Cluster Difference Imaging Photometric Survey. II. TOI 837: A Young Validated Planet in IC 2602

Acquisition and reduction—We observed four transits with the 0.36 m telescope at Observatorio El Sauce, located in the Río Hurtado Valley in Chile and operated by coauthor P. Evans. The observations were obtained in the Cousins-R band on the nights of 2020 April 1 and 26, the Cousins-I band on the night of 2020 May 21, and the Johnson-B band on the night of 2020 June 14. The final June 14 transit began shortly after twilight.

We scheduled our transit observations using the TESS Transit Finder, which is a customized version of the Tapir software package (Jensen 2013). The photometric data were calibrated and extracted using AstroImageJ (Collins et al. 2017). Comparison stars of similar brightness were used to produce the final light curves, each of which showed a roughly 4 ppt dip near the expected transit time. The data are reported in Table 1 and plotted in Figure 4.

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Custom aperture analysis—Based solely on the TESS data, both Star A and Star B were possible sources of blended eclipsing binary signals. The typical FWHM for stars in the El Sauce observations was ≈23, with a variance of ≈02. Star B is resolved in the 0.36 m images; Star A is not.

To rule out blend scenarios with the ground-based photometry, we produced light curves centered on TOI 837 with circular apertures of radii ranging from 07 to 51. We did not detect any statistically significant variation in the depth of the transits with aperture size. Beyond the difference image centroiding test performed by the SPOC pipeline, two additional lines of evidence ruled out Star B as the eclipsing source: first, the transits were detected in the smallest apertures. Second, we made light curves with 21 apertures centered on Star B, and they did not show the transit.

To assess the possibility that Star A is an eclipsing body, we created light curves with a custom set of circular apertures with radii of 21 and positions ranging from Star A (23 west of TOI 837) to 23 east of TOI 837. We did not detect any variation of the transit depth along this line of light curves. The apertures east of TOI 837 excluded over 90% of the flux from Star A. The eclipse on Star A would therefore need to have depth greater than unity to produce the observed eclipse depth. We therefore interpret the lack of asymmetry between the westernmost (centered on Star A) and easternmost (furthest from Star A) light curves as conclusive evidence that TOI 837 is the source of the transit signal to within ≈20. To verify self-consistency, we checked that the maximum dilution from Star A (≈1%) is less than the uncertainty of the transit depth measurements (≈15%), and so the lack of variation of transit depth with aperture location is consistent with TOI 837 being the source of transits.

An additional line of evidence for Star A not being the transit host was also noted by the referee. The G-band magnitude and the parallax suggest that Star A is an M dwarf. As a probable cluster member, it would have Bp − Rp ≈ 2.8 (see Section 4.1.2), which corresponds roughly to a mass in the range of 0.15–0.45 M_⊙, or to densities roughly in the range of 2–3 g cm⁻³ based on the Padova–Trieste Stellar Evolution Code (PARSEC) isochrones (Bressan et al. 2012; Chen et al. 2014, 2015; Marigo et al. 2017). These densities are inconsistent with those inferred from the transit fits in Section 4.3.

We observed three transits with the 0.40 m Antarctic Search for Transiting Exoplanets (ASTEP) telescope at the Concordia base on the Antarctic Plateau (Daban et al. 2010). The Concordia base is operated by the French and Italian polar institutes, IPEV and PNRA. Its position on the Antarctic Plateau allows it to take advantage of the continuous night during austral winter. The weather is of photometric quality for about two-thirds of each winter (Crouzet et al. 2018).

ASTEP is equipped with an FLI ProLine science camera with a KAF-16801E, 4096 × 4096 front-illuminated CCD. The camera has an image scale of 093 pixel⁻¹, resulting in a 1° × 1° corrected field of view. The focal instrument's dichroic plate splits the beam into a blue wavelength channel for guiding and a non-filtered red science channel roughly matching a Cousins-R transmission curve (Abe et al. 2013; Mékarnia et al. 2016). The images were processed on site using an automated aperture photometry pipeline based on the daophot package of the IDL Astronomy User's Library (Landsman 1995).

TOI 837 was observed with ASTEP on 2020 May 12, May 29, June 14, and June 23 (Universal Time). Except for May 12, our observations were conducted under stable weather conditions, with clear skies, temperatures of about −70°C, and wind speeds less than 5 m s⁻¹. Due to their poor quality, we excluded from the analysis all data collected on May 12. We found that the optimal calibrated light curves of TOI 837 correspond to an 11 pixel (10'') and 14 pixel (12'') radius aperture for the observations carried out on June and May, respectively. The data are reported in Table 1 and plotted in Figure 4.

We acquired nine spectra using CHIRON at the SMARTS 1.5 m telescope at the Cerro Tololo Inter-American Observatory (CTIO), Chile (Tokovinin et al. 2013). Six met our signal-to-noise requirements for RV measurements and stellar parameter extraction. We used CHIRON in its image slicer configuration, yielding a spectral resolution of ≈79,000 across 415–880 nm.

We derived RVs and spectroscopic line profiles from the CHIRON observations using a least-squares deconvolution (LSD) of the spectra against nonrotating synthetic spectral templates (Donati et al. 1997). The spectral templates were generated using ATLAS9 atmosphere models (Castelli & Kurucz 2004) with the SPECTRUM script (Gray & Corbally 1994). These line profiles were fitted with a broadening kernel that describes the rotational, radial–tangential macroturbulent, and instrumental broadening of the spectrum. The rotational and macroturbulent broadening were computed as per Gray (2005), following the methods described in Zhou et al. (2018). We fitted the line profile from each observation independently, yielding the RVs listed in Table 2 and shown in Figure 5. We found a mean rotational broadening velocity of v sin i_⋆ = 16.2 ± 1.1 km s⁻¹ and a macroturbulent broadening of v_mac = 8. 4 ± 2.9 km s⁻¹.

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To derive the stellar parameters, we matched the set of CHIRON spectra against a library of observed spectra, previously obtained using the Tillinghast Reflector Echelle Spectrograph (Fűrész et al. 2008) on the 1.5 m reflector at the Fred Lawrence Whipple Observatory, Arizona, USA, and classified using the Stellar Parameter Classification pipeline (Buchhave et al. 2010). We found the best-matching stellar parameters to be T_eff = 5899 ± 55 K, log g = 4.496 ± 0.011 dex, and [Fe/H] = −0.069 ± 0.042 dex. We ultimately adopted a different set of stellar parameters for our analysis (see Section 4.2.4).

The spectroscopic line profiles were thoroughly examined for any signs of secondary lines that might indicate the presence of another star, either associated or in chance alignment with TOI 837. No such set of lines was found. To set limits on the contributions of a close-by star to the observed spectrum, we injected a secondary signal into the mean LSD profile derived from the CHIRON observations. The injection spanned 10,000 different combinations of line broadening, velocity separation, and flux ratio F₂/F₁. The recovery results showed that for rotational broadenings of the secondary of 5, 15, and 25 km s⁻¹, we were able to exclude sources with flux fractions ${F}_{2}/{F}_{1}$ brighter than roughly 0.03, 0.08, and 0.20, provided that the secondary was separated from the primary by at least ≈15 km s⁻¹. At smaller velocity separations, the injected lines began to blend with the target spectrum. We verified these results by injecting secondary lines directly into the spectrum and then deriving their LSD broadening profile as we would for a normal observation. The results were nearly identical, save for greater computational cost.

TOI 837b was monitored with the FEROS echelle spectrograph (Kaufer et al. 1999), mounted on the MPG $2.2$ m telescope at the European Southern Observatory's (ESO) La Silla Observatory in Chile. FEROS has a resolution of ≈48,000 across a spectral range of 350–920 nm. It has a high efficiency of ≈20%. We obtained 13 spectra of TOI 837 between 2019 July 5 and 2020 March 14 in the context of the Warm Giants with TESS collaboration, which focuses on the systematic characterization of TESS transiting giant planets with moderately long orbital periods (e.g., Brahm et al. 2019; Jordán et al. 2020). We adopted exposure times of 500 and 600 s, and the observations were performed with the simultaneous calibration mode for tracing the instrumental velocity variations with a comparison fiber illuminated with a ThAr lamp. FEROS data were processed with the ceres pipeline (Brahm et al. 2017), which delivers precision RVs and bisector span measurements through cross-correlation of the extracted spectra with a binary mask resembling the properties of a G2V star. The RVs are given in Table 2 and shown in Figure 5. To check for the presence of secondary lines, we performed an injection–recovery exercise similar to that with the CHIRON data. We achieved slightly worse limits, likely due to the lower spectral resolution of FEROS, and therefore adopted the CHIRON limits.

We acquired 34 spectra over 10 visits of TOI 837 using the Veloce spectrograph, mounted on the 3.9 m Anglo-Australian Telescope (AAT) at Siding Spring Observatory near Coonabarabran, Australia (Gilbert et al. 2018). The currently operational "Veloce Rosso" channel provides coverage from 600 to 950 nm at a spectral resolution of ≈80,000. Many of the exposures were taken in average or poor seeing conditions, when the signal-to-noise ratio (S/N) was lowest and the fiber-to-fiber cross-contamination on the integral field unit–style fiber feed was strongest. To reduce the spectra to velocities, we cross-correlated against a template of δ Pavonis, because with spectral type G8 IV it was the closest high-S/N TOI 837 analog available in the Veloce spectral database. The velocity rms seen across each visit was hundreds of meters per second, likely due to uncorrected fiber-to-fiber cross-contamination. This cross-contamination severely affected the wavelength solutions for the 19 individual science fibers, ultimately leading to significantly increased RV scatter. For analysis purposes, we averaged the single-shot RVs across each visit and set the velocity uncertainties to be the standard deviation of the per-visit exposures. The velocities are given in Table 2 and shown in Figure 5.

In HEB and BEB scenarios, the flux from TOI 837 and the true eclipsing binary host blend together and reduce the "true" TESS-band eclipse depth δ_true to the observed depth δ_obs:

$$\begin{eqnarray}&&{\delta }_{\mathrm{obs}}={\delta }_{\mathrm{true}}\displaystyle \frac{{F}_{\mathrm{comp}}}{{F}_{\mathrm{total}}},\end{eqnarray} \tag{ 1 }$$

where the total system flux and the flux from only the companion binary are labeled as such. The requirement that the eclipse is produced by fusion-powered stars and that δ_true < 0.5 translates to a bound on the faintest possible blended companion system:

$$\begin{eqnarray}&&{\rm{\Delta }}m\lt -\displaystyle \frac{5}{2}{\mathrm{log}}_{10}\left(\displaystyle \frac{0.5}{{\delta }_{\mathrm{obs}}}\right).\end{eqnarray} \tag{ 2 }$$

For TOI 837 (T = 9.93), this implies that any stellar companion invoked to explain the transit depth must be brighter than T = 15.07. In Figure 6, we set the spatial limit to 2'' based on the precision at which we have localized the transits using seeing-limited ground-based photometry.

If the transit were box-shaped, this argument could be extended to even more restrictive depths (e.g., Seager & Mallén-Ornelas 2003; Vanderburg et al. 2019; Rizzuto et al. 2020). Since the transits of TOI 837 could be grazing, the second and third contact points do not necessarily occur, and the shape of the transit is not particularly restrictive.

The contrast limits obtained through the SOAR I-band speckle imaging (Section 2.3) are shown in Figure 6. While "Star A" was detected in the SOAR images, our ground-based photometry rules it out as a possible source of the eclipse signal (Section 2.4). To convert the remaining contrast constraints to limits on the masses of bound companions, we used the Baraffe et al. (2003) models for substellar-mass objects and the MESA Isochrones and Stellar Tracks (MIST) models for stellar-mass objects (Paxton et al. 2011, 2013, 2015; Choi et al. 2016; Dotter 2016). We assumed that the system age was 35 Myr, so that companions would be at a plausible state of contraction.

To convert from theoretical effective temperatures and bolometric luminosities to expected magnitudes in instrumental bandpasses, we made the simplifying assumption that all sources had blackbody spectra. Using the theoretical stellar parameters and the measured transmission functions (Tokovinin 2018), we then calculated the apparent magnitudes of stellar companions of different masses and interpolated to produce the scale shown on the upper right in Figure 6.

We derived limits on blended spectroscopic companions using the stacked CHIRON spectra (see Section 2.5.1). For a slowly rotating stellar companion well separated in velocity, the spectra would have revealed companions with flux fractions F₂/F₁ ≳ 3%. For a companion with rotational broadening of 15 km s⁻¹, roughly equivalent to that of TOI 837, we were able to exclude companions with flux fractions exceeding ≈8%. For plotting purposes, in Figure 6 we assume the latter flux-fraction limit of 8% (Δmag ≈ 2.7). The outer limit in projected separation for associated companions is the distance at which the Keplerian orbital velocity is well below the rotational broadening. This condition translates to a projected separation of 10–20 au, depending on the companion mass. For chance alignments, the same restrictions on velocity separation apply, but out to a projected separation equal to the CHIRON slit width of ≈1''.

The RVs from FEROS, CHIRON, and Veloce can be used to detect massive bound companions orbiting TOI 837. We searched for planetary- and stellar-mass companions in two different regimes: first at the orbital period of the transiting object and second at longer orbital periods to constrain the presence of a massive bound companion.

For the first fit we set a prior on the period and time of conjunction using the known ephemeris from the transit. We then fitted for the semi-amplitude, instrument offsets, and jitter parameters using radvel (Fulton et al. 2018) and assuming circular orbits. This yielded a nondetection of the planet's orbit. The corresponding 3σ (99.7th percentile) upper limit on M_p sin i is 1.20 M_Jup. The data and corresponding model are shown in Figure 5.

The above exercise ruled out the possibility that the observed eclipses were caused by a stellar-mass object orbiting TOI 837. The lack of a linear RV trend, particularly in the FEROS data, further constrains the presence of a hierarchical binary system. Fitting a line to the FEROS velocities yielded a 3σ limit on linear RV trends of $| \dot{\gamma }| \lt 0.82\,{\rm{m}}\,{{\rm{s}}}^{-1}\,{\mathrm{day}}^{-1}$, over the 253 day FEROS baseline. The agreement between the mean Gaia DR2 velocity (17.44 ± 0.64 km s⁻¹) and that from FEROS (18.0 ± 0.1 km s⁻¹) in theory places an additional limit on linear trends, since the two observation epochs are separated by roughly 5 years.

To place limits on the properties of a possible bound hierarchical companion, we performed the following injection–recovery exercise. We simulated 10⁶ two-body systems with random orbital phases and inclinations and drew their semi-amplitudes and periods from logarithmic distributions: $K\ [{\rm{m}}\,{{\rm{s}}}^{-1}]\sim \mathrm{log}{ \mathcal U }(1,{10}^{7})$ and $P\ [\mathrm{days}]\sim \mathrm{log}{ \mathcal U }(1,{10}^{15})$. Again assuming circular orbits, we then analytically evaluated what the RVs would have been at the observed FEROS times if the system had the assumed parameters. We then calculated what the linear slope would have been for each simulated system. If the absolute value of the slope exceeded our 3σ limit of $| \dot{\gamma }| \lt 0.82\,{\rm{m}}\,{{\rm{s}}}^{-1}\,{\mathrm{day}}^{-1}$, we assumed that we would have detected such a system. Figure 6 shows the resulting limits; weakened sensitivity at harmonics of the baseline occurred at lower masses and smaller projected separations than shown on the plot. The interpolation from mass to brightness contrast was performed using the same isochrone models and assumptions in Section 3.1.2.

Multicolor photometry and HEB scenarios—The most plausible HEB scenarios for TOI 837 involve pairs of eclipsing M dwarfs (Figure 6). Eclipses of such stars are much redder than eclipses of the G dwarf TOI 837. Limits on whether the transit depth decreases in bluer bandpasses can therefore rule out certain HEB scenarios.

We fitted for the observed depths in different bandpasses using machinery similar to that described in Section 4.3. We fitted each ground-based transit individually for the planet-to-star size ratio, the impact parameter, and a local quadratic trend (the ephemeris was assumed from an initial fit of only the TESS data). The corresponding 2σ lower limits on the transit depths in Cousins-R and Johnson-B band light curves were 2.82 and 1.77 ppt, respectively, and are shown in Figure 4. Particularly in our Johnson-B light curve, the transit depth is correlated with the mean and linear slope of the light curve: a smaller depth is allowed if the data are fitted with a larger linear slope and a larger mean. Our quoted limits marginalize over these correlations, and the depth measurement itself is nearly Gaussian.

To determine what classes of HEB are eliminated by these limits, we performed the following calculation. We assumed that each system was composed of the primary (TOI 837), plus a tertiary companion eclipsing a secondary companion every 8.3 days. For secondary masses ranging from 0.07 to 1.10 M_⊙ and mass ratios (M₃/M₂) ranging from 0.1 to 1, we then calculated the observed maximal eclipse depth caused by Star 3 eclipsing Star 2 in each observed bandpass. As before, we interpolated between mass, effective temperature, and radius assuming the MIST isochrones for a 35 Myr old system and also assumed that each source had a blackbody spectrum. We used the transmission functions from the Spanish Virtual Observatory (SVO) Filter Profile Service.³⁰ For a typical HEB system (e.g., M₂ = M₃ = 0.2 M_⊙), the bluest optical bandpasses produced eclipses with roughly a tenth of the depth of those in the TESS band, because the M-dwarf blackbody function turns over at much redder wavelengths than the G-dwarf blackbody (Wien's law).

For a fixed secondary mass, we then asked whether any tertiary companions existed for which the maximal expected eclipse depth could have been larger than the observed depth. We could not rule out hierarchical eclipsing binary systems in cases for which the answer was yes. Conversely, we ruled out systems for which at fixed secondary mass no tertiary mass could enable eclipses of the necessary depth (in the R_C band or B_J band). The R_C-band limit corresponded to a secondary-mass limit of M₂ > 0.27 M_⊙, and the B_J-band limit corresponded to a stronger limit of M₂ > 0.70 M_⊙.

Multicolor photometry and BEB scenarios—While the above constraints rule out HEBs, certain configurations of BEB systems (e.g., a background G0V+K3V binary) can produce blue eclipses while remaining undetected along the line of sight. Such scenarios are constrained by the lack of an observed secondary eclipse and therefore require either eccentric orbits to avoid secondary eclipses or else a background twin-binary system at double the orbital period. The only way to definitively rule out such scenarios is to prove that the loss of light is from the target star, for instance by detecting the Rossiter–McLaughlin (RM) effect during a transit and confirming that the spectroscopic transit is consistent with the photometric transit.

The "Gaia" curve in Figure 6 combines both point-source detections from imaging and sources showing an astrometric noise excess relative to the single-source astrometric model. The curve was interpolated from Figure 4 of Rizzuto et al. (2018). TOI 837 has a RUWE statistic of 1.022, indicating that there are no obviously present astrometric companions. The unit weight error statistic (square root of the reduced astrometric χ²) is 1.38, which is consistent with stars of similar brightness and color (Lindegren et al. 2018, Appendix A).

Archival SERC-J and AAO-SES plates are available for the TOI 837 field.³¹ These plates were acquired in 1982 and 1992, respectively. For high proper motion stars, archival imagery can be used to detect slowly moving background stars that might be an astrophysical false-positive source (e.g., Bakos et al. 2006; Huang et al. 2018a; Vanderburg et al. 2019). However TOI 837 has only moved ≈07 between 1982 and the present, in comparison to the ≈20 FWHM of the target on the plates. We therefore cannot resolve it from background sources not already resolved through more modern imaging.

The IC 2602 cluster is about 150 pc from the Earth and is near the galactic plane with (l, b) ≈ (2896, −50) (Cantat-Gaudin et al. 2018). It is also sometimes called the θ Carinae cluster, after its brightest member, or the "Southern Pleiades." While IC 2602 is close to the Lower Centaurus–Crux subgroup of the Scorpius–Centaurus OB2 association in terms of both position and proper motion space, its older age and clear kinematic separation indicate that it is a distinct stellar population (de Zeeuw et al. 1999; Damiani et al. 2019).

Reliable ages reported for IC 2602 range from 30 to 46 Myr. We have collected ages reported over the years in Table 3. The lithium depletion boundary technique yields slightly older absolute ages than isochrone fitting (Dobbie et al. 2010; Randich et al. 2018). Rather than redetermine the age of the cluster and add another line to the table, we simply adopt an absolute-age range for TOI 837 of 30–46 Myr.

Table 3.  Previously Reported Ages for the Open Cluster IC 2602

Method	Age (Myr)	Reference
MSTO isochrone	36.3	Mermilliod (1981)
PMS+MSTO isochrone	30 ± 5	Stauffer et al. (1997)
Isochrone (a)	67.6	Kharchenko et al. (2005)
Isochrone (b)	221	Kharchenko et al. (2013)
Isochrone	67.6	van Leeuwen (2009)
LDB (c)	${46}_{-5}^{+6}$	Dobbie et al. (2010)
MSTO isochrone (d)	41–46	David & Hillenbrand (2015)
MSTO isochrone (e)	37–43	David & Hillenbrand (2015)
Li selection + isochrone	${43.7}_{-3.9}^{+4.3}$	Bravi et al. (2018)
Isochrone (f)	${30}_{-7}^{+9}$	Randich et al. (2018)
LDB	${43.7}_{-3.9}^{+4.3}$	Randich et al. (2018)
Isochrone	${35.5}_{-1.6}^{+0.8}$	Bossini et al. (2019)
Isochrone	${35.5}_{-10.4}^{+14.6}$	Kounkel & Covey (2019)

Note. MSTO ≡ main-sequence turn-off. PMS ≡ pre-main-sequence. LDB ≡ lithium depletion boundary. (a) Based on location in Hertzsprung–Russell (HR) diagram of just two stars. (b) Notes major age change since Kharchenko et al. (2005). (c) Dobbie et al. (2010) performed a dedicated study of the LDB in IC 2602. Their resulting LDB age was slightly larger than previously reported isochrone ages, which they noted is consistent with similar discrepancies seen in the Pleiades, α-Per, IC 2391, and NGC 2457. (d) Using Ekström et al. (2012) evolutionary models. (e) Using PARSEC evolutionary models (Bressan et al. 2012). (f) Averaged across PROSECCO, PARSEC, and MIST models in $(J,H,{K}_{{\rm{s}}})$ and $(J,H,{K}_{{\rm{s}}},V)$ planes.

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Reported mean metallicity values [Fe/H] for the cluster range between slightly supersolar (0.04 ± 0.01; Baratella et al. 2020) and slightly subsolar (−0.02 ± 0.02; Netopil et al. 2016). The extinction E(B − V) is rather low, with reported values ranging from 0.03 to 0.07 (e.g., Randich et al. 2018).

Kinematically, IC 2602 seems to be supervirial, in the sense that the observed stellar velocity dispersion is larger than the value expected if it were in virial equilibrium by about a factor of two (Bravi et al. 2018). Damiani et al. (2019) also reported evidence for the ongoing evaporation of IC 2602, in the form of a diffuse ≈10° halo of young stars around the central density cusps. A gyrochronological study of these stars could confirm that these stars are truly coeval with the cluster.

Figure 7 shows an HR diagram of TOI 837, the IC 2602 cluster, and the neighborhood of spatially nearby stars. Stars labeled as cluster members are those reported by Cantat-Gaudin et al. (2018) based on Gaia DR2 positions, proper motions, and parallaxes. We included candidate members with a formal membership probability exceeding 10%. Most members appear to be young and coeval. TOI 837 lies on the single-star sequence. Any hypothetical companions to TOI 837 must therefore have ≲50% of its brightness; brighter companions would have made the total system ≳0.44 mag brighter than the single-star sequence, which can be ruled out based on the photometric uncertainties and the intrinsic scatter in the HR diagram.

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Figure 7 suggests that the membership census of IC 2602 is incomplete. We defined the reference neighborhood as the group of at most 10⁴ randomly selected non-member stars within five standard deviations of the mean IC 2602 R.A., decl., and parallax. In other words, the neighborhood members were chosen based on the observed spread in the cluster's parameters. We queried Gaia DR2 for these stars using astroquery (Ginsburg et al. 2018). Many low-mass stars appeared above the main sequence, even though they were not identified as five-dimensional kinematic members through the unsupervised Cantat-Gaudin et al. (2018) membership assignment process.

Figure 7 also compares the data to the MIST isochrones (Choi et al. 2016). We used the web interface³⁴ to interpolate isochrones at 10, 20, 30, and 40 million years. We assumed solar metallicity and a fixed extinction value of A_V = 0.217 (Randich et al. 2018). The 30 and 40 Myr models align well with the data for stars with masses of roughly 0.7–7 M_⊙. The PMS K- and M-dwarf models are bluer than observed in the Gaia photometry. This discrepancy was noted and discussed at length by Choi et al. (2016). One suggested explanation was that strong magnetic fields in low-mass PMS stars inhibit convection and produce a high filling factor of starspots (e.g., Stauffer et al. 2003; Feiden & Chaboyer 2013). This explanation however fails to explain poor isochrone fits in both old open clusters (e.g., M67) and the field, particularly in blue bandpasses. An alternative explanation is that the molecular line lists for M-dwarf atmospheres are incomplete in these wavelength ranges (Mann et al. 2013; Rajpurohit et al. 2013).

TOI 837 has been reported as a member of IC 2602 by many independent investigators (e.g., Kharchenko et al. 2013; Oh et al. 2017; Cantat-Gaudin et al. 2018; Damiani et al. 2019; Kounkel & Covey 2019). The simplest way to verify the membership is through inspection of the Gaia DR2 position and kinematics. Figure 8 shows the six-dimensional positions and kinematics of TOI 837, IC 2602 members, and nearby stars. The "neighborhood" is defined as in Figure 7. The axis limits for the R.A., decl., and parallax dimensions are set to within five standard deviations of the mean IC 2602 R.A., decl., and parallax. The axis limits for the proper motion and RV dimensions are set at the 25th and 75th percentiles, in order to give a sense of the population's distribution while excluding outliers. The RVs suffer the greatest incompleteness due to the current G ≈ 12 mag limit of the Gaia DR2 data processing.

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Figure 8 provides strong evidence that TOI 837 is a member of IC 2602. The only dimension that could lead to some doubt is the parallax, as TOI 837 is one of the closest IC 2602 members reported by Cantat-Gaudin et al. (2018). Fortunately, there are independent means of verifying the star's youth.

As stars get older, their rotation rates incrementally slow due to magnetic braking (Skumanich 1972; Weber & Davis 1967). One way to verify the youth of TOI 837 is by comparing its rotation period to those of other stars with known ages.

We measured the rotation period from the TESS PDCSAP light curve using the Lomb–Scargle periodogram implemented in astropy (Lomb 1976; Scargle 1982; VanderPlas & Ivezić 2015). We fitted the light curve without masking out the transits or flares, as these represented a small fraction of the overall time series. To derive the uncertainty on the best period, we fitted a Gaussian to the dominant peak, after first ensuring that we had oversampled the initial frequency grid. This gave a rotation period of P_rot = 2.987 ± 0.056 days when allowing for a single Fourier term in the periodogram model, and P_rot = 3.004 ± 0.053 days when allowing for two Fourier terms. As the latter model provides a better fit to the data, we adopt it as the rotation period.

As we discuss in Section 4.2.4, we measured the star's radius by combining the spectroscopic effective temperature with a broadband photometry spectral energy distribution (SED) fit. We would expect, by combining our R_⋆ and P_rot measurements, that the equatorial velocity v of the star would be 17.67 ± 0.32 km s⁻¹. Our spectroscopically measured $v\sin i$ from CHIRON, 16.2 ± 1.1 km s⁻¹, agrees reasonably well with this expectation.

The star is clearly a rapid rotator. Figure 9 compares its rotation period with rotation periods that have been measured in a number of well-studied open clusters. TOI 837 seems to be gyrochronologically coeval with the Pleiades sequence. This is not to say that TOI 837 is "Pleaides-aged," because the observed scatter in the rotation period diagram for the first 10–100 Myr is quite high (see Figure 9 of Rebull et al. 2020). Instead, we interpret the rotation period as evidence to support the claim that TOI 837 is younger than ∼500 Myr.

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Lithium depletion for early G dwarfs like TOI 837 requires hundreds of megayears (Soderblom et al. 2014). This is because their convective envelopes are shallow, and so transport of photospheric lithium to the hot core takes place over diffusive timescales, rather than convective timescales. Nonetheless, comparison of early G dwarfs in the field to, e.g., 600 Myr old Hyads has shown that the depletion does indeed happen over many gigayears (Berger et al. 2018).

The spectra of TOI 837 all show the 6708 Å lithium doublet in absorption. Opting to use our FEROS spectra because of their high S/N, we measured the line's EW to be 154 ± 9 mÅ. Figure 9 compares this EW to those of stars in the field and other young open cluster members. The field star measurements were collected by Berger et al. (2018); we show their reported lithium detections with S/N > 3. The young open cluster members were selected based on the presence of lithium, as described by Randich et al. (2018). The measured TOI 837 lithium EW is much larger than those observed for field stars and is consistent with the lithium absorption seen in stars with similar colors in sub-100 Myr moving groups.

Select properties of TOI 837 from the literature and our analysis are presented in Table 4. We calculated the stellar parameters using two different approaches.

Table 4.  Literature and Measured Properties for TOI 837

Other Identifiers
TIC 460205581
GAIADR2 5251470948229949568
Parameter	Description	Value	Source
${\alpha }_{J2015.5}$	R.A. (hh:mm:ss)	10:28:08.95	1
${\delta }_{J2015.5}$	Decl. (dd:mm:ss)	−64:30:18.76	1
${l}_{J2015.5}$	Galactic longitude (deg)	288.2644	1
${b}_{J2015.5}$	Galactic latitude (deg)	−5.7950	1
B	Johnson-B mag.	11.119 ± 0.107	2
V	Johnson-V mag.	10.635 ± 0.020	2
$G$	Gaia-G mag.	10.356 ± 0.020	1
${Bp}$	Gaia-Bp mag.	10.695 ± 0.020	1
${Rp}$	Gaia-Rp mag.	9.887 ± 0.020	1
$T$	TESS mag.	9.9322 ± 0.006	2
J	2MASS-J mag.	9.392 ± 0.030	3
H	2MASS-H mag.	9.108 ± 0.038	3
${K}_{{\rm{S}}}$	2MASS-${K}_{{\rm{S}}}$ mag.	8.933 ± 0.026	3
W1	WISE1 mag.	8.901 ± 0.023	4
W2	WISE2 mag.	8.875 ± 0.021	4
W3	WISE3 mag.	8.875 ± 0.020	4
W4	WISE4 mag.	8.936 ± N/A	4
π	Gaia DR2 parallax (mas)	6.989 ± 0.022	1
d	Distance (pc)	143.1 ± 0.5	1
${\mu }_{\alpha }$	Gaia DR2 proper motion	−18.017 ± 0.039	1
	in R.A. (mas yr−1)
${\mu }_{\delta }$	Gaia DR2 proper motion	11.307 ± 0.037	1
	in decl. (mas yr−1)
RV	Systemic RV	17.44 ± 0.64a	1
	(km s−1)
$v\sin {i}_{\star }$	RV (km s−1)	16.2 ± 1.1	5
${v}_{\mathrm{mac}}$	Macroturbulence velocity (km s−1)	8.4 ± 2.9	5
$[\mathrm{Fe}/{\rm{H}}]$	Metallicity	−0.069 ± 0.042	5
${T}_{\mathrm{eff}}$	Effective temperature (K)	6047 ± 162	6
$\mathrm{log}{g}_{\star }$	Surface gravity (cgs)	4.467 ± 0.049	6
Li EW	6708 Å EW (mÅ)	154 ± 9	7
${P}_{\mathrm{rot}}$	Rotation period (day)	3.004 ± 0.053	8
Age	Adopted stellar age (Myr)	30–46	9
Spec. type	Spectral type	G0/F9 V	5
${R}_{\star }$	Stellar radius (${R}_{\odot }$)	1.022 ± 0.083	6
${M}_{\star }$	Stellar mass (${R}_{\odot }$)	1.118 ± 0.059	6
${A}_{V}$	Interstellar reddening (mag)	0.20 ± 0.03	10

Notes.

^aSystemic RV uncertainty is the standard deviation of single-transit RVs, as quoted from Gaia DR2. The sources are (1) Gaia Collaboration et al. (2018), (2) Stassun et al. (2019), (3) Skrutskie et al. (2006), (4) Wright et al. (2010), (5) CHIRON spectra, (6) Method 2 (cluster isochrone, Section 4.2.4), (7) FEROS spectra, (8) TESS light curve, (9) IC 2602 ages from isochrone and lithium depletion analyses (Section 4.1.1), and (10) Method 1 (photometric SED fit, Section 4.2.4).

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In "Method 1," we measured the spectroscopic parameters from each of the CHIRON spectra (Section 2.5.1). We then calculated the stellar radius and reddening following Stassun et al. (2017). We first derived the bolometric flux by combining available broadband magnitudes from Gaia, Tycho-2, the AAVSO Photometric All-sky Survey, the Two Micron All Sky Survey (2MASS), and the Wide-field Infrared Survey Explorer (WISE). We then fitted the SED with the Kurucz (2013) stellar atmosphere models and summed it to find F_bol. When fitting the atmosphere model, we varied the extinction (A_V) and the overall normalization. This procedure yielded A_V = 0.20 ± 0.03, which agrees with the average from the IC 2602 isochrone fits of Randich et al. (2018). Combining the spectroscopic effective temperature, bolometric flux, and Gaia distance, we determined the stellar radius using the Stefan–Boltzmann law. Combining this radius with the spectroscopic log g also yielded a stellar mass. The stellar mass however seemed to be high relative to the observed CHIRON effective temperature (1.21 M_⊙ to 5946 K, with relative uncertainties of a few percent on each). We therefore explored a second method and ultimately adopted it because its systematic uncertainties were easier to quantify.

In "Method 2," we used the observed location of TOI 837 in the HR diagram and interpolated it against the 40 Myr MIST isochrone. This method leverages the relative location of TOI 837 within the IC 2602 isochrone to derive precise, theoretically self-consistent constraints on all of the stellar parameters. Although this approach would fail for a low-mass star, TOI 837 is above the stellar masses where the Gaia photometry and isochrone models begin to diverge. The statistical uncertainties yielded by this approach are of order 1% for the stellar mass and radius. To quantify the systematic uncertainties, we compared the parameters derived from the MIST isochrones with those from the PARSEC³⁵ isochrones (Bressan et al. 2012; Chen et al. 2014, 2015; Marigo et al. 2017). The PARSEC isochrones gave a stellar mass 5% lower, an effective temperature 3% lower, a logarithmic surface gravity 1% lower, and a radius 8% smaller than that given by the MIST isochrones. For the sake of self-consistency, in Table 4 and in the ensuing analysis we adopt the stellar parameter values from MIST. We took the uncertainties to be the quadrature sum of the statistical and systematic components.