Geomagnetism and Aeronomy, 2022, Vol. 62, No. 7, pp. 903–910. DOI:
10.1134/S0016793222070131 Activity of Selected Solar Twins M. M. Katsovaa,*,
B. A. Nizamova, and A. A. Shlyapnikovb solar twins, stars: activity, stars:
coronae, stars: rotation, stellar flares, lithium abundance We analyze various
tracers of magnetic activity for 23 solar twins which are characterized by
significant scatter of lithium abundance in their atmospheres. A level of
coronal and chromospheric activity has been studied from available X-ray and
UV-archival data. It gives us a chance to compare coronae of solar twins of
various ages with the solar case. We found a scatter in the X-ray to
bolometric luminosity ratio $L_{\rm X}/L_{\rm bol}$ by several orders of
magnitude, which exists in these stars along with a significant spread in Li
abundance. This may link the surface activity of stars with phenomena at the
base of their convective zones. The TESS data allowed us to reveal rotation
modulation of stellar brightness associated with starspots. For some twins of
our samples, periods of axial rotation are detected around 6 days, i.e. these
stars rotate almost 4 times faster than the contemporary Sun. This indicates
their relative youth. Flare activity of solar twins is discovered in the TESS
data; we showed existence of various kinds of flares, and present temporal
profiles for some of them. We obtained the energy about of $8\times
10^{33}\,$erg for the largest flare of our samples, lasting longer than 4 h.
In addition, we discuss also magnetic fields and exoplanets, orbiting these
stars. DOI 10.1134/S0016793222070131

##  1 INTRODUCTION

The solar-like magnetic activity phenomena are inherent in stars on the lower
part of the main sequence. Among solar-type stars there are solar analogues
with fundamental parameters similar to the solar ones, and the solar twins can
be identified as stars which have the same physical properties as those of the
Sun: mass, radius, luminosity, chemical composition, rotation, and activity.
This should mean that the spectrum of a solar twin should be identical to that
of the Sun. However there is a set of solar twins that have a significant
scatter in the lithium abundance in their atmospheres (Mishenina et al.,
2020). Understanding the reasons for this behaviour of lithium is important in
studying the stellar evolution and the chemical evolution of the Galaxy.
Insofar as 7Li is destroyed at temperatures $\sim 2.5\times 10^{6}\,$K,
knowledge of the abundance of lithium provides an effective tool for studying
the various mixing processes inside solar-type stars that lead to changes in
its abundance. These processes include, first of all, convection, microscopic
diffusion, meridional circulation, and chromospheric activity. In addition to
the initial conditions with which a star enters the main sequence, one of the
factors affecting the abundance of lithium may be the activity (Mishenina et
al., 2012). The latter is important point in understanding the evolution of
solar-type activity during the further life of a star on the main sequence
(Katsova et al., 2013).

Figure 1:  The left panel: the coronal activity index, $L_{\rm X}/L_{\rm bol}$
for solar twins versus rotation velocities $v\sin i$; two values for the Sun
at minimum and maximum activity level are also plotted as crosses (Peres et
al., 2000). The right panel: the near UV- to the bolometric luminosity ratio
versus the velocities $v\sin i$.

We consider here evidences for activity of 23 solar twins out of 55 solar
analogues for which effective temperature, gravity $\log g$, and metallicity
[Fe/H] differ from the solar values by maximum 100 K, 0.1 dex, and 0.1 dex
respectively (Mahdi et al., 2016). Mishenina et al. (2020) found significant
scatter of lithium abundance in their atmospheres. These targets are proxies
of the Sun that essentially differ only in their rotation periods (and,
therefore, age) and hence in the efficiency of the magnetic dynamo. For a
given main-sequence stellar mass, the rotation period is a rather well defined
function of the star’s age if the latter exceeds a few 100 Myr. Magnetic
activity expresses itself in the outer stellar atmospheres of these stars
through various phenomena such as dark magnetic spots, bright chromospheric
plages, chromospheric emission lines, and coronal radio and X-ray emissions.
These phenomena are characterized by several key tracers such as axial
rotation, X-ray and UV-radiation, magnetic fields, and non-stationary events
as well. In particular, now it became clear that the coronal emission displays
the largest range of variation depending on the surface magnetic activity
level. The saturated regime of activity changes to the unsaturated mode, when
the solar-type activity is formed. We analyze here relevant characteristics of
these stars, compare them with the contemporary Sun and discuss them in the
context of an evolution of solar-stellar activity. It is obviously that both
X-rays and UV-radiation from the stellar coronae can affect the planet
atmospheres, therefore this study is significant for stars with various
activity levels.

##  2 THE X-RAY AND UV-EMISSION OF SOLAR TWINS WITH THE DETECTED LITHIUM

We analyzed available data for solar twins with detected lithium and found 23
stars out of 55 solar analogues, for which the X-ray emission was registered
during such space missions as Einstein, EXOSAT, ROSAT, XMM-Newton and Chandra.
Besides, definite information about UV-radiation of these stars can be derived
from the GALEX archival data. Because both kinds of high energy radiation
determine properties of outer atmospheres of low mass stars, they allowed us
to judge about a level of their activity.

The general parameters of these stars are given in Table 1 together with data
about Li abundances. The coronal index, the X-ray to bolometric luminosity
ratio, $R_{\rm X}=L_{\rm X}/L_{\rm bol}$, we estimated for several samples of
solar twins from the above mentioned X-ray archival data (Evans et al., 2010;
Boller et al., 2016; Traulsen et al., 2020; the corresponding references are
given in the description to Table 1). Dependence of the obtained coronal
indices on rotational velocities is presented in Fig. 1 (the left panel).The
corresponding values for the Sun at minimum and maximum activity level are
also plotted for comparison by crosses (after Peres et al., 2000). In spite of
spread of our values, definite trend of increase of the X-ray luminosities for
stars with the faster rotation does exist.

Table 1:  Physical parameters of the stars

HD |  $d$, pc | $\log A_{\rm Li}$ |  $v\sin i$,  km/s | $L_{\rm bol}/L_{\rm Sun}$ |  $L_{\rm X}$, $10^{27}\>$erg/s | $\log L_{\rm X}/L_{\rm bol}$ | $\log L_{\rm FUV}/L_{\rm bol}$ | $\log L_{\rm NUV}/L_{\rm bol}$
---|---|---|---|---|---|---|---|---
5 294 | 30 | 2.17 | 3.35 | 0.84 | 43 | –4.861 | –4.9 | –2.3
9 986 | 25 | 1.75 | 2.07 | 1.10 | 37 | –5.051 | –5.1 | –2.7
24 409 | 23 | 1.15 | 1.92 | 1.11 | 3.0 | –6.143 | –5.1 | –2.6
29 150 | 34 | 1* | — | 0.93 | 13 | –5.421 | — | —
42 618 | 24 | 1.3 | 1.28 | 0.94 | 0.9 | –6.604 | — | —
42 807 | 19 | 2.1 | 3.59 | 0.81 | 49 | –4.801 | — | —
56 124 | 27 | 2.0 | 1.33 | 1.07 | 23 | –5.251 | –5.0 | –2.7
75 767 | 23 | 1.45 | 3.1 | 1.07 | 97 | –4.622 | — | —
76 151 | 17 | 1.75 | 1.44 | 0.97 | 21 | –5.254 | –5.0 | –2.7
95 128 | 14 | 1.8 | 2.14 | 1.58 | 0.15 | –7.615 | — | –3.1
117 176 | 18 | 1.78 | — | 3.04 | 0.93 | –7.095 | –5.5 | –3.4
140 538 | 15 | 1.5 | — | 0.86 | 25 | –5.121 | –5.2 | –2.7
146 233 | 14 | 1.6 | 1.79 | 1.09 | 0.60 | –6.844 | — | —
159 222 | 24 | 2.0 | 2.74 | 1.24 | 235 | –4.301 | –5.1 | –2.5
168 009 | 23 | 1* | 1.92 | 1.41 | 0.43 | –7.106 | –5.1 | –3.0
181 655 | 25 | 1.93 | 1.81 | 1.72 | 71 | –4.961 | — | —
186 408 | 21 | 1.45 | 2.08 | 1.57 | 1.1 | –6.749 | — | —
186 427 | 21 | 0.8* | 2.27 | 1.25 | 0.30 | –7.205 | — | —
187 237 | 26 | 2.15 | 2.35 | 1.01 | 7.8 | –5.694 | — | —
222 143 | 23 | 2.0 | 2.93 | 1.05 | 186 | –4.332 | — | —
224 465 | 24 | 0.8* | 1.42 | 1.02 | 6.5 | –5.777 | — | —
146 362 | 23 | 2.43 | 2.14 | 1.02 | 5300 | –2.864 | — | –2.4
187 123 | 46 | 1.2 | 1.66 | 1.34 | 2.0 | –6.48 | — | —

The following data are given: Henry Draper catalog id, distance, lithium
abundance (asterisks denote upper limits), rotation velocity projection,
bolometric luminosity in solar units, logarithms of the ratios of the X-ray,
far-ultraviolet (1350–1750 Å) and near-ultraviolet (1750–2750 Å) luminosities
to the bolometric one. Distances are taken from the SIMBAD database, lithium
abundances from the work by Mishenina et al. (2020), bolometric luminosities
from the TIC catalog, UV luminosities from GALEX. The sources of the X-ray
luminosity are denoted by upper numbers as follows:

1Second ROSAT all-sky survey (2RXS) source catalog (Boller+, 2016)
2016A&A…588A.103,

2XMM-Newton slew survey Source Catalogue, version 2.0 (XMM-SSC, 2017),

3ROSAT All-Sky Survey Faint Source Catalog (Voges+ 2000), IAU Circ., No. 7432,
#3 (2000),

4XMM-Newton Serendipitous Source Catalogue 4XMM-DR9 (Webb+, 2020)
2020A&A…641A.136,

5Chandra observations of solar analogs (Miller+, 2015) 2015ApJ…799..163,

6The Chandra Source Catalog (CSC), Release 2.0. Evans, et al., 2019, HEAD,
114.01,

7The WGACAT version of ROSAT sources (White+ 2000)
https://heasarc.gsfc.nasa.gov/wgacat/,

8Kashyap et al. 2008 ApJ 687, 1339,

9Classification of Swift and XMM-Newton sources (Tranin+2022)
2022A&A…657A.138.

This agrees with well known rotation-activity relation, indicated that late-
type stars (G to M) have X-ray luminosities strongly dependent on rotation
rate $L_{\rm X}\sim(v\sin i)^{1.9\pm 0.5}$ and independent on bolometric
luminosity (Pallavicini et al., 1981).

The UV-radiation characterizes activity levels of the chromosphere and the
chromosphere-corona transition region. Therefore we estimated also the UV-
radiation for our stars in two spectral ranges: far-ultraviolet (FUV:
1350–1750 Å) and near-ultraviolet (NUV: 1750–2750 Å) bands observed with GALEX
(Bianchi et al., 2011). The FUV-and NUV-luminosities are derived by us for
several stars. We obtained that the minimal value of the FUV-luminosity
differs from the maximal one by a factor of 1.8, while the similar difference
for $L_{\rm NUV}$ reaches 4. The ratio of both parameters, $L_{\rm NUV}$ and
$L_{\rm FUV}$ to the bolometric luminosities, are listed in Table 1. The
available values of $\log L_{\rm NUV}/L_{\rm bol}$ are presented in Fig. 1
(the right panel). Although there is scatter in data, one can trace that the
faster the rotation, the larger the UV-luminosity.

Figure 2:  The coronal index versus lithium abundances for solar twins
considered. The solar Li content A(Li) = 1.05 is adopted from Asplund et al.
(2009).

Thus, we found that the X-ray luminosities of the solar twins cover the wide
range of values from the saturation limit in young stars, $R_{\rm X}$ around
$10^{-3}$, to levels approximately 4 orders of magnitude lower. This
significant scatter may mean that among the solar twins exist stars both more
active and even less active than the Sun.

Analyzing the activity of stars, in which the abundance of lithium shows a
scatter of almost an order of magnitude, we note that among our twins there
are objects of different ages from 1.5 to 5 Gyr (Fig. 4 in Mishenina et al.,
2020). Further comparison of the coronal X-ray emission with lithium
abundances for stars of our samples and the Sun shows that despite the spread,
a certain trend can be traced, indicating a relationship between the coronal
indices, the Li content and stellar ages. Indeed, Fig. 2 demonstrates that the
higher coronal indices correspond in general to larger values of the Li
content. This reflects the dependence of the activity level on stellar age.
Thus, among the solar twins, we have identified stars with a more powerful
corona, i.e. more active and relatively younger stars, apparently rotating a
few times faster than the nowadays Sun. At the same time, there are solar
twins, which have a lower level of activity than that of the contemporary Sun;
their soft X-ray radiation is almost an order of magnitude weaker than the
solar value.

##  3 THE TESS BRIGHTNESS VARIABILITY OF SOLAR TWINS

###  3.1 Rotational Modulation

The data from the TESS observatory, after preprocessing and filtering, make it
possible to obtain the optical light curves for the considered stars (Ricker
et al., 2014). We present as preliminary results a few examples of rotational
modulation associated with spots. So, in the upper panel in Fig. 3 the TESS
light curves for two solar twins HD 5294 and HD 24409 is shown. It is seen
that HD 5294 demonstrates the higher amplitude of rotational modulation as
compared with HD 24409 where both the level of the flux and amplitude
variations are significantly lower. Thus, HD 5294 can be considered as more
active star. This point is supported by comparison of their coronal indices
which differ by more than one order of magnitudes. Note also that HD 5294 has
twice higher Li abundance relatively to the solar value.

Figure 3:  Samples of the TESS light curves for several solar twins. The upper
panel: rotational modulation of HD 5294 and HD 22409. The lower panel –
brightness variations of HD 42807, which is known as a chromospherically
active RS CVn-type star (the left graph), and a component of spectral binary
HD 159222 (on the right).

The light curve in Fig. 3 (left in the lower panel) for HD 42807 presents a
more complicated shape of the brightness variation with presence of flare
events. This star has twice higher flux level than that from HD 5294, more
expressed rotational modulation, and similar coronal indices, rotational
velocity and lithium abundance as well. It should be noted here that HD 42807
is known as a chromospherically active RS CVn-type binary. The bottom right
panel in Fig. 3 shows the TESS light curve for HD 159222 where the flux is
also by a factor 2 more than that for HD 5294, and activity parameters are
similar to those in other stars in this Fig. 3. It cannot be excluded that
this star can be a spectroscopic binary.

We estimated the period of axial rotation for two stars HD 5294 and HD 159222
using a discrete Fourier transform algorithm (Lenz and Breger, 2014). We
obtained the axial rotation period for HD 5294 is 6d.526949 for this set of
observations. The accuracy of the frequency from which the period was found is
0d.011368. HD 159222 rotates with the period of 5d.92057. The accuracy of the
frequency from which the period was found is 0d.008882. Results of convolution
with found periods for both stars are presented in Figs. 4 and 5. Note that
possible rotation periods for HD 5294 and HD 159222 were given also in the
catalogue by Oelkers et al. (2018). However, period 0d.920615 for HD 5294 is
found there in 47 more stars, and period 29d.533400 for HD 159222 is found in
792 stars. This calls into question the reliability of these periods.
Convolutions with these periods do not show a real result. Thus, these quite
active solar twins rotate with periods of around 6 days, i.e. 4 times faster
than the contemporary Sun. This fact as well as their other tracers of
activity indicates their comparative youth.

Figure 4:  Frequency analysis diagram of time series for the HD 5294 star
(constructed from the TESS data obtained in sector 17) on the left panel.
Convolution with a period of 6d.526949 on the right panel. The accuracy of the
frequency from which the period was found is 0d.011368.

###  3.2 Optical Flares on Solar Twins Registered with the TESS Observatory

Considering flare activity of solar analogues, we have to keep in mind that
the most powerful flares on the Sun are rare phenomena. Flares in optical
continuum emission which are analogues of solar white-light flares have not
been seen on single main sequence G stars until the Kepler mission. Their
detection both on the Sun and on these stars is difficult because a source of
the flare optical continuum emission has a low contrast against the
photosphere, a small flare area, and lives a short time (a few minutes).
Nevertheless, an existence of optical flares in G stars can be suspected in
the UV data supports by recent study by Kashapova et al. (2021) where was
shown that time profiles of solar flares in the UV-continuum emission are
similar to impulsive flare light curves registered on the red dwarf during the
Kepler mission. Indeed, flares on G stars were found in GALEX NUV-data
(Brasseur et al., 2019).

The only recently a definite information appears about flare activity of these
stars from other observations, including ground-based monitoring (Jackman et
al., 2018; Bondar’ et al., 2021; Koller et al., 2021). However, until now
these surveys do not contain data for solar twins of our sample.

The first Kepler data about flares on G dwarfs were reported by Maehara et al.
(2012, 2015). Later on it was found that the energy of some of flares can
reach a few times of $10^{36}\,$erg (e.g. Wu et al., 2017).

After completion the Kepler mission, the TESS space observatory provides
possibility to continue permanent monitoring of larger number of stars that
allows searching for flares on these stars. We have analyzed TESS light curves
for some of our stars. We selected several high amplitude, non-single-impulse
events, using the $3\sigma$-criterion and give some samples of TESS flare
light curves. The temporal profiles for 3 flare events on the solar twins HD
24409 and HD 75767 registered with time resolution 120 s are presented in Fig.
6a. Note the quite complicated shape of the flare light curve in the middle of
this figure. The third flare sample on the HD 75767 star looks like a
classical impulsive flare on red dwarfs, but it occurs on the G star. We have
been estimated the energy of these non-stationary events. For the HD 24409
star, the lower limit of the total energy of the larger flare (in the middle
of the left panel) is $8\times 10^{33}\,$erg, its duration is 4.32 h. The two
flares to the right and left of it are about of 2 times weaker in the energy,
around $4\times 10^{33}\,$erg, and last 0.5–1 h less. As for the flares on the
HD 75767 star, the flare, demonstrating quite complicated light curve shape,
has the energy $4.12\times 10^{33}\,$erg and its duration is 12 h, while the
next sample of flares on the left panel in Fig. 6 looks like a classical
impulsive flare on red dwarfs, but it occurs on the G star. This flare of the
larger amplitude with the total energy of $4.3\times 10^{33}\,$erg lasts 21.6
h.

Figure 5:  Frequency analysis diagram of time series for the HD 159222 star
(constructed from the TESS data obtained in sector 26) on the left panel.
Convolution with a period of 5d.9205 on the right panel. The accuracy of the
frequency from which the period was found is 0d.008882.

##  4 ON THE MAGNETIC FIELD OF SOLAR TWINS

There is reason to believe that activity of solar analogues at various levels
from the highest one to low activity of the contemporary Sun is caused by
local magnetic fields with a definite governing role of the large-scale
magnetic field. Therefore, analyzing the factors determining activity, it
needs to know information about stellar magnetic fields. Earlier, we compared
data for magnetic fields obtained in the frameworks of the ”Bcool
collaboration” by Marsden et al. (2014) for several active G stars with data
on the general magnetic field of the Sun as a star. We obtained the average
value of the modulus of the magnetic field $|B_{l}|=4.72\pm 0.53\,$G for G
stars (Katsova and Livshits, 2014). The obtained average value corresponds to
a rotation rate of about 4 km/s. Thus, the mean value of the longitudinal
fields for active G stars, rotating slower than 5 days, is of one order of
magnitudes stronger than the mean daily magnetic field of the Sun as a star,
which does not exceed 0.5 G near the maximum of the cycle. Now we considered
these data for the solar twins, and it turned out that for only a few stars
measurements can be considered reliable.

We chose value of mean surface longitudinal magnetic field, $B_{l}$, exceeding
$3\sigma$ from Table 3 of Marsden et al. (2014), which are marked as a
”definite detection”. The only 5 of our 23 solar twins possess observable
magnetic fields. These stars with magnetic fields are HD 9986: $B_{l}=+2.5\pm
0.5\;$G; HD 56124: $B_{l}=+4.9\pm 0.8\;$G, HD 76151: $B_{l}=-3.7\pm 0.2\;$G,
HD 146233: $B_{l}=-2.3\pm 0.4\;$G, and HD 222143: $B_{l}=-5.2\pm 0.8\;$G. Note
that all these stars differ from other solar twins in two significant factors.
Firstly, they possess an enhanced Li abundance relatively to the Sun: $\log
A_{\rm Li}$ from 1.6 to 2.0. The second difference is that the radius of the
convective zones of these stars in the range $0.260-0.289\;R_{\rm Sun}$, while
estimates for the rest twins are from 0.325 to $0.371\;R_{\rm Sun}$, as it
follows from Table 1 in Marsden et al. (2014). Both circumstances point to
relative youth of these stars as compared with other solar twins.

Figure 6:  The TESS light curves for one of the flareson the HD 24409 star
(the left panel) and two flareson HD 75767 registered with time-resolution 120
s. The green line corresponds to the mean level of stellar brightness in
quiescence; two blue lines indicate the $\pm 1\sigma$-variability level, and
red line is the $3\sigma$-level.

##  5 DISCUSSION AND CONCLUSION

Thus, our analysis of various tracers of stellar activity for solar twins with
detected lithium abundances shows that this group of twins contains definitely
stars of various ages. It follows from a significant scatter in the coronal
indices, which are close to the saturation activity level for the most active
young dwarfs. This spread reflects similar dispersion in the lithium content.
Besides, magnetic field measurements showed that mean longitudinal magnetic
fields can be 5–10 times stronger as compared with the nowadays solar value,
that also indicates that these stars are younger that the others. Such
magnetic fields can be able, in principle, to provide the energy for powerful
flares, much stronger than the solar ones. Studying flare activity and other
powerful non-stationary phenomena is of importance for atmospheres of
exoplanets orbiting similar stars. Note that because ages and mass of solar
twin are defining in lithium abundance (do Nascimento et al., 2009), non-
standard mixing is required to explain the low Li abundances observed in solar
twins. So, for example, the 16 Cygni system consists of two stars HD 186408
(16 Cyg A is a good candidate for the most Sun-like star) and HD 186 427
having the same age, the same initial composition, and the Li abundance
differences currently observed must be due to their various paths of
evolution, related to the fact that one of them hosts a planet while the other
does not. By the way, note here that 6 solar twins have exoplanets orbiting
these stars. The corresponding information can be found, for instance, in
https://exoplanets.nasa.gov/discovery/exoplanet-catalog/, http://exoplanet.eu.
The following objects orbiting our stars are two Neptune-like exoplanet around
HD 42618 and HD 164595, three gas giants 47 UMa b, c and d around HD 95128, a
gas giant exoplanet 70 Vir b around HD 117176, a gas giant exoplanet 16 Cyg B
b around HD 186427, and two gas giant exoplanets around HD 187123. Since
activity phenomena on hosts of exoplanets can play role in influence on
planetary environments, further investigations of stellar activity are of
interest.

##  6 ACKNOWLEDGMENTS

This paper includes data collected with the TESS mission, obtained from the
MAST data archive at the Space Telescope Science Institute (STScI). Funding
for the TESS mission is provided by the NASA Explorer Program. STScI is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5–26555. This research has made use of data obtained
from the Chandra Source Catalog, provided by the Chandra X-ray Center (CXC) as
part of the Chandra Data Archive.

##  7 FUNDING

MMK and BAN acknowledge the support of Ministry of Science and Higher
Education of the Russian Federation under the grant 075-15-2020-780.

##  8 CONFLICT OF INTEREST

The authors declare that they have no conflicts of interest.

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