11institutetext: INAF – Osservatorio Astrofisico di Catania, via S. Sofia 78,
95123 Catania, Italy
11email<EMAIL_ADDRESS>22institutetext: INAF – Osservatorio di
Astrofisica e Scienza dello Spazio, Via P. Gobetti 93/3, 40129 Bologna, Italy
33institutetext: Department of Physics, University of Rome Tor Vergata, via
della Ricerca Scientifica 1, 00133, Rome, Italy 44institutetext: INAF –
Osservatorio Astronomico di Padova, Vicolo dell2̆019Osservatorio 5, 35122,
Padova, Italy 55institutetext: Purple Mountain Observatory, Chinese Academy of
Sciences, Nanjing 210023, China 66institutetext: Fundación Galileo
Galilei–INAF, Rambla José Ana Fernández Pérez 7, 38712 Breña Baja, Tenerife,
Spain 77institutetext: INAF – Osservatorio Astronomico di Roma, Via Frascati
33, 00078 Monte Porzio Catone, Italy

# TIC 43152097
The first eclipsing binary in NGC 2232 ††thanks: Based on observations made
with the Italian Telescopio Nazionale Galileo (TNG), operated on the island of
La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di
Astrofisica) at the Observatorio del Roque de los Muchachos. Based on
photometry collected at the INAF - Osservatorio Astrofisico di Catania.

A. Frasca TIC 43152097 The first eclipsing binary in NGC 2232 ††thanks: Based
on observations made with the Italian Telescopio Nazionale Galileo (TNG),
operated on the island of La Palma by the Fundación Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Observatorio del Roque de los
Muchachos. Based on photometry collected at the INAF - Osservatorio
Astrofisico di Catania.TIC 43152097 The first eclipsing binary in NGC 2232
††thanks: Based on observations made with the Italian Telescopio Nazionale
Galileo (TNG), operated on the island of La Palma by the Fundación Galileo
Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Observatorio
del Roque de los Muchachos. Based on photometry collected at the INAF -
Osservatorio Astrofisico di Catania. J. Alonso-Santiago TIC 43152097 The first
eclipsing binary in NGC 2232 ††thanks: Based on observations made with the
Italian Telescopio Nazionale Galileo (TNG), operated on the island of La Palma
by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di
Astrofisica) at the Observatorio del Roque de los Muchachos. Based on
photometry collected at the INAF - Osservatorio Astrofisico di Catania.TIC
43152097 The first eclipsing binary in NGC 2232 ††thanks: Based on
observations made with the Italian Telescopio Nazionale Galileo (TNG),
operated on the island of La Palma by the Fundación Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Observatorio del Roque de los
Muchachos. Based on photometry collected at the INAF - Osservatorio
Astrofisico di Catania. G. Catanzaro TIC 43152097 The first eclipsing binary
in NGC 2232 ††thanks: Based on observations made with the Italian Telescopio
Nazionale Galileo (TNG), operated on the island of La Palma by the Fundación
Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the
Observatorio del Roque de los Muchachos. Based on photometry collected at the
INAF - Osservatorio Astrofisico di Catania.TIC 43152097 The first eclipsing
binary in NGC 2232 ††thanks: Based on observations made with the Italian
Telescopio Nazionale Galileo (TNG), operated on the island of La Palma by the
Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at
the Observatorio del Roque de los Muchachos. Based on photometry collected at
the INAF - Osservatorio Astrofisico di Catania. A. Bragaglia TIC 43152097 The
first eclipsing binary in NGC 2232 ††thanks: Based on observations made with
the Italian Telescopio Nazionale Galileo (TNG), operated on the island of La
Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di
Astrofisica) at the Observatorio del Roque de los Muchachos. Based on
photometry collected at the INAF - Osservatorio Astrofisico di Catania.TIC
43152097 The first eclipsing binary in NGC 2232 ††thanks: Based on
observations made with the Italian Telescopio Nazionale Galileo (TNG),
operated on the island of La Palma by the Fundación Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Observatorio del Roque de los
Muchachos. Based on photometry collected at the INAF - Osservatorio
Astrofisico di Catania. V. D’Orazi TIC 43152097 The first eclipsing binary in
NGC 2232 ††thanks: Based on observations made with the Italian Telescopio
Nazionale Galileo (TNG), operated on the island of La Palma by the Fundación
Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the
Observatorio del Roque de los Muchachos. Based on photometry collected at the
INAF - Osservatorio Astrofisico di Catania.TIC 43152097 The first eclipsing
binary in NGC 2232 ††thanks: Based on observations made with the Italian
Telescopio Nazionale Galileo (TNG), operated on the island of La Palma by the
Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at
the Observatorio del Roque de los Muchachos. Based on photometry collected at
the INAF - Osservatorio Astrofisico di Catania.TIC 43152097 The first
eclipsing binary in NGC 2232 ††thanks: Based on observations made with the
Italian Telescopio Nazionale Galileo (TNG), operated on the island of La Palma
by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di
Astrofisica) at the Observatorio del Roque de los Muchachos. Based on
photometry collected at the INAF - Osservatorio Astrofisico di Catania.TIC
43152097 The first eclipsing binary in NGC 2232 ††thanks: Based on
observations made with the Italian Telescopio Nazionale Galileo (TNG),
operated on the island of La Palma by the Fundación Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Observatorio del Roque de los
Muchachos. Based on photometry collected at the INAF - Osservatorio
Astrofisico di Catania. X. Fu TIC 43152097 The first eclipsing binary in NGC
2232 ††thanks: Based on observations made with the Italian Telescopio
Nazionale Galileo (TNG), operated on the island of La Palma by the Fundación
Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the
Observatorio del Roque de los Muchachos. Based on photometry collected at the
INAF - Osservatorio Astrofisico di Catania.TIC 43152097 The first eclipsing
binary in NGC 2232 ††thanks: Based on observations made with the Italian
Telescopio Nazionale Galileo (TNG), operated on the island of La Palma by the
Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at
the Observatorio del Roque de los Muchachos. Based on photometry collected at
the INAF - Osservatorio Astrofisico di Catania.TIC 43152097 The first
eclipsing binary in NGC 2232 ††thanks: Based on observations made with the
Italian Telescopio Nazionale Galileo (TNG), operated on the island of La Palma
by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di
Astrofisica) at the Observatorio del Roque de los Muchachos. Based on
photometry collected at the INAF - Osservatorio Astrofisico di Catania.TIC
43152097 The first eclipsing binary in NGC 2232 ††thanks: Based on
observations made with the Italian Telescopio Nazionale Galileo (TNG),
operated on the island of La Palma by the Fundación Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Observatorio del Roque de los
Muchachos. Based on photometry collected at the INAF - Osservatorio
Astrofisico di Catania. A. Vallenari TIC 43152097 The first eclipsing binary
in NGC 2232 ††thanks: Based on observations made with the Italian Telescopio
Nazionale Galileo (TNG), operated on the island of La Palma by the Fundación
Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the
Observatorio del Roque de los Muchachos. Based on photometry collected at the
INAF - Osservatorio Astrofisico di Catania.TIC 43152097 The first eclipsing
binary in NGC 2232 ††thanks: Based on observations made with the Italian
Telescopio Nazionale Galileo (TNG), operated on the island of La Palma by the
Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at
the Observatorio del Roque de los Muchachos. Based on photometry collected at
the INAF - Osservatorio Astrofisico di Catania. G. Andreuzzi TIC 43152097 The
first eclipsing binary in NGC 2232 ††thanks: Based on observations made with
the Italian Telescopio Nazionale Galileo (TNG), operated on the island of La
Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di
Astrofisica) at the Observatorio del Roque de los Muchachos. Based on
photometry collected at the INAF - Osservatorio Astrofisico di Catania.TIC
43152097 The first eclipsing binary in NGC 2232 ††thanks: Based on
observations made with the Italian Telescopio Nazionale Galileo (TNG),
operated on the island of La Palma by the Fundación Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Observatorio del Roque de los
Muchachos. Based on photometry collected at the INAF - Osservatorio
Astrofisico di Catania.TIC 43152097 The first eclipsing binary in NGC 2232
††thanks: Based on observations made with the Italian Telescopio Nazionale
Galileo (TNG), operated on the island of La Palma by the Fundación Galileo
Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Observatorio
del Roque de los Muchachos. Based on photometry collected at the INAF -
Osservatorio Astrofisico di Catania.TIC 43152097 The first eclipsing binary in
NGC 2232 ††thanks: Based on observations made with the Italian Telescopio
Nazionale Galileo (TNG), operated on the island of La Palma by the Fundación
Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the
Observatorio del Roque de los Muchachos. Based on photometry collected at the
INAF - Osservatorio Astrofisico di Catania.

(Received 19 June 2023 / Accepted 24 July 2023)

We report the discovery of a low-mass totally eclipsing system in the young
($age\simeq 28$ Myr) open cluster NGC 2232, during an examination of their
TESS photometry. The follow-up study of this detached system, TIC 43152097, is
based on photometry and high-resolution spectra from the literature and
collected by us. The radial velocity of the center of mass and the
photospheric lithium abundance of the binary components confirm its membership
to NGC 2232. By analyzing the existing photometric and spectroscopic data, we
obtain orbital elements and fundamental stellar parameters for the two stars.
The primary component of TIC 43152097 is a late F-type dwarf ($T_{\rm eff}$ =
6070 K), while the lower-mass secondary is a late K-type star ($T_{\rm eff}$ =
4130 K) that is still in the pre-main-sequence phase. The precise measurements
of the radii, masses, and effective temperatures, enabled by the simultaneous
solution of light and radial velocity curves, indicate radius inflation for
the K-type component, which turns out to be 7–11 % larger than that predicted
by standard evolutionary models. More sophisticated models incorporating both
the inhibition of convective energy transport caused by sub-photospheric
magnetic fields and the effects of cool starspots covering a substantial
fraction of the stellar surface (30–60 %) allow the position of the secondary
component to be reproduced in the Hertzsprung-Russell and mass-radius
diagrams.

###### Key Words.:

stars: binaries: eclipsing – stars: binaries: spectroscopic – stars: low-mass
– stars: pre-main sequence – stars: individual: TIC 43152097 – open clusters
and associations: individual: NGC 2232

##  1 Introduction

Precise measurements of stellar parameters are of paramount importance for
studying the physics and evolution of stars and their environment,
specifically, circumstellar protoplanetary disks and planetary systems.
Eclipsing binaries represent unparalleled targets for achieving the most
precise determinations of fundamental stellar parameters, such as effective
temperature ($T_{\rm eff}$), mass ($M_{\ast}$), and radius ($R_{\ast}$). These
quantities can be directly measured from the analysis of the radial velocity
(RV) and light curves, eliminating the need for calibration relationships or
complex models of stellar structure and evolution. Furthermore, these
precisely derived parameters serve as a means to validate the accuracy and
reliability of internal structure models, providing a valuable opportunity to
assess the fidelity of our understanding of stellar interiors.

One of the most relevant results that emerged from the study of binaries with
late spectral type (KM) components is the disagreement between the theoretical
and observed radii of young magnetically active stars. For a fixed mass, the
observed radii are 10–20% larger than the model predictions and hence, for a
given luminosity, the effective temperature can be overestimated by $\sim$5%
(e.g., Morales et al., 2009; Kraus et al., 2011; Torres, 2013). On the other
hand, the radii of single slowly rotating stars derived from interferometric
measurements (e.g., Demory et al., 2009; Boyajian et al., 2012) are in close
agreement with standard models, suggesting that the high level of magnetic
activity induced by tidal coupling is the main effect responsible for the
radius inflation in the components of close binary systems. Strong support for
this hypothesis comes from observations of late-type members of young
clusters, which have not yet spun down via magnetic braking and display a
strong magnetic activity. Their color-magnitude diagrams (CMD) and lithium
abundance distributions are reproduced satisfactorily, considering only radius
inflation of approximately 10% (e.g., Jeffries et al., 2017; Somers & Stassun,
2017; Jackson et al., 2018).

Eclipsing binaries with components in the pre-main sequence (PMS) or in the
zero-age main sequence (ZAMS) phase, and in particular those belonging to
clusters with a known age and metallicity, are of great help in this respect,
because they offer the possibility for direct measures of $T_{\rm eff}$,
$M_{\ast}$, and $L_{\ast}$ for objects in these evolutionary phases. This is
particularly relevant for PMS binaries, because the components of the already
known binaries with radius inflation are mostly main-sequence (MS) stars.

We report here the discovery and study of an eclipsing binary, TIC 43152097,
in NGC 2232, a young open cluster ($\text{age}\simeq$ 28–38 Myr) with a solar
metallicity (e.g., Binks et al., 2021; Jeffries et al., 2023), whose late-type
members are still in the PMS phase. TIC 43152097 was initially selected as a
target for high-resolution spectroscopic observations of members of young open
clusters tentatively associated with the Radcliffe Wave (Alves et al., 2020),
with the aim of determining their kinematic and chemical properties. For this
purpose, we selected slowly rotating G-type members of five clusters,
including NGC 2232, from the high-probability candidates proposed by Cantat-
Gaudin et al. (2018, 2020). Therefore, among the stars with Transiting
Exoplanet Survey Satellite (TESS; Ricker et al. 2015) photometry, we searched
for those with rotation periods long enough to expect a small projected
rotation velocity ($v\sin i$ $\leq 20$ km s-1), which would allow a good
determination of atmospheric parameters and abundances to be made. In the
course of this search, we came across an eclipsing binary that was not known
in the literature and that had all the characteristics of a bona fide member
of NGC 2232, as clearly shown by its position in the Gaia CMD (Fig. 1). The
main properties of this source from the literature are summarized in Table 1.
We acquired three spectra of this star during our observing run with High
Accuracy Radial velocity Planet Searcher North spectrograph (HARPS-N), which,
together with another spectrum available in the literature, are well enough
distributed in the orbital phase to trace the RV curve. We solved for the TESS
light curve and the RV curve to obtain the orbital and physical parameters of
this system.

The paper is organized as follows. In Sect. 2 ,we present our observations and
the data retrieved from the literature. In Sect. 3, we show the results of our
work, describing the analysis carried out on both the photometric and
spectroscopic data. We discuss our results in Sect. 4. Finally, in Sect. 5, we
summarize the main results and present our conclusions.

Figure 1: Gaia CMD for the members of NGC 2232 (open circles) selected by
Cantat-Gaudin et al. (2020). The position of TIC 43152097 is marked with a red
dot.

##  2 Observations

Table 1: Properties of TIC 43152097 from the literature.

Gaia DR3 ID | RA | DEC | Plxa | pmRA | pmDEC | $G^{a}$ | $G_{\rm BP}-G_{\rm RP}^{a}$ | $V^{b}$ | $B-V^{b}$
---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) | (mas) | (mas yr-1) | (mag) | (mag) | (mag) | (mag)
3104591653648488192 | 06 29 38.05 |  $-$04 03 59.2 | 2.9119 | $-4.556$ | $-1.864$ | 11.771 | 0.791 | 11.871 | 0.613

Notes. a From the Gaia DR3 catalog (Gaia Collaboration, 2022). b From the
APASS Catalog (Henden et al., 2018).

Figure 2: SAP TESS light curves of TIC 43152097 in 2018 (top) and 2020
(bottom). Low-amplitude out-of-eclipse variation is visible in both epochs.
The higher data cadence in 2020 is apparent.

###  2.1 Photometry

Space-born accurate photometry was obtained with TESS (Ricker et al., 2015).
TIC 43152097 was observed in sector 6 with 1800 s exposure times between 15
December 2018 and 6 January 2019, as well as in sector 33 with 600 s exposure
times between 17 December 2020 and 12 January 2021. As NGC 2232 is a sparse
cluster, there is no severe star crowding, particularly considering the large
pixel size of TESS (21″). Moreover, TIC 43152097 is located far from the
central region of the cluster, at about 40 ′ from 10 Mon, which is the
brightest star of the cluster. Indeed, searching in the Gaia DR3 catalog (Gaia
Collaboration, 2022), no star with a comparable magnitude can be found within
21″of TIC 43152097. We downloaded the TESS light curves reduced by the MIT
Quick Look Pipeline (QLP, Huang et al., 2020) from the
MAST111https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html archive
and used the simple aperture photometry (SAP) flux and the KSPSAP flux. The
latter was obtained from the SAP flux by applying a high-pass filter that
removes the low-frequency variability originating from stellar activity or
instrumental effects.

To obtain the color information that is lacking in the TESS data, we planned
multiband photometric observations of TIC 43152097 at the M. G. Fracastoro
station (Serra La Nave, Mt. Etna, 1750 m. a.s.l.) of the Osservatorio
Astrofisico di Catania (OACT, Italy) in the winter season of 2022-23. We used
the facility imaging camera at the 0.91 m telescope with a set of broadband
Bessell filters ($B$, $V$, $R_{\rm C}$, and $I_{\rm C}$). Due to bad weather
and time constraints, we were only able, apart from some scattered data points
outside eclipses, to acquire useful data during a secondary eclipse on 7
January 2023 whose egress, observed at high values of airmass, was not fully
covered. Although their cadence is higher than that of TESS, the photometric
precision is lower. Therefore, we used this multiband photometry only to
verify whether the light-curve solution made on the TESS data was able to
reproduce them (see Fig. 12).

###  2.2 Spectroscopy

High-resolution spectroscopy ($R\simeq 115,000$) was performed with the High
Accuracy Radial velocity Planet Searcher North spectrograph (HARPS-N,
Cosentino et al. 2012), which is mounted at the 3.6-m Telescopio Nazionale
Galileo (TNG), at the Roque de los Muchachos Observatory (La Palma, Spain).
Three spectra were acquired during three consecutive nights from 27 to 29
October 2022, with 1800 s exposure time. These spectra were automatically
reduced using the instrument pipeline.

Searching in the literature for additional high-resolution spectra, we found
only one spectrum, which is the sum of three individual spectra taken on the
same night with HERMES at AAT in the framework of the Galactic Archeology with
HERMES survey (GALAH), De Silva et al. (2015), (see Buder et al., 2021, for
the third GALAH release). HERMES (Sheinis, 2016) is a multi-object
spectrograph ($R\simeq 28,000$) mounted at the 3.9-m telescope of the Anglo
Australian Observatory. The secondary component was not detected by the
automatic pipeline, which has basically derived the atmospheric parameters,
element abundances, and RV of the primary component of TIC 43152097. We used
this spectrum to measure the RV of the system components, adding another
useful point to their RV curves.

The Gaia DR3 catalog (Gaia Collaboration, 2022) reports an RV=36.46 $\pm$
19.43 km s-1, which was obtained with the Radial Velocity Spectrometer (RVS)
as the mean of the values measured in eight different epochs. The large error
for such a bright source is suggestive of a variable RV. Unfortunately, the
individual values of RV, which would have been helpful to cover the RV curve
of the primary component, will only be available in the fourth Gaia data
release.

##  3 Results

###  3.1 Light-curve solution

The SAP TESS light curves (Fig. 2) clearly show that this star is indeed an
eclipsing binary with the primary minimum much deeper than the secondary one,
indicating a very different temperature for the two system components. In the
SAP data, a low-amplitude variation is also visible outside the eclipses that
can be ascribed to starspots in one of the components and to instrumental
effects. For the purpose of studying the eclipses, it is advantageous to use
the KSPSAP flux, in which low-frequency variations, whatever their origin,
have been filtered out and the out-of-eclipse part of the light curve appears
flat.

The first parameter we measured was the orbital period, $P_{\rm orb}$. To this
aim, we determined the times of primary and secondary minima with the method
of eclipse bisector (e.g., Covino et al., 2004), which allowed us to reduce
the uncertainties on the mid-eclipse epochs due to the measurement errors and
the coarse data sampling (see Fig. 13 for an example). The errors of the mid-
eclipse epochs, measured as the standard deviation of the values of eclipse
bisector, range from approximately 25 to 300 s, depending on the signal-to-
noise ratio (S/N) and the data cadence.

The epochs of the primary and secondary minima allowed us to find the
constant-period ephemeris, which provided the best match to the data (minimum
residuals):

$BJD_{\rm minI}=2\,459\,225.6410(1)+3.718265(7)\times E.$ (1)

The residuals between observed and calculated epochs (O–C) of primary (blue
dots) and secondary (red circles) minima (Fig. 3) are flat and scattered
around zero, which means no relevant period variation occurred during the time
spanned by the TESS observations. A very small systematic offset between the
primary and secondary minima observed in sector 33 seems to be visible in the
O–C, which could suggest a very small eccentricity or could be the effect of
an uneven distribution of starspots in the secondary component. However, this
is well within the error bars, and it is likely to be not significant.

Figure 3: Observed minus calculated times of minima for TIC 43152097. Primary
and secondary minima are represented with blue dots and red circles,
respectively. The orbital period appears to be constant within the errors.

We used the KSPSAP TESS data from 2020, which have a higher cadence, for the
light-curve solution. The phase-folded light curve around the primary and
secondary minimum is shown in Fig. 4 (black dots), along with the synthetic
light curve (solid red lines). Given the large separation of the two
components, suggested by the short duration of the eclipses in units of the
orbital period, we adopted a model with spherical limb-darkened stars. We used
the quadratic limb-darkening coefficients calculated for the TESS passband by
Claret (2017), who adopted quasi-spherical PHOENIX-COND stellar atmosphere
models with solar metallicity, $\log g$ = 4.5, and mixing-length parameter
$\alpha=2$. The occulted fraction of the limb-darkened star disk at each
orbital phase was calculated from numerical integrations following the
prescriptions of Kopal (1990) and dividing the stellar disk into 1000
concentric rings. The surface brightness ratio between the two stars, $J$, was
calculated, as a function of $T_{\rm eff}$, by integrating BT-Settl models
(Allard et al., 2012) through the TESS passband. We fixed the temperature of
the primary component as $T_{1}=6070\pm 70$ K (see Sect. 3.3) and left the
temperature $T_{2}$ of the secondary component free to vary. The system
inclination, $i$, and the fractional radii of the primary and secondary
components in units of the separation, $r_{1}=R_{1}/a$ and $r_{2}=R_{2}/a$,
were also free variables. We minimized the residuals in the part of the light
curve encompassing the two eclipses (magenta dots in Fig. 4), using as a
goodness-of-fit parameter the $\chi^{2}$ defined as

$\chi^{2}=\frac{1}{N}\sum\left(\frac{F_{\rm obs}-F_{\rm mod}}{\sigma_{\rm
obs}}\right)^{2},$ (2)

where $N$ is the total number of points selected for the fit, $F_{\rm obs}$
and $F_{\rm mod}$ are the observed and model fluxes, respectively, and
$\sigma_{\rm obs}$ is the data uncertainty.

Figure 4: Primary (left panel) and secondary (right panel) eclipse in the
phased KSPSAP TESS light curve of sector 33 (black dots). The solid red lines
represent the solution, and the blue dots at nearly zero level are the
residuals (observed$-$model). The magenta dots are those used to calculate the
$\chi^{2}$ of the fit. Table 2: Best-fit parameters from the model solution of
the KSPSAP TESS light curve of TIC 43152097 in 2020.

Parameter | Best-fit value
---|---
(units) |
BJD${}_{0}^{(a)}$ | 2225.641$\pm$0.001
$P_{\rm orb}$ ($d$) | 3.718265$\pm$0.000007
$e$ | 0
$\omega$ (∘) | …
$i$ (∘) | $90^{+0}_{-0.4}$
$r_{1}$ | 0.0894$\pm$0.0006
$r_{2}$ | 0.0706$\pm$0.0004
$T_{1}^{(b)}$ (K) | 6070$\pm$70
$T_{2}$ (K) | 4130$\pm$30
$a_{1}$, $b_{1}^{(c)}$ | 0.3276, 0.2297
$a_{2}$, $b_{2}$ | 0.3955, 0.2618
$J^{(d)}$ | 0.194

Notes. (a) Barycentric Julian date (BJD-2 457 000) of the primary minimum; the
subscripts 1 and 2 refer to the primary (more massive) and secondary
component, respectively. (b) $T_{1}$ fixed based on spectral analysis. (c)
Quadratic limb-darkening coefficients. (c) Surface brightness ratio
$J=F_{2}/F_{1}$ calculated in the TESS passband from BT-Settl models.

We also tried a solution with linear limb darkening for both stars and found a
slightly worse fit, especially at eclipse contacts. However, the parameters of
the final model changed very little:$i$ and $T_{2}$ did not change,
$r_{1}=0.0890$ (approximately 0.4% smaller), and $r_{2}=0.0725$ (2.7% larger).
The contour maps of the $\chi^{2}$ for various pairs of parameters are shown
in Fig. 14, where the 1$\sigma$ confidence level is marked with a thick red
line. The best-fit parameters are listed in Table 2, together with their
standard errors, which correspond to the 1$\sigma$ confidence levels.

We used also the v43 version of the fortran code
JKTEBOP222https://www.astro.keele.ac.uk/jkt/codes/jktebop.html (Southworth et
al., 2004; Southworth, 2013) to verify our results. This code uses a biaxial
ellipsoidal model (Nelson & Davis, 1972) and is particularly suitable for very
fast modeling of detached eclipsing binaries. We first ran JKTEBOP with the
same assumptions of our code, that is, considering spherical stars with a
quadratic limb-darkening law with Claret (2017) coefficients. The stellar
radii, the system inclination, and the surface brightness ratio were left as
free parameters in the fit; the results are very similar to those of our code,
$r_{1}=0.0898\pm 0.0025$, $r_{2}=0.0730\pm 0.0024$, $i=90.0^{+0.0}_{-0.8}$
degrees, and $J=F_{2}/F_{1}=0.190\pm 0.003$. The 1$\sigma$ uncertainties in
the fitted parameters were determined by means of 1000 Monte Carlo
simulations. The radius of the secondary component is only 3.4% larger than
the one derived with our code. Relaxing the hypothesis of spherical stars and
leaving $P_{\rm orb}$ and BJD0 free to vary did not appreciably change the
final parameters. We also tried with an eccentric orbit, but this did not
improve the fit. Another trial was performed leaving the third light, $L_{3}$,
as a free parameter and we in fact found a better fit, with a small negative
value, $L_{3}=-0.094\pm 0.007$. Small $L_{3}$ values have been found in the
solution of TESS light curves (e.g., Southworth & Van Reeth, 2022) and could
be related to sky background estimation. If, on the other hand, this third
light were to be real, it would leave $r_{1}$ nearly unchanged and would have
a detectable effect only on the flux ratio ($J=0.1951\pm 0.0007$) and on the
radius of the secondary component ($r_{2}=0.06895\pm 0.0001$), making it
closer to and slightly smaller ($\sim$ 2%) than the value reported in Table 2.
In the following section, we use the parameters derived with our model and
reported in Table 2, but we also consider the values of $r_{2}$ derived with
JKTEBOP, both assuming $L_{3}=0$ and adopting the best-fit value.

###  3.2 Radial velocity

The RV was measured by cross-correlating the target spectra with late-type
stellar templates, which are ATLAS9 (Kurucz, 1993) synthetic spectra with
solar metallicity and $T_{\rm eff}$ in the range 4000–6000 K calculated with
SYNTHE (Kurucz & Avrett, 1981). This analysis was carried out with the
IRAF333IRAF is distributed by the National Optical Astronomy Observatory,
which is operated by the Association of Universities for Research in
Astronomy, Inc. task fxcor, excluding very broad features that can blur the
peaks of the cross-correlation function (CCF). To measure the centroids of the
CCF peaks of the two components, we applied a two-Gaussian fit. The RV error,
$\sigma_{\rm RV}$, was computed by fxcor according to the fitted peak height
and the antisymmetric noise as described by Tonry & Davis (1979).

Table 3: Barycentric RVs of the two components of TIC 43152097.

BJD | RV1 | $\sigma_{\rm RV_{1}}$ | RV2 | $\sigma_{\rm RV_{2}}$ | Instrument | S/N(a)
---|---|---|---|---|---|---
(2 450 000+) | (km s-1) | (km s-1) |  |
8145.0608 | $-17.15$ | 0.43 | 93.70 | 2.83 | HERMES | 105
9879.7243 | 61.54 | 1.64 | $-30.26$ | 4.06 | HARPS-N | 41
9880.7015 | $-33.89$ | 0.27 | 118.17 | 2.73 | HARPS-N | 43
9881.6640 | $-1.66$ | 0.38 | 68.52 | 1.08 | HARPS-N | 33

Notes. (a) Signal-to-noise ratio per pixel at 6500 Å.

Figure 5: Barycentric RV curve (circles = HARPS-N, squares = HERMES) of TIC
43152097. Filled and open symbols are used for the primary (more massive) and
secondary component, respectively. The blue and red lines represent the
orbital solution (Table LABEL:Tab:Param) for the primary and secondary
component, respectively.

The individual values of RV measured for the two system components are listed
in Table 3. These data, folded with the ephemeris in Eq. 1, are displayed in
Fig. 5 along with the circular orbital solution. The latter was fitted to the
data by means of the curvefit routine (Bevington & Robinson, 2003), allowing
us to determine the orbital parameters and their standard errors, which are
reported in Table LABEL:Tab:Param.

Table 4: Orbital and stellar parameters of TIC 43152097.

Orbital parameters
---
BJD${}_{0}^{(a)}$ | 2225.641$\pm$0.001
$P_{\rm orb}$ ($d$) | 3.718265$\pm$0.000007
$e$ | 0
$\omega$ (∘) | …
$\gamma$ (km s-1) | 26.27$\pm$0.58
$K_{\rm 1}$ (km s-1) | 67.48$\pm$0.78
$K_{\rm 2}$ (km s-1) | 103.28$\pm$3.32
$M_{\rm 1}\sin^{3}i$ (M☉) | 1.160$\pm$0.083
$M_{\rm 2}\sin^{3}i$ (M☉) | 0.758$\pm$0.033
$q=M_{\rm 2}/M_{\rm 1}$ | 0.653$\pm$0.022
$a\sin i$ (R☉) | 12.54$\pm$0.25
Stellar parameters
M1 (M☉) | 1.160$\pm$0.083
M2 (M☉) | 0.758$\pm$0.033
R1 (R☉) | 1.121$\pm$0.022
R2 (R☉) | 0.885$\pm$0.021
$\log g$1 (cgs) | 4.423$\pm$0.020
$\log g$2 (cgs) | 4.440$\pm$0.016
$T_{1}$ (K) | 6070$\pm$70
$T_{2}$ (K) | 4130$\pm$60
$L_{1}$ (L⊙) | 1.531$\pm$0.093
$L_{2}$ (L⊙) | 0.204$\pm$0.015

Notes. (a) Barycentric Julian date (BJD-2 457 000) of the primary minimum;
subscripts 1 and 2 refer to the primary (more massive) and secondary
component, respectively.

Combining the light-curve and RV solutions, we derived the absolute parameters
of the system components, which are reported in Table LABEL:Tab:Param. As the
inclination is $i=90\degr$, the masses are the same as $M_{1,2}\sin^{3}i$; the
relative errors of the radii are the quadratic sum of the relative errors of
the fractional radii, $r_{1,2}$ (reported in Table 2) and that of the
separation, $a$ (Table LABEL:Tab:Param). The stellar luminosity was calculated
as $L=4\pi R^{2}\sigma$$T_{\rm eff}$4 and its error was estimated by
propagating the $T_{\rm eff}$ and $R$ errors.

###  3.3 Stellar parameters from the spectral analysis

As a first approach, we used the code ROTFIT (Frasca et al., 2006) to
determine the atmospheric parameters and $v\sin i$ of the brighter component
of TIC 43152097. For a description of the version of ROTFIT working on HARPS-N
spectra, the reader is referred to Frasca et al. (2019). We analyzed, for the
three spectra, the spectral segments with a wavelength shorter than 5500 Å, to
minimize the contribution of the cooler secondary component, and found as
average parameters of the primary component $T_{1}=6110\pm 80$ K, $\log
g$${}_{1}=4.18\pm 0.13$ dex, [Fe/H]${}_{1}=0.07\pm 0.10$ dex, and $v\sin
i$$=16.0\pm 0.9$ km s-1.

In the case of double-lined spectroscopic binaries (SB2), we used COMPO2, a
code similar to ROTFIT that was also developed in the IDL444IDL (Interactive
Data Language) is a registered trademark of Harris Corporation. environment
(Frasca et al., 2006, 2019). COMPO2 adopts a grid of non-active templates to
reproduce the observed spectrum, which is split into segments of 100 Å each
that are independently analyzed. The grid of templates, as for ROTFIT, is
composed of ELODIE spectra of low-active slowly rotating FGKM stars. The
resolution of the HARPS-N spectra was degraded to that of the ELODIE templates
($R=42,000$) by convolution with a Gaussian kernel with the proper width.
COMPO2 did not derive the projected rotation velocities of the two components,
which are fixed parameters. In this case, with $i=90\degr$, we used the values
of $v\sin i$ that could be derived from the light-curve solution, assuming
spin-orbit synchronization (see Sect. 3.4), as

$v\sin i=v_{\rm eq}\sin i=v_{\rm eq}=\frac{2\pi R_{*}}{P_{\rm orb}},$ (3)

finding $v_{1}\sin i=15.0$ km s-1 (in agreement with the values derived with
ROTFIT) and $v_{2}\sin i=11.9$ km s-1. The RV separation of the two components
is well known from the CCF analysis and was used to build the composite
”synthetic” spectrum. The flux contribution of the primary component in units
of the continuum, $w_{\rm 1}$, is normally free to vary in COMPO2. In the case
of a totally eclipsing binary such as TIC 43152097, we can fix this value
using the light-curve solution. For instance, at the central wavelength of the
$R_{\rm C}$ band, the secondary component contributes to only 7% of the total
flux, that is, $w_{\rm 1}=0.93$; at shorter wavelengths, the contribution of
the secondary component is still smaller (5% in the $V$ and 3% in the $B$
band). Keeping the flux contribution fixed (per each analyzed spectral
segment), only the templates reproducing the primary and secondary components
were variable inside COMPO2. We ran the code on the spectrum acquired on JD=2
459 880.7, which has the largest S/N and RV separation of the components. The
stellar parameters produced by COMPO2 for the primary component, namely
spectral type F9V, $T_{1}=6070\pm$70 K, and $\log g$1 = 4.20$\pm$0.16 dex,
closely agree with those found with ROTFIT. Moreover, they share a remarkable
level of agreement with the values of $T_{\rm eff}$=6053$\pm$87 K and $\log
g$=4.07$\pm$0.22, reported in the GALAH DR3 catalog (Buder et al., 2021). The
atmospheric parameters of the secondary component are only indicative values,
given its very low flux contribution and the fairly low S/N of the HARPS-N
spectra. However, they are compatible with those derived from the light-curve
solution, as we found a spectral type K9V, $T_{2}=4370\pm$450 K and $\log g$2
= 4.5$\pm$0.3 dex.

Figure 6: Subtraction of the synthetic composite spectrum (red line) generated
by COMPO2 from the spectrum of TIC 43152097 observed on 28 October 2022 (black
dots). In each panel, the residual spectrum is shown by the blue line. The
chromospheric emission (bottom panel) in the H$\alpha$ core of the primary and
the secondary component, which has been integrated to provide $W_{\rm
H\alpha}^{em}$, is shown by the hatched green and magenta areas, respectively.
The Li i $\lambda$6708 Å absorption lines of the two components (top panel)
are marked with ”P” and ”S” in the residual spectrum.

Equivalent widths of the Li i 6708Å line, $W_{\rm Li}$, for the components of
TIC 43152097 were measured in the residual spectrum (blue line in Fig.6),
which was obtained by subtracting the synthetic template generated by COMPO2
from the observed spectrum. This procedure offers the advantage of removing
possible contamination from nearby iron lines and is particularly helpful in
the case of SB2 systems, as it allows us to remove different lines of the two
components, which, due to the different Doppler shifts, can overlap the Li i
lines of the two components. The error of the equivalent width was estimated
as the product of the integration range and the mean error per spectral point,
which results from the standard deviation of the flux values of the residual
spectrum measured at the two sides of the line. The $W_{\rm Li}$ values, as
well as their errors, were corrected for the flux contribution to the
composite spectrum by dividing them by $w_{\rm 1}$ and $w_{\rm 2}$ for the
primary and secondary component, respectively. Both the measured and corrected
values of $W_{\rm Li}$ are listed in Table 5.

Table 5: H$\alpha$, Li i$\lambda$6708 Å equivalent widths, and lithium abundance for the components of TIC 43152097. Comp | $T_{\rm eff}$ | $W_{\rm H\alpha}^{em}$ | err | $W_{\rm Li}$ | err |  $A$(Li) | err
---|---|---|---|---|---|---|---
| (K) | (mÅ) | (mÅ) | (dex)
|  | Measured values |  |
1 | 6070 | 101 | 15 | 107 | 6 | … | …
2 | 4130 | 85 | 17 | 25 | 6 | … | …
|  | Corrected values |  |
1 | 6070 | 109 | 17 | 116 | 7 | 2.95 | 0.07
2 | 4130 | 1209 | 247 | 361 | 81 | 1.97 | 0.35

The spectral subtraction was also used to measure the excess emission in the
core of the H$\alpha$ line ($W_{\rm H\alpha}^{em}$), which is an indicator of
chromospheric activity. As is apparent in Fig. 6, the H$\alpha$ core of the
primary component is filled in by emission, while a redshifted H$\alpha$
emission bump is clearly visible at the wavelength corresponding to the
secondary component. The net H$\alpha$ emission cores of the two components
are displayed by the hatched areas in the residual spectrum (blue line in the
bottom panel of Fig. 6). They were integrated to provide the values of $W_{\rm
H\alpha}^{em}$, which are reported in Table 5. We corrected these values for
the flux contribution of the two stars to the observed spectrum, as we did for
$W_{\rm Li}$.

###  3.4 Out-of-eclipse variations

Figure 7: TESS SAP light curve of TIC 43152097 in 2018 (sector 6) where the
eclipses have been removed. The inset in the upper left corner shows the
cleaned periodogram; the rotational and orbital periods are marked with
vertical red and blue lines, respectively. The inset in the upper right corner
displays the data phased with the orbital period. Figure 8: Same as Fig. 7 but
for 2020 (sector 33) TESS SAP data.

The out-of-eclipse variations visible in the SAP fluxes (Fig. 2) are
reminiscent of rotational modulation produced by starspots in one or both of
the system components. Indeed, proximity effects (ellipticity and reflection)
are negligible for this very detached system (amplitude $\sim$ 3 mmag), as
indicated by the synthetic light curve produced by JKTEBOP. We applied a
periodogram analysis (Scargle, 1982) and the CLEAN deconvolution algorithm
(Roberts et al., 1987) to the TESS SAP light curves where the eclipses were
removed. The out-of-eclipse variations and the results of the period search
are depicted in Fig. 7 and Fig. 8 for sectors 6 and 33, respectively. The
cleaned power spectrum displays a peak at a period very close to the orbital
one in both TESS epochs (3.88$\pm$0.20 and 3.77$\pm$0.15 days, in 2018 and
2020, respectively). This could be related to the rotation of the primary
component, which is the component contributing the largest flux (more than 90
%) in the TESS bandpass. However, given the very low peak-to-peak amplitude of
the observed modulation (15–20 mmag), we cannot exclude a relevant
contribution from the secondary component, which displays an active
chromosphere in the H$\alpha$ line (see Fig. 6). This suggests that at least
one component has attained spin-orbit synchronization.

The timescales for synchronization, calculated for the primary and secondary
components according to Zahn (1989), are $\tau_{\rm sync}\sim 0.3$ Myr and 8
Myr, respectively. At NGC2232’s age of 28 Myr, both components should already
be synchronized or close to the spin-orbit synchronization, as found from the
out-of-eclipse variations.

##  4 Discussion

The center-of-mass velocity of the TIC 43152097 system ($\gamma$ = 26.3$\pm
0.6$ km s-1, Table LABEL:Tab:Param) is consistent with the cluster mean
velocity RV=25.38$\pm$0.18 km s-1 derived by Jackson et al. (2022) for 697
members of NGC 2232 observed as a part of the Gaia-ESO Survey (GES); it also
agrees with the value of 25.35$\pm$0.85 km s-1 based on Gaia DR2 data
(Soubiran et al., 2018). This reinforces the membership of TIC 43152097 to NGC
2232. We note that the GES observations in the field of NGC 2232 did not
include TIC 43152097.

From the corrected values of $W_{\rm Li}$ (Table 5), we derived a lithium
abundance, $A$(Li), of 2.95$\pm$0.07 and 1.97$\pm$0.35 for the primary and
secondary component, respectively, by using the curves of growth of Lind et
al. (2009). The different lithium abundance for the two components follows the
general trend of lithium depletion as a function of $T_{\rm eff}$ displayed by
clusters of similar ages (e.g., Sestito & Randich, 2005). To estimate the age
of the system from the lithium content in the photospheres of its components,
we used the EAGLES code (Jeffries et al., 2023). This code fits Li-depletion
isochrones to the values of $T_{\rm eff}$ and $W_{\rm Li}$ of a coeval star
group, such as the members of a cluster or the components of a binary system,
as in the present case. We found $age=25^{+9}_{-19}$ Myr (see Fig. 15), which
is in very close agreement to the age of 28 Myr estimated with EAGLES by
Jeffries et al. (2023) for the members of NGC 2232 observed as a part of the
GES.

The position of the two components of TIC 43152097 in the Hertzsprung-Russell
(HR) diagram is shown in Fig. 9, along with the PMS evolutionary tracks and
isochrones from Baraffe et al. (2015). We note that the cooler component lies
close to the isochrone at 20 Myr and very close to the evolutionary track for
0.8 $M_{\odot}$, suggesting that it is slightly overluminous and a little bit
hotter than a standard model would predict for a 0.76 $M_{\odot}$ star with an
age of $\simeq$30 Myr. The primary component appears to have already reached
the MS, since for this mass, all PMS isochrones with $age\geq$ 30 Myr overlap
the ZAMS ($age\simeq 300$ Myr). It is very likely too hot to produce a strong
magnetic activity and display significant radius inflation. Furthermore, its
position in the HR diagram rules out an age $\leq 20$ Myr, at which the object
should have a noticeably higher luminosity and a lower temperature, according
to the tracks and isochrones from Baraffe et al. (2015).

Figure 9: Position of the primary (blue dot) and secondary (red dot) component
of TIC 43152097 in the HR diagram. Isochrones and evolutionary tracks from
Baraffe et al. (2015) are overlaid as dashed and solid lines; the labels give
their age and mass.

A better agreement between the position of the secondary component and the
isochrone at 30 Myr is found considering the effects of radius inflation (Fig.
10). To this purpose, we used the SPOTS models (Somers et al., 2020) that
incorporate both the inhibition of convective energy transport caused by sub-
photospheric magnetic fields and the effects of cool ($T_{\rm spot}/T_{\rm
phot}=0.8$) starspots.

Figure 10: Position of the components of TIC 43152097 in the HR diagram.
Isochrones and evolutionary tracks from Somers et al. (2020) for a spot
covering fraction of 34 % are overlaid. Symbols and line styles are as in Fig.
9.

A more effective way to highlight the radius inflation for the secondary
component is to compare $M_{2}$ and $R_{2}$ \- quantities directly obtained
from the light-curve and RV curve solutions - with the SPOT isochrones. To
this purpose, we plotted the mass-radius diagram, which is displayed in
Fig.11. In this diagram, the SPOTS isochrones at 28 Myr ($\log(age)=7.45$) for
three spot-covering factors (0%, 34% , and 68 %) are overplotted on the
position of the secondary component. For each spot coverage, we considered an
age uncertainty $\Delta\log(age)=0.05$ (hatched strips in Fig. 11), which is a
more conservative value compared to that of $\pm 0.02$ reported by Jeffries et
al. (2023). Figure 11 clearly displays the discrepancy between the observed
radius and the one predicted by models that neglect the effects of magnetic
activity555The SPOT tracks and isochrones with a spot-filling factor $F_{\rm
spot}=0$% are nearly identical to the tracks from Baraffe et al. (2015), as
also shown by Frasca et al. (2021).. A radius inflation of approximately 8 %
can be deduced. It is notable that a spot coverage of $\sim 40$ % is
sufficient to explain the discrepancy, while a 68 % spot fraction would give
rise to a too-high radius inflation. If we adopt instead the slightly larger
radius derived with JKTEBOP, assuming a third light $L_{3}=0$, the radius
inflation, with respect to the isochrone without spots, would be approximately
11 %, which is compatible with a larger spot coverage ($\sim 60\,\%)$. If we
adopt the JKTEBOP solution with the best-fit value of $L_{3}$, we find a
smaller value of radius inflation of about 7 %, compatible with a spot
coverage of about 30 %. This result indicates that radius inflation on the
order of of 7–11 % is already occurring in late K-type stars at ages
considerably earlier than the ZAMS, when these objects are still in the PMS
evolutionary phase. The direct measure of the stellar radius for the
components of PMS eclipsing binaries strongly supports radius inflation as the
most likely cause of disagreement between the ages inferred from CMDs and the
lithium depletion pattern in the PMS cluster Gamma Vel (Jeffries et al.,
2017). This, along with the problem of spectroscopic $T_{\rm eff}$
determination in heavily spotted stars, has a strong impact on the
determination of ages and masses of PMS stars from their position in the HR
diagram (see, e.g., Gully-Santiago et al., 2017; Gangi et al., 2022).

Figure 11: Mass–radius diagram for the secondary component of TIC 43152097
(red dot). SPOT isochrones (Somers et al., 2020) at 28 Myr ($\log(age)=7.45$)
for a spot covering factor of 0 %, 34 %, and 68 % are overlaid with different
colors, as indicated in the legend. The hatched areas delimit, per each value
of $F_{\rm spot}$, an age uncertainty of $\Delta\log(age)=0.05$. As a
comparison, the value derived with JKTEBOP assuming a third light $L_{3}=0$
($R_{2}=0.915$ $R_{\odot}$) is also shown by the white dot. A larger spot
coverage is necessary to reproduce the observations in this case. The value of
$R_{2}=0.865$ $R_{\odot}$, derived with JKTEBOP with the best-fit value of
$L_{3}=-0.094$, is also overlaid with a cyan dot.

##  5 Summary

We have reported the discovery and follow-up study of the eclipsing binary
system TIC 43152097, which is composed of low-mass stars in a well-detached
configuration and belongs to the young open cluster NGC 2232.

High-resolution spectra purposely collected with HARPS-N allowed us to measure
the RV of the two components and determine their basic properties (atmospheric
parameters, lithium abundance, and chromospheric emission). The RV of the
center of mass of the system and the age derived from the photospheric lithium
abundance fully agree with the cluster values, which confirms the membership
of TIC 43152097 to NGC 2232.

We used the very precise TESS photometry to study the out-of-eclipse
modulation and to determine the orbital period from the eclipse timing. The
low-amplitude (15–20 mmag) modulation observed out of the eclipses shows a
regular behavior with a period close to the orbital one and can be ascribed to
cool starspots in one or both components, which are in a synchronous (or
quasi-synchronous) rotation.

The combined analysis of light and RV curves allowed us to derive orbital
elements as well as fundamental stellar parameters of the two stars,
particularly their masses and radii. The primary component of TIC 43152097 is
a late F-type dwarf ($T_{\rm eff}$ = 6070 K, from the spectral analysis with
COMPO2), while the lower-mass secondary is a late K-type PMS star ($T_{\rm
eff}$ = 4130 K). The precise measurements of $R_{\ast}$ ($\simeq$2 %) and
$M_{\ast}$ ($\simeq$4 %) indicate radius inflation for the secondary
component, which turns out to be 7–11 % larger than predicted by standard
evolutionary models. The SPOT evolutionary models, which incorporate both
inhibition of convective energy transport caused by sub-photospheric magnetic
fields and the effects of cool starspots covering a substantial fraction of
the stellar surface (30–60 %), allow for reproduction of the stellar
parameters of the secondary component at the age of NGC2232, 28 Myr.

###### Acknowledgements.

We are grateful to the referee, Dr. John Southworth, for his very useful
comments and suggestions. This research made use of SIMBAD and VIZIER
databases, operated at the CDS, Strasbourg, France.
This paper includes data collected by the TESS mission which are publicly
available from the Mikulski Archive for Space Telescopes (MAST). Funding for
the TESS mission is provided by the NASA’s Science Mission Directorate.
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.
This research used the facilities of the Italian Center for Astronomical
Archive (IA2) operated by INAF at the Astronomical Observatory of Trieste.
This work has been supported by the PRIN-INAF 2019 STRADE (Spectroscopically
TRAcing the Disk dispersal Evolution), the Large-Grant INAF YODA (YSOs
Outflow, Disks and Accretion), and by the Mini-Grant INAF 2022 “High
resolution spectroscopy of Open Clusters”. X.F. thanks the support of the
National Natural Science Foundation of China (NSFC) No. 12203100 and the China
Manned Space Project with NO. CMS-CSST-2021-A08.

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##  Appendix A Additional figures

Figure 12: Multiband ground-based light curve of TIC 43152097 during the
secondary eclipse of 7 January 2023. The model light curves with the same
elements as those listed in Table 2 are overplotted with solid lines.  Figure
13: Example of the determination of the time of a light-curve minimum with the
bisector method for the primary eclipse observed by TESS in sector 33 on 7
January 2021. The horizontal magenta lines connect points at the same flux
level in the descending (blue dots) and rising (red dots) branch of the
eclipse, interpolating between the two. The vertical green line represents the
eclipse bisector.

Figure 14:  $\chi^{2}$ contour maps for different pairs of parameters. In each
panel, the blue dot marks the best-fit values, while the 1$\sigma$ confidence
level is denoted by the red contour.  Figure 15: Fit to the lithium depletion
pattern of the two components of TIC 43152097 made with the EAGLES code
(Jeffries et al. 2023).