Revised temperatures for two benchmark M-dwarfs – outliers no more

ABSTRACT

Well-characterized M-dwarfs are rare, particularly with respect to effective temperature. In this letter, we re-analyse two benchmark M-dwarfs in eclipsing binaries from Kepler/K2: KIC 1571511AB and HD 24465AB. Both have temperatures reported to be hotter or colder by |$\approx 1000$| K in comparison with both models and the majority of other M-dwarfs in the literature. By modelling the secondary eclipses with both the original data and new data from TESS, we derive significantly different temperatures: |$2865\pm 27$| for KIC 1571511B and |$3081\pm 32$| for HD 24465B from the Transiting Exoplanet Survey Satellite (TESS) and |$3114\pm 32$| K for HD 24465B from K2. These new temperatures are not outliers. Removing this discrepancy allows these M-dwarfs to be truly benchmarks. Our work also provides relief to stellar modellers. We encourage more measurements of M-dwarf effective temperatures with robust methods.

1 INTRODUCTION

There is a lack of precisely characterized M-dwarfs in the literature. This inhibits our ability to constrain models of stellar structure for low-mass stars. Exoplanet studies are also hampered because our knowledge of the planets is limited by our knowledge of the host star. In the era of the Transiting Exoplanet Survey Satellite (TESS) and the James Webb Space Telescope (JWST), where M-dwarfs are popular targets for exoplanet studies, this is particularly problematic. In addition to poor statistics, there exist discrepancies between observations and theory. The most thoroughly studied is the so-called radius inflation problem, where M-dwarfs have been often observed with radii a few per cent higher at a given mass than expected by theoretical models (Chabrier et al. 2000; Torres et al. 2014). In this paper, we tackle a different yet just as fundamental property: effective temperature. Like with the mass–radius relationship, we expect M-dwarfs to follow a mass–temperature relationship, with more massive stars being expected to be hotter. So far, for the small number (a few dozen) of eclipsing M-dwarfs with measurement temperatures, theoretical models have largely matched observations (Fig. 1). In this paper, we will study the only two cases of extreme outliers.

Eclipsing binaries remain the most robust avenue for precise M-dwarf characterization (e.g. Triaud et al. 2017; von Boetticher et al. 2019). We can measure M-dwarf temperatures if we can observe the occultation of the M-dwarf by the companion star. In our study, the M-dwarf is the smaller and cooler star in the binary, so its occultation is referred to as the secondary eclipse. The ratio between the primary and secondary eclipse depths provides the brightness ratio between the two stars, in a given observing passband. To convert to an effective temperature ratio we can use models of stellar atmospheres as a function of |$T_{\rm eff}$| to predict the observed brightness ratio, and hence match it to the data. To obtain the M-dwarf’s effective temperature, |$T_{\rm eff,B}$|⁠, we use a measurement from |$T_{\rm eff,A}$| from spectral characterization. This has been the method employed by the EBLM (eclipsing binary low mass) survey (Triaud et al. 2017; Maxted, Triaud & Martin 2023; Davis et al. 2024).

With only a single passband the resulting M-dwarf temperature will suffer from some model dependence. This is nevertheless still better than say fitting a spectral energy distribution (SED) to a single M-dwarf, where both |$T_{\rm eff}$| and R are unknown; for an eclipsing binary |$R_{\rm B}$| is well constrained. The model dependence in eclipsing binaries can be alleviated with multicolour photometry. The number of eclipsing binaries with such photometry is rare, but there is a growing list of binaries with at least two bands, e.g. TESS and CHEOPS, (Sebastian et al. 2023), or as for one target in this paper, TESS and K2.

Regardless of the method used to derive the M-dwarf’s effective temperature, the results need to be consistent across different instruments and analyses by different groups. An M-dwarf in the G + M eclipsing binary EBLM J0113+31 was found to have an effective temperature of |$3922\pm 42$| K (Gómez Maqueo Chew et al. 2014), roughly 600 K hotter than expected for a |$0.186\, \mathrm{ M}_\odot$| star. This irregularity was later shown to be erroneous by Swayne et al. (2020), who calculated |$T_{\rm eff,B}=3208\pm 40$| K, in line with expectations. The difference between the two studies was that Swayne et al. (2020) used TESS space-based photometry, whereas Gómez Maqueo Chew et al. (2014) only had ground-based photometry. It was suggested that systematic errors in the J-band photometry created the error. A third analysis, Maxted et al. (2022), added CHEOPS photometry and near-infrared SPIRou radial velocities. They derived a slightly higher temperature than Swayne et al. (2020) of |$3375\pm 40$| K. However, this is consistent with their heavier mass measurement of |$0.197\, \mathrm{ M}_\odot$|⁠.

In this paper, we study two other benchmark M-dwarfs with outlier temperatures: KIC 1571511B (Ofir et al. 2012) and HD 24465B (Chaturvedi et al. 2018). The outlier nature of these targets is demonstrated in Fig. 1. KIC 1571511B has |$M_{\rm B}=0.14136\, \mathrm{ M}_\odot$| and |$T_{\rm eff,B}=$|4030–4150, which is ∼1000 K hotter than expected from models and the bulk of the literature. Conversely, HD 24465B has |$M_{\rm B}=0.233\, \mathrm{ M}_\odot$| and |$T_{\rm eff,B}=2335.6\pm 8.6$| K, which makes it |$\sim 800$| K colder than expected. This temperature error is also underestimated since it does not incorporate uncertainty in the primary star’s temperature.

Both KIC 1571511AB and HD 24465AB were first analysed using space-based photometry (Kepler and K2, respectively). The majority of the analysis from Ofir et al. (2012) and Chaturvedi et al. (2018) focussed on the mass and radius of the M-dwarf, which are very precisely measured owing to a high signal-to-noise radial velocity signal and exquisite space-based photometry. In these respects, they truly are benchmark M-dwarfs. Only a simple analysis was provided of the M-dwarf effective temperatures; Ofir et al. (2012) applied a ‘toy model’ with a uniform passband to the observed secondary eclipse and Chaturvedi et al. (2018) did not use the secondary eclipse but allowed the M-dwarf temperature as a free parameter in their phoebe fit of the photometry and spectroscopy.

In this paper, we provide the first thorough analysis of the secondary eclipses, using methods applied in several earlier studies (Gill et al. 2019; Swayne et al. 2020, 2021) that involve fitting model PHOENIX spectra to the measured secondary eclipse depth. We analyse both the existing Kepler/K2 data and, for HD 24465, new data from TESS. We demonstrate that, as was the case with EBLM J0113+31, the original published temperatures are erroneous. We derive M-dwarf temperatures in line with theoretical models and the rest of the literature.

2 TARGETS AND OBSERVATIONS

Observational and stellar properties are catalogued in Table 1. The photometric and spectroscopic data are shown in Fig. 2.

2.1 KIC 1571511AB

This is a 14.0-d eclipsing binary containing |$1.265$| and |$0.141\, \mathrm{ M}_\odot$| stars, discovered using data from the original Kepler mission (Ofir et al. 2012). KIC 1571511B is considered a ‘benchmark’ M-dwarf, which we define as having mass and radius errors less than 5 per cent. For KIC 1571511B: |$\delta M_{\rm B}/M_{\rm B}=3.18~{{\ \rm per\ cent}}$| and |$\delta R_{\rm B}/R_{\rm B}=0.78~{{\ \rm per\ cent}}$|⁠. The secondary star mass comes from six RV measurements from the FIbre-fed Echelle Spectrograph (FIES) on the Nordic Optical Telescope (NOT). KIC 1571511AB is a single-lined spectroscopic binary (SB1), i.e. only the primary star’s spectrum is visible. This means that radial velocities only provide the mass function |$f(m)=M_{\rm B}^3\sin I/(M_{\rm A}+M_{\rm B})^2$|⁠. The inclination comes from the eclipses. To get the primary mass Ofir et al. (2012) follow a standard procedure of deriving effective temperature, metallicity, and surface gravity from the FIES spectra and then fitting a Yonsei–Yale model isochrone.

Ofir et al. (2012) derive a temperature of |$T_{\rm eff,B}=$| 4030–4150, which is roughly 1000 K hotter than expected. KIC 1571511AB has since been observed by the TESS space telescope. Unfortunately, the faintness of the target (Tmag = 12.95) means that we can see primary but not secondary eclipses, so we do not use these data.

2.2 HD 24465AB

This target comes from the Chaturvedi et al. (2018) study of four eclipsing binaries containing M-dwarfs. It is the only one which can be truly considered a benchmark M-dwarf, owing to precise K2 photometry. HD 24465AB is a 7.20-d binary consisting of 1.337 and |$0.233\, \mathrm{ M}_\odot$| stars, where the M-dwarf is constrained to a precision of |$\delta M_{\rm B}/M_{\rm B}=0.86~{{\ \rm per\ cent}}$| and |$\delta R_{\rm B}/R_{\rm B}=0.4~{{\ \rm per\ cent}}$|⁠. However, these are formal errors on the fitted parameters and they do not account for the modelling uncertainties in the primary star’s parameters (Duck et al. 2023). The mass is derived from 14 radial velocities taken with the PARAS (PRL Advanced Radial-velocity Abu-sky Search) spectrograph on the 1.2-m telescope at Gurushikhar, Mount Abu, India. HD 24465AB is an SB-1, so just like for KIC 1571511AB a model-fit to the primary star’s spectrum was required to derive its mass, and consequently the mass of the secondary star too.

HD 24465AB was observed by TESS in sectors 42 and 43, both in short cadence (120 s). Unlike for KIC 1571511AB, these data are sensitive to the secondary eclipse because this is a much brighter target (Tmag = 8.50). This provides an opportunity to measure the secondary eclipse depth in two different passbands, since TESS has a significantly redder sensitivity than Kepler (Fig. 3). If the results match across both passbands then this partially alleviates the model-dependency issues of converting a surface brightness ratio to an effective temperature ratio using a single passband.

3 METHODS

3.1 Light-curve processing

For the Kepler, K2, and TESS data we use the lightkurve software package (Lightkurve Collaboration 2018) to download the data. For KIC 1571511AB we use the Keplerpdcsap flux. For HD 24465AB we use the everest flux (Luger et al. 2016) for K2 and the pdcsap flux for TESS. We flatten all three light curves using the wotan detrending software (Hippke et al. 2019). We apply a Tukey’s biweight filter with a 1 d window length. This will remove out of eclipse variability, both instrumental and astrophysical (e.g. ellipsoidal variations and spot modulations) but will not affect the eclipse depths. For HD 26645AB we manually removed the first few days of K2 data (⁠|$T-2455\,000 \lt 2065$|⁠). The original light curves and the fitted trends are shown in Fig. 2.

3.2 exoplanet fit

We use the exoplanet software (Foreman-Mackey et al. 2021) to create joint photometry and radial-velocity fits. The fitted light curve, with primary and secondary eclipses, is calculated using starry (Luger et al. 2019), with quadratic limb-darkening parameters calculated using Kipping (2013). The primary star mass and radius are fixed to the original literature values. This is because these are model-dependent values from spectral fitting, so if we were to derive our own values they would likely be slightly different. By fixing |$M_{\rm A}$| and |$R_{\rm A}$| then we can better localize the cause of a different |$M_{\rm B}$| and |$R_{\rm B}$|⁠. The free parameters in our joint fit are: |$M_{\rm B}$|⁠, |$R_{\rm B}$|⁠, impact parameter b, period, eccentricity vectors (⁠|$e\cos \omega$| and |$e\sin \omega$|⁠), primary eclipse time, and secondary eclipse depth (used for temperature calculation, see Section 3.3). After first estimating the maximum a posteriori parameters, we derive a posterior distribution and |$1\sigma$| errorbars using pymc3.

For HD 22465 we do separate fits for the K2 and TESS data. The secondary eclipse depth will change in different passbands (Fig. 3), but as a test of the robustness of our temperature analysis (Section 3.3), we should retrieve the same temperature with both data sets. Furthermore, by analysing the two data sets individually rather than as an ensemble we can directly compare our K2 fit to that of Ofir et al. (2012).

We note one issue with the radial velocity fits to HD 24465AB. We were unable to exactly replicate the fit of Chaturvedi et al. (2018) with their published data. In particular, our values for K differ by |$\approx 700$| m s⁻¹. In their fig. 2 there are essentially no residuals to the RV fit, but in our best exoplanet fit we have residuals of hundreds of m s⁻¹. We attempted an RV-only fit with the generic algorithm yorbit (Ségransan et al. 2011), but obtained the same fit as with exoplanet. Ultimately, our derived value for |$M_{\rm B}$| is consistent with theirs, so for the purposes of this paper exploring the |$T_{\rm eff}$| versus M relationship our fit is sufficient. We had no such issues with the radial velocity fits of KIC 1571511AB.

Despite the exoplanet code being written primarily for exoplanet science, its validity for eclipsing binaries has been demonstrated several times. First, the tutorial provided for fitting eclipsing binaries¹ replicates the parameters of HD 23642 from Southworth, Maxted & Smalley (2005) within |$\approx 1\sigma$|⁠. The radius ratio for HD 23642 is |$R_{\rm B}/R_{\rm A} = 0.85$|⁠, whereas for our two systems it is |$\approx 0.15-0.2$|⁠, i.e. our binaries are more ‘planet-like’. exoplanet was also used in the study of CM Draconis by Martin et al. (2023), where the radius ratio is |$\approx 1$|⁠, and the study of a Jupiter-sized planet around an M-dwarf by Kanodia et al. (2023), where the radius ratio is |$\approx 0.25$|⁠. Finally, exoplanet was used in the Duck et al. (2023) study of eclipsing binaries similar to this paper, to independently verify the results calculated using exofastv2.

3.3 M-dwarf effective temperature derivation

The secondary eclipse depth is related to the brightness ratio of the two stars by

where k is the radius ratio, S is the surface brightness ratio, and |$A_{\rm g}$| is the geometric albedo (Charbonneau et al. 2005; Cañas et al. 2022). In the first line the |$k^2S$| factor is the contribution from the intrinsic brightness of the M-dwarf. The |$A_{\rm g}(R_{\rm B}/a)^2$| factor is light from the primary star reflected off the M-dwarf. Owing to the relatively wide separation of the binaries and a typical albedo of |$A_{\rm g}=0.1$| (Marley et al. 1999; Cañas et al. 2022), the reflection effect can be considered negligible. For example for KIC 1571511 the reflection effect is |$\approx 4$| ppm, relative to a |$\approx 200$| ppm secondary eclipse.

To derive the secondary star’s effective temperature we first calculate S from equation (1) and then solve for |$T_{\rm eff,B}$| in

where |$\tau$| is the instrumental transmission function for Kepler/K2/TESS² and |$F_{\lambda }$| is the flux of each star as a function of wavelength |$\lambda$|⁠, effective temperature, and surface gravity. The factor of |$\lambda$| inside each integral is the same correction as made in Duck et al. (2023), based on Bessell & Murphy (2012). This is because CCDs are photon-counting devices the energy flux |$F_{\lambda }$| is divided by |$hc/\lambda$| to convert it to photon flux. We calculate |$F_{\lambda }$| using an interpolated grid of PHOENIX stellar spectra models (Husser et al. 2013). In equation (2), we convolve these theoretical spectra with the instrument’s bandpass to predict the star’s observed brightness. This is done for both stars. For the primary star we take the published value of |$T_{\rm eff,A}$| and |$\log {g_{\rm A}}$|⁠. For the secondary star we calculate |$\log {g_{\rm B}}$| from our fitted values of |$M_{\rm B}$| and |$R_{\rm B}$|⁠, use the literature value for [Fe/H] and test a grid of |$T_{\rm eff,B}$| between 2500 and 4000 K. We then solve equation (2) for |$T_{\rm eff}$|⁠. The error bar on |$T_{\rm eff,B}$| comes from applying equation (2) with the |$1\sigma$| errors on S, [Fe/H], |$T_{\rm eff,A}$|⁠, |$\log {g_{\rm A}}$|⁠, and |$\log {g_{\rm B}}$|⁠.

For KIC 1571511 B we derive a secondary star effective temperature of |$2865\pm 27$| K. For HD 24465 B we derive a secondary star effective temperature of |$3081\pm 32$| K, based on TESS data, and |$3114\pm 32$| K, based on K2 data. In all three cases our values are close to both the rest of the literature values and the theoretical prediction from MIST models.

As an additional, independent confirmation, we also determined the effective temperatures via fitting of the broad-band stellar SED, following the methodology of Miller, Maxted & Smalley (2020) as implemented in Stassun et al. (2022). Briefly, the combined-light SED is fitted with two stellar model atmospheres constrained by the fundamental parameters of the eclipse solution, namely the sum of radii, the surface brightness ratio, as well as the distance via the Gaia parallax (see also Stassun et al. 2023). For KIC 1571511, we obtain |$T_{\rm eff,A} \approx 6200$| K, |$R_{\rm A} \approx 1.35$| R|$_\odot$|⁠, |$T_{\rm eff,B} \approx 3050$| K, and |$R_B \approx 0.18$| R|$_\odot$|⁠. For HD 24465, we obtain |$T_{\rm eff,A} \approx 6250$| K, |$R_{\rm A} \approx 1.46$| R|$_\odot$|⁠, |$T_{\rm eff,B} \approx 3225$| K, and |$R_B \approx 0.25$| R|$_\odot$|⁠. These estimates are consistent with those determined as above.

4 RESULTS AND DISCUSSION

We derive effective temperatures that are significantly different to the Ofir et al. (2012) and Chaturvedi et al. (2018) results, but in line with expectations from both models and the rest of the literature. This difference is highlighted in Fig. 1. All of the results are provided in Table 2. In Fig. 4, we show zoomed fits to the primary and secondary eclipses for both targets.

Our fractional uncertainty on |$D_{\rm sec}$| for HD 24465AB is 0.4 per cent for K2, compared with 1.7 per cent for TESS. The higher precision of K2 compensates for the deeper secondary eclipse in TESS’s redder bandpass (Fig. 3), such that the overall temperature error on each measurement is almost identical.

For HD 24465AB our TESS and K2 temperatures are |$\approx 1\sigma$| different. Whilst this is not a statistically significant difference, we speculate on some possible causes of a discprency between the two instruments. It may be an artefact of our light-curve detrending; whilst the wotan filter was chosen to preserve eclipse depths according to Hippke et al. (2019), any slight distortion of the eclipse depths would affect the derived temperature. The temperature difference may also arise from different levels of dilution from neighbouring stars. Whilst we did not see any neighbouring stars that we believe bright enough to affect the eclipse depths, TESS does ultimately have much larger pixels (21 arcsec) compared with K2 (4 arcsec). Another possibility is that the K2 and TESS observations are over 6 yr apart. During this time star-spots may have evolved (changed location and/or changed coverage fraction). This could affect the photometry (Martin et al. 2023; Sethi & Martin 2024). One final possibility is that our PHOENIX stellar spectral models (Husser et al. 2013) are not a perfect representation of the M-dwarf, the spectrum of which we cannot directly see. This might be due to imprecise measurements and/or assumptions with respect to the M-dwarf’s metallicity. This would mean that different bandpasses may yield different temperatures. Ultimately, the differences between |$T_{\rm eff,B}$| in K2 and TESS are very small relative to the difference with the value from Chaturvedi et al. (2018). The differences are also similar to what Sebastian et al. (2023) found when comparing M-dwarf temperatures from TESS and CHEOPS observations, using the same approach as ours.

Our fitted parameters for the M-dwarf mass and radius match the discovery papers within |$1\sigma$|⁠. This suggests consistency with the fitting of the radial velocities and the primary eclipse, at least.

One additional discrepancy with our results is the measured orbital period of KIC 1571511B. Our joint fit of FIES radial velocities and K2 photometry measures |$P=14.022452\pm 0.00000067$|⁠, which is a factor of 34 times more precise than the Ofir et al. (2012) measurement of |$14.02248^{+0.000023}_{-0.000021}$|⁠. In Ofir et al. (2012) they only had a baseline of observations of about 40 d (roughly three orbits), since it was a discovery in the early days of the Kepler spacecraft. Comparatively, we have the benefit of a photometric baseline of nearly 1600 d, consisting of roughly 100 orbits. From this we would expect a precision increase around a factor of 30 due to the increase in our sample size. As an additional test for our precision estimate, we create a fit solely to the six FIES radial velocities and obtained |$P=14.021\pm 0.014$|⁠, which is within 1σ of the Ofir et al. (2012) value. This measurement lies within the expected uncertainty range on the period using only the RV data. It is likely that the precision of the uncertainty in the period is dominated by the fit of the photometric data in our joint fit model. Despite the increase in precision, since the actual value of the period matches it should not affect the results.

We have made the first robust measurements of the two M-dwarf temperatures using a thorough analysis of the secondary eclipse depth. Whilst the past works openly only used simplistic methods to derive |$T_{\rm eff}$|⁠, it is nevertheless of interest to try to reproduce their results and investigate the large discrepancy. Specifically, why was the Ofir et al. (2012) temperature for KIC 1571511B roughly 1000 K too hot, and the Chaturvedi et al. (2018) result for HD 24465B roughly 800 K too cold?

4.1 KIC 1571511B

Ofir et al. (2012) derive an M-dwarf temperature of 4030–4150 K, which is more than 1000 K hotter than our value of |$2970\pm 17$| K. There are three differences between our studies. First, their secondary eclipse depth (⁠|$D_{\rm sec}=0.000275\pm 0.000019$|⁠) is roughly |$3\sigma$| deeper than ours (⁠|$D_{\rm sec}=0.0002043\pm 0.0000059$|⁠), despite both values being derived from Kepler data. We re-do our analysis with the Ofir et al. (2012) |$D_{\rm sec}$| and derive only a slightly hotter temperature of |$3075\pm 18\mathrm{ K}$|⁠, which would still be within theoretical expectations, and hence does not significantly change the 1000 K discrepancy.

A second difference is that Ofir et al. (2012) derive |$T_{\rm eff,B}$| assuming blackbodies, as opposed to our phoenix model spectra (comparison in Fig. 3). We re-do our analysis with this assumption and actually obtain a colder temperature of |$2695\pm 15$| K. This would be an outlier, but in the opposite direction of the Ofir et al. (2012) result.

The third difference is that Ofir et al. (2012) assume a uniform Kepler passband between 420 and 900 nm. By applying this assumption, we obtain |$2884\pm 15$|⁠. Again, this simplying assumption actually acts to make the M-dwarf cooler. This can be seen in Fig. 3 where the assumption of a uniform bandpass would imply a higher Kepler sensitivity at redder wavelengths. Overall, we cannot explain the much higher temperature from Ofir et al. (2012). However, we do note that Ofir et al. (2012) describe their temperature derivation as a ‘toy model’, so such a large difference between their value and both ours and that from theory may not be surprising.

4.2 HD 26645

Chaturvedi et al. (2018) derive |$T_{\rm eff,B}=2335.60\pm 8.56$|⁠, which is 865 K cooler than our value from K2. It is stated that ‘we also searched for the secondary eclipse but did not find any significant evidence’. Fig. 4 shows that the secondary eclipse is in fact clear in our K2 data. However, Chaturvedi et al. (2018) do not appear to be using the everest pipeline, and hence the secondary eclipse may have been hidden to them behind telescope systematics.

Chaturvedi et al. (2018) use the phoebe (Prsa et al. 2011) package to model the photometry and radial velocities, and state that |$T_{\rm eff,B}$| is ‘kept free for fitting’. However, since the fit was only of the primary eclipse and the radial velocities, there is essentially no information in the light curve concerning |$T_{\rm eff,B}$| except a note that ‘the secondary depth or HD 24465 as modelled from KEPLER data is 18 ppm’. An 18 ppm secondary eclipse is much shallower than ours measured secondary eclipse, but this is consistent with Chaturvedi et al. (2018)’s much cooler temperature. It is beyond the scope of our work but it would be an interesting project to fit the everest pipeline K2 photometry with phoebe, directly fitting both the primary and secondary eclipses.

5 CONCLUSION

We have studied two benchmark M-dwarfs: KIC 1571511B (Ofir et al. 2012) and HD 24465B (Chaturvedi et al. 2018). The former had a reported temperature about 1000 K hotter than expected. The latter was about 800 K colder than expected. Such discoveries would have posed significant challenges to stellar models. We re-analyse the original Kepler/K2 data to derive the M-dwarf effective temperature based on the secondary eclipse depth. Our results differ significantly from the original studies, and instead match the temperatures expected from both models and the majority of other literature M-dwarfs. With these new precise and reliable M-dwarf temperatures, these two targets can be truly considered benchmarks.

ACKNOWLEDGEMENTS

Support for DVM was provided by NASA through the NASA Hubble Fellowship grant HF2-51464 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. This research is also supported work funded from the European Research Council (ERC) the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 803193/BEBOP). Partial support for AD, RRM, and BSG was provided by the Thomas Jefferson Chair Endowment for Discovery and Space Exploration. MIS acknowledges support from STFC grant number ST/T506175/1.

DATA AVAILABILITY

All radial velocities and light curves will be made available online.

Footnotes

REFERENCES

APPENDIX A: CORNER PLOTS

Figs A1, A2, and A3 show corner plots to demonstrate the quality of fit to the two targets.

Author notes