20XX Vol. X No. XX, 000–000

11institutetext:  Department of Space Sciences and Technologies, Faculty of
Sciences, Çanakkale Onsekiz Mart University, Terzioǧlu Campus, TR 17100,
Çanakkale, Turkey<EMAIL_ADDRESS>
Received 20XX Month Day; accepted 20XX Month Day

# Six Newly Discovered Eclipsing Binary Systems in the TESS field

Burak Ulaş∗00footnotetext: $*$ Corresponding author. and Vildan Ayan

###### Abstract

We present the first detailed investigation of six eclipsing binary systems in
the TESS field. The TESS light curves of the targets are analysed by
determining the initial effective temperatures via SED fits. The absolute
parameters are derived and the systems are compared to well-known binaries of
the same type. Results show that CD-58 791, CD-62 1257 and TYC 9356-355-1 are
detached binary systems. CD-54 942 and UCAC4 136-007295 are contact binaries
while TYC 8508-1413-1 is a semidetached system.

###### keywords:

binaries: eclipsing — stars: fundamental parameters — stars: individual: CD-54
942, CD-58 791, CD-62 1257, TYC 8508-1413-1, TYC 9356-355-1 and UCAC4
136-007295

##  1 Introduction

Studies on eclipsing binary systems improved our understanding of the
structure and evolution of stars in various circumstances. Since the
observation of Mizar, more than four hundred years of effort given by
researchers to observe, discover, classify and reveal the characteristics of
binary systems resulted in an ability to determine the light and absolute
parameters, thus, making incisive estimations on their structural properties
and evolutional paths. Being powerful tools for deriving the crucial
properties of the stars, binary star systems still hold their solid ground as
one of the leading research topics in stellar astrophysics.

Space observations are a milestone in finding a chance to look at the binary
stars in a different way. They allow us to determine the variations with small
amplitudes and discover very faint binaries that can be improbable to detect
with numerous ground-based instruments. The discoveries made by using the data
from Kepler (Borucki et al. 2010) and Transiting Exoplanet Survey Satellite
(TESS, Ricker et al. 2015) missions played an important role in improving our
knowledge of various types of stars, as well as binary systems. They also
provided a dramatic increment in the number of known systems. As of the
moment, Kepler Eclipsing Binary Catalog of Kirk et al. (2016) contains 2920
systems while Prša et al. (2022) cataloged 4584 binaries in their TESS
Eclipsing Binary catalog.

The systems investigated in this paper were first validated as eclipsing
binaries in the eclipsing binary catalog of Prša et al. (2022) where authors
classified the targets based on their TESS light curves. The targets were also
cataloged by the Gaia data releases (Gaia Collaboration et al. 2016, 2018,
2022). CD-54 942, CD-58 791 and TYC 9356-355-1 also appeared in the releases
of the RAVE (Kordopatis et al. 2013; Kunder et al. 2017; Steinmetz et al.
2020). Sharma et al. (2018) listed UCAC4 136-007295 in their High Efficiency
and Resolution Multi-Element Spectrograph (HERMES) catalog.

The lack of detailed information on the systems in the literature motivated us
to study them in detail. Our study is the first one that focuses on the
analyses of the light curves and the determination of binary parameters. The
next section gives the details of the data used in the study while Sec. 3
deals with the derivation of the initial effective temperatures, calculation
of the orbital periods and the analyses of the light curves. In the last
section, we conclude the results and compare the systems with the well-known
binaries with the same morphologies.

##  2 Light Curves

We collected the TESS light curve data of the systems via Mikulski Archive for
Space Telescopes (MAST)
portal111mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. The magnitude
values were derived following the TESS magnitudes (Stassun et al. 2019) and
using the formula $-2.5\log F$ where $F$ is the Pre-search Data Conditioning
Simple Aperture Photometry (PDC SAP) flux values stored in the data files. The
data are from sectors 3, 4, 5, and 6 for CD-54 942, sectors 2,3 and 4 for
CD-58 791, sector 13 for CD-62 1257, sectors 3 and 4 for TYC 8508-1413-1,
sectors 1 and 13 for TYC 9356-355-1, sectors 9, 10 and 11 for UCAC4
136-007295. The TESS magnitudes are 10.785m, 9.718m, 9.891m, 10.787m, 10.238m,
12.406m for CD-54 942, CD-58 791, CD-62 1257, TYC 8508-1413-1, TYC 9356-355-1
and UCAC4 136-007295, respectively.

The one orbital period long light curves of the systems are shown in Fig. 1.
As seen from the figure, the shapes of the curves resemble the typical
variation of eclipsing binary systems in several morphologies. The depths of
primary and secondary minimums are 0.31m and 0.26m for CD-54 942, 0.283m and
0.282m for CD-58 791, 0.24m and 0.20m for CD-62 1257, 0.42m and 0.16m for TYC
8508-1413-1, 0.40m and 0.14m for TYC 9356-355-1, 0.22m and 0.21m for UCAC4
136-007295. The durations are 3.8h and 3.4h, 5.5h and 5.4h, 5.6h and 5.3h,
2.9h and 2.8h, 3.5h and 3.8h, 6.1h and 5.9h for the primary and secondary
minimum of CD-54 942, CD-58 791, CD-62 1257, TYC 8508-1413-1, TYC 9356-355-1
and UCAC4 136-007295, respectively. 967 times of minimum light for the targets
were also calculated from the TESS light curves using the method of Kwee & van
Woerden (1956) and listed in Table 1

Figure 1: TESS light curve in the time interval equals to one orbital period
for CD-54 942 (a), CD-58 791 (b), CD-62 1257 (c), TYC 8508-1413-1 (d), TYC
9356-355-1 (e) and UCAC4 136-007295 (f).

Table 1: Calculated times of minimum light for the systems. TYC 8508, TYC 9356
and UCAC4 136 refer to TYC 8508-1413-1, TYC 9356-355-1 and UCAC4 136-007295,
respectively. This table is for guidance, its full version is available in
electronic form.

System |  BJD-2457000 | Error | Min. type
---|---|---|---
CD-54 942 |  1386.126517 |  0.000001 | I
CD-54 942 |  1385.971296 |  0.000001 | II
CD-54 942 |  1386.436137 |  0.000001 | I
CD-54 942 |  1386.281039 |  0.000001 | II
CD-54 942 |  1386.745805 |  0.000001 | I
CD-54 942 |  1386.590640 |  0.000001 | II
$\vdots$ | $\vdots$ | $\vdots$ | $\vdots$

##  3 Analyses of the Light Curves

The systems were recently classified as eclipsing binary candidates by Prša et
al. (2022), however, their binary parameters were not determined in the
literature. The lack of detailed information about the systems necessitates
the derivation of some crucial parameters prior to the light curve analyses.
We first determined the mass ratio for the systems via $q$-search procedure by
using the 2015 version of Wilson-Devinney code (Wilson & Devinney 1971; Wilson
et al. 2020) on 1000 normalized data points of the light curves. A lack of
morphological classes of the systems directed us to apply $q$-search in two
different morphological assumptions for each system. Contact and semidetached
approach used for CD-54 942 and UCAC4 136-007295. The q-searches with the
contact approach were applied in the range of $q$=0.0-2.0 to avoid missing the
more accurate value larger than 1.0. The process output unphysical results for
the q values larger than 0.5 for CD-54 942. The q-search for CD-58 791, CD-62
1257, TYC 8508-1413-1 and TYC 9356-355-1, on the other hand, was made in
detached and semidetached mode. The results of the $q$-search are shown in
Fig. 2 which indicates that CD-54 942 and UCAC4 136-007295 are probably
contact binary systems whereas detached morphology is more accurate for CD-58
791, CD-62 1257 and TYC 9356-355-1. TYC 8508-1413-1 are found to be
semidetached binary based on our $q$-search results. However, one must bear in
mind that the light curve is not sensitive to mass ratio for detached binaries
and semidetached systems that show partial eclipses (Terrell & Wilson 2005),
therefore, some further properties must be taken into account to decide the
morphology as we remark in corresponding subsections.

The effective temperature also significantly impacts deriving physically
meaningful results by light curve analysis. The systems were not studied in
detail previously, thus, we faced the lack of reliable effective temperature
values for the components in the literature as expected. We constructed
spectral energy distributions (SEDs) through Virtual Observatory SED Analyzer
(VOSA, Bayo et al. 2008) using the photometric data given by the VizieR
database (Ochsenbein et al. 2000) to derive the temperatures for the
components of the systems. During the SED analysis, the data were fitted using
chi-squared fit or binary fit (two components approach) with a parameter-grid
search to obtain the optimized Kurucz atmosphere model (Kurucz 1979). The
search domain for the temperatures was set between 3500 and 10000 K while the
interval for log $g$ values, which has a minor effect on SED, was between
2.5-5.0. A good fit corresponds to the Vgfb value, a value for estimating the
goodness of fit, that is smaller than 10-15 (Bayo et al. 2008). The error in
the temperature and the gravity values calculated by the SED analyses are
$\Delta T$=125 K and $\Delta$ log $g$=0.25. The results of the SED analyses
are given in corresponding subsections while the fits are shown in Fig. 3.

Orbital periods of the systems were determined by calculating averages of the
differences between two consecutive minima times of the same type. Frequency
analyses using Period04 software (Lenz & Breger 2005) were also applied to the
light curves to confirm the calculated orbital period values. The calculated
times of minima (Table 1) were also used for a period analysis with the linear
variation assumption and variation in orbital period $\Delta P$ and time of
minimum light, $\Delta T_{0}$ were derived utilizing the equation $O-C=\Delta
T_{0}+\Delta P\cdot E$, with the cycle number $E$. The standard errors ($SE$)
for the orbital periods were derived by using the equation containing standard
deviation ($\sigma$) and the number of derived period values ($N$),
$SE=\sigma/N$. The calculated values are given in the following subsections as
well as Table 2.

The analyses were applied by using PHOEBE (Prša & Zwitter 2005) which analyse
the input light curve by using Wilson-Devinney method (Wilson & Devinney
1971). The inclination $i$, the temperature of the secondary component
$T_{2}$, mass ratio $q$, the surface potential values of the primary component
$\Omega_{1}$ and the luminosity of the primary component $L_{1}$ were the
adjustable parameters of the solutions. $\Omega_{2}$ was also set as
adjustable in the analyses with detached approximation. The albedos ($A_{1}$,
$A_{2}$) were adopted from Ruciński (1969) and the gravity darkening
coefficients ($g_{1}$, $g_{2}$) for the systems were taken from von Zeipel
(1924) and Lucy (1967) by taking account of the fact that the granulation
boundary at about F0 spectral type (Gray & Nagel 1989). Logarithmic limb
darkening coefficients ($x_{1}$ and $x_{2}$) were derived from Claret (2017)
based on the initial temperatures of the components. The light curve data
covering more than 50000 data points were reduced to 50000, the input limit of
the software, during the solution.

Figure 2: Results of the $q$-search for CD-54 942 (a), CD-58 791 (b), CD-62
1257 (c), TYC 8508-1413-1 (d), TYC 9356-355-1 (e) and UCAC4 136-007295 (f).
The sub-indices C, D and SD indicate contact, detached and semidetached
morphologies, respectively. Note that the procedure output unphysical results
for CD-62 1257 in semidetached assumption other than the initial value.

###  3.1 CD-54 942

The analysis was applied to 50000 data points which are binned from originally
59124. The orbital period was set to 0.309691 days, the value derived by using
the previously discussed method. Binary fit in the SED analysis resulted in
the effective temperatures of the two components as 7250 and 5000 K. However,
the first one is quite large compared to the values 5502 K (Steinmetz et al.
2020), 5244 K (Gaia Collaboration et al. 2016, 2022) and 5241 (Stassun et al.
2019) given in the literature. Therefore, we applied a chi-square fit to
determine a more realistic temperature and derived the value of 5250 K. The
log $g$ was also found to be 4.5. The distance is 157.4(3) based on the Gaia
DR3 parallax (Gaia Collaboration et al. 2016, 2022) and the extinction is
0$\overset{m}{.}$0342, derived by using the Galactic Dust Reddening and
Extinction interface of NASA/IPAC Infrared Science
Archive222https://irsa.ipac.caltech.edu/applications/DUST/. The components are
assumed to be in solar abundance. The Vgfb of the resulting fit is 0.704,
which is agree with the criterion for the good fit. The result is shown in
Fig.3.

Figure 3: SED fits applied to the available photometric data for CD-54 942
(a), CD-58 791 (b), CD-62 1257 (c), TYC 8508-1413-1 (d), TYC 9356-355-1 (e)
and UCAC4 136-007295 (f). The red lines refer to the model fits. The dashed
and dotted lines in d, e and f represent the best model fits for the hotter
and the cooler components, respectively.

The effective temperature of the hotter component is adjusted to 5250 K during
the light curve solution following the SED analysis. The light curve solution
was conducted in contact and semidetached approximations with the initial
value of the mass ratios of 0.25 and 0.2 considering the $q$-search. A
significantly better fit with smaller squared residuals was achieved with the
contact approach. Additionally, a spotted area on the cooler components was
hypothesized to fit the difference between the maxima of the light curve. The
parameters of the spot are found to be $\beta$=45∘, $\lambda$=90∘, $r$=25∘ and
$t$=0.9, where $\beta$, $\lambda$, $r$ and $t$ are co-latitude, longitude,
fractional radius and temperature factor, respectively. The results of the
analysis are listed in Table 2 while the agreement of the final fit to the
observations is shown in Fig. 4. We conclude that the target can be considered
as a contact binary system.

Figure 4: Calculated light curve (red lines) is plotted with the observations
and the agreement at the minimum phases are represented for CD-54 942 (a, c)
and CD-58 791 (b, d).

Table 2: Results of the light curve analyses. TYC 8508, TYC 9356 and UCAC4 136
refer to TYC 8508-1413-1, TYC 9356-355-1 and UCAC4 136-007295, respectively.
The standard deviations, 3$\sigma$ for the last digits of light parameters are
given in parentheses. The errors in the effective temperature, $T_{1}$, are
from the corresponding SED analyses. See text for the error determination for
orbital period values, $P$.

Parameter | CD-54 942 | CD-58 791 | CD-62 1257
---|---|---|---
T0 (BJD) | 1435.365982(3) | 1355.68657(2) | 1654.92067(2)
$P$ (days) | 0.309691(4) | 1.82630(2) | 2.71459(4)
$i$ ${({{}^{\circ}})}$ | 66.81(2) | 77.922(4) | 83.41(1)
$q$ | 0.237(1) | 0.789(1) | 0.608(1)
$T_{1}$ (K) | 5250(125) | 6500(125) | 6500(125)
$T_{2}$ (K) | 4963(21) | 6448(10) | 6273(33)
$\Omega_{1}$ | 2.293(1) | 5.022(2) | 6.630(6)
$\Omega_{2}$ | $\Omega_{1}$ | 4.896(2) | 7.90(1)
${L_{1}}/({L_{1}+L_{2}})$ | 0.832(1) | 0.5701(4) | 0.804(1)
$r_{1}$ | 0.5164(6) | 0.2381(7) | 0.166(2)
$r_{2}$ | 0.271(3) | 0.2097(9) | 0.091(4)
$x_{1},~{}x_{2}$ | 0.646, 0.659 | 0.558, 0.558 | 0.568, 0.581
| TYC 8508 | TYC 9356 | UCAC4 136
T0 (BJD) | 1386.143736(7) | 1325.984991(7) | 1544.00685(2)
$P$ (days) | 0.64191(3) | 1.31699(3) | 0.52391(8)
$i$ ${({{}^{\circ}})}$ | 69.86(2) | 79.67(3) | 67.46(3)
$q$ | 0.580(1) | 0.517(1) | 0.102(1)
$T_{1}$ (K) | 6500(125) | 7000(125) | 7000(125)
$T_{2}$ (K) | 5058(36) | 5548(21) | 6682(51)
$\Omega_{1}$ | 3.848(6) | 5.244(3) | 1.956(1)
$\Omega_{2}$ |  $\Omega_{cr}$=3.027 | 4.137(3) | $\Omega_{1}$
${L_{1}}/({L_{1}+L_{2}})$ | 0.743(1) | 0.796(1) | 0.905(2)
$r_{1}$ | 0.311(3) | 0.212(1) | 0.583(1)
$r_{2}$ | 0.331(1) | 0.179(2) | 0.210(6)
$x_{1},~{}x_{2}$ | 0.570, 0.617 | 0.547, 0.670 | 0.548, 0.601

###  3.2 CD-58 791

The SED analysis for the system resulted in two temperature values, 7750 and
6500 K, using the binary fit approach. However, the former temperature are
contrary to the values given by Gaia Collaboration et al. (2016, 2022),
Stassun et al. (2019) and Kordopatis et al. (2013) which are between 6000 and
6600 K. Therefore, we decided to analyse the SED by using the chi-square fit
option. The result indicated that log $g$=4.0 with the temperature value of
6500 K which we set as the temperature of the primary component in our light
curve analysis. The extinction was set to 0$\overset{m}{.}$0736 and the
distance was taken as 416(2) pc following (Gaia Collaboration et al. 2016,
2022). The Vgfb of the solution, 0.81, corresponds to a good fit. The SED fit
is plotted in Fig. 3. The orbital period of the system, on the other hand, was
calculated as 1.82630 by following the method described earlier.

The light curve analyses were conducted on 44540 data points in two
morphologies, detached and semidetached, individually. Although the
semidetached configuration shows relatively small squared residuals in the min
of $q$-search curve, the detached configuration fits the observations better
in the light curve analysis. The reason may rise from the fact that the mass
ratio is not sensitive to the light curve in detached configuration and weakly
depend on it in the semidetached binaries showing partial eclipses (Terrell &
Wilson 2005). The results are shown in Table 2 as well as in Fig. 4.
Considering the above-mentioned arguments, we accomplish that the system is a
detached binary.

###  3.3 CD-62 1257

The temperature of the primary components was derived in the same method that
was described in previous subsections. The chi-square fit resulted in log
$g$=4.5 and T=6500 K which is agree with the values given by Gaia
Collaboration et al. (2016, 2022) and Stassun et al. (2019). The distance of
the system was set to 455(7) pc based on the parallax byGaia Collaboration et
al. (2016, 2022), thus, the extinction is 0$\overset{m}{.}$1629\. The Vgfb was
derived as 0.577, which quite agrees with the acceptable interval.
Furthermore, the orbital period of the system was calculated to be 2.71459
days using the method discussed above.

The light curve of the binary was analysed by assuming that the system is a
detached binary considering not only the $q$-search but also the period value
and the shape of the light curve. The number of data in the solution was
19581. The calculated light curve is shown with the observations in Fig. 5
while the results are listed in Table 2.

Figure 5: Same as 4, but for CD-62 1257 (a, c) and TYC 8508-1413-1 (b, d).

###  3.4 TYC 8508-1413-1

SED analysis applied to available photometric data by using binary fit which
resulted in $T_{1}$=6500 K, $T_{2}$=5750 K and log $g_{1}$=log $g_{2}$=4.5,
the values assumed as the initial parameters for the components during the
light curve analysis. The Vgfb of the fit was calculated as 4.81, smaller than
10-15. The distance of the system was adopted as 374(2) pc (Gaia Collaboration
et al. 2016, 2022) that corresponds to the extinction value of
$A_{V}$=0$\overset{m}{.}$04.

The analysis was applied to 12399 data points with detached and conventional
semidetached approaches individually. Although the residuals of the light
curve solution were close in two morphologies, the fillout factor for the
secondary component was calculated to be 99%, using the equation,
$1-[(\Omega_{2}-\Omega_{cr})/\Omega_{cr}]$ in detached approximation, where
$\Omega_{cr}$ denotes the critical potential value for the corresponding mass
ratio. In addition, the K spectral type of the secondary is typical for the
secondaries of the Algol-type binaries. Therefore, the semidetached
configuration was supposed to be a more reliable morphology of the system. The
initial mass ratio was set to 0.35 and the orbital period was taken as 0.64191
days during the solution. The albedo of the secondary component was set as a
free parameter for the first couple of runs in order to achieve a better fit
around the secondary minimum. A hot spotted area on the primary component,
which may have been the result of the mass transfer from the secondary, was
also included in the solution to fit the difference between levels at maximum
phases. The spot parameters are $\beta$=90∘, $\lambda$=240∘, $r$=15∘ and
$t$=1.05. The resulting parameters are listed in Table 2. The calculated and
observational light curves are shown in Fig. 5.

###  3.5 TYC 9356-355-1

A binary fit with Vgfb=0.35 in the SED analysis corresponded to that the
temperature of the primary and secondary components are $T_{1}$=7000 K,
$T_{2}$=4750 K whilst the log $g$ values were found to be 4.5 for both of the
components. The extinction was adopted to 0$\overset{m}{.}$2026 and the
distance of the system is 320(4) pc (Gaia Collaboration et al. 2016, 2022).
The orbital period was calculated as 1.31699 by using the method mentioned
earlier in the text.

The orbital period value, the result of the q-search and the shape of the
light curve led us to analyse the light curve, which covers 37859 data points,
in detached mode and, therefore, the initial value for the mass ratio was set
to 0.5. The calculated light curve was plotted with observations in Fig. 6 and
the light parameters found by the solution are given in Table 2.

Figure 6: Same as 4, but for TYC 9356-355-1 (a, c) and UCAC4 136-007295 (b,
d).

###  3.6 UCAC4 136-007295

The temperatures and the gravities of the components were calculated as
$T_{1}$=7000 K, $T_{2}$=4250 K and log $g_{1}$=log $g_{2}$=4.0 during the SED
analysis, the former is relatively close to the value given by Sharma et al.
(2018), 6529 K, in their catalog. The distance of the system is 1295(68) pc
(Gaia Collaboration et al. 2016, 2022) and the extinction through the
direction is $A_{V}$=0$\overset{m}{.}$1195 that yielded using the same method
given above. The goodness of fit for the solution, Vgfb=0.218, corresponds to
a good fit.

We analysed the light curve in two morphological assumptions; semidetached
(with a secondary filling its Roche lobe) and contact. The semidetached
analysis resulted in a warning that the primary component exceeds its
corresponding Roche lobe. Thereby, the solution was conducted using 41110
light curve data with an approach that the binary is a contact system. The
calculated light curve is plotted with the observations in Fig. 6 and the
results are listed in Table 2.

##  4 Conclusion

We presented a comprehensive study on the binary properties of six eclipsing
binary systems. The absolute parameters (Table 3) are derived based on the
light parameters by using the AbsParEB program (Liakos & Niarchos 2015). It is
worth emphasizing that the errors in Table 2 and 3 are unphysical since the
uncertainties in the Wilson-Devinney method are underestimated. Furthermore,
the relatively poor fit caused deviations from the observations around the
minimum phases of some systems. The maximum value of the amplitude of
deviation was calculated as 0$\overset{m}{.}$02 for CD-58 791 and TYC
8508-1413-1, while it was 0$\overset{m}{.}$03 for CD-62 1257 and TYC
9356-355-1. The masses of the primary components of contact and semidetached
systems (CD-54 942, TYC 8508-1413-1 and UCAC4 136-007295) were estimated among
204930 binary star models created by using the Binary Star Evolution code by
Hurley et al. (2002, 2013) by setting the initial parameters of the orbital
period between 0.5 d and 7 d, the eccentricity between 0 and 0.5, the mass of
the primary component, $M_{1}$, between 0.5 M⊙ and 5.0 M⊙, the mass of the
secondary component between 0.1 M⊙ and $M_{1}$. The masses for the primaries
of the detached systems (CD-58 791, CD-62 1257 and TYC 9356-355-1), were
calculated from the stellar tracks of Bertelli et al. (2009) according to
their log $g$ and effective temperature values. The stars are assumed to be in
solar abundance during calculations.

Table 3: Absolute parameters of the systems. TYC 8508, TYC 9356 and UCAC4 136
refer to TYC 8508-1413-1, TYC 9356-355-1 and UCAC4 136-007295, respectively.
The standard errors are given in parentheses for the last digits

Parameter |  CD-54 942 | CD-58 791 | CD-62 1257
---|---|---|---
M1 (M⊙) | 0.8 | 1.5 | 2.1
M2 (M⊙) | 0.190(1) | 1.183(2) | 1.277(2)
R1 (R⊙) | 1.015(2) | 2.13(1) | 2.09(9)
R2 (R⊙) | 0.53(1) | 1.87(2) | 1.1(3)
L1 (L⊙) | 0.701(2) | 7.2(1) | 6.9(6)
L2 (L⊙) | 0.154(7) | 5.4(1) | 1.8(9)
$a$ (R⊙) | 1.965(2) | 8.943(4) | 12.57(1)
|  TYC 8508 | TYC 9356 | UCAC4 136
M1 (M⊙) | 1.3 | 1.5 | 1.6
M2 (M⊙) | 0.754(1) | 0.776(2) | 0.163(2)
R1 (R⊙) | 1.27(2) | 1.44(2) | 1.972(4)
R2 (R⊙) | 1.35(1) | 1.22(4) | 0.71(5)
L1 (L⊙) | 2.57(9) | 4.4(1) | 8.36(3)
L2 (L⊙) | 1.07(1) | 1.26(9) | 0.9(1)
$a$ (R⊙) | 4.074(2) | 6.807(4) | 3.382(3)

The fill-out factor, which indicates the degree of contact between components,
for the contact binaries CD-54 942 and UCAC4 136-007295 were found 0.19 and
0.42 by using the equation
${f=(\Omega_{i}-\Omega)\mathbin{/}(\Omega_{i}-\Omega_{o})}$ (Kallrath & Milone
2009), where $\Omega_{i}$ and $\Omega_{o}$ are the inner and outer Lagrangian
potentials. The filling factor ($f=r/r_{L}$) for the primary component of the
semidetached system TYC 8508-1413-1, on the other hand, was calculated by
using the relation
${r_{L}=0.49q^{\frac{2}{3}}\mathbin{/}[0.6q^{\frac{2}{3}}+\ln(1+q^{\frac{1}{3}})]}$
given by Eggleton (1983), where $r_{L}$ is the Roche lobe radius. The $f$ was
found to be 0.93 which indicates that the component is close to its Roche lobe
and the binary can be considered as a V1010 Oph type near-contact binary group
based on the classification of Shaw (1994). The difference between the
maximums of the light curve also supports this classification.

The systems were compared to the known binaries with the same morphological
type in Fig. 7. The plots confirm that the components of the systems are in
good agreement with 100 contact (Yıldız & Doğan 2013), 162 detached
(Southworth 2015) and 119 semidetached (Malkov 2020) binary systems. We also
compare TYC 8508-1413-1 to 26 known near-contact systems given by Yakut &
Eggleton (2005) in Fig. 8 in order to check its possible near-contact
candidacy remarked in the previous paragraph. The components of the target are
in accordance with the other near-contact binaries. A further statistical
comparison was made through the known systems’ mass, radius and temperature
distributions similar to those done by Ulaş & Ulusoy (2023). Fig. 9
illustrates the distributions and the box plots calculated by using the data
of corresponding stellar parameters. The masses, radii and temperatures of our
target systems are well inside the minimum and maximum values although the
secondary component of CD-54 942 seems to be cooler than most of its cousins.
The parameters of the box plots are given in Table 4.

Figure 7: The upper panel shows the Hertzsprung-Russell diagrams while the
lower panel indicates the mass-radius planes for contact (a,d), semidetached
(b,e) and detached (c,f) binary systems. Plus and cross signs denote the
primaries and secondaries of well-known systems with the corresponding
morphology. Full and open signs refer to primary and secondary components.
Squares, circles, triangles, diamonds, pentagons and upside-down triangles
denote CD-54 942, CD-58 791, CD-62 1257, TYC 8508-1413-1, TYC 9356-355-1 and
UCAC4 136-007295, respectively. Note that the location of the primary
components of CD-58 791 and CD-62 1257 overlap on the Hertzsprung-Russell
diagram (c). The data for ZAMS (thick solid line) and TAMS (dashed line) are
taken from Bressan et al. (2012) with $Y=0.267$ and $Z=0.01$ abundance. Figure
8: same as Fig. 7, but for TYC 8508-1413-1 and the known near-contact
binaries.  Figure 9: Mass, radius and temperature distributions (left panes)
and corresponding box plots (right panes) for primary (blue) and secondary
(red) components of known contact (a, b, c), detached (d, e, f) and
semidetached (g, h, i) binary systems. The other symbols are the same as those
displayed in Fig. 7. Some extreme values are excluded in plots, however, boxes
are calculated using all available data.

Table 4: Parameters of box plot calculated by using data from 100 contact
(Yıldız & Doğan 2013), 162 detached (Southworth 2015) and 119 semidetached
(Malkov 2020) binaries. $Q1$, $Q2$, $Q3$ and $IQR$ refer to lower quartile,
median, upper quartile and interquartile range values.

| $Q1$ |  $Q2$ |  $Q3$ |  min. |  max. |  $IQR$
---|---|---|---|---|---|---
Contact |  |  |  |  |  |
M1 (M⊙) | 1.09 | 1.36 | 1.61 | 0.56 | 2.09 | 0.52
M2 (M⊙) | 0.27 | 0.40 | 0.55 | 0.10 | 0.88 | 0.28
R1 (R⊙) | 1.16 | 1.40 | 1.58 | 0.71 | 2.20 | 0.43
R2 (R⊙) | 0.69 | 0.78 | 0.89 | 0.40 | 1.19 | 0.21
T1 (K) | 5860 | 6100 | 6500 | 5012 | 7300 | 640
T2 (K) | 5982 | 6180 | 6453 | 5380 | 7102 | 472
Detached |  |  |  |  |  |
M1 (M⊙) | 1.13 | 1.56 | 2.33 | 0.12 | 4.12 | 1.19
M2 (M⊙) | 0.97 | 1.41 | 2.10 | 0.11 | 3.60 | 1.13
R1 (R⊙) | 1.31 | 1.92 | 2.98 | 0.25 | 5.41 | 1.67
R2 (R⊙) | 1.04 | 1.59 | 2.43 | 0.24 | 4.29 | 1.38
T1 (K) | 5798 | 6471 | 9094 | 2892 | 12303 | 3296
T2 (K) | 5191 | 6375 | 8133 | 2851 | 11912 | 2942
Semidetached |  |  |  |  |  |
M1 (M⊙) | 2.01 | 2.71 | 5.69 | 0.97 | 10.70 | 3.68
M2 (M⊙) | 0.48 | 0.88 | 2.03 | 0.18 | 4.10 | 1.55
R1 (R⊙) | 2.00 | 2.74 | 4.50 | 1.20 | 8.00 | 2.50
R2 (R⊙) | 2.41 | 4.01 | 6.12 | 0.96 | 11.02 | 3.70
T1 (K) | 8283 | 9660 | 15498 | 4570 | 25200 | 7215
T2 (K) | 4465 | 4803 | 7615 | 3650 | 10900 | 3150

We concluded that TYC 8508-1413-1 is a semidetached system with the
probability of being a V1010 Oph type near-contact system. CD-54 942 and UCAC4
136-007295 are contact binaries and CD-58 791, CD-62 1257 and TYC 9356-355-1
are detached systems. Spectroscopic studies in combination with our results
may lead to determining the characteristics of the systems more precisely.

###### Acknowledgements.

This work was supported by Çanakkale Onsekiz Mart University, The Scientific
Research Coordination Unit, Project number: 2022-FBA-3851. The numerical
calculations reported in this paper were partially performed at TUBITAK
ULAKBIM, High Performance and Grid Computing Center (TRUBA resources). This
paper includes data collected by the TESS mission. Funding for the TESS
mission is provided by the NASA’s Science Mission Directorate. Some/all of the
data presented in this paper were obtained from the Mikulski Archive for Space
Telescopes (MAST). STScI is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST
for non-HST data is provided by the NASA Office of Space Science via grant
NNX13AC07G and by other grants and contracts. This research has made use of
the NASA/IPAC Infrared Science Archive, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This publication makes use
of VOSA, developed under the Spanish Virtual Observatory project supported by
the Spanish MINECO through grant AyA2017-84089. VOSA has been partially
updated by using funding from the European Union’s Horizon 2020 Research and
Innovation Programme, under Grant Agreement nº 776403 (EXOPLANETS-A). This
research has made use of NASA’s Astrophysics Data System. This research has
made use of the VizieR catalogue access tool, CDS, Strasbourg, France.This
work has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

## References

  * Bayo et al. (2008) Bayo, A., Rodrigo, C., Barrado Y Navascués, D., et al. 2008, A&A, 492, 277
  * Bertelli et al. (2009) Bertelli, G., Nasi, E., Girardi, L., & Marigo, P. 2009, A&A, 508, 355
  * Borucki et al. (2010) Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Claret (2017) Claret, A. 2017, A&A, 600, A30
  * Eggleton (1983) Eggleton, P. P. 1983, ApJ, 268, 368
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2022, arXiv e-prints, arXiv:2208.00211
  * Gray & Nagel (1989) Gray, D. F., & Nagel, T. 1989, ApJ, 341, 421
  * Hurley et al. (2002) Hurley, J. R., Tout, C. A., & Pols, O. R. 2002, MNRAS, 329, 897
  * Hurley et al. (2013) Hurley, J. R., Tout, C. A., & Pols, O. R. 2013, BSE: Binary Star Evolution
  * Kallrath & Milone (2009) Kallrath, J., & Milone, E. F. 2009, Eclipsing Binary Stars: Modeling and Analysis (Springer)
  * Kirk et al. (2016) Kirk, B., Conroy, K., Prša, A., et al. 2016, AJ, 151, 68
  * Kordopatis et al. (2013) Kordopatis, G., Gilmore, G., Steinmetz, M., et al. 2013, AJ, 146, 134
  * Kunder et al. (2017) Kunder, A., Kordopatis, G., Steinmetz, M., et al. 2017, AJ, 153, 75
  * Kurucz (1979) Kurucz, R. L. 1979, ApJS, 40, 1
  * Kwee & van Woerden (1956) Kwee, K. K., & van Woerden, H. 1956, Bull. Astron. Inst. Netherlands, 12, 327
  * Lenz & Breger (2005) Lenz, P., & Breger, M. 2005, Communications in Asteroseismology, 146, 53
  * Liakos & Niarchos (2015) Liakos, A., & Niarchos, P. 2015, in Astronomical Society of the Pacific Conference Series, Vol. 496, Living Together: Planets, Host Stars and Binaries, ed. S. M. Rucinski, G. Torres, & M. Zejda, 195
  * Lucy (1967) Lucy, L. B. 1967, ZAp, 65, 89
  * Malkov (2020) Malkov, O. Y. 2020, MNRAS, 491, 5489
  * Ochsenbein et al. (2000) Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23
  * Prša & Zwitter (2005) Prša, A., & Zwitter, T. 2005, ApJ, 628, 426
  * Prša et al. (2022) Prša, A., Kochoska, A., Conroy, K. E., et al. 2022, ApJS, 258, 16
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003
  * Ruciński (1969) Ruciński, S. M. 1969, Acta Astron., 19, 245
  * Sharma et al. (2018) Sharma, S., Stello, D., Buder, S., et al. 2018, MNRAS, 473, 2004
  * Shaw (1994) Shaw, J. S. 1994, Mem. Soc. Astron. Italiana, 65, 95
  * Southworth (2015) Southworth, J. 2015, in Astronomical Society of the Pacific Conference Series, Vol. 496, Living Together: Planets, Host Stars and Binaries, ed. S. M. Rucinski, G. Torres, & M. Zejda, 164
  * Stassun et al. (2019) Stassun, K. G., Oelkers, R. J., Paegert, M., et al. 2019, AJ, 158, 138
  * Steinmetz et al. (2020) Steinmetz, M., Guiglion, G., McMillan, P. J., et al. 2020, AJ, 160, 83
  * Terrell & Wilson (2005) Terrell, D., & Wilson, R. E. 2005, Ap&SS, 296, 221
  * Ulaş & Ulusoy (2023) Ulaş, B., & Ulusoy, C. 2023, MNRAS, 518, 4180
  * von Zeipel (1924) von Zeipel, H. 1924, MNRAS, 84, 665
  * Wilson & Devinney (1971) Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605
  * Wilson et al. (2020) Wilson, R. E., Devinney, E. J., & Van Hamme, W. 2020, WD: Wilson-Devinney binary star modeling
  * Yakut & Eggleton (2005) Yakut, K., & Eggleton, P. P. 2005, ApJ, 629, 1055
  * Yıldız & Doğan (2013) Yıldız, M., & Doğan, T. 2013, MNRAS, 430, 2029