campaigns used in this work
are listed in Table 2.

###  2.1 Flare Detection and Rotational Periods

To detect flares, for each light curve of a TESS sector or K2 campaign, we
used a cubic B-spline to fit the out-of-flare variability, and then removed
the fitted B-spline from the light curve. In the residual of a light curve,
flares can be detected by residual fluxes larger than 3$\sigma$, where
$\sigma$ is the standard deviation of the out-of-flare residual. At last, the
stellar rotational period was calculated from the out-of-flare variability.
Detailed steps are as follows:

  * •

Step 1: Remove the points with fluxes greater than the top $2\%$ flux from the
light curve ($l_{0}$), the new light curve is denoted as $l_{1}$.

  * •

Step 2: Calculate the Lomb-Scargle periodogram (LS; Lomb 1976; Scargle 1982)
of $l_{1}$ using the code LombScargle in the python package astropy.timeseries
(Astropy Collaboration et al. 2013, 2018), then determine the preriod $P_{0}$
of the light curve.

  * •

Step 3: A cubic B-Spline curve with a knot interval of 0.1$P_{0}$ is used to
fit the $l_{1}$, and denote the new B-Spline as $S_{1}$ and
$R_{1}=l_{1}-S_{1}$. Calculate the standard deviation $\sigma_{1}$ of $R_{1}$,
and remove the points with $R_{1}$ values greater than 2$\sigma_{1}$. The new
light curve is denoted as $l_{2}$, and $l_{1}:=l_{2}$. Then repeat this step
again, and obtain the the standard deviation $\sigma$ of $l_{1}$, B-Spline
$S$, and $R=l_{0}-S$ for finding flares.

  * •

Step 4: A flare is detected from $R$ if there are at least 3 (for curves of 2
minutes cadence) or 2 (for curves of 30 minutes cadence) successive fluxes
greater than 2$\sigma$ and the flare peak is greater than 3$\sigma$.

  * •

Step 5: After all flares were removed from the light curve, the rotational
period $P$ was calculated from the out-of-flare light curve by LS.

Figure 1 shows the results of our algorithm. In the upper panel, the red line
is the fitted cubic B-spline, and flares detected are shown in blue. All
flares detected were inspected by eye, and finally obtained 931 flares.

The rotational periods of 31 stars were obtained by the above algorithm, and
the periods of 3 eclipsing binaries were calculated in Section 4. Star #3 (HAT
178-02667) is not observed by TESS and K2, but it has a period of 1.717885
days from Hartman et al. (2011), which may be the orbital period (see Section
4 for details), so there are total 35 GWAC flare stars have periods. Among the
31 stars that have rotational periods, 30 stars have periods less than 5.4
days, and the left one has a period of about 10.42 days, and thus all are
rapid rotators.

Flares and periods detected in TESS and K2 light curves by the above
algorithm, the 43 GWAC flare light curves and the flare movie of Star #4 (G
176-59), #7 LSPM J1542+6537), #28 (G 235-65), and #39 (1RXS J064358.4+704222)
are all given in https://nadc.china-vo.org/res/r101145/.

Figure 1:  Upper panel: the black dots are from a part of the light curve of
Star #1 (TIC 141533801) in Sector 19 of TESS. The red curve is the fitted
cubic B-Spline curve. Lower panel: the black dots are the residuals of the
fluxes minus the fitted cubic B-Spline curve, and the two red lines indicate
$\pm 3\sigma$ positions. In both panels, the detected flares are shown in blue
lines and their peaks are indicted by red dots.

###  2.2 Flare Energy

The equivalent duration (ED) (Gershberg 1972) was used to calculate a flare
energy. ED is defined as: $\sum_{i}\frac{\bigtriangleup
f_{i}}{f}\times\bigtriangleup t$, where, $\bigtriangleup f_{i}$ is a flux
variation at time $t_{i}$ in the flare, $f$ is the quiescent flux and
$\bigtriangleup t$ is the cadence. Then the flare energy is $E=ED\times f$.

GWAC has no filter, and the Gaia $G$ photometry of Gaia DR3 (Gaia
Collaboration 2022) was used to calibrate the GWAC photometry by the GWAC
pipeline, with a photometric accuracy better than 0.1 mag. Thus, we used the
Gaia $G$ band filter and passband zero to calculate the quiescent flux $f$ of
a GWAC flare star. The Gaia $G$ band filter was from Riello et al. (2021), the
Vega spectrum was from Castelli & Kurucz (1994), and the Gaia $G$ magnitude of
Vega was set 0.03 mag (Jordi et al. 2010). As a result, the passband zero
$p_{0}$ of Gaia $G$ band is $9.12\times 10^{-6}$ erg cm-2 s-1.

The distances of GWAC flare stars were calculated from parallaxes of Gaia DR3,
but there are three stars (Star #8 (HAT 149-01951), #14 (HAT 149-01951), and
#29 (HAT 149-01951)) without available parallaxes in Gaia DR3. Then we used
the equation of $M_{Ks}=1.844+1.116(V-J)$ given by Raetz et al. (2020), and
$d=10^{0.2(M_{Ks}-Ks-5)}$ in pc to calculate their distances, where Ks and J
are from 2MASS (Skrutskie et al. 2006), and V is from APASS (Henden et al.
2015). As a result, the quiescent flux in the $G$ band of a star is: $f=\pi
d^{2}p_{0}10^{-0.4G}$ erg s-1.

To obtain flare energies of TESS flares, the TESS response function and the
passband zero from Sullivan et al. (2017) were used. The observed quiescent
flux $f_{o}$ of a star in the TESS passband was the median value of its light
curve multiplied by the TESS passband zero. Thus the the quiescent flux is
$f=\pi d^{2}f_{o}$.

Two stars: Star #15 (HAT 307-06930) and #36 (CU Cnc) only have K2 light
curves. Then the formulae (1) - (6) in Shibayama et al. (2013) were used to
calculate quiescent fluxes in the Kepler passband444The Kepler response
function was from https://keplergo.github.io/KeplerScienceWebsite/the-kepler-
space-telescope.html, with the surface temperatures and stellar radii from
Huber et al. (2016).

We assumed the fare energy was from a blackbody radiation with a temperature
of 9000 K, and then used observed flare energies in Gaia $G$, TESS or $K2$
filters to calculate whole white light flare energies, which should be lower
than the true released flare energies (e.g. Hawley & Pettersen 1991;
Kretzschmar 2011).

###  2.3 Spectra

The Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic
Telescope, LAMOST; Cui et al. 2012) can obtain 4000 spectra in one exposure,
and is located at the Xinglong Observatory, the same place as GWAC and the
2.16m telescope. In LAMOST DR8 555http://www.lamost.org/dr8/v1.1/, there are
about 11 million low-resolution spectra (LRS, $R\sim 1800$) and 6 million
medium-resolution spectra (MRS, $R\sim 7500$). We searched spectra of GWAC
flare stars in LAMOST DR8, and obtained available LRS for 25 stars, and MRS
for 13 stars. Because 11 stars have available both LAMOST LRS and MRS, there
are 27 stars have LAMOST spectra. We also obtained LRS of another 7 flare
stars by the 2.16m telescope with the instrument G5. The spectral resolution
is about 2.34 Å pixel-1, and the wavelength coverage is 5200 Å- 9000 Å(Zhao et
al. 2018). In sum, 32 of 43 flare stars have LSR, and 7 have LAMOST MRS.

The spectroscopic standards from Kirkpatrick et al. (1991) were used to assign
spectral types of M stars that have LRS from LAMOST or the 2.16m telescope.
For stars that have spectral types earlier than M0, their spectral types are
from LAMOST DR8.

The Color-Magnitude Diagram (CMD) of flare stars with their spectra types are
shown in Figure 2, where Gaia $G$, parallax $\varpi$ ( in milliarcsecond),
$G_{bp}-G_{rp}$ are from Gaia DR3, and the absolute magnitude $M_{G}=G+5{\rm
log}_{10}(\varpi)-10$. For 32 stars that have LRS, their H$\alpha$ are all
shown in emission, which indicate they are all active stars. Among them,
thirty-one stars were assigned spectral types and are shown in different
symbols and colors in Figure 2. Star #21 was assigned a spectral type of M3,
but with a bluer color in Figure 2. We found that its $ruwe=2.478$ in Gaia
DR3, which implies that there may be some astrometric problems or it is not a
single star, thus the Gaia photometry is unreliable. Star #18 (DR Tau) is not
in Figure 2, because it is a T Tauri star (Chavarria-K. 1979), and there is no
available absorption line in its spectrum for spectral classification.

For the other 11 stars without available spectra in this paper, their spectral
types were also assigned by their $G_{bp}-G_{rp}$ in Figure 2. Among them,
Star #9 (2MASS J04542368+1709534; Herczeg & Hillenbrand 2014), #23 (1RXS
J101627.8-005127; Zickgraf et al. 2005), #27 (1RXS J120656.2+700754; Christian
et al. 2001), #28 (G 235-65; Reid et al. 2004), #30 (1RXS J082204.1+744012;
Fleming et al. 1988), and #35 (1RXS J075554.8+685514; Zickgraf et al. 2005)
had been identified as active stars in the literature.

Figure 2: The Color-Magnitude Diagram (CMD) of flare stars with their spectral
types. $M_{G}$ is the absolute magnitude of Gaia $G$. $G$, $G_{bp}$ and
$G_{rp}$ are from Gaia DR3. The 31 stars that have LRS are shown in different
symbols and colors for different spectral types. The black dots are the stars
that have not available spectra in this paper.

In sum, there are one G type star, four K type stars, thirty-seven M type
stars, and one T Tauri in our sample. Figure 3 shows the distribution of
spectral types of GWAC flare stars, except one T Tauri (Star #18; DR Tau).

Figure 3: The distribution of spectral types of GWAC flare stars, except one T
Tauri (Star #18; DR Tau).

To calculate the Hα emission luminosity $L_{\rm H_{\alpha}}$, the Sérsic
function (Sersic 1968) was used to fit Hα emission profiles. The function is:
$F(\lambda)=A_{0}\exp(Z^{A_{3}}/A_{3})+A_{4}+A_{5}\lambda$, where
$Z=|(\lambda-A_{1})/A_{2}|$, $\lambda$ is wavelength in Å, and $A_{i}$,
$i=0,\cdots,5$ are coefficients to be fitted. The wavelength range was set to
$6564.61\pm 20$ Å(6564.61 Åis the vacuum wavelength of H$\alpha$), and the
LAMOST spectral luminosity of H$\alpha$: $L^{\prime}_{\rm
H_{\alpha}}=\int_{6544.61}^{6584.61}A_{0}\exp(Z^{A_{3}}/A_{3})d\lambda$. The
fluxes of LAMOST spectra are not calibrated, but there is only a constant
ratio between each spectrum and its true flux. For each star that has LAMOST
LRS, we calculated its spectral flux $f_{L}$ from its LRS spectrum in the SDSS
r′ filter (Fukugita et al. 1996), and its observed flux $f_{A}$ from r′ given
by APASS (Henden et al. 2015). Then its $L_{\rm H\alpha}=L^{\prime}_{\rm
H\alpha}*f_{A}/f_{L}$.

To obtain the quiescent bolometric luminosity $L_{\rm bol}$ of a star,
photometric data from r′, g′ and i′ of APASS (Henden et al. 2015), J, H, and
Ks of 2MASS (Skrutskie et al. 2006), and W1, W2, W3, and W4 of WISE (Jarrett
et al. 2011) for each star, were fitted by a blackbody irradiation function.
In the calculation, the reference wavelengths and the zero points of all
filters were from the SVO Filter Profile Service 666http://svo2.cab.inta-
csic.es/theory/fps/ (Rodrigo & Solano 2020). Finally, $L_{\rm H\alpha}/L_{\rm
bol}$ can be obtained. $L_{\rm H\alpha}/L_{\rm bol}$ that can be calculated
from spectra are listed in Table 3. Because one star can have several LAMOST
spectra, and one spectra has one $L_{\rm H\alpha}/L_{\rm bol}$, so there are
several $L_{\rm H\alpha}/L_{\rm bol}$ for a star in Table 3.

The information of GWAC flare stars with their GWAC flares are given in Table
LABEL:tab:gwacflare.

##  3 Flare Profiles

###  3.1 Sympathetic or homologous flares

Based on an enormous amount of observations, solar flares are well known to be
produced by magnetic reconnections in active regions (ARs; Toriumi & Wang
2019). Solar ARs are the regions full of intense magnetic fields with complex
morphologies (McIntosh 1990; Sammis et al. 2000). Successive flares are often
observed on the Sun and are identified as sympathetic activity from different
regions with physical causal links (Pearce & Harrison 1990; Moon et al. 2002;
Schrijver & Higgins 2015; Hou et al. 2020), or homologous ones occurring in
the same AR (e.g. Louis & Thalmann 2021; Xu et al. 2014).

It is interesting that there are three pairs of flares successively appearing
among the 43 GWAC samples as shown in Figure 4. Each pair of flares occurred
following a similar profile of light curves in the interval of 20-50 minutes.
The morphology of the light curves during a flare may reflect the release
processes of magnetic energies, and manifest complex magnetic topology of the
intense magnetic fields. The successive occurrence of three pairs of stellar
flares indicate that the cool stars may share the similar physical magnetic
explosions to those sympathetic flares or homologous ones happening on the
Sun. With the development of future imaging observations for the other stars,
it is anticipated to unveil these possibly universal physical mechanisms.

Figure 4: Successive flares from Star #16 (TIC 29172363), #19 (TIC 274086357;
1RXS J031750.1+010549), and #39 (TIC 289040091; 1RXS J064358.4+704222).

###  3.2 Quasi-periodic pulsation

Quasi-periodic pulsations (QPPs) are very common phenomenons in solar flares
(Van Doorsselaere et al. 2016; Simões et al. 2015; Kupriyanova et al. 2010),
but QPPs in stellar white light flares are still rare (Howard & MacGregor
2022; Pugh et al. 2016). More than a dozen of mechanisms were suggested to
trigger QPPs (Kupriyanova et al. 2020). Coronal loop lengths can be derived
from periods of QPPs from some mechanisms with some theoretical considerations
(Ramsay et al. 2021). The periods of QPPs in white light curves are of tens
minutes (Ramsay et al. 2021; Pugh et al. 2016), but at short cadence (20
seconds) of TESS, QPP periods less than 10 minutes were also found (Howard &
MacGregor 2022).

GWAC has a cadence of 15 seconds, shorter than TESS, and make it possible to
find QPPs with short periods in GWAC white light flares. One flare occurring
on Star #16 (TIC 29172363) was found to indicate a QPP process as shown by the
red light curve in the left panel of Figure 5. The function
$f(t)=A_{0}\times\exp(A_{1}t)+A_{2}$ was used to fit the background of the QPP
signal, and shown by the blue curve in the left panel of Figure 5. Here,
$A_{0},A_{1}$ and $A_{2}$ are parameters to be fitted, and $t$ is time in
seconds. According to the light curve after subtracting the background
information, a character manifested by QPP process is shown in the middle
panel of Figure 5, and is analyzed by using the LS periodogram. The right
panel of Figure 5 shows the periodogram result. A period of $13.0\pm 1.5$
minutes is obtained for the QPP process.

Figure 5: The QPP of Star #16 (TIC 29172363). Left panel: the QPP position in
the flare is indicated in red. The blue curve is the fitted background. Middle
panel: the QPP signal without background. The blue curve is the fitted QPP
with a period of 13.0 minutes; Right panel: the LS periodogram of the QPP
signal in the middle panel.

##  4 Binary and multiple systems

We inspected all GWAC flare stars in Aladin (Bonnarel et al. 2000) and Gaia
DR3, and found that there are 11 binaries and one triple system. Among them,
Star #27 (TIC 142979644; 1RXS J120656.2+700754), #32 (TIC 382379884) and #36
(EPIC 211944670; CU Cnc) hold close eclipsing binaries. To obtain periods of
binaries, we fitted the eclipse minimum times by quadratic polynomials of
light curves, and ephemerides were calculated by fitting the eclipse minimum
times. The ephemerides (in BJD) of Star #27 (TIC 142979644; 1RXS
J120656.2+700754), #32 (TIC 382379884) and #36 (EPIC 211944670; CU Cnc) are

$T_{min}-2457000=1683.36653104(\pm 0.00002399)+4.17903758(\pm 0.00000027)E$

,

$T_{min}-2457000=2144.48865796(\pm 0.00010348)+0.45825824(\pm 0.00000316)E$

, and

$T_{min}-2454833=2306.95408506(\pm 0.00199451)+2.77147142(\pm 0.00001076)E$

, respectively. Here, $E$ is the circle number, and $T_{min}$ is the eclipse
minimum time. O - C diagrams and light curves in phase are shown in Figure 6.
Star #36 (EPIC 211944670; CU Cnc) is a triple system in Gaia DR3, so its
ephemerides may be disturbed by the third star.

The secondary eclipse minimum of Star #27 (TIC 142979644; 1RXS
J120656.2+700754) deviate from the phase 0.5 in Figure 6, so it has an
eccentricity. We used the formulae 1 and 2 in Lei et al. (2022) to calculate
its eccentricity ($e$) and periastron angle ($\omega$). From our calculation,
its secondary eclipse phase $\phi_{2}=0.518$ (its primary eclipse phase
$\phi_{1}=0$), and the widths of the primary and secondary eclipses were
determined by eye, which are $w_{1}\sim 0.0176$ and $w_{2}\sim 0.018$,
respectively. Then,
$e\cos(\omega)=\frac{\pi}{2}\left[\phi_{2}-\phi_{1}-0.5\right]=0.028274$ and
$e\sin(\omega)=\frac{w_{2}-w_{1}}{w_{2}+w_{1}}\sim 0.011236$. As a result,
$e\sim 0.03$ and $\omega\sim 0.387$.

Figure 6: O - C diagrams and light curves in phases of Star #27 (TIC
142979644; 1RXS J120656.2+700754), #32 (TIC 382379884) and #36 (EPIC
211944670; CU Cnc) are shown in the left and right columns, respectively.

Star #3 (HAT 178-02667) has no Li I 6708 line in its LAMOST MRS as shown in
the right panel of Figure 7, which implies that it is not a young star, and
thus it unlikely holds a curcumstellar disk. Its $ruve=7.65$ in Gaia DR3 and
there are double H$\alpha$ emissions in its LAMOST MRS as shown in the left
panel of Figure 7, so it is likely a binary system and double H$\alpha$
emissions indicate both components are active stars. In Hartman et al. (2011),
it has a period of 1.717885 days.

Figure 7: The LAMOST MRS of Star #3 (HAT 178-02667). Left panel: Double
H$\alpha$ emissions of Star #3 (HAT 178-02667); Right panel: There is no Li I
6708. The positions of H$\alpha$ and Li I 6708 in vacuum are indicated in red
lines.

##  5 H$\alpha$

H$\alpha$ is a very important indicator of stellar activity. Stars with strong
H$\alpha$ emissions in their quiescent spectra are very likely to show strong
flare activities (Kowalski et al. 2009). Figure 8 shows the relationship
between H$\alpha$ luminosity from 44 spectra of 21 M dwarfs and $Ro=P_{\rm
rot}/\tau$, where $P_{\rm rot}$ is the stellar rotational period and $\tau$ is
the convective turnover time calculated from Equation 10 in Wright et al.
(2011). For M type stars, their $L_{\rm X}/L_{\rm bol}$ shows saturation (e.g.
Wright et al. 2018; Pizzolato et al. 2003) and even supersaturation (e.g.
Jeffries et al. 2011) for rapid rotators. Compared to Figure 7 in Newton et
al. (2017), our sample stars are all rapid rotators, and in the saturation
region as shown In Figure 8.

Figure 8: The relationship between $Ro$ and $L_{\rm H\alpha}/L_{\rm bol}$. The
red line and dotted lines are the relationship and 1$\sigma$ contours given in
(Newton et al. 2017).

##  6 Habitablity

Stellar activity is a double-edged sword for life on a habitable planet. On
one hand, flare activities can contribute the generation and development of
life (Rimmer et al. 2018), on the other hand erode and even destroy the ozone
of a habitable-zone exoplanet (Tilley et al. 2019). We used Equation 10 in
Günther et al. (2020) to delineate ”abiogenesis zone,” which means the flare
frequency in this zone can contribute the prebiotic chemistry and then promote
life generation.

The flare frequency distribution (FFD) is the cumulative flare energy
frequency in per day (Gershberg 1972; Günther et al. 2020), and often used to
show how often a flare energy higher than a given value is. We obtained FFDs
of 13 single stars with more than 20 flares detected in TESS or $K2$ light
curves, and a power law function ${\rm log}_{10}(\nu)=\alpha{\rm
log}_{10}(E_{\rm bol})+\beta$ was used to fit each FFD, where $\nu$ is the
cumulative flare frequency in day-1, $E_{\rm bol}$ is the flare energy in erg,
$\alpha$ and $\beta$ are parameters to be fitted. We also calculated the flare
frequency $\nu$ of the GWAC flare energy using the fitted $\alpha$ and $\beta$
for each star, and found GWAC flares can occur at a frequency of 0.5 to 9.5
yr-1.

Flares with $E_{\rm bol}\geqslant 10^{34}$ erg can impact atmospheres of
habitable planets. The cumulative flare frequency of $\nu\geqslant 0.4$ day-1
can remove more than 99.99% of the ozone layer of a habitable-zone exoplanet
as suggested by Tilley et al. (2019), and a more permissive frequency limit is
$\nu\geqslant 0.1$ day-1.Though the flare temperature of 9000 K is popularly
used in literature, but the flare temperature can reach as high as 30000 K and
even 42000 K (Howard et al. 2020b). In Figure 9, blue lines for a flare
temperature of 9000 K, while pink lines for 30000 K. We can see that for the
flare temperature of 9000 K, two stars (TIC 88723334 and TIC 416538839)
produce flares with energies greater than $10^{34}$ erg in the highest
frequencies, but still can not destroy ozone layers of their habitable
planets. However, for the flare temperature 30000 K, almost all stars can
produce energetic flares to destroy ozone layers of their habitable planets,
except Star #28 (TIC 103691996).

Equation 10 in Günther et al. (2020) was also used to calculate the flare
frequency limit for prebiotic chemistry. These frequency limits are shown by
brown lines in Figure 9, and there is no star having enough high energetic
flares to trigger prebiotic chemistry on its habitable planets.

Figure 9: FFDs of 13 flaring single stars with flare numbers greater than 20.
The grey dots are the flare frequency obtained from TESS or $K2$ light curves,
and their fitted power law functions are shown by blue lines for a flare
temperature of 9000 K, while pink lines for 30000 K. The yellow line is
log${}_{10}(E_{\rm bol})=34$, and $\nu=0.1$ and 0.4 are shown in cyan and
green lines, respectively. The brown lines represent the abiogenesis zones for
flare stars calculated by Equation 10 in Günther et al. (2020).

##  7 Conclusion

In this paper, we studied the 43 flares from 43 stars found in the GWAC
archive between December 2018 and May 2019, by combining light curves from
TESS and $K2$, spectra from LAMOST and the 2.16m telescope the Xinglong
Observatory, and parallax and photometry from Gaia DR3, and obtained the
following results:

  1. 1.

We found 19 new active stars.

  2. 2.

We found 3 sympathetic or homologous flares, which imply that the cool stars
may share the similar physical magnetic explosions to those happening on the
Sun.

  3. 3.

We found a white light QPP in the sympathetic or homologous flare of Star #16
(RX J0903.2+4207) with a period of $13.0\pm 1.5$ minutes, which shows the
advantage of GWAC with a cadence of 15 seconds in discovering white light QPPs
with short periods.

  4. 4.

Thirty-four stars have rotational or orbital periods less than 5.4 days and
only one star has a period of $\sim$10.42 days.

  5. 5.

Eleven stars are binaries and one is a triple system. The ephemerides of three
binaries are calculated from their light curves, and one of them (Star #27;
1RXS J120656.2+700754) also has an eccentricity of $e\sim 0.03$. Star #3 (HAT
178-02667) has no light curve, but double H$\alpha$ emissions in its LAMOST
medium-resolution spectrum imply a binary.

  6. 6.

$L_{\rm H\alpha}/L_{\rm bol}$ shows that the rapid rotators in GWAC flare
stars are in the saturation region in the rotation-activity diagram.

  7. 7.

Some of GWAC flare stars may produce enough energetic flares to destroy the
ozone layer, but none can trigger prebiotic chemistry on its habitable planet.

Big flares with amplitudes greater than 1 mag detected by GWAC, can trigger
telescopes in the Xinglong Observatory to follow up. Some research results
have been obtained based on these observations (Xin et al. 2021; Wang et al.
2021, 2022). In future, we will continue to analysis these big flares to study
their generation mechanisms and impacts on habitable planets.

Table 1: GWAC flare stars # | Name | Other Name | New | R.A. J2000 | Decl. J2000 | Dis | Gmag | bp-rp | SpT | Multi | Period | Date | Start | End | Flare Energy | ED
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  | degree | degree | pc | mag | mag |  |  | days | yyyymmdd | hhmmss | hhmmss | $\rm log_{10}(erg)$ | seconds
1 | TIC 141533801 | PM J06521+7908 |  | 103.040098 | 79.14838 | 39.98 | 10.514 | 1.68 | M0 |  | 5.20898(0.42182) | 20190223 | 123107 | 141352 | 35.09(0.10) | 4485
2 | TIC 8688061 | PM J09108+3127 |  | 137.701223 | 31.45744 | 27.04 | 12.506 | 2.653 | M3 |  | 4.24599(0.27568) | 20190225 | 134702 | 150947 | 33.6(0.17) | 2028
3 |  | HAT 178-02667 | Y | 131.491539 | 36.59261 | 96.88 | 13.465 | 2.391 | (M2.5) | Binary | 1.717885 | 20190225 | 134702 | 150947 | 34.69(0.47) | 4626
4 | TIC 253050844 | G 176-59 | Y | 177.70409 | 45.56739 | 29.6 | 14.033 | 3.029 | M4.5 |  |  | 20190403 | 144350 | 180450 | 33.82(0.59) | 11285
5 | TIC 392402786 | BD+48 1958 |  | 174.352417 | 47.46249 | 33.47 | 10.034 | 1.687 | M0 | Binary | 1.03001(0.01528) | 20190403 | 144350 | 180450 | 34.98(0.09) | 1851
6 | TIC 416538839 | StKM 2-809 |  | 183.914031 | 52.65242 | 25.1 | 11.373 | 2.608 | M3 |  | 0.72597(0.00680) | 20190403 | 144350 | 180450 | 34.3(0.13) | 4151
7 | TIC 334637014 | LSPM J1542+6537 |  | 235.554214 | 65.61809 | 38.92 | 13.233 | 2.889 | M4.5 |  | 0.61722(0.00399) | 20190403 | 180612 | 205708 | 34.07(0.40) | 5561
8 | TIC 162673744 | HAT 149-01951 | Y | 246.061458 | 48.39066 | 59.69 | 13.615 | 2.482 | M3 |  | 1.63170(0.04786) | 20190502 | 165833 | 200324 | 34.22(0.37) | 4755
9 | TIC 436680588 | 2MASS J04542368+1709534 |  | 73.598678 | 17.16485 | 143.62 | 16.617 | 2.365 | (M2.5) | Binary |  | 20190113 | 102051 | 134136 | 35.37(0.51) | 9090
10 | TIC 20161577 | HAT 138-01877 | Y | 145.345992 | 43.97308 | 99.51 | 12.793 | 1.78 | (M1) |  | 3.13022(0.14959) | 20190125 | 151425 | 170400 | 34.19(0.08) | 746
11 | TIC 88723334 | G 196-3 | Y | 151.089429 | 50.38705 | 21.81 | 10.615 | 2.35 | M2.5 |  | 1.31341(0.02628) | 20190125 | 151425 | 201525 | 34.56(0.09) | 4946
12 | TIC 323688555 | GJ 3537 |  | 137.413115 | 6.70305 | 23 | 12.081 | 2.629 | M3 |  | 4.06548(0.30373) | 20190224 | 135938 | 153823 | 33.36(0.10) | 1068
13 | TIC 318230983 | HAT 140-00487 | Y | 162.861825 | 48.69546 | 79.05 | 11.429 | 1.817 | M1 |  | 4.06913(0.25229) | 20190124 | 175515 | 211330 | 35.53(0.19) | 7433
14 |  | 1RXS J075908.2+171957 |  | 119.779882 | 17.32982 | 24.16 | 12.706 | 2.8 | (M4) |  | 0.48204(0.00411) | 20190113 | 135650 | 185505 | 33.5(0.29) | 2382
15 | EPIC 210701183 | HAT 307-06930 | Y | 55.739582 | 18.37965 | 132.82 | 14.414 | 2.184 | M1 |  | 1.67409(0.01648) | 20190112 | 102758 | 141043 | 34.75(0.69) | 6870
16 | TIC 29172363 | RX J0903.2+4207 |  | 135.811479 | 42.12356 | 79.49 | 11.647 | 1.703 | M0 |  | 1.49055(0.03069) | 20190201 | 170000 | 193443 | 35.44(0.13) | 7350
17 | TIC 283729913 |  | Y | 63.455228 | 9.21321 | 104.41 | 14.03 | 2.222 | M2.5 |  |  | 20190114 | 113000 | 140052 | 34.36(0.42) | 3188
18 | TIC 436614005 | DR Tau |  | 71.775897 | 16.97856 | 192.97 | 11.651 | 1.621 | T Tau |  |  | 20190114 | 101252 | 154952 | 36.71(0.24) | 23321
19 | TIC 274086357 | 1RXS J031750.1+010549 | Y | 49.457729 | 1.10221 | 151.67 | 12.219 | 1.38 | K3 |  | 0.63653(0.01102) | 20181223 | 125610 | 162440 | 35.72(0.29) | 6484
20 | TIC 427020004 | HAT 307-01221 | Y | 49.572707 | 18.40566 | 94.92 | 11.693 | 1.495 | K5 |  | 3.16524(0.22178) | 20190111 | 120004 | 151035 | 35.22(0.09) | 3200
21 | TIC 114059158 |  | Y | 55.304975 | 20.85436 | 140.32 | 13.862 | 1.96 | M3 |  | 0.31366(0.00193) | 20181230 | 145636 | 162551 | 34.88(0.28) | 4953
22 | TIC 195188536 | DF Cnc |  | 128.870322 | 18.20561 | 49.23 | 12.906 | 2.376 | M3 |  | 5.35280(0.62707) | 20190112 | 144958 | 195145 | 34.11(0.15) | 2810
23 | TIC 77644831 | 1RXS J101627.8-005127 |  | 154.112263 | -0.86091 | 60.15 | 12.329 | 2.136 | (M1.5) |  | 0.74709(0.00835) | 20190114 | 155759 | 191159 | 34.58(0.11) | 3307
24 |  |  | Y | 153.304236 | 2.80498 | 105.46 | 17.593 | 3.115 | (M5) |  |  | 20190213 | 170041 | 180211 | 34.04(0.27) | 1780
25 | TIC 374270454 | 1RXS J103715.4+020612 | Y | 159.314334 | 2.09753 | 71.84 | 11.829 | 1.951 | M1 |  | 3.51123(0.28641) | 20190106 | 175650 | 205650 | 34.59(0.06) | 1491
26 | TIC 142877499 | G 236-81 |  | 176.772653 | 70.03285 | 30.62 | 13.093 | 2.856 | (M4) | Binary | 10.42161(0.9949) | 20190121 | 153702 | 205732 | 34.73(0.54) | 16582
27 | TIC 142979644 | 1RXS J120656.2+700754 |  | 181.73505 | 70.13054 | 17.37 | 10.892 | 2.845 | (M4) | Binary | 4.17903758(0.00000027) | 20190318 | 134018 | 190333 | 33.65(0.12) | 1065
28 | TIC 103691996 | G 235-65 |  | 154.787606 | 66.49275 | 29.26 | 13.053 | 2.662 | (M3.5) |  |  | 20190216 | 164856 | 195511 | 34.14(0.37) | 9772
29 | TIC 99173696 |  | Y | 123.681926 | 46.84348 | 39.3 | 13.745 | 2.84 | M4 |  | 1.78860(0.01522) | 20190206 | 162410 | 185425 | 33.37(0.25) | 1733
30 | TIC 153858162 | 1RXS J082204.1+744012 |  | 125.533783 | 74.67285 | 47.66 | 12.264 | 2.266 | (M3) |  | 1.97116(0.05626) | 20190121 | 154417 | 183817 | 34.00(0.24) | 1297
31 | TIC 270478293 | LP 589-69 | Y | 34.197584 | 1.2126 | 31.51 | 12.476 | 2.532 | M3 |  | 4.49044(0.33040) | 20181224 | 120134 | 142234 | 33.31(0.21) | 735
32 | TIC 382379884 |  | Y | 45.066475 | -3.04574 | 114.87 | 12.073 | 1.53 | M0 | Binary | 0.45825824(0.00000316) | 20190127 | 102150 | 140010 | 35.48(0.14) | 4360
33 | TIC 435308532 | LP 413-19 |  | 54.392052 | 17.85 | 38.8 | 12.079 | 2.712 | M3 | Binary | 0.47630(0.00278) | 20190204 | 113935 | 131650 | 34.12(0.06) | 890
34 | TIC 440686488 | V660 Tau |  | 57.116786 | 23.30076 | 134.02 | 12.242 | 1.319 | K5 |  | 0.23520(0.00104) | 20190204 | 113935 | 131650 | 35.54(0.24) | 5538
35 | TIC 457100137 | 1RXS J075554.8+685514 |  | 118.972289 | 68.9069 | 29.2 | 13.056 | 2.844 | (M4) |  | 0.53285(0.00445) | 20 |  |  | 33.18(0.16) | 1077
36 | EPIC 211944670 | CU Cnc |  | 127.906559 | 19.39428 | 16.65 | 10.576 | 2.861 | M3.5 | Triple | 2.7714842(0.00001076) | 20190101 | 145240 | 190810 | 33.96(0.09) | 1565
37 | TIC 224304406 | 1RXS J123415.2+481306 |  | 188.564232 | 48.21862 | 46.83 | 13.135 | 2.675 | M3 |  | 0.94869(0.01295) | 20190206 | 191205 | 221635 | 33.71(0.18) | 1535
38 |  | BX Ari |  | 44.546799 | 20.50087 | 234.85 | 11.921 | 1.541 | K3 | Binary | 2.83690(0.14557) | 20181229 | 135121 | 163451 | 36.35(0.16) | 6342
39 | TIC 289040091 | 1RXS J064358.4+704222 |  | 100.994199 | 70.70326 | 59.56 | 13.348 | 2.402 | M3 |  | 0.54374(0.00562) | 20181215 | 162100 | 174019 | 34.42(0.62) | 5981
40 | TIC 16246712 |  | Y | 153.803156 | 37.86495 | 95.42 | 12.945 | 2.066 | M1 | Binary |  | 20 |  |  | 34.78(0.14) | 1756
41 | TIC 445830121 |  | Y | 173.045411 | 52.09011 | 42.3 | 13.465 | 2.503 | M3 | Binary |  | 20190106 | 210011 | 222626 | 33.59(0.48) | 1790
42 | TIC 197251248 | G 9-38 |  | 134.558692 | 19.76258 | 5.15 | 11.966 | 3.777 | M7 | Binary | 0.25397(0.00150) | 20190211 | 150414 | 155014 | 32.51(0.15) | 1704
43 | TIC 316276917 |  | Y | 133.388088 | 56.78993 | 225.65 | 12.087 | 1.042 | G7 |  | 0.65862(0.00688) | 20181227 | 165728 | 211943 | 35.56(0.15) | 1797

0.86 1, The bolometric flare energies were calculated from GWAC flares
assuming a blackbody with a temperature of 9000 K. The fraction of the
bolometric energy in the Gaia $G$ band is $\frac{f_{G}}{f_{\rm bol}}\approx
0.3$.
2, Spectral types in parentheses are assigned based on $G_{\rm rp}-G_{\rm
bp}$.
3, The period of Star #3 is from Hartman et al. (2011).

Table 2: Data of which TESS Sector and K2 Campaign was used

Star # | Name | Sectors
---|---|---
1 | TIC 141533801 | 19,20,26,40
2 | TIC 8688061 | 21
3 |  |
4 | TIC 253050844 | 22
5 | TIC 392402786 | 22
6 | TIC 416538839 | 22
7 | TIC 334637014 | 14,15,16,17,21,22,23,24,41
8 | TIC 162673744 | 23,24,25
9 | TIC 436680588 | (43),(44)
10 | TIC 20161577 | 21
11 | TIC 88723334 | 21
12 | TIC 323688555 | 8,34,45
13 | TIC 318230983 | 21
14 |  | 44,45,46
15 | EPIC 210701183 | 4
16 | TIC 29172363 | 21
17 | TIC 283729913 | 5,23
18 | TIC 436614005 | (43),(44)
19 | TIC 274086357 | 4,31
20 | TIC 427020004 | 42,43
21 | TIC 114059158 | 42,43,44
22 | TIC 195188536 | 44,45
23 | TIC 77644831 | 8,35,45
24 |  |
25 | TIC 374270454 | 35,45
26 | TIC 142877499 | 21
27 | TIC 142979644 | 14,15,21,41
28 | TIC 103691996 | 14,21,40,41
29 | TIC 99173696 | 20
30 | TIC 153858162 | 20,26,40,47,53
31 | TIC 270478293 | 4,31
32 | TIC 382379884 | (4),31
33 | TIC 435308532 | 42,43,44
34 | TIC 440686488 | 42,43,44
35 | TIC 457100137 | 20,26,40
36 | EPIC 211944670 | 5,18
37 | TIC 224304406 | 22
38 |  | (42),(43),(44)
39 | TIC 289040091 | 19,20,26
40 | TIC 16246712 | 21
41 | TIC 445830121 | 21,(22)
42 | TIC 197251248 | 44,45
43 | TIC 316276917 | 20

0.86 The TESS sectors in parentheses mean that the data of these sectors are
not available for this work.

Table 3: H$\alpha$ luminosity.

Star # | R. A. J2000 | Decl. J2000 | $\lg(L_{\rm H\alpha}/L)$
---|---|---|---
| degree | degree |
2 | 137.702323 | 31.457447 | -3.78(+0.01),-3.79(+0.01),-3.58(+0.00)
4 | 177.704090 | 45.567390 | -3.63(+0.01)
5 | 174.352814 | 47.462439 | -5.05(+0.01)
6 | 183.914032 | 52.652434 | -3.69(+0.00),-3.68(+0.00),-3.78(+0.01)
7 | 235.554210 | 65.618100 | -3.15(+0.00)
8 | 246.061805 | 48.390525 | -3.66(+0.01)
9 | 73.598465 | 17.162068 | -4.22(+0.02)
11 | 151.089442 | 50.387056 | -3.67(+0.01),-3.65(+0.00)
12 | 137.413190 | 6.703040 | -3.63(+0.00),-3.64(+0.00),-3.68(+0.00)
13 | 162.861881 | 48.695440 | -4.01(+0.01),-4.09(+0.01)
15 | 55.739577 | 18.379597 | -3.83(+0.01),-3.92(+0.01),-3.94(+0.01)
16 | 135.811466 | 42.123555 | -3.82(+0.01)
17 | 63.455420 | 9.213330 | -4.30(+0.01)
18 | 71.775872 | 16.978558 | -2.47(+0.01),-2.75(+0.01)
19 | 49.457706 | 1.102194 | -3.80(+0.01)
20 | 49.572717 | 18.405648 | -4.07(+0.02)
21 | 55.306192 | 20.854802 | -3.48(+0.00),-4.60(+0.05),-3.56(+0.01),-3.83(+0.02)
22 | 128.870334 | 18.205612 | -3.84(+0.01),-3.86(+0.01),-3.87(+0.01)
26 | 159.314354 | 2.097543 | -4.21(+0.03),-4.21(+0.02)
30 | 123.681884 | 46.843252 | -3.67(+0.00)
32 | 34.197623 | 1.212631 | -3.94(+0.01)
35 | 57.116787 | 23.300774 | -3.85(+0.01),-3.82(+0.01)
37 | 127.906510 | 19.394273 | -3.78(+0.00),-3.76(+0.00),-3.73(+0.00)
38 | 188.564219 | 48.218640 | -3.74(+0.01),-3.74(+0.01),-3.59(+0.01)
39 | 44.546799 | 20.500874 | -3.58(+0.01)
40 | 100.993690 | 70.702840 | -3.69(+0.00),-3.82(+0.01)
41 | 153.802305 | 37.864154 | -3.76(+0.02),-3.98(+0.05),-3.61(+0.02)

0.86Each spectrum provides one $\lg(L_{\rm H\alpha}/L)$, with the error in the
following parenthesis.

###### Acknowledgements.

We thank our anonymous referee for the insightful comments. This work is
supported by the National Natural Science Foundation of China (NSFC) with
grant No. 12073038. This work is supported by the Joint Research Fund in
Astronomy U1931133 under cooperative agreement between the National Natural
Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS). Chen
Yang, Chao-Hong Ma, Xu-Kang Zhang, Xin-Li Hao, and Xiao-Feng Meng acknowledges
the NSFC with grant No. 61941121. Jie Chen acknowledges the Beijing Natural
Science Foundation, No. 1222029. Guang-Wei Li thanks Dr. Ting Li for helpful
discussions. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber
Spectroscopic Telescope LAMOST) is a National Major Scientific Project built
by the Chinese Academy of Sciences, Funding for the project has been provided
by the National Development and Re- form Commission. LAMOST is operated and
managed by the National Astronomical Observatories, the Chinese Academy of
Sciences. We acknowledge the support of the staff of the Xinglong 2.16m
telescope. This work was partially supported by the Open Project Program of
the Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences. This research has made use of ”Aladin sky atlas”
developed at CDS, Strasbourg Observatory, France.

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