# Eight exoplanet candidates in SAO survey

O. Ya. Yakovlev∗1,2, A. F. Valeev2,3,4, G. G. Valyavin2, A. V. Tavrov1,5,
V. N. Aitov2, G. Sh. Mitiani2, G. M. Beskin2,6, V. V. Vlasyuk2,
O. I. Korablev1, G. A. Galazutdinov4,2, E. V. Emelyanov2, T. A. Fatkhullin2,
V. V. Sasyuk6, A. V. Perkov7, S. F. Bondar†7, T. E. Burlakova2,4, S. N.
Fabrika2, I. I. Romanyuk2

1Space Research Institute, Moscow, 2Special Astrophysical Observatory, Nizhnii
Arkhyz,
3St. Petersburg University, St. Petersburg, 4Crimean Astrophysical
Observatory, Nauchny,
5Moscow Institute of Physics and Technology, Dolgoprudny, 6Kazan Federal
University, Kazan,
7Research and Production Corporation “Precision Systems and Instruments”,
Moscow
<EMAIL_ADDRESS>

Accepted by Astrophysical Bulletin, November 29, 2022

###### Abstract

Here we present eight new candidates for exoplanets detected by the transit
method at the Special Astrophysical Observatory of the Russian Academy of
Sciences. Photometric observations were performed with a 50-cm robotic
telescope during the second half of 2020. We detected transits with depths of
$\Delta m=0\,.\\!\\!^{\rm m}056$–$0\,.\\!\\!^{\rm m}173$ and periods
$P=18\,.\\!\\!^{\rm h}8$–$8\,.\\!\\!^{\rm d}3$ in the light curves of stars
with magnitudes of $m=14\,.\\!\\!^{\rm m}3$–$18\,.\\!\\!^{\rm m}8$. All
considered stars are classified as dwarfs with radii of
$R_{*}=0.4$–$0.6R_{\odot}$ (with the uncertainty for one star up to
$1.1\,R_{\odot}$). We estimated the candidate radii (all are greater than 1.4
times the Jovian radius), semi-major axes of their orbits (0.012–0.035 AU),
and other orbital parameters by modelling. We report the light curves with
transits for two stars obtained in 2022 based on individual observations.

##  1 Introduction

The first optical robotic telescope with 50-cm mirror at the Special
Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) aimed
at studies of exoplanets started operating in 2020. Its primary purpose is to
find new exoplanet candidates. Transit photometry technique is used — an
exoplanet is found and further studied by analyzing photometric data acquired
during the transit. It also observes stars with known confirmed exoplanets.

To discover exoplanet candidates, photometric monitoring of a selected sky
area was performed during the second half of 2020 (hereafter referred to as
survey-mode observations). So far, no confirmed exoplanet of exoplanet
candidate has been found in this field according to the NASA Exoplanet Archive
data [NASA, 2022]. As a result of the analysis of about 30 000 light curves of
$m=13\,.\\!\\!^{\rm m}5$–$19\,.\\!\\!^{\rm m}5$ stars in the area studied we
found eight objects exhibiting periodic brightness variations typical of
planet transit events (in terms of periodicity, amplitude, duration, and
form). The objects are designated as SOI-N, i.e “SAO Object of Interest”
followed by the candidate number $N$. Since the beginning of 2022 dedicated
observations of these objects are performed at the SAO RAS including
multicolor photometry (50-cm and 1-m telescopes) and spectroscopy (the 6-m
telescope BTA).

The area that we selected for preliminary study is centered on the magnetic
white dwarf WD 0009$+$501 ($m_{G}\approx 14\,.\\!\\!^{\rm m}2$) with eight-
hour periodic light variations with an amplitude of $\Delta m\approx
0\,.\\!\\!^{\rm m}01$ [Valeev et al., 2015]. This result is confirmed by the
structure of the light curve obtained. In the process of our search for
transit events we detected more than 100 new variable stars with $\Delta
m\approx 0\,.\\!\\!^{\rm m}01$–$0\,.\\!\\!^{\rm m}1$ light variations. We will
present results of their studies in a separate paper.

The transits of the exoplanet candidates discussed in this paper have depths
in the range $0\,.\\!\\!^{\rm m}06$–$0\,.\\!\\!^{\rm m}17$. Such a brightness
decrease corresponds to a transit of a giant planet the size of 1.5–2 times
that of Jupiter across the disk of a solar-radius or smaller star [Yakovlev et
al., 2022].

The duration of survey-mode observations (5 months) and their duty cycle (on
the average, every third night) determine the possible intervals of detectable
transit-event periods in the objects found — 1–2 days and up to slightly more
than a week. Such a period corresponds to planets with orbit semi-major axes
smaller than 0.1 AU. These observed parameters (the depth and period of
brightness decrease) are consistent with earlier preliminary estimates [Valeev
et al., 2015] and with statistical data for confirmed exoplanets discovered
using the same technique (i.e., via transit observations on ground-based
instruments) taken from the Exoplanet Archive data [NASA, 2022] and [Yakovlev
et al., 2022].

For each of the exoplanet candidates presented in this paper light curves
covering three or more complete transits are available that were fitted to
model curves in order to determine the radius of the candidate and its orbital
parameters, primarily the semi-major axis of the orbit. According to these
models, the observed transit events can be caused by transits of planets
across the stellar disk. The currently available data are insufficient to
confidently reject the hypothesis about the planetary nature of the candidates
considered.

Here we publish coordinates and other information about stars SOI-1–SOI-8, as
well as the ephemerides of the transit events. See [Yakovlev et al., 2022] for
details of observations and data reduction procedure. Further observations
with other instruments will be useful for confirming or discarding the
hypothesis about the planetary nature of the candidates discovered.

##  2 Observations and data processing

Observations were carried out in two stages. At the first stage, from August
25, 2020 to January 21, 2021, light curves for more than 35 000 stars were
acquired with a total duration of up to $22\,.\\!\\!^{\rm d}8$ over 56 nights.
Observations were performed for a total of 84 nights. These were wide-field
($\Delta\alpha=2\,.\\!\\!^{\circ}45$, $\Delta\delta=1\,.\\!\\!^{\circ}56$)
survey-mode observations on a large scale
($1\,.\\!\\!^{\prime\prime}34/$pixel) performed on a 50-cm telescope with 60-s
exposure using a detector located in the primary focus. Since February 2022
the second stage began — $BVRI$-band observations of individual objects
discovered during the survey with same and another 50-cm telescope (equipped
with a detector placed at the secondary focus with a scale of
$0\,.\\!\\!^{\prime\prime}93/$pixel after binning $2\times 2$) (see Table 1).
We will use the results of more precise transit photometry based on the data
from the 1-m telescope and the SOI spectra acquired with the 6-m telescope to
refine the parametes of exoplanet candidates and publish them in the future.

Table 1: Log of individual observations
of exoplanet candidates

Date | Filters | Object
---|---|---
22.02.11 | B, V, R | SOI-3
22.02.13 | B, V, R | SOI-3
22.05.29 | B, V, R, I | SOI-8
22.06.02 | B, V, R, I | SOI-3
22.06.05 | V, I | SOI-8
22.06.28 | V, R, I | SOI-2*
22.07.04 | R | SOI-7, SOI-8
22.07.08 | I, V | SOI-7, SOI-8

* transit was not observed

Photometric data were processed in pipeline mode using standard procedures:
dark-frame subtraction (no flat field frames were obtained), identification of
sources in the frame and coordinate fitting, aperture photometry, and cross-
matching. To perform data reduction we used a Python script with standard
programs: Astrometry.net [Lang et al., 2009], SExtractor [Bertin and Arnouts,
1999], and CCDPACK [Warren-Smith et al., 2014].

These procedures were followed by light-curve calibration. We used bright
stars ($14\,.\\!\\!^{\rm m}0$–$15\,.\\!\\!^{\rm m}5$) with high correlation
coefficient between instrumental light curves and the star compared, and with
many observational data points (close to the maximum number).

##  3 Analysis of light curves

We investigated the resulting light curves for periodic brightness dips
expected in the case of an exoplanet transit across the stellar disk. To this
end, we employed the simple Box Least Squares algorithm (BLS) [Kovacs et al.,
2002], which we used to select the parameters of the two-level model fitting
the light curve phase-folded with the trial period [Yakovlev et al., 2022]. In
this model the outside-transit light curve is approximated by a single (zero)
level, and the inside-transit part of the light curve, by another level (Fig.
1).

Figure 1: Models fitting the transit events: box-shape [Kovacs et al., 2002],
[Astropy Collaboration et al., 2022] (the thick line), trapezium-shaped (the
dashed line) and batman [Kreidberg, 2015] (the thin line). The dots show a
fragment of the SOI-3 light curve with a transit.

The search for light curves with transit events is performed by analyzing the
periodograms that statistically characterize the agreement between the phased
light curve and the adopted model. The main parameter determined at this stage
using the BLS algorithm is the period $P$, i.e., the time interval between two
consecutive transits (the orbital period of the body that causes the
darkening). The remaining parameters of this model (duration $\tau$, depth
$\Delta m$, and the position of the central transit point $t_{0}$) are refined
using other models described below.

We use astropy (Python) library [Astropy Collaboration et al., 2022] to
implement the BLS algorithm. The input parameters are the light curve and the
period $P$ and transit duration $\tau$ grids. We proceeded from the duration
and duty cycle of observations, photometric precision, statistical data about
the parameters of known exoplanets, and simple estimates (see Fig. 9 in
[Yakovlev et al., 2022]) to select the following intervals of inferred
parameters: $P=0.5$–$5$ days and $\tau=0.1$–$5$ hours (candidates SOI-4 and
SOI-5 with periods longer than five days were initially found with shorter
multiple periods).

Hereafter to determine the parameters of transit events and the physical and
orbital parameters of exoplanet candidates we convert the relative magnitudes
$\Delta m$ into relative flux units $\Delta F$. The zero (outside-transit)
level is set equal to 1.

The next approximation is the trapezium-shaped light curve. It differs from
the previous model (BLS) by the presence of transition fragments between the
zero level and the “flat bottom”, during which only a part of the body lies in
front of the stellar disk. This model is described by four time parameters:
the beginning and end of the transit, $t_{1}$, $t_{4}$, and the beginning and
end of maximum brightness decrease phase, $t_{2}$, $t_{3}$. The depth of the
transit $\Delta F$ is, like in the previous model, determined as the median
value in the $t_{2}$–$t_{3}$ interval.

The radius of the body, $R_{{p}}$, and the semi-major axis of its axis, $sma$,
in the units of stellar radius $R_{*}$ can be determined from the shape and
amplitude of the light curve ($t_{1}$, $t_{2}$, $t_{3}$, $t_{4}$, $\Delta F$)
assuming that the orbit is circular [Seager and Mallen-Ornelas, 2003]:

$R_{{p}}/R_{*}=\sqrt{\Delta F},$ (1) $sma/R_{*}=\sqrt{\frac{(1+\sqrt{\Delta
F})^{2}-b^{2}(1-f_{1})}{f_{2}}},$ (2)

where $f_{1}=\sin^{2}(\pi\,t_{T}/P)$ and $f_{2}=\sin^{2}(\pi\,t_{F}/P)$ are
functions that depend on the total duration of the transit,
$t_{T}=t_{4}-t_{1}$, and the duration of the maximum transit depth phase,
$t_{F}=t_{3}-t_{2}$, and  $b=f(\Delta F,f_{1},f_{2})$ is the projected
distance between the planet and the center of the star at time $t_{0}$ (see
equations (6)–(8) in [Seager and Mallen-Ornelas, 2003]:

The third model, which describes best the transit compared to the above two
models is batman (BAsic Transit Model cAlculatioN) [Kreidberg, 2015]. The
light curve is determined by eight parameters: the central point of the
transit, $t_{0}$, radius of the planet $R_{{p}}/R_{*}$ and semi-major axis of
its orbit $sma/R_{*}$ in the units of stellar radius; inclination $i$ (angle
between the orbital and sky planes); eccentricity $e$ and longitude of the
ascending node $\Omega$ of the orbit, and the coefficients of the quadratic
limb-darkening function of the star, $a$ and $b$.

We used the algorithm of the first (Box-shape) model to find more than 30
stars with transit events. For each of these stars we determined the transit
epoch ${\mathrm{JD}_{0}}$, period $P$, and the depth $\Delta m$ and duration
$\tau$ of the brightness dip. We then used the inferred estimates of these
parameters to distinguish stars with exoplanet candidates (SOI) from eclipsing
variables with $\Delta m\geq 0\,.\\!\\!^{\rm m}2$, $P\geq 5^{\rm h}$,
$\tau/P\geq 0.25$ and V-shaped transit light curves or with different depths
$\tau$ of odd and even transits.

We determined the parameters of the second (trapezium-shaped) and third
(batman) models via the maximum-likelihood method. We used the $t_{1}$–$t_{4}$
and $\Delta F$ estimates of the second model to determine the intervals of
inout parameter values for the third model: ($t_{0}$, $R_{{p}}/R_{*}$ from Eq.
(1) and $sma/R_{*}$ from Eq. (2)). The intervals of orbital parameters are
$i=75$–$90^{\circ}$, $e=0$–$1$ and $\Omega=0$–$360^{\circ}$. We adopted the
coefficients $a$ and $b$ of the star’s quadratic limb-darkening function from
the table published by [Claret, 2000] based on the following stellar
parameters: effective temperature $T_{\mathrm{eff}}$, surface gravity $g$, and
metallicity [M/H] [Gaia Collaboration et al., 2016], [Gaia Collaboration et
al., 2022].

The aim of this modeling stage was to estimate the period, duration, and depth
of the transit, the radii of exoplanet candidates, and the semi-major axes of
their orbits in order to test the hypothesis of the planetary nature of these
bodies (other, orbital, parameters are accompanying quantities). We will
perform further refining modeling with error estimates based on photometric
and spectroscopic data obtained with the 1-m Zeiss-1000 and 6-m telescopes of
the SAO RAS.

##  4 Results

Analyzing the light curves of stars in the field studied, we found eight stars
exhibiting periodic light dips characteristic of transit events. Fig. 2 shows
the light curves of these stars (with individual nightly trend subtracted and
outliers and data obtained during nights with bad weather conditions removed).
The transit depth $\Delta m$ for the brightest stars SOI-3, SOI-5 ($m<15^{\rm
m}$), and SOI-8 ($m\approx 17^{\rm m}$) exceeds $3\sigma$. The other
candidates are fainter ($m\approx 18^{\rm m}$–$19^{\rm m}$), we estimate the
transit depths for them as $\Delta m<3\sigma$.

We present the data for stars SOI-1–SOI-8 including IDs from Gaia DR3
(Vallenari et al. 2022), magnitudes, coordinates, physical parameters and the
inferred estimates of the observed parameters of transit events (zero epoch,
period, and depth) below in this Section and also in summary Tab. 2, 3.
Partial differences of the values of the above parameters for SOI-1–SOI-5 from
the estimates earlier published by [Yakovlev et al., 2022] can be explained by
the use of a different Gaia data release (DR3 instead of EDR 3) and different
transit models — the trapezium-shaped and batman model [Kreidberg, 2015].

Table 2:  Parameters of stars with exoplanet candidates: Gaia DR3 ID, coordinates RA and Dec, and apparent magnitude $m_{G}$ from Gaia database [Gaia Collaboration et al., 2022] and parameters of transit events, including zero epoch ${\mathrm{JD}_{0}}$ of one of the transits, period $P$ between the transits observed, duration $\tau$ and maximum depth $\Delta m$ of the transit SOI | Gaia ID | RA, hh:mm:ss | Dec, dd:mm:ss |  $m_{G}$, mag | ${\mathrm{JD}_{0}}$ |  $P$, h |  $\tau,$ h |  $\Delta m,$ mag
---|---|---|---|---|---|---|---|---
1 | 395249244499720320 | 00:10:30.08 | +50:27:54.0 | 18.81 | 2459202.090069 | 26.085 | 1.56 | 0.14
2 | 395239868590825472 | 00:12:31.18 | +50:27:21.3 | 18.83 | 2459219.105861 | 50.358 | 2.97 | 0.17
3 | 395281753112434304 | 00:08:26.77 | +50:28:23.9 | 14.30 | 2459189.314361 | 45.988 | 2.17 | 0.06
4 | 395220833295162112 | 00:11:10.60 | +50:16:21.6 | 17.81 | 2459171.403981 | 126.844 | 1.49 | 0.08
5 | 395229079635160320 | 00:13:17.88 | +50:15:43.9 | 15.17 | 2459221.434447 | 198.309 | 3.81 | 0.06
6 | 395282813962513536 | 00:07:59.73 | +50:31:19.9 | 17.96 | 2459202.386315 | 49.645 | 2.79 | 0.06
7 | 394596585565904000 | 00:16:33.19 | +50:41:10.1 | 18.24 | 2459236.309815 | 97.670 | 2.55 | 0.15
8 | 394573186584164096 | 00:16:01.05 | +50:32:24.1 | 16.94 | 2459221.159153 | 18.768 | 1.47 | 0.09

### SOI-1

The candidate SOI-1 with $m_{G}=18\,.\\!\\!^{\rm m}81$ was found to exhibit
brightness dips with the period of $P=26\,.\\!\\!^{\rm h}09$, duration
$\tau=1\,.\\!\\!^{\rm h}56$, and depth $\Delta m=0\,.\\!\\!^{\rm m}144$ (Fig.
3). A total of 12 complete transits (from the beginning to the end) were
detected for this star during survey-mode observations.

The limb-darkening coefficients for SOI-1 are: $a~{}=~{}0.354$ and
$b~{}=~{}0.374$ (with $\log g~{}=~{}4.90$ and $\log{\rm(M/H)}=-1.69$). The
fitted model transit curve corresponds to the following parameters:
$\phi_{0}\\!=\\!0.7501$, $R_{{p}}/R_{*}=0.38$, $sma/R_{*}=7.85$,
$i=83\,.\\!\\!^{\circ}3$, $e=0.60$, and $\Omega=307^{\circ}$.

### SOI-2

The period of transits for SOI-2 with $m_{G}=18\,.\\!\\!^{\rm m}83$ was
initially estimated as $P=25\,.\\!\\!^{\rm h}2$ (this period is reported in
[Yakovlev et al., 2022]). After the subtraction of the daily trend the period
corresponding to the maximum of the periodogram increase twofold (Fig. 4).

The phased light curve with $P=50\,.\\!\\!^{\rm h}36$ reveals a secondary
minimum (Fig. 5, $\phi\approx 0.25$), which was mistaken for the primary
minimum along with the minimum at $\phi\approx 0.75$. The transit duration and
depth are equal to $\tau=2\,.\\!\\!^{\rm h}97$ and $\Delta m=0\,.\\!\\!^{\rm
m}173$, respectively. A total of eight complete transits were registered
during survey-mode observations.

The limb-darkening coefficients for SOI-2 are derived to be $a=0.22$, $b=0.44$
($\log g=4.77$ and $\log{\rm(M/H)}=-2.52$). The fitted model transit curve
corresponds to the following parameters: $\phi_{0}\\!=\\!0.7500$,
$R_{{p}}/R_{*}=0.42$, $sma/R_{*}=8.47$, $i=83\,.\\!\\!^{\circ}7$, $e=0.50$,
and $\Omega=219^{\circ}$.

### SOI-3

SOI-3 is the brightest among the eight studied ($m_{G}=14\,.\\!\\!^{\rm
m}30$). Its light curve was found to exhibit brightness dips with the period,
duration, and depth equal to $P=45\,.\\!\\!^{\rm h}99$, $\tau=2\,.\\!\\!^{\rm
h}17$, and $\Delta m=0\,.\\!\\!^{\rm m}056$, respectively (Fig. 6). A total of
eight complete and four partial transits were detected during survey-mode
observations.

Temporary flux increase by $0\,.\\!\\!^{\rm m}01$–$0\,.\\!\\!^{\rm m}02$ is
observed at the periods of 16, 28, and 53 during the transit. This effect can
be due to the flare activity in the stellar atmosphere.

The limb-darkening coefficients for SOI-3 are: $a=0.59$, $b=0.19$ ($\log
g\\!=\\!4.20$, $\log{\rm(M/H)}\\!=\\!-0.99$). The fitted model transit curve
corresponds to the following parameters: $\phi_{0}=0.7489$,
$R_{{p}}/R_{*}=0.24$, $sma/R_{*}=4.50$, $i=81\,.\\!\\!^{\circ}2$, $e=0.45$,
and $\Omega=90^{\circ}$.

In the case of SOI-3 the light curves for three nights in 2022 were obtained
with predicted transit event (Fig. 7). All three detected transits were
observed at phases $\phi<0.5$, i.e., so far no predicted transit could be
observed completely. The beginning of the transit is present in the light
curve.

### SOI-4

The star SOI-4 with $m_{G}=17\,.\\!\\!^{\rm m}81$ was found to exhibit
transits with the period $P=126\,.\\!\\!^{\rm h}85\approx 5^{\rm d}6^{\rm h}$,
duration $\tau=1\,.\\!\\!^{\rm h}95$, and depth $\Delta m=0\,.\\!\\!^{\rm
m}071$ (Fig. 8). A total of six transits were detected during survey-mode
observations.

The limb-darkening coefficients we derived for SOI-4 are: $a=0.27$, $b=0.48$
(with $\log g=4.63$, $\log{\rm(M/H)}\\!=\\!-0.33$). The fitted transit curve
corresponds to the following parameters: $\phi_{0}=0.7493$,
$R_{{p}}/R_{*}=0.30$, $sma/R_{*}=13.22$, $i=79\,.\\!\\!^{\circ}8$, $e=0.85$,
and $\Omega=195^{\circ}$.

### SOI-5

The star SOI-5 (ID 395229079635160320 in Gaia DR3, ID 395229079633073024 in
EDR3) with $m_{G}=15\,.\\!\\!^{\rm m}17$ was found to manifest transit events
with the longest — more than one week — period among the eight stars
considered, $P\\!=\\!198\,.\\!\\!^{\rm h}31\\!\approx\\!8^{\rm d}6^{\rm h}$,
with the duration $\tau=3\,.\\!\\!^{\rm h}81$ and depth $\Delta
m=0\,.\\!\\!^{\rm m}060$ (Fig. 9). One complete transit and three partial
transits with phases up to $\phi\approx 0.85$ were found during survey-mode
observations.

The fitted model transit curve corresponds to the following parameters:
$\phi_{0}=0.7501$, $R_{{p}}/R_{*}=0.24$, $sma/R_{*}=14.34$,
$i=85\,.\\!\\!^{\circ}4$, $e=0.30$, $\Omega=170^{\circ}$, $a=0.25$, and
$b=0.42$. The parameters of the star SOI-5 are unknown and that is why the
parameters $a$ and $b$ were inferred in the process of modeling.

### SOI-6

Transits events with the period $P=49\,.\\!\\!^{\rm h}65$, duration
$\tau=2\,.\\!\\!^{\rm h}79$, and depth $\Delta m=0\,.\\!\\!^{\rm m}060$ (Fig.
10) were found for the star SOI-6 ($m_{G}=17\,.\\!\\!^{\rm m}96$). During
survey-mode observations a total of four complete transits were registered.

The limb-darkening coefficients for the object are: $a=0.25$, $b=0.42$ ($\log
g\\!=\\!4.72$, $\log{\rm(M/H)}\\!=\\!-2.78$). The fitted model transit curve
corresponds to the following parameters: $\phi_{0}=0.7413$,
$R_{{p}}/R_{*}=0.25$, $sma/R_{*}=9.58$, $i=87\,.\\!\\!^{\circ}6$, $e=0.60$,
and $\Omega=238^{\circ}$.

### SOI-7

In studies of the star SOI-7 with $m_{G}=18\,.\\!\\!^{\rm m}24$ transit events
with the period $P=97\,.\\!\\!^{\rm h}67\approx 4^{\rm d}17^{\rm h}$, duration
$\tau=2\,.\\!\\!^{\rm h}55$, and depth $\Delta m=0\,.\\!\\!^{\rm m}153$ were
revealed (Fig. 11). During survey-mode observations we registered a total of
three complete transits and one with transit phase before $\phi\approx 0.5$.

The limb-darkening coefficients for SOI-7 are estimated as $a=0.37$, $b=0.37$
($\log g=4.79$ and $\log{\rm(M/H)}=-1.52$). The fitted model transit curve
corresponds to the following parameters: $\phi_{0}=0.7493$,
$R_{{p}}/R_{*}=0.39$, $sma/R_{*}=8.24$, $i=81\,.\\!\\!^{\circ}5$, $e=0.55$,
and $\Omega=40^{\circ}$.

### SOI-8

The star SOI-8 with $m_{G}=16\,.\\!\\!^{\rm m}94$ was found to exhibit transit
events with the shortest period — less than one day or $P=18\,.\\!\\!^{\rm
h}77$ — among the eight stars studied (Fig. 12). The transit duration and
depth are $\tau=1\,.\\!\\!^{\rm h}47$ and $\Delta m=0\,.\\!\\!^{\rm m}089$,
respectively. A total of 19 complete and three partial transits were detected
during survey-mode observations.

The limb-darkening coefficients for SOI-8 are: $a=0.50$, $b=0.25$ ($\log
g\\!=\\!4.72$, $\log{\rm(M/H)}\\!=\\!-1.03$). The fitted model transit curve
corresponds to the following parameters: $\phi_{0}=0.7452$,
$R_{{p}}/R_{*}=0.30$, $sma/R_{*}=4.59$, $i=82\,.\\!\\!^{\circ}8$, $e=0.05$,
and $\Omega=273^{\circ}$.

In 2022 light curves for SOI-8 were obtained for four nights during which
transit events were predicted (Fig. 15). Two of these were observed completely
in two filters ($V$, $R$), and two, partially in three filters ($B$, $V$,
$R$).

Besides transits, SOI-8 also manifests brightness variations (inferred from an
analysis of the Lomb–Scargle periodogram in [VanderPlas, 2017]) with the
period $P=18\,.\\!\\!^{\rm h}688$ and amplitude $\Delta m\approx 0.1$ (Fig. 15
and Fig. 15). This period is shorter than the period of transits
$P_{\mathrm{tr}}=18\,.\\!\\!^{\rm h}768$ by about 4.5 minutes. Fig. 15 also
shows the phase-folded light curve for $P=P_{\mathrm{tr}}$ with the transit-
event phase excluded.

##  5 Discussion

In the cases where two transits of the same shape were registered with
consistent periodicity over a long time interval the hypotheses that light
variations may be caused by star spots, phenomena in terrestrial atmosphere,
or arose in the process of observations or data reduction can be discarded.
Hence the brightness dip is cased by the apparent transit of a body that is
gravitationally bound to the star and may be a star, brown dwarf, or planet.
These conditions are satisfied for all SOI: four or more transits (at least
three complete ones) were detected over several months, for two objects (SOI-3
and SOI-8) including transits observed in 2022 at times predicted based on the
data of 2020 survey-mode observations, and recurrent shape of transits (during
transit time the light curve deviates from the mode curve by no more than
$3\sigma$). A transit is observed at any time epoch separated from the zero
epoch by integer number of periods (in the cases where data are available).

The transit technique makes it possible to determine only the radius, whereas
the mass of the body remains unknown. If the transit is caused by a body
comparable in size with gas giants, we can exclude the presence of a stellar
component. If the radius of the body is significantly smaller than the radius
of Jupiter, we can conclude that the body is an exoplanet. All candidates
found in this study have radii greater than that of Jupiter and therefore we
cannot rule out the possibility that they may be brown dwarfs or small stars.

Mass is the physical parameter that distinguishes planets from brown dwarfs.
The adopted conventional boundary is set at $13\,M_{\mathrm{Jup}}$: if the
mass of the object exceeds this value, the hypothesis of its planetary nature
is not confirmed. The mass of the object can be inferred from radial-velocity
measurements of the star orbited by the body. Perturbations of the radial
velocity of a star caused by an exoplanet do not exceed 15 m s-1 according to
the [NASA, 2022]. High-resolution spectra are needed to measure such
velocities. However, the stars studied are rather faint: $m=14^{\rm
m}$–$15^{\rm m}$ for SOI-3, SOI-5; $m=17^{\rm m}$–$18^{\rm m}$ for SOI-4,
SOI-6, and SOI-8, and $m\approx 19^{\rm m}$ for SOI-1 and SOI-2 — their light
curves have low $S/N$.

Instead of measuring stellar radial velocities from high-resolution spectra
other techniques can be used to test the hypothesis about the planetary
nature, e.g., an analysis of the dependence of the transit depth on
photometric band (transmission spectroscopy). If the transit depths in
different filters do not differ then the transiting body can be considered to
be gray and the hypothesis that it may be a star can be rejected. If transit
depths differ in different filters (and does not agree with the wavelength
dependence of limb darkening or the assumption that the exoplanet has
atmosphere) then the planetary hypothesis is not confirmed. Note that one
transit event in SOI-8 was observed with the 50-cm telescope in three filters
(Fig. 15) however, the number of data points is insufficient to draw
conclusions.

Another option is to measure the star’s spectrum at different phases with
respect to the transit. If the second component is a star of a significantly
different spectral type then the shifts of spectral line should differ at
different phases of the orbit of the body.

Yet another option consists in determining the upper limit for the radial
velocity of the star from low-resolution spectra. If the second component is a
star then the radial-velocity amplitude of the observed star (several tens of
km s-1) can be measured, whereas no radial-velocity curve will be observed if
the body is a planet.

We plan to use these methods to test the hypothesis about the planetary nature
of the exoplanet candidates discovered.

We used modeling (see Section 4 and Tab. 3) to determine for all SOI the
radius $R_{{p}}/R_{*}$ and semi-major axis of the orbit of the second
component, $sma/R_{*}$, in the units of the radius of the star it orbits (Tab.
3). To determine the size of the second component, we must known the radius of
the star studied. According to Vallenari et al. (2022), the radii of SOI-1,
SOI-2, SOI-4, SOI-6, SOI-7, and SOI-8 lie in the 0.4–0.58 interval; that of
SOI-3 is equal to $0.64\,R_{\odot}$ or $1.14\,R_{\odot}$, and the radius of
SOI-5 is unknown. Hereafter to test the hypothesis, we use the above estimates
of the radii and sizes of orbits of secondary components to a first
approximation by formulas (1) and (2) and compare then with the values of
these parameters for confirmed exoplanets.

Table 3: Radii $R_{*}$ of the stars according to Gaia DR3 [Gaia Collaboration et al., 2022] and parameter estimates for exoplanet candidates: the radius $R_{{p}}$ of the planet and the semi-major axis $sma$ of its orbit. For SOI-3 the radius from Gaia EDR 3 is given in parentheses.  SOI | $R_{*},R_{\odot}$ | $R_{{p}}/R_{*}$ | $sma/R_{*}$
---|---|---|---
1 | 0.40 | 0.38 | 7.85
2 | 0.55 | 0.42 | 8.47
3 | 1.14 (0.64) | 0.24 | 4.50
4 | 0.57 | 0.27 | 13.22
5 | – | 0.24 | 14.34
6 | 0.58 | 0.25 | 9.58
7 | 0.52 | 0.39 | 8.24
8 | 0.57 | 0.30 | 4.59

The radii $R_{{p}}$ of four exoplanet candidates, SOI-6, SOI-4, SOI-1, SOI-8,
lie in the $1.39$–$1.64R_{\mathrm{Jup}}$ interval. The radius of SOI-7
candidate is $R_{{p}}=1.96\,R_{\mathrm{Jup}}$, that of SOI-3candidate
$R_{{p}}$ is equal to $1.46\,R_{\mathrm{Jup}}$ or $2.62\,R_{\mathrm{Jup}}$,
and that of exoplanet candidate SOI-2 is equal to
$R_{{p}}=2.22\,R_{\mathrm{Jup}}$. Currently, there are only two and six
exoplanets with the radii $R_{{p}}\\!\approx\\!2.7\,\\!R_{\mathrm{Jup}}$ and
$R_{{p}}\\!=\\!2.0$–$2.2\,\\!R_{\mathrm{Jup}}$, respectively, presented in the
[NASA, 2022], with masses estimated to be $M\leq 13M_{\mathrm{Jup}}$, all
other known exoplanets are less massive. Our inferred estimates of SOI
exoplanet candidate radii lie within the interval of radii of confirmed
exoplanets. Thus the eight stars studied can be subdivided into two groups
based on how the radius of the exoplanet candidate is consistent with possible
exoplanet radii: SOI-6, SOI-4, SOI-1, SOI-8, and SOI-7 are of greatest
interest for further study, followed by SOI-3, SOI-2, and SOI-5.

The minimum orbital period and minimum semi-major axis of known transiting
exoplanets (with $M\leq 13\,M_{\mathrm{Jup}}$) are
$P_{\mathrm{min}}=4\,.\\!\\!^{\rm h}3$ [NASA, 2022] and
$sma_{\mathrm{min}}=0.0058$ AU, respectively. The minimum values of these
parameters for the candidates SOI-1–SOI-8 are
$P_{\mathrm{SOI8}}=18\,.\\!\\!^{\rm h}8$ and $sma_{\mathrm{SOI8}}=0.012$ AU,
respectively. A total of 76 transiting exoplanets are known to have
$P_{\mathrm{SOI8}}<P<P_{\mathrm{min}}$ and 26 (the same except three) have
$sma_{\mathrm{SOI8}}<sma<sma_{\mathrm{min}}$. Hence the periods and orbital
semi-major axes of SOI-1–SOI-8 candidates are consistent with the
corresponding values for confirmed exoplanets.

Other parameters ($e$, $\Omega$, $i$) determined in the process of modeling
are of no importance for the tested hypothesis. The orbital eccentricities of
SOI-1–SOI-7 are greater than 0.3. Less than 3% of transiting exoplanets are
known to have such orbital eccentricities [NASA, 2022]. The longitude of the
ascending node is in no way restricted and it is uniformly distributed in the
$\Omega=0$–$360^{\circ}$ interval. These two parameters have the greatest
fractional uncertainty. Orbital inclinations $i$ of the candidates discussed
lie in the $79\,.\\!\\!^{\circ}8$–$87\,.\\!\\!^{\circ}6$ interval, which
accounts for 26% of transiting exoplanets [NASA, 2022].

The stellar radii used here (Vallenari et al. 2022) are inferred from the
$B-R$ color index and star parallax assuming that the object is a single star.
Therefore the inferred estimates of the sizes semi-major axes of exoplanets
cannot be considered to be sufficiently reliable. However, at the same time,
the available data do not allow us to fully reject the hypothesis about the
planetary nature of the secondary SOI components.

It is also possible to solve the inverse problem of the determination of the
maximum stellar radius $R_{\mathrm{*max}}$ given the $R_{{p}}/R_{*}$ ratio and
adopting $2.5\,R_{\mathrm{Jup}}$ as the maximum possible radius of an
exoplanet. We thus infer the following maximum radii $R_{\mathrm{*max}}$ for
SOI-1–SOI-8: 0.66, 0.61, 1.07, 0.95, 0.66, 1.03, 0.66, and 0.86 $R_{\odot}$.
We can consider rejecting the tested hypothesis if future radius estimates
will exceed the above values.

## Conclusions

In this study we performed a complete cycle of the search for and analysis of
exoplanet candidates by means of transit photometry: photometric monitoring,
photometry and searching for transit events in the light curves, predicting
upcoming transits and conducting further photometric observations of
candidates, and modeling of transits.

We have discovered eight new exoplanet candidates. The inferred transit
parameters, the radii, orbital periods and semi-major axes are consistent with
the parameters of the already known exoplanets. We plan to study the spectra
of the stars considered and acquire photometric data with the 1-m telescope in
order to more accurately model the transits and determine the parameters of
the stars and exoplanet candidates.

The depth of brightness dip during the transit in the stars found corresponds
to the cases of giant planets passing across the discs of small stars
($0\,.\\!\\!^{\rm m}06$–$0\,.\\!\\!^{\rm m}17$). This proves that exoplanet
observations with the 50-cm robotic telescope of the Special Astrophysical
Observatory of the Russian Academy of Sciences can be used to discover
exoplanets larger than Jupiter. And this is true even if the planetary nature
of these exoplanet candidates will not be confirmed in the future.

## Acknowledgments

This study makes use of the results from the European Space Agency (ESA) space
mission Gaia. Gaia data are being processed by the Gaia Data Processing and
Analysis Consortium (DPAC). This study also makes use of the NASA Exoplanet
Archive, which is operated by the California Institute of Technology, under
contract with the National Aeronautics and Space Administration under the
Exoplanet Exploration Program.

## Funding

Authors acknowledge the support of Ministry of Science and Higher Education of
the Russian Federation under the grant 075-15-2020-780 (No 13.1902.21.0039).

## References

  * [Astropy Collaboration et al., 2022] Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., Earl, N., Starkman, N., Bradley, L., Shupe, D. L., Patil, A. A., Corrales, L., Brasseur, C. E., N”othe, M., Donath, A., Tollerud, E., Morris, B. M., Ginsburg, A., Vaher, E., Weaver, B. A., Tocknell, J., Jamieson, W., van Kerkwijk, M. H., Robitaille, T. P., Merry, B., Bachetti, M., G”unther, H. M., Aldcroft, T. L., Alvarado-Montes, J. A., Archibald, A. M., B’odi, A., Bapat, S., Barentsen, G., Baz’an, J., Biswas, M., Boquien, M., Burke, D. J., Cara, D., Cara, M., Conroy, K. E., Conseil, S., Craig, M. W., Cross, R. M., Cruz, K. L., D’Eugenio, F., Dencheva, N., Devillepoix, H. A. R., Dietrich, J. P., Eigenbrot, A. D., Erben, T., Ferreira, L., Foreman-Mackey, D., Fox, R., Freij, N., Garg, S., Geda, R., Glattly, L., Gondhalekar, Y., Gordon, K. D., Grant, D., Greenfield, P., Groener, A. M., Guest, S., Gurovich, S., Handberg, R., Hart, A., Hatfield-Dodds, Z., Homeier, D., Hosseinzadeh, G., Jenness, T., Jones, C. K., Joseph, P., Kalmbach, J. B., Karamehmetoglu, E., Kaluszy’nski, M., Kelley, M. S. P., Kern, N., Kerzendorf, W. E., Koch, E. W., Kulumani, S., Lee, A., Ly, C., Ma, Z., MacBride, C., Maljaars, J. M., Muna, D., Murphy, N. A., Norman, H., O’Steen, R., Oman, K. A., Pacifici, C., Pascual, S., Pascual-Granado, J., Patil, R. R., Perren, G. I., Pickering, T. E., Rastogi, T., Roulston, B. R., Ryan, D. F., Rykoff, E. S., Sabater, J., Sakurikar, P., Salgado, J., Sanghi, A., Saunders, N., Savchenko, V., Schwardt, L., Seifert-Eckert, M., Shih, A. Y., Jain, A. S., Shukla, G., Sick, J., Simpson, C., Singanamalla, S., Singer, L. P., Singhal, J., Sinha, M., SipHocz, B. M., Spitler, L. R., Stansby, D., Streicher, O., Sumak, J., Swinbank, J. D., Taranu, D. S., Tewary, N., Tremblay, G. R., Val-Borro, M. d., Van Kooten, S. J., Vasovi’c, Z., Verma, S., de Miranda Cardoso, J. V., Williams, P. K. G., Wilson, T. J., Winkel, B., Wood-Vasey, W. M., Xue, R., Yoachim, P., Zhang, C., Zonca, A., and Astropy Project Contributors (2022).  The Astropy Project: Sustaining and growing a community-oriented open-source project and the latest major release (v5.0) of the core package.  Astrophys. J., (2):167.
  * [Bertin and Arnouts, 1999] Bertin, E. and Arnouts, S. (1999).  SExtractor: Software for source extraction.  Astron. and Astrophys. Suppl.
  * [Claret, 2000] Claret, A. (2000).  A new non-linear limb-darkening law for lte stellar atmosphere models ii.  Astron. and Astrophys., pages 1081–1190.
  * [Gaia Collaboration et al., 2016] Gaia Collaboration, Prusti, T., de Bruijne, J., Brown, A., Vallenari, A., Babusiaux, C., Bailer-Jones, C., Bastian, U., Biermann, M., Evans, D., Eyer, L., Jansen, F., Jordi, C., Klioner, S., Lammers, U., Lindegren, L., Luri, X., Mignard, F., Milligan, D., Panem, C., and Zschocke, S. (2016).  The Gaia mission.  Astron. and Astrophys.
  * [Gaia Collaboration et al., 2022] Gaia Collaboration, Vallenari, A., Brown, A., Prusti, T., de Bruijne, J., Arenou, F., Babusiaux, C., Biermann, M., Creevey, O., Ducourant, C., Evans, D., Eyer, L., Guerra, R., Hutton, A., Jordi, C., Klioner, S., Lammers, U., Lindegren, L., Luri, X., and Zwitter, T. (2022).  Gaia Data Release 3: Summary of the content and survey properties.  arXiv e-prints astro-ph:2208.00211.
  * [Kovacs et al., 2002] Kovacs, G., Zucker, S., and Mazeh, T. (2002).  A box-fitting algorithm in the search for periodic transits.  Astron. and Astrophys.
  * [Kreidberg, 2015] Kreidberg, L. (2015).  batman: BAsic Transit Model cAlculatioN in Python.  Publ. Astron. Soc. Pacific, (957):1161–1165.
  * [Lang et al., 2009] Lang, D., Hogg, D., Mierle, K., Blanton, M., and Roweis, S. (2009).  Astrometry.net: Blind astrometric calibration of arbitrary astronomical images.
  * [NASA, 2022] NASA (2022).  NASA Exoplanet Archive.
  * [Seager and Mallen-Ornelas, 2003] Seager, S. and Mallen-Ornelas, G. (2003).  A Unique Solution of Planet and star parameters from an extrasolar planet transit light curve.  Astrophys. J., (2):1038–1055.
  * [Valeev et al., 2015] Valeev, A., Antonyuk, K., Pit, N., Solovyev, V., Burlakova, T., Moskvitin, A., Grauzhanina, A., Gadelshin, D., Shulyak, D., Fatkhullin, T., Galazutdinov, G., Malogolovets, E., Beskin, G., Karpov, S., Dyachenko, V., Rastegaev, D., Rzaev, A., and Valyavin, G. (2015).  Detection of regular low-amplitude photometric variability of the magnetic dwarf wd0009+501. on the possibility of photometric investigation of exoplanets on the basis of 1-meter class telescopes of the special and crimean astrophysical observatories.  Astrophysical Bulletin, pages 318–327.
  * [VanderPlas, 2017] VanderPlas, J. (2017).  Understanding the Lomb-Scargle Periodogram.  Astrophys. J. Suppl.
  * [Warren-Smith et al., 2014] Warren-Smith, R., Draper, P., Taylor, M., and Allan, A. (2014).  CCDPACK: CCD Data Reduction Package.
  * [Yakovlev et al., 2022] Yakovlev, O., Valeev, A., Valyavin, G., Tavrov, A., Aitov, V., Mitiani, G., Korablev, O., Galazutdinov, G., Beskin, G., Emelianov, E., Fatkhullin, T., Vlasyuk, V., Sasyuk, V., Perkov, A., Bondar, S., Burlakova, T., Fabrika, S., and Romanyuk, I. (2022).  Exoplanet two square degree survey with sao ras robotic facilities.  Front. Astron. Space Sci.

Figure 2:  Light curves of eight exoplanet candidates during the entire time
of the monitoring. The solid horizontal lines show the zero level and maximum
transit depth, and the dashed lines, the $\pm 3\sigma$ levels. The labels
under the light curves indicate the nights during which the transit was
observed: only the beginning (leftward arrow), only the end (rightward arrow),
mid-transit with the beginning or end (“plus” symbol) or complete transit
(upward arrow).

Figure 3: Light curve of SOI-1. Left: phase folded (dots), median values (the
black line), and model curve (the white line). Right: fragments for individual
transits with the same model curve (the black line), the period numbers for
each transit are indicated. Tick marks and labels are omitted not to clutter
the plots. Figure 4: BLS periodograms for SOI-2 without (bottom) and with
(top) subtraction of the nightly trend.

Figure 5: Light curve of SOI-2 (see the caption to Fig. 3).

Figure 6: Light curve of SOI-3 (see the caption to Fig. 3). Figure 7: Phased
light curve of SOI-3 based on individual observations made in 2022 ($V$-band
filter) and the model curve based on the data of 2020 survey-mode observations
(see Fig. 6).

Figure 8: Light curve of SOI-4 (see the caption to Fig. 3).

Figure 9: Light curve of SOI-5 (see the caption to Fig. 3).

Figure 10: Light curve of SOI-6 (see the caption to Fig. 3).

Figure 11: Light curve of SOI-7 (see the caption to Fig. 3).

Figure 12: The light curve of SOI-8 (see the caption to Fig. 3).

Figure 13: Phased curve for SOI-8 based on individual $B$, $V$, $R$ band
observations (circles, triangles, and crosses, respectively) in 2022 and the
model curve based on the 2020 data (survey-mode observations, see Fig. 12).

Figure 14: The BLS periodogram of SOI-8 (the thin line) after the subtraction
of the daily trend and the Lomb–Scargle periodogram (the thick line) without
the subtraction of this trend and without taking transits into account (data
points with phases $\phi=0.693$–$0.807$ excluded).

Figure 15: Phased light curves for SOI-8 without the subtraction of the trend
and without transits (data points with phases $\phi=0.693$–$0.807$ excluded):
folded with the period of $P=18\,.\\!\\!^{\rm h}688$ (top) and with the period
of transits $P=18\,.\\!\\!^{\rm h}768$ (bottom).