COol Companions ON Ultrawide orbiTS (COCONUTS). III. A Very Red L6 Benchmark Brown Dwarf around a Young M5 Dwarf

We present the third discovery from the COol Companions ON Ultrawide orbiTS (COCONUTS) program, the COCONUTS-3 system, composed of a young M5 primary star UCAC4 374-046899 and a very red L6 dwarf WISEA J081322.19$-$152203.2. These two objects have a projected separation of 61$''$ (1891 au) and are physically associated given their common proper motions and estimated distances. The primary star, COCONUTS-3A, has a mass of $0.123\pm0.006$ M$_{\odot}$ and we estimate its age as 100 Myr to 1 Gyr based on its kinematics and spectrophotometric properties. We derive its metallicity as $0.21 \pm 0.07$ dex using empirical calibrations established by older higher-gravity M dwarfs and find this [Fe/H] could be slightly underestimated according to PHOENIX models given COCONUTS-3A's younger age. The companion, COCONUTS-3B, has a near-infrared spectral type of L6$\pm$1 INT-G, and we infer physical properties of $T_{\rm eff} = 1362^{+48}_{-73}$ K, $\log{(g)}= 4.96^{+0.15}_{-0.34}$ dex, $R = 1.03^{+0.12}_{-0.06}$ R$_{\rm Jup}$, and $M = 39^{+11}_{-18}$ M$_{\rm Jup}$, using its bolometric luminosity, its host star's age, and hot-start evolution models. We construct cloudy atmospheric model spectra at the evolution-based physical parameters and compare them to COCONUTS-3B's spectrophotometry. We find this companion possesses ample condensate clouds in its photosphere with the data-model discrepancies likely due to the models using an older version of the opacity database. Compared to field-age L6 dwarfs, COCONUTS-3B has fainter absolute magnitudes and a 120 K cooler $T_{\rm eff}$. Also, the J-K color of this companion is among the reddest for ultracool benchmarks with ages older than a few 100 Myr. COCONUTS-3 likely formed in the same fashion as stellar binaries given the companion-to-host mass ratio of 0.3 and represents a valuable benchmark to quantify the systematics of substellar model atmospheres.


INTRODUCTION
Wide-field sky surveys have been a powerful means to construct a large census of planetary-mass and substellar objects in the solar neighborhood, allowing us to investigate star formation at the very low-mass end. These surveys also have helped to establish a photometric sequence of ultracool dwarfs spanning M, L, T, and Y dwarfs (e.g., Vrba et al. 2004;Best et al. 2021;Kirkpatrick et al. 2021), as well as to find peculiar objects, including L dwarfs with much redder infrared colors and fainter absolute magnitudes than field objects with similar spectral types (e.g., Gizis et al. 2012;Kellogg et al. 2015;Schneider et al. 2014Schneider et al. , 2017Faherty et al. 2016;Liu et al. 2013Liu et al. , 2016.
The anomalous photometry of these unusually red L dwarfs suggest they have more dusty atmospheres (e.g.,  or a stronger thermo-chemical instability in their atmospheres (e.g., Tremblin et al. 2016) than normal field dwarfs. Many unusually red L dwarfs have low surface gravities and their anomalous spectrophotometry thus suggests a gravity dependence of ultracool dwarfs' atmospheric properties during the L/T tradition (e.g., Metchev & Hillenbrand 2006;Faherty et al. 2016;Liu et al. 2016;Tremblin et al. 2017). However, a number of red L dwarfs likely have old ages ( 1 Gyr) as they are not associated with any young stars or moving groups and have no low-gravity spectral features (e.g., Looper et al. 2008;Kirkpatrick et al. 2010;Allers & Liu 2013). Spectroscopic characterization of unusually red L dwarfs rely on cloudy and dis-equilibrium model atmospheres. However, these models are challenged by the uncertainties in opacity line lists, the assumption of radiative-convective equilibrium, and the presence of complex, patchy, timeevolving clouds (e.g., Marley & Robinson 2015;Showman et al. 2020;Zhang 2020). Also, modeling efforts are still needed to reconcile the discrepancies between model predictions and the observed photometric sequence of ultracool dwarfs, particularly near the L/T transition (e.g., Figures 22-24 of Liu et al. 2016). To improve the performance of these models, ultracool dwarfs that are either wide-orbit companions to stars or members of nearby associations are essential benchmarks. The ages and metallicities of these objects can be independently inferred from their associated stars and can therefore identify specific shortcomings of model assumptions and directly quantify the systematic errors of model predictions (e.g., Zhang et al. 2020Zhang et al. , 2021c. To establish a large census of wide-orbit ( 500 au) benchmark companions, we are conducting the COol Companions ON Ultrawide orbiTS (COCONUTS) program, by targeting 300,000 stars within 100 pc selected from Gaia. Mining astrometry and photometry from wide-field sky surveys (e.g., Pan-STARRS1 [PS1; Chambers et al. 2016], AllWISE (Wright et al. 2010;Cutri 2014), and CatWISE2020 [Cat-WISE hereafter; Marocco et al. 2021]), we have searched for candidate companions which have consistent proper motions as their host stars (with projected separations < 10 4 au) and have optical and infrared colors and magnitudes expected for planetary-mass objects and brown dwarfs (e.g., Best et al. 2018). We have then conducted ground-based follow-up observations to confirm the companionship and substellar nature of new wide-orbit companions. Our first discovery COCONUTS-1AB ) is composed of a very old (7.3 +2.8 −1.6 Gyr) white dwarf primary and a T4 brown dwarf companion (69 +2 −3 M Jup ), which we use to test the highgravity regime of cloudless model atmospheres (Marley et al. 2021). Our second discovery COCONUTS-2Ab (Zhang et al. 2021b) is composed of a young (100 − 800 Myr) M3 primary star with a T9 super-Jupiter companion (6 ± 2 M Jup ), which is the nearest imaged planetary-mass object to our Solar System and also the second imaged exoplanet whose physical properties overlap both hot-start and cold-start formation models.
Here, we report the third COCONUTS discovery, a system with a young M-dwarf primary star (UCAC4 374−046899; hereafter COCONUTS-3A) with a very red L-dwarf companion (WISEA J081322.19−152203.2; hereafter COCONUTS-3B), which was previously identified as a freefloating object by Schneider et al. (2017). We describe the system in Section 2 and our spectroscopic follow-up observations in 3. We then study the physical properties of the primary star and the companion in Sections 4 and 5, respectively, followed by a brief summary in Section 6. Figure 1 shows the COCONUTS-3 system and its neighborhood.
COCONUTS-3B is a previously known, very red L dwarf, WISEA J081322.19−152203.2 (WISE J0813−1522), identified by Schneider et al. (2017) using 2MASS and AllWISE photometry. Schneider et al. (2017) assigned an L7 spectral type using R ≈ 3500 CTIO/ARCoIRIS near-infrared (0.8 − 2.4 µm) spectra with a signal-to-noise ratio (S/N) of only 8 per pixel near the J-band peak. Based on proper motions computed from 2MASS and AllWISE astrometry, they suggested this L dwarf is a possible member of the Argus (with a 87% membership probability from BANYAN II; Malo et al. 2013;Gagné et al. 2014) or Carina-Near (with a 97% mem-bership probability from the Rodriguez et al. 2013 convergent point tool) moving group. However, Schneider et al. (2017) cautioned the distances predicted by BANYAN II (15 ± 2 pc) and the Rodriguez et al. (2013) convergent point tool (17 pc), assuming young moving group membership, are both significantly closer than the object's photometric distance of 31 ± 6 pc (derived using K S,2MASS , spectral type, and empirical relations between absolute magnitudes and spectral types by Dupuy & Liu 2012). We update this object's photometric distance to be 32 ± 7 pc based on our analysis in Section 5.2, which is independent from the physical association between this object and COCONUTS-3A (see below). Using BANYAN Σ ) and this L dwarf's photometric distance, we find its CatWISE proper motion, (µ α cos δ, µ δ ) = (−120.8 ± 6.9, +92.5 ± 7.6) mas yr −1 , corresponds a 30% Carina-Near and a 28% Argus membership. In addition, this object's PS1 proper motion, (−112.6± 21.0, +101.1 ± 21.0) mas yr −1 , corresponds a 19% Carina-Near and 57% Argus membership. Thus, young moving group membership for WISE J0813−1522 seems unlikely, but this object's photometric distance and proper motions agree very well with those of COCONUTS-3A.
We conclude WISE J0813−1522 is a co-moving companion to the field dwarf COCONUTS-3A ( Figure 2). Based on their CatWISE coordinates, the A and B components are separated by 61.46 ±0.04 , meaning a projected physical separation of 1891±2 au at the primary star's distance. Properties of COCONUTS-3AB are summarized in Table 1 We obtained optical (3500 − 9100 Å) spectra of COCONUTS-3A on UT 2019 October 7 using the Super-Nova Integral Field Spectrograph (SNIFS; Aldering et al. 2002;Lantz et al. 2004) mounted on the University of Hawai'i's 2.2m telescope. SNIFS is a 6 × 6 integral field spectrograph and provides a spectral resolution of R ≈ 1200. We took one 1800-second exposure for our target and then followed the pipeline described in Bacon et al. (2001) to extract the one-dimensional spectrum, comprising dark, bias, and flat-field corrections, wavelength calibration, and sky subtraction. The dispersion in wavelength calibration is 0.55 Å for the blue channel (3500 − 4700 Å) and 0.08 Å for the red channel (5300 − 9100 Å). We flux-calibrated the 1D spectrum using spectrophotometric standard stars observed during the same night, LTT 2415, Feige 110, HR 3454, and GD 71. Although the night was non-photometric, only relative fluxes of SNIFS spectra (and GMOS spectra in Section 3.1.2) are used in our subsequent analysis and are thus reliable. Our resulting SNIFS spectrum has air wavelengths, with S/N = 28 at 6700 Å and 74 at 8200 Å, and also exhibits Hα emission.

Gemini/GMOS
The optical (6400 − 8900 Å) spectra of COCONUTS-3A was also acquired with the GMOS spectrograph (Hook et al. 2004) at the Gemini-North Telescope (queue program GN-2019B-Q-139; PI: Z. Zhang) on UT 2019 December 12, in order to search for lithium λλ6708 absorption. The R831 grating was used in conjunction with the GG-455 filter and the 0.5 long slit (R ≈ 4400). One 330-second exposure was taken with a central wavelength of 7600 Å, 7650 Å, and 7700 Å (i.e., 3 exposures in total). Such wavelength dithering compensates for the detectors' inter-chip gaps (≈ 38 Å in our data), enabling continuous wavelength coverage. Using the Gemini IRAF data reduction package, we performed dark, bias, and flat-fielding corrections, cosmic-ray rejec-tion, wavelength calibration, and sky subtraction. The dispersion in the wavelength calibration is 0.01 Å. We then flux-calibrated our extracted spectra by using a spectrophotometric standard, Feige 34, observed on UT 2019 November 28. This calibration produces reliable relative fluxes for the GMOS spectra for our subsequent analysis, which does not require absolute fluxes. We computed the weighted average of all three spectra with flux uncertainties propagated to provide the final GMOS spectrum of COCONUTS-3A, with air wavelengths and S/N = 125 at 6700 Å and 380 at 8200 Å.

IRTF/SpeX
Near-infrared (0.7 − 2.5 µm) spectra of COCONUTS-3A were observed using the NASA Infrared Telescope Facility (IRTF) on UT 2019 April 26. We used the SpeX spectrograph  in the short wavelength crossdispersed (SXD) mode with the 0.3 slit (R ≈ 2000) and took six 120-second exposures in a standard ABBA nodding pattern. We contemporaneously observed an A0V standard star HD 67725 within 0.01 airmass of COCONUTS-3A for telluric correction. We reduced the data using version 4.1 of the Spextool software package (Cushing et al. 2004) and obtained a 0.122 Å dispersion in the wavelength calibration. Our resulting SpeX SXD spectrum has vacuum wavelengths, with a median S/N of 135 and 146 per pixel in J and K band, respectively.

IRTF/SpeX
We acquired near-infrared (0.7 − 2.5 µm) spectra of COCONUTS-3B using IRTF/SpeX in prism mode with the 0.8 slit (R ≈ 75) on UT 2019 April 07 and UT 2019 November 02. We took a total of 74 exposures with 120 seconds each in a ABBA pattern, and contemporaneously observed multiple A0V standard stars (HD 78955, HD 82724, HD 89911, HD 72366, and HD 71580) to perform the telluric correction, given that the airmass of the companion spanned a wide range over long exposures. We divided raw spectroscopic data of COCONUTS-3B into five subsets, with each set calibrated by a telluric standard with a < 0.1 airmass difference. The dispersion in wavelength calibration of the prism data is 5.9 Å. Combining all the five telluriccorrected spectra using a robust weighted mean, we obtained the SpeX prism spectrum with vacuum wavelengths and a median S/N= 53 per pixel in J band.

Gemini/GNIRS
The near-infrared (0.9 − 2.5 µm) spectra of COCONUTS-3B was observed with the Gemini-North GNIRS spectrograph (Elias et al. 2006) on UT 2019 November 12 (queue program GN-2019B-Q-139; PI: Z. Zhang) with a higher spectral resolution (R ≈ 750) than the SpeX prism data. The cross-dispersed (XD) mode was used with the 32 I/mm grating, short camera (0.15 per pixel), 0.675 slit. Eight exposures were taken with 222 seconds in an ABBA pattern. Also, an A0V telluric standard star, HIP 37787, was contemporaneously observed within 0.05 airmass of COCONUTS-3B. We reduced the data using a modified version of Spextool (K. Allers, private communication; also see Vacca et al. 2003;Cushing et al. 2004;Section 4.4 of Kirkpatrick et al. 2011) and obtained a dispersion of 0.8 Å in wavelength calibration. Our resulting GNIRS XD spectrum has vacuum wavelengths and a median S/N= 45 per pixel in J band. We convert spectra of COCONUTS-3A to the stellar rest frame by comparing with spectral templates. For the optical spectrum, we use templates from PyHammer (Kesseli et al. 2017), a modified version of the Hammer spectral classification tool (Covey et al. 2007). These templates are constructed using the Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey (Dawson et al. 2013), spanning 3650 − 10200 Å wavelengths in vacuum (R ∼ 2000), O5−L3 spectral types, and [Fe/H]= −2 to +1 dex (with intervals of 0.5 dex). We first put our SNIFS and GMOS spectra in vacuum following Ciddor (1996). Given that COCONUTS-3A has an optical spectral type of M5.5 ± 0.5 (Section 4.2), we cross-correlate with all M5 and M6 Py-Hammer templates (with [Fe/H]= −0.5, 0, +0.5 dex at each spectral type) over a wavelength range of 6500 − 8800 Å for both SNIFS and GMOS spectra. We then shift these spectra using the averaged radial velocity of 120.4 km s −1 (SNIFS) and 15.0 km s −1 (GMOS), after confirming no > 5σ outliers exist.
For the near-infrared spectrum, we use Gl 213 (M4), Gl 268AB (M4.5), and Gl 51 (M5) from the IRTF Spectral Library (Cushing et al. 2005;Rayner et al. 2009) as templates, given that COCONUTS-3A has a near-infrared spectral type of M4.5 ± 0.5 (Section 4.2). We cross-correlate the SpeX SXD spectrum of COCONUTS-3A with each template over individual orders 3−7 and then shift the spectrum by using the averaged value of 58.8 km s −1 among all computed radial velocities (no > 5σ outliers are detected).
Based on the size of one resolution pixel, we assign an uncertainty of 250 km s −1 , 68 km s −1 , and 150 km s −1 to the estimated radial velocity by SNIFS, GMOS, and SpeX SXD spectra, respectively. We further apply the barycentric correction to each measured radial velocity using Astropy (Astropy Collaboration et al. 2013, 2018 and compute their weighted mean and weighted error, leading to a radial velocity of 41 ± 60 km s −1 for COCONUTS-3A.  (Kesseli et al. 2017) are overlaid and scaled by the averaged flux at 6500 − 9000 Å. We only show templates with the solar metallicity (orange) since the overall morphology of these templates at a given spectral type do not vary significantly with metallicities from −0.5 to +0.5 dex. The spike shown at the short wavelength of our observed GMOS spectrum is the Hα emission line discussed in Section 4.5.1. We derive a visual optical spectral type of M5.5±0.5 for COCONUTS-3A.

Spectral Type
We determine the optical spectral type of COCONUTS-3A using PyHammer (Kesseli et al. 2017), which measures a suite of indices and then compares to those of spectral templates via a weighted least-squares approach. PyHammer contains templates with a range of metallicities, thereby enabling a metallicity estimate along with the spectral type. Kesseli et al. (2017) suggested the spectral types and metal-licities estimated by PyHammer are accurate to ±1.5 subtypes and ±0.4 dex, respectively. We find COCONUTS-3A has an index-based spectral type of M6 using both SNIFS and GMOS spectra, with a metallicity of −0.5 dex and 0 dex, respectively. Visually comparing our observed spectra with PyHammer spectral templates, we assign a visual type of M5.5±0.5 ( Figure 3) and adopt this as the final optical spectral type of the primary star. Given the large metallicity uncertainties from PyHammer, we subsequently determine the bulk metallicity of COCONUTS-3A using narrow-band spectroscopic features (Section 4.3).
We determine the near-infrared spectral type of COCONUTS-3A following Allers & Liu (2013), who derived empirical polynomials between optical spectral types and four H 2 O-band indices using IRTF/SpeX spectra of young and field-age M4−L8 ultracool dwarfs. Allers & Liu (2013) also includes a gravity classification system, based on strengths of gravity-sensitive spectral features. We compute an index-based spectral type of M4.2 ± 0.5 and an intermediate gravity class INT-G (see Section 4.5.8 for further discussion) and caution such a spectral type is near the margin of the applicable range (M4−L8) for the Allers & Liu (2013) classification. We also measure the H 2 O-K2 index, a spectral type indicator for M0−M9 dwarfs calibrated by Rojas-Ayala et al. (2012) and derive M4.5 ± 1.3. We further compare our SpeX SXD spectrum to M3−M7 spectral standards from the IRTF Spectral Library (Cushing et al. 2005;Rayner et al. 2009) in J, H, and K bands and assign a visual type of M4.5 ± 0.5 (Figure 4), which we adopt as the final near-infrared spectral type of COCONUTS-3A.

Metallicity
We compute the bulk metallicity of COCONUTS-3A by using empirical calibrations established using binaries composed of FGK primary stars (with independently measured [Fe/H]) and M dwarf secondaries. Such M-dwarf metallicity calibrations were originally developed for photometry (e.g., Bonfils et al. 2005;Schlaufman & Laughlin 2010;Johnson et al. 2012;Neves et al. 2012) and then extended to moderate-resolution spectroscopy (R ∼ 2000; e.g., Rojas-Ayala et al. 2010Terrien et al. 2012;Mann et al. 2013Mann et al. , 2014Newton et al. 2014). Using a sample of 112 binaries, Mann et al. (2013) derived metallicity calibrations for objects with optical spectral types of K5−M5 using either optical, J-, H-, or K-band spectra as observed by UH 2.2m/SNIFS or IRTF/SpeX SXD. They also used their sample to update calibrations in previous work (Lépine et al. 2007;Dhital et al. 2012;Johnson et al. 2012;Terrien et al. 2012). Mann et al. (2014) further extended the calibration to near-infrared spectral types of M4.5−M9.5 using sodium and calcium features in K-band SXD spectra. A metallicity calibration for nearinfrared spectral types of M1−M5 was also established by Newton et al. (2014) using the sodium doublet in K-band SXD spectra.
Given that COCONUTS-3A has an optical spectral type of M5.5 and a near-infrared spectral type of M4.5 (Section 4.2), we apply both the Mann et al. (2014) and Newton et al. (2014) calibrations and obtain metallicities of 0.23 ± 0.08 dex and 0.16 ± 0.12 dex, respectively, with spectral flux uncertainties and calibration errors propagated in a Monte Carlo fashion. We adopt the weighted mean and weighted standard deviation of [Fe/H] = 0.21 ± 0.07 dex as the final metallicity of the COCONUTS-3 system (also see Table 2). Our adopted empirical calibrations were established using field M dwarfs with slightly higher surface gravities and older ages than COCONUTS-3A (see Sections 4.5), so we explore the potential surface-gravity dependence of our derived [Fe/H] in Appendix A. Based on the PHOENIX stellar models, our bulk metallicity could be under-estimated by 0.2 − 0.3 dex. A more accurate estimate of [Fe/H] would benefit from an empirical calibration customized for young low-mass stars, which is unfortunately not available to date, given that the existing sample of nearby young stars lacks sufficiently large variations in [Fe/H] and mostly has solar metallicity.
While the spectral type of our primary star is just outside the applicable range (K5−M5) of the Mann et al. (2013) calibrations, we applied them to our SNIFS and SpeX SXD spectra and obtained [Fe/H] = −0.22 ± 0.16 dex in the optical, 0.09 ± 0.13 dex in J band, −0.17 ± 0.11 dex in H band, and 0.12 ± 0.09 dex in K band. Using the Terrien et al. (2012) Hand K-band calibrations as updated by Mann et al. (2013), we obtain [Fe/H] = 0.11 ± 0.15 dex and 0.15 ± 0.14 dex, respectively. Most of these values are < 1σ consistent with our adopted metallicity. We find the spectral features traced by the Mann et al. (2013) optical-and H-band calibrations are not prominent in COCONUTS-3A's spectra, likely leading to less accurate metallicity estimates.

Physical Properties
We derive physical properties of COCONUTS-3A using its broadband photometry and empirical relations. We first synthesize its 2MASS and MKO JHK photometry using our SpeX SXD spectra and measured J and K S from the VISTA Hemisphere Survey (VHS; McMahon et al. 2013), given that this star lacks MKO photometry and its 2MASS photometry is contaminated by a diffraction spike from a nearby source. We use the Vega spectrum and obtain 2MASS, MKO, and VHS filters from Cohen et al. (2003), Hewett et al. (2006), and the ESO VISTA instrument webpage 2 , respectively. We propagate the uncertainties in VHS magnitudes and spectral fluxes in a Monte Carlo fashion, and when the VHS photometry and the synthesized ones are in different bandpasses, we add a 0.05 mag error in quadrature (e.g., Dupuy & Liu 2012). We find using VHS J and K S lead to very similar magnitudes in each band and we adopt their average and standard deviation as the final synthetic photometry (see Table 1).
Following of R = 0.151 ± 0.004 R and a mass of M = 0.123 ± 0.006 M , leading to a surface gravity of log(g )= 5.17 ± 0.03 dex. We also compute a bolometric luminosity of log(L bol, /L )= −2.80 ± 0.04 dex by using the Cifuentes et al. (2020) empirical relation between L bol and J 2MASS -band absolute magnitudes, which is robust over a range of stellar metallicities spanning from −1.0 dex to +0.6 dex (see their Section 4). We then use the Stefan-Boltzmann law to compute an effective temperature of T eff, = 2966±85 K. All measurement uncertainties and calibration errors are propagated in a Monte Carlo fashion.

Hα Emission
The chromospheric Hα emission probes stellar activity which is correlated with stellar ages (e.g., Soderblom 2010). Based on Hα measurements of a large M-dwarf sample from SDSS,  noted the activity fraction of these objects decreases with vertical distance from the Galactic midplane, and the slope of such a decrease depends on spectral type. Using one-dimensional dynamical simulations encoded with a correlation between stellar ages and Galactic positions,  derived a model-based activity lifetime for a given M subtype. More recently, an empirical calibration between stellar age and Hα-based activity has been established by Kiman et al. (2021) using M dwarfs that are either members of young moving groups or companions to white dwarfs. Kiman et al. (2021) fitted a broken powerlaw to the fractional Hα luminosity (L Hα /L bol ) as a function of age and found that L Hα /L bol stays in a saturation regime with a little evolution at < 1 Gyr but decreases more rapidly at older ages.
To assess the Hα emission of COCONUTS-3A, we measure the equivalent width (EW) using SNIFS and GMOS spectra (with rest-frame vacuum wavelengths), following definitions of the Hα line and continuum by Schmidt et al. (2015). We integrate the line flux over 6557.61 − 6571.61 Å with the pseudo-continuum approximated by the mean flux across two surrounding wavelength regions of 6530−6555 Å and 6575 − 6600 Å. We measure EW(Hα) = −2.9 ± 0.2 Å (SNIFS) and −7.18±0.02 Å (GMOS) with flux uncertainties propagated in a Monte Carlo fashion. Using slightly different line and continuum definitions by West et al. (2011) and Newton et al. (2017), as well as fitting a Gaussian function for the Hα line, we obtain similar EW Hα values with a < 1 Å difference for each spectrum. Therefore, COCONUTS-3A is active, with its Hα emission from the stellar chromosphere rather than disk accretion (e.g., Barrado y Navascués & Martín 2003). We attribute the EW(Hα) difference of 4.3 Å between the SNIFS and GMOS spectra to variability and note such a strong variability tends to occur for relatively young stars ( 100 Myr; see Figure 7 of Kiman et al. 2021).
We compute L Hα /L bol = −EW(Hα) × χ, with χ being a factor calibrated against broadband colors and spectral types (e.g., Walkowicz et al. 2004;. We use the Douglas et al. (2014) relation between χ and optical spectral types and obtain χ = (2.1065 ± 0.4167) × 10 −5 , with both the value and error computed as the average of those at M5 and M6 types. We derive log(L Hα /L bol ) = −4.22 ± 0.09 dex (SNIFS) and −3.79 ± 0.09 dex (GMOS), and then estimate the stellar age using the Kiman et al. (2021) Hα activity-age relation in a Bayesian framework (also see Zhang et al. 2021b). We evaluate the age (t) based on the following log-likelihood function: where log(L Hα /L bol ) obs = −4.22 (SNIFS) or −3.79 (GMOS), and σ obs = 0.09. We use the best-fit model parameters of Kiman et al. (2021) to compute log(L Hα /L bol ) model as a function of stellar age (t), with σ V = 0.22 dex. We use the Markov Chain Monte Carlo (MCMC) algorithm emcee (Foreman-Mackey et al. 2013) and assume a uniform prior of [1.5 Myr, 10 Gyr] in age. Running MCMC with 20 walkers and 5000 iterations (with the first 100 iterations excluded as burn-in), we obtain an age estimate of 2.9 +2.4 −1.4 Gyr and 870 +940 −570 Myr using the SNIFS and GMOS spectra, respectively. Both these estimates are consistent with M5 and M6 dwarfs' model-based activity lifetime of < 7 ± 0.5 Gyr computed by .
We caution that the older derived age from the SNIFS spectrum is primarily constrained by a power-law component of Kiman et al. (2021) models at ages >1 Gyr, which is not well constrained by their very small sample size of 6 old M dwarfs. Also, the measured log(L Hα /L bol ) obs = −4.22 ± 0.09 dex from the SNIFS spectrum is in fact consistent with young M dwarfs spanning ages of 10 Myr to 1 Gyr, considering the large scatter in the Hα activity-age relation. Therefore, we adopt an Hα-based age of 870 +940 −570 Myr as determined from the GMOS spectrum.

X-ray Emission
As another indicator of stellar magnetic activity, coronal X-ray emission has a qualitatively similar behavior with stellar age as Hα emission. At young ages ( 100 Myr−1 Gyr), the X-ray-to-bolometric luminosity ratio log (R X )=log (L X /L bol ) exhibits a plateau and the specific saturation level tends to increase with lower stellar masses (e.g., Jackson et al. 2012). This plateau is then followed by a power-law decline toward older ages, with a slope weakly dependent on spectral type (e.g., Booth et al. 2017).
To estimate the X-ray emission of COCONUTS-3A, we query the Second ROSAT All-Sky Survey (Boller et al. 2016) using a 30 matching radius and follow Fleming et al. (1995) to convert the measured count rate and hardness ratio (HR1) into a flux F X = (1.70 ± 0.96) × 10 −13 erg s −1 cm −2 . Multiple background sources are near the ROSAT X-ray detection, which we find make a negligible contribution to our measured X-ray emission (see Appendix B). We derive an X-ray luminosity of log (L X )= 28.3 ± 0.2 dex, similar to M dwarfs in the Pleiades (112 ± 5 Myr; Dahm 2015) and the Hyades (750 ± 100 Myr; Brandt & Huang 2015) according to Preibisch & Feigelson (2005). Based on Malo et al. (2014), the log (L X ) of COCONUTS-3A is fainter than members of AB Doradus moving group (149 +51 −19 Myr; Bell et al. 2015) and younger associations but brighter than the inactive field population. We compute log (R X )= −2.7 ± 0.3 dex, suggesting COCONUTS-3A is in the saturation regime of the X-ray activity-age relation. We also derive flux ratios between X-ray and 2MASS J and K S bands as log (F X /F J )= log F X + 0.4J + 6.3 = −1.6 ± 0.2 dex and log (F X /F KS )= log F X +0.4K S +7.0 = −1.2±0.2 dex, which are comparable with members of the β Pictoris moving group (24 ± 3 Myr; Bell et al. 2015) and the Pleiades (e.g., Shkolnik et al. 2009;Schlieder et al. 2012b). The coronal X-ray activity of COCONUTS-3A thus suggests an age of 850 Myr.

UV Emission
We also study the stellar activity of COCONUTS-3A through UV emission as measured by the Galaxy Evolution Explorer (GALEX; Martin et al. 2005). Using the Milkulski Archive for Space Telescopes (MAST), we find COCONUTS-3A was observed in the near-UV (NUV ) band by the GALEX All-Sky Imaging Survey (AIS) but not detected. We also note the sources within 1 are all fainter than the GALEX 5σ detection limit of 20.5 mag in NUV . To estimate an upper limit of NUV emission from COCONUTS-3A, we extract all GALEX sources within 10 and exclude problematic photometry with a bright star window reflection, dichroic reflection, detector run proximity, or bright star ghost. We then fit a linear function between these objects' NUV magnitudes and the logarithmic photometric S/N. We adopt an upper limit of NUV > 22.3 mag, which corresponds to the predicted value at S/N= 2 (e.g., Schneider & Shkolnik 2018).

Kinematics
Combining Gaia EDR3 astrometry and our estimated radial velocity (Section 4.1), we compute the space position and motion of COCONUTS-3A as XY Z = (−16.899 ± 0.011, −25.311 ± 0.016, 5.542 ± 0.004) pc and UVW = (−41 ± 33, −22 ± 49, −2 ± 11) km s −1 . Such a space motion is outside but consistent within uncertainties with the "good box" of young stars as assigned by Zuckerman & Song (2004) To revisit the ages of objects within the good box, we study the mean space motions of 28 nearby young moving groups from  and Gagné et al. (2020 Kraus et al. 2017;Zhang et al. 2018). We note the Taurus mean space motion is only 0.7 km s −1 outside the border. The fact that the mean UVW of COCONUTS-3A is outside the good box suggests it has an age of 150 Myr, although a more precise radial velocity measurement is needed for verification. We also run BANYAN Σ  and LACEwING (Riedel et al. 2017), finding COCONUTS-3A is not associated with any nearby young moving groups.

HR Diagram Position
According to the MESA isochrones (Paxton et al. 2011;Dotter 2016;Choi et al. 2016), M dwarfs with comparable masses and metallicities as COCONUTS-3A remain in the pre-main sequence evolutionary stage for ∼ 1.5 Gyr. As shown in Figure 5, COCONUTS-3A is located near the upper envelope of the main sequence, indicating it is younger than a few Gyrs. Comparing the Gaia G-band absolute magnitude (11.5826 ± 0.0015 mag) and BP−RP color (3.088±0.004 mag) to empirical isochrones of nearby young moving group members compiled by Kiman et al. (2021), we find COCONUTS-3A has similar photometry as members of  Douglas et al. 2019), and the Hyades (750 ± 100 Myr), and has a fainter absolute magnitude than younger association members. This suggests an age estimate of 100 Myr−1.5 Gyr.

Lithium Absorption
Approaching the main sequence, young M dwarfs contract and increase their core temperatures, which then burns their initial lithium via convective mixing (e.g., Soderblom 2010). Based on the Chabrier & Baraffe (1997) models, the lithiumburning would occur after ∼ 10−15 Myr for M2−M3 dwarfs and ∼ 100 Myr for M5−M6 dwarfs (also see Mentuch et al. 2008;Binks & Jeffries 2014, 2016. We measure the equivalent width of lithium EW Li for COCONUTS-3A using the GMOS spectrum. To approximate the pseudo continuum at the Lithium absorption feature, we fit a PyHammer template (M6 and [Fe/H]= 0) to the GMOS spectrum, with the scaling factor determined by Equation 2 of Cushing et al. (2008). Both GMOS and template spectra have vacuum wavelengths in the rest frame, and we compute EW(Li) over 6708.8 − 6710.8 Å, leading to an upper limit of 4 mÅ. The absence of lithium absorption in COCONUTS-3A suggests an age of 100 Myr.

Optical Sodium Doublet
The sodium doublet (λλ8183, 8195; all wavelengths discussed in this subsection are in the air) is gravity-sensitive and thereby an indicator of stellar age. To quantify the strength of this doublet, Lyo et al. (2004) proposed a Na I index= F λ8148−8172 / F λ8176−8200 , computed as the ratio between the averaged fluxes over 8148 − 8172 Å and 8176 − 8200 Å. They found such indices for giant stars are significantly lower than those of higher-gravity main-sequence dwarfs for early-to-mid-M types, with young pre-main sequence stars falling between these two classes of objects. Riedel et al. (2014) revisited the Na I index with the addition of nearly 50 main-sequence stars and 25 association members, and they cautioned the interpretation of this index at V − K S 5 mag ( M3.5). Also, Slesnick et al. (2006a) proposed a Na-8189 index= F λ8174−8204 /F λ8135−8165 , defined as the ratio between integrated fluxes over 8174 − 8204 Å and 8135 − 8165 Å. This index is quantitatively equivalent to the inverse of the Lyo et al. (2004) Na I index and is gravity-sensitive, particularly for M2−M7 spectral types (e.g., Slesnick et al. 2006b;Kraus et al. 2017). In addition, Schlieder et al. (2012a) defined an equivalent width of the Na doublet EW Na8200 , with the absorption line computed from the integrated flux over 8179 − 8201 Å and the pseudo-continuum approximated by the mean flux over 8149−8169 Å and 8236−8258 Å. Based on stellar model at- mospheres, they suggested EW Na8200 can robustly distinguish 100 Myr stars from the field population at V − K S 5 mag.
Here we perform the largest examination of all these Na spectral indices and equivalent widths by combining spectra of giant and dwarf stars from the Ultracool RIZzo Spectral Library (Cruz & Gagné 2014) and the Montreal Spectral Library. 3 We make use of all optical and near-infrared spectra which cover the sodium feature and have S/N>10 at 8190 Å, including 131 giants (K4−M9), 581 main-sequence field dwarfs (K0−T2), and 56 young dwarfs (M3−L5), which either have β, γ, or δ gravity classes or are kinematic members of 200 Myr young moving groups (based on a crossmatch with the young moving group census from Faherty 2018). We homogeneously determine the Na I index, Na-8189 index, and EW Na8200 values of these objects, with spectral flux uncertainties propagated in a Monte Carlo fashion and with the vacuum wavelengths of near-infrared spectra put in the air following Ciddor (1996). These spectra were obtained by various instruments that span spectral resolutions of R ∼ 100 − 2000, with the most common instruments being the Ritchey-Chrétien (RC) spectrograph (504 objects), the GoldCam spectrograph (148 objects), and the SpeX spectrograph (47 objects). Within each dataset of giants, main-sequence dwarfs, and young dwarfs, we find our measured Na indices and equivalent widths ex-3 https://jgagneastro.com/the-montreal-spectral-library/. hibit no systematic offsets between the different spectrographs. Figure  (2012a) EW Na8200 as a function of spectral types. We note the Na doublet strengths of giants and main-sequence dwarfs are distinct, while those of pre-main sequence dwarfs bridge these two populations with a very large scatter. We also measure these Na features for COCONUTS-3A using its SNIFS, GMOS, and SpeX SXD spectra and find a < 3% discrepancy in a given feature among different spectra. Compared to the library M dwarfs, the strength of COCONUTS-3B's Na doublet λλ8183, 8195 is located near the low-gravity envelope of main-sequence stars and similar to several young pre-main sequence M dwarfs with β and γ gravity classes. These suggest an age of a few 100 Myr (e.g., Cruz et al. 2009) but cannot rule out the much older ages given the large scatter of Na indices and equivalent widths of main-sequence stars.  Table 3). Such gravity class is determined primarily by its low Na I equivalent width at 1.138 µm. All the other gravity-sensitive features cannot be applied to the M4.5 near-infrared spectral type (Section 4.2), but we find those measured values mostly fall in the low-gravity envelope of the field sequence (also see Artigau et al. 2015) and line up with an INT-G classification. These suggest COCONUTS-3A likely has an age of ≈ 30 − 200 Myr but could be younger or older, given its too early spectral type and the uncertainties in the age-gravity class relation.

Rotation
This object (TIC 125245420) was observed by the Transiting Exoplanet Survey Satellite (TESS) in sectors 7 and 34 with a 30-minute cadence. However, according to Stassun et al. (2019), 83% of the measured flux from the TESS pixels It is unclear if the two bright g-band points are due to flare activity or contamination by the nearby bright source, but regardless are ignored during the calculation of periodograms. Right: Periodograms for the ZTF light curve with all combined g and r photometry (grey), the light curve with all but the high-cadence, deep-drilling data (light blue), and the light curve with only high-cadence photometry (dark blue). We detect a tentative period of 2.7 ± 0.2 hours from the r-band deep-drilling light curve and adopt this value as a lower limit for the stellar rotation period of COCONUTS-3A.
covering COCONUTS-3A is in fact from nearby contaminating sources, especially the close (10 )  We also query the Infrared Science Archive (IRSA) to obtain time-series photometry from DR11 of the Zwicky Transient Facility survey (ZTF; Bellm et al. 2019;Masci et al. 2019) in g and r bands (Figure 7). The ZTF images have 1.0 pixels and a FWHM typically less than 3.0 , allowing for COCONUTS-3A and the nearby bright star to be resolved on most nights. Following recommendations in the ZTF Science Data System explanatory supplement 4 , we removed poor-quality detections from the ZTF light curve by requiring catflags = 1. The resulting light curve has 478 data points (g = 98, r = 380) spanning 1430 days, although 274 of the r-band data come from the 3-hour continuous, deepdrilling observations on 2019 Jan 11 as part of the highcadence galactic plane survey (Kupfer et al. 2021). All ZTF images have exposure times of 30 seconds, and we applied barycentric corrections to the UTC timestamps of each im-4 http://web.ipac.caltech.edu/staff/fmasci/ztf/ztf_pipelines_deliverables.pdf age using the Astropy python package (Astropy Collaboration et al. 2013Collaboration et al. , 2018. We do not detect a significant stellar rotation period based on the Lomb-Scargle periodograms derived from the light curves of combined g and r photometry or from the ones of individual bands, likely because the observed time-series photometry is sparsely sampled. Excluding the high-cadence data, the ZTF light curve for COCONUTS-3A has an average observing cadence of 4.7 days. However, the r-band deepdrilling light curve itself exhibits variations that are consistent with a period of 2.7 ± 0.2 hours. This period is very tentative, given that the entire baseline of the high-cadence light curve is only 3 hours. We therefore place a lower limit of P rot, 2.7 hours for COCONUTS-3A, meaning its stellar rotation can be broadly consistent with M dwarfs spanning ages of a few Myr to Gyr (e.g., Rebull et al. 2018). Table 2 summarizes the age estimates from stellar activity (Hα, X-ray, and UV emission), kinematics, photometry, and spectroscopic features. We adopt a final age of 100 Myr−1 Gyr for the COCONUTS-3 system.

Spectral Type and Surface Gravity Classification
We first determine the quantitative near-infrared spectral type of COCONUTS-3B using two index-based methods from Burgasser et al. (2006) and Allers & Liu (2013). Burgasser et al. (2006) (2007) later extended this system to spectral types of L0−T8 using polynomial fits to these indices. Following this system, we determine a spectral type of L6.1±1.8 and L6.0±1.3 for COCONUTS-3B based on its SpeX prism and GNIRS XD spectra, respectively, with the uncertainties in spectral fluxes and polynomial calibrations propagated in an analytic fashion ( Table 4).

established a near-infrared classification system for T dwarfs based on five H 2 O-band and CH 4 -band features, and Burgasser
The Allers & Liu (2013) classification system is based on four H 2 O-band indices and is applicable to spectral types of M4−L8. Only one index (H 2 OD) provides a reliable classification for >L2 dwarfs as the other three indices saturate at L2−L8 types (see Figure 6 of Allers & Liu 2013). We determine an H 2 OD-based spectral type of L5.0±0.8 and L5.2±0.7 for COCONUTS-3B using its SpeX and GNIRS spectra, respectively, which are consistent with those derived from the Burgasser et al. (2006) system.
We then derive the Allers & Liu (2013) gravity classification (see Section 4.5.8) of INT-G for both SpeX prism and GNIRS XD spectra. The derived gravity class lines up with the moderately young age of the primary star COCONUTS-3A (Section 4.5). While field-age, dusty L dwarfs can have similar spectral slopes as their young, low-gravity counterparts (e.g., Looper et al. 2008;Kirkpatrick et al. 2010; also see In Figures 8 and 9, we determine the visual spectral type and gravity class of COCONUTS-3B by comparing its SpeX prism and GNIRS XD data to the following spectral standards: (1) L5−L8 FLD-G dwarfs (Kirkpatrick et al. 1999;Cruz et al. 2003;Cushing et al. 2005 Kirkpatrick et al. (2010) spectral standards based on χ 2 values. Their derived spectral type was based on the best match, 2MASS 0103 + 1935, which had an L7 spectral type initially assigned by Kirkpatrick et al. (2010) but then became the L6 INT-G standard later suggested by Allers & Liu (2013). The Schneider et al. (2017) spectral type is therefore the same as our visual classification result. Cruz et al. (2018) have suggested that 2MASS 0103+1935 has no low-gravity spectral features in the optical wavelengths and thus might not be an appropriate L6 INT-G standard. This will only impact our visual gravity classification of COCONUTS-3B, but the low surface gravity of our companion is also supported by the quantitative spectral indices and equivalent widths of its gravity-sensitive features based on Allers & Liu (2013), its very red near-infrared colors, and the moderately young age of COCONUTS-3A.
Combining our index-based and visual spectral classification, we adopt an L6±1 INT-G as the final near-infrared spectral type for COCONUTS-3B.

Bolometric Luminosity and Synthesized Photometry
We determine the bolometric luminosity of COCONUTS-3B by integrating its spectral energy distribution (SED). We first flux-calibrate both SpeX prism and GNIRS XD spectra of the companion using its observed VHS K S magnitude. Then we construct an SED by combining the object's 0.9 − 2.4 µm SpeX prism spectrum with broadband fluxes from z P1 and CatWISE W 1 and W 2 photometry. We linearly interpolate fluxes to fill in the wavelength gaps between spectra and broadband fluxes. At shorter wavelengths than z P1 , we linearly extrapolate the SED to zero flux at zero wavelength, and at longer wavelengths beyond W 2 (with a cut at 1000 µm), we append a Rayleigh-Jeans tail. We compute the bolometric luminosity of log(L bol /L )= −4.451 ± 0.002 dex, with the uncertainties of SED fluxes and the host star's parallax propagated in a Monte Carlo fashion. We also construct the SED using the companion's GNIRS XD data with wavelengths of 0.95 − 1.35 µm, 1.45 − 1.8 µm, and 1.95 − 2.4 µm to avoid spectra with low S/N and significant telluric features. Integrating this GNIRS-based SED leads to a consistent L bol with the SpeX-based value within 1σ.
To examine the systematic error of our computed L bol , we apply the same SED analysis to a set of  atmospheric model spectra whose fluxes are scaled at the substellar surface, spanning T eff = 1000 − 1600 K (100 K intervals), log(g)= 4 and 5 dex, and f sed = 1 and 2. These physical parameters are close to properties of COCONUTS-3B (see Sections 5.3 and 5.4). We synthesize z P1 , W 1, and W 2 broadband fluxes for each model spectrum, and then we tailor the spectral resolution and wavelength range of the models to match those of our SpeX and GNIRS data used for the aforementioned SED construction. We also conduct the same linear interpolation and extrapolation to generate model-based SED fluxes spanning 0−1000 µm. By integrating our emulated SED at each model grid point, we compute the bolometric flux F bol and then compare with the original model value of F bol,true = σT 4 eff , where σ is the Stefan-Boltzmann constant. Among all grid points, we find the mean and standard deviation of log (F bol,true )−log (F bol ) is −0.003 ± 0.033 dex for SpeX-based SEDs, and is −0.010 ± 0.033 dex for GNIRS-based SEDs. These differences in logarithmic bolometric fluxes between the computed values from emulated SEDs and the original values equal to the differences in logarithmic bolometric luminosities. We therefore adopt a systematic error of 0.03 dex for our SED-based L bol and derive a bolometric luminosity of log(L bol /L )= −4.45 ± 0.03 dex for COCONUTS-3B.
We also synthesize 2MASS and MKO magnitudes for COCONUTS-3B using its spectra and VHS photometry following Section 4.4. For each broadband X in {J 2MASS , H 2MASS , K S,2MASS , Y MKO , J MKO , H MKO , K MKO }, we use each of the companion's SpeX prism and GNIRS XD spectra to compute two colors, X − J and X−K S , with J and K S bands from VHS. Spectral flux uncertainties are propagated into these computed colors in a Monte Carlo fashion. For this calculation, we use the Vega spectrum and obtain 2MASS, MKO, and VHS filters from Cohen et al. (2003), Hewett et al. (2006), and the ESO VISTA instrument webpage (see Section 4.4), respectively. We thus obtain four estimates of the X-band magnitude by computing J + (X − J) and K S + (X − K S ) using the SpeX and GNIRS spectra. We con-firm all these four estimates in a given band X are consistent within 1σ and compute their average and the standard deviation. For X that is not J or K band, we follow Dupuy & Liu (2012) and incorporate an additional 0.05 mag systematic error to the final synthetic photometry (see Table 1).
We find our synthesized H 2MASS = 15.89 ± 0.06 mag is brighter than the observed H 2MASS = 16.25 ± 0.18 mag by 0.36 mag (2.0σ) and our synthesized K S,2MASS = 15.02 ± 0.03 mag is fainter than the observed K S,2MASS = 14.86 ± 0.13 mag by 0.16 mag (1.2σ). These indicate that the observed H 2MASS −K S,2MASS is ∼ 0.5 mag redder than the color from our SpeX prism and GNIRS XD data, although these two spectra have consistent morphology and do not exhibit noticeable spectral variability. In addition, if we compute the VHS J−K S color using our SpeX and GNIRS spectra, then these values are both consistent with the observed J−K S color within 0.05 mag. The observed H 2MASS and K S,2MASS magnitudes of COCONUTS-3B are not blended or affected by artifact, but have modest S/N (≈ 5 − 8). We therefore recommend using our synthetic photometry in 2MASS bands. Photometric variability monitoring of this object will be valuable to investigate this discrepancy.
We compute the photometric distance of COCONUTS-3B as 32 ± 7 pc, by using its synthetic J MKO magnitude and the typical J MKO -band absolute magnitude of L6 INT-G dwarfs provided by Table 10 of Liu et al. (2016). As discussed in Section 2, this distance for COCONUTS-3B is consistent with that of COCONUTS-3A (d = 30.88 ± 0.02 pc) and validates their physical association.

Physical Properties based on Evolution Models
We infer COCONUTS-3B's effective temperature (T eff ), surface gravity (log(g)), radius (R), and mass (M) by using the hot-start  cloudy evolutionary models. These models parameterize the sedimentation efficiency of condensate particles via f sed using the Ackerman & Marley (2001) framework and include a grid of f sed = 1, 2, 3, 4, with higher f sed meaning a larger average cloud particle size, higher sedimentation efficiency, and thereby less cloud effect on the photosphere. To reproduce the photometric sequence of MLT-type ultracool dwarfs,  also produced a suite of "hybrid" models with f sed = 1 for T eff 1400 K and f sed = 4 for T eff 1200 K. For 1200 < T eff < 1400 K, they interpolated the surface boundary condition in T eff using the f sed = 2 models at T eff = 1400 K and the cloudless models at T eff = 1200 K.
We assume COCONUTS-3B's age follows a uniform distribution spanning [0.1, 1.0] Gyr (Section 4.5) and its log(L bol /L ) follows a normal distribution of N(µ = −4.45, σ 2 = 0.03 2 ). We draw random age and log(L bol /L ) values from these distributions to linearly interpolate the grid of physical parameters predicted by the  hybrid evolution models at these ages and log(L bol /L ). Such interpolation is conducted logarithmically for the T eff values. Computing the median and 16to-84 percentile intervals of the interpolated model parameters, we derive T eff = 1362 +48 −73 K, log(g)= 4.96 +0.15 −0.34 dex, R = 1.03 +0.12 −0.06 R Jup , and M = 39 +11 −18 M Jup as the evolutionbased physical properties of COCONUTS-3B.
Our derived physical properties will inevitably carry any systematic errors in the evolution model predictions. Dupuy et al. (2009Dupuy et al. ( , 2014 measured dynamical masses of two binaries composed of mid-L brown dwarfs, HD 130948BC (L4+L4) and Gl 417BC (L4.5+L6), based on orbit monitoring. These two binaries are both companions to solar-mass host stars and thus have independently known ages. Simi-lar to our analysis of COCONUTS-3B, Dupuy et al. used these L dwarfs' ages and observed bolometric luminosities to infer their masses from several evolution models. However, they found the evolution-based masses are higher than their directly measured values by ≈ 25% for the  hybrid evolution models. Recently, Brandt et al. (2019) and Brandt et al. (2021) further expanded the dynamical mass sample by combining radial velocities, relative astrometry, and the Hipparcos-Gaia accelerations of several systems hosting brown dwarf companions, including three L dwarfs, HR 7672B (L4.5; Liu et al. 2002), HD 33632Ab (L9.5 +1.0 −3.0 ; Currie et al. 2020), and HD 72946B (L5.0±1.5; Maire et al. 2020). These objects' masses predicted by  hybrid evolution models given their ages and L bol are all consistent with their dynamical masses, although these L dwarfs have older ages (≈ 2 Gyr) than HD 130948BC and Gl 417BC (≈ 800 Myr). If the evolution-based properties of COCONUTS-3B suffer from the same systematic errors as HD 130948BC and Gl 417BC, then its true mass might be as low as ∼ 30 M Jup .
In addition, we note our derived physical properties of COCONUTS-3B are based on solar-metallicity evolution models while its host star has slightly super-solar bulk metallicity (Section 4.3). To estimate this metallicity effect, we re-compute the physical properties of COCONUTS-3B using two classes of the cloudless  evolution models with [Fe/H]= 0 dex and +0.3 dex. Switching models from solar to a super-solar metallicity, COCONUTS-3B will have a 21 K cooler T eff , a 0.04 dex lower log (g), a 0.03 R Jup larger R, and a 2 M Jup smaller M. These systematic differences are all much smaller than the uncertainties of our derived properties.

Model Spectra
To examine whether the  models can sufficiently interpret the atmospheres of mid-to-late-L dwarfs like COCONUTS-3B, we construct the  atmospheric model spectra at this companion's evolution-based physical properties. Specifically, we linearly interpolate the model spectra using the distributions of T eff and log(g) computed in Section 5.3 and then scale these models by the companion's evolution-based R and COCONUTS-3A's parallax. As demonstrated in Zhang et al. (2020) and Zhang et al. (2021c), the difference between these evolution-based model spectra and the objects' observed spectra can reveal the shortcomings of the assumptions adopted by model atmospheres. Figure 10 compares the SpeX prism spectrum and broadband fluxes of COCONUTS-3B to the evolution-based  model spectra with f sed = 1, 2, 3.

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x R p w F 7 L 0 q P n / b 2 y / T g p O Z P K 9 + 8 d 9 9 3 C + w + L S 8 u N j y u f V t e a 6 x u X s q g E h T 4 t e C G u E y K B s x z 6 i i k O 1 6 U A k i U c r p L b 7 9 P + 1 R 8 Q k h X 5 h Z q U M M z I O G c p o 0 R Z K 2 6 a i 1 h H I s O Q p g b 3 c B B 2 2 7 / 1 1 8 6 R i f X + Y W g i P O v + N H s R t o s X Y z 0 2 v Y 7 3 r W s p 3 w s O p p z v h Z 1 n c g R / a / a 8 F 3 h + W F P t m v K 7 z 9 R 5 r E + r 0 p i 4 2 b L 2 r P B b E c x F C 8 3 r L G 7 e R a O C V h n k i n I i 5 S D w S z X U R C h G O Z h G V E k o C b 0 l Y x h Y m Z M M 5 F D P Y j J 4 1 z o j n B b C 7 l z h m f v v h C a Z l J M s s W R G 1 I 1 8 3 Z u a / + s N K p U e D T X L y 0 p B T u u D 0 o p j V e B p 5 n j E B F D F J 1 Y Q K p i 9 K 6 Y 3 R B C q 7 M 8 0 b A j B 6 y e / F Z d t L w i 9 9 q 9 O 6 / h k H s c S 2 k G f 0 R c U o E N 0 j H 6 g M 9 R H F D 0 4 y 8 6 G s + k 8 u q v u l r t d o 6 4 z n 9 l E L 8 r F T 0 T U s Y A = < / l a t e x i t > P1 W1 W2 Figure 10. The SpeX prism spectrum of COCONUTS-3B (black) as compared to the evolution-based  model spectra described in Section 5.4.1, with fsed= 1, 2, 3 models displayed in red, brown, and blue, respectively. We use colored solid lines and shadows to present the median and 68% confidence intervals of the model spectra constructed at the evolution-based Teff, log(g), R of COCONUTS-3B. We also synthesize zP1, W 1, and W 2 fluxes using these models (colored circles) and compare them with the observed photometry (black circles). The SED of COCONUTS-3B can be best matched by atmospheric models with fsed= 1, suggesting the companion retains ample condensate clouds in its photosphere. Figure 11 further examines the moderate-resolution spectral features by comparing these models to the GNIRS XD data. The spectrophotometry of COCONUTS-3B is best described by dusty atmospheres with f sed = 1, although such models produce slightly brighter z P1 -band and fainter W 1band fluxes than observed values. Also, these f sed = 1 models predict too shallow depths for Na I and K I resonance lines in J band and a slightly bluer K-band spectral slope than the data. These differences are very likely due to the older version of the opacity database (e.g., Freedman et al. 2008) for the alkali lines (in red optical and J bands), CH 4 (in H, K, and W 1 bands), and collision-induced H 2 absorption (in K band) adopted by . New sets of cloudy models that incorporate the updated opacities (e.g., Saumon et al. 2012;Ryabchikova et al. 2015;Allard et al. 2016Allard et al. , 2019Yurchenko et al. 2013;Yurchenko & Tennyson 2014) will likely improve the consistency between model predictions and observations, leading to more reliable estimates of these objects' physical properties via atmospheric modeling.

Comparison with Previously Known Ultracool Benchmarks
To place our discovery in the context, we compare the photometry of COCONUTS-3B to that of L6−Y1 benchmarks compiled by Zhang et al. (2020) and Zhang et al. (2021a) in Figure 12. These benchmarks include wide-orbit comoving companions to stars, kinematic members of nearby young moving groups, and components of substellar binaries with dynamical masses. All of these objects have independently known ages or masses which are usually impossible to determine for free-floating single brown dwarfs in the field. We also compare the J-band absolute magnitude and J − K color of COCONUTS-3B to the photometric sequences of FLD-G, INT-G, and VL-G ultracool dwarfs from Liu et al. (2016). COCONUTS-3B has slightly brighter and bluer near-infrared photometry than L6 VL-G objects, but is much fainter and redder than their FLD-G counterparts. Also, the J MKO − K MKO = 2.11 ± 0.02 mag of COCONUTS-3B is among the reddest of all ultracool benchmarks with ages older than a few 100 Myr. COCONUTS-3B is in fact simi-  Figure 11. The GNIRS XD spectrum of COCONUTS-3B (black) as compared to the evolution-based  model spectra (colored; same as those shown in Figure 10) in individual JHK bands. All spectra are normalized by their mean values within each band. The data are best matched by fsed= 1 models, although these models predict too shallow depths in Na I and K I resonance lines in J band and slightly bluer spectral slope in K band than the observation. The absorption feature at ∼ 1.66 µm predicted by models is likely due to the incomplete CH4 line list used by  models. lar to the brown dwarf companion HD 206893B, which has a moderately young age (50 − 700 Myr based on its host star) and an extremely red near-infrared color (Milli et al. 2017;Delorme et al. 2017). 5 Field-age, high-gravity L6 dwarfs have a typical log(L bol /L ) of −4.37 ± 0.14 dex and a T eff of 1483 ± 113 K based on polynomial fits in Zhang et al. (2020) and Filippazzo et al. (2015), respectively. COCONUTS-3B has a 0.08 dex (0.5σ) fainter bolometric luminosity and a 121 K (1.0σ) cooler effective temperature compared to its high-5 Delorme et al. (2017) synthesized HD 206893B's J S -band magnitude from their VLT/SPHERE IFS spectroscopy (R ∼ 30) with S/N≈ 10 and measured K1 and K2-band magnitudeS using IRDIS data, leading to very red colors of J S − K1 = 3.13 ± 0.20 mag and J S − K2 = 3.45 ± 0.19 mag. We synthesize the J S − K1 = 1.969 ± 0.004 mag and J S − K2 = 2.220 ± 0.004 mag for COCONUTS-3B using its SpeX prism spectrum, the dualband K12 filters of SPHERE IRDIS, and a virtual J S filter with 100% transmission spanning 1.2−1.3µm adopted by Delorme et al. (2017). COCONUTS-3B is thus bluer than HD 206893B, but still redder than fieldage late-L dwarfs (see Figure 7 of Delorme et al. 2017).

COCONUTS-3B (GNIRS XD
gravity counterparts with similar spectral types. The companion's lower T eff , faint absolute magnitude, and red colors are in accord with its moderately young age, intermediate surface gravity, and dusty atmospheres, given that properties of L/T transition objects are known to be surface gravity dependent (e.g., Metchev & Hillenbrand 2006;Marley et al. 2012;Faherty et al. 2016;Liu et al. 2016).

Formation Scenario
Formation of planetary-mass and substellar companions that reside on very wide orbits (a few 100−1000 au) is intriguing. These companions might form in situ like components of stellar binaries via fragmentation of the collapsing proto-stellar clouds (e.g., Kroupa 2001;Chabrier 2003). Alternatively, they might form like closer-in exoplanets via core/pebble accretion or disk gravitational instability and then scatter outward to large orbital separations due to dynamical interactions with other system components (e.g., Boss 2006;Veras et al. 2009). For the COCONUTS-3 system, it is very likely that the companion formed in a star-  Zhang et al. (2020) and Zhang et al. (2021a) with ages of > 300 Myr (orange) and 300 Myr (blue), as well as the photometric sequences of L1−L6 dwarfs with FLD-G (orange), INT-G (black), and VL-G (blue) gravity classes. We overlay the photometry of field dwarfs (grey) with M, L, T, Y spectral types obtained from the UltracoolSheet (Best et al. 2020b), which have S/N> 5 in MJ and J − K and are not young, binaries, or subdwarfs. We label all benchmarks with the same spectral type (L6) as COCONUTS-3B, including HIP 9269B   Chiu et al. 2006;Dupuy et al. 2015), LP 261−75B (Kirkpatrick et al. 2000;Reid & Walkowicz 2006), 2MASS J2244+2043 (Dahn et al. 2002), andCalar 21 andCalar 22 (Zapatero Osorio et al. 2014). The J − K color of COCONUTS-3B is among the reddest compared to all benchmarks with ages of a few 100 Myr or older. like fashion, given that the companion's mass of ≈ 40 M Jup is 10× larger than the expected total mass of protoplanetary disks surrounding low-mass (≈ 0.1 M ) M dwarfs like COCONUTS-3A (e.g., Ansdell et al. 2016;Pascucci et al. 2016;Manara et al. 2018). In addition, a companion-tohost mass ratio of 0.29 ± 0.10 for the COCONUTS-3 system is much higher than those of directly imaged exoplanets ( 0.04; e.g., Marois et al. 2008Marois et al. , 2010Macintosh et al. 2015;Bohn et al. 2020Bohn et al. , 2021; also see Figure 3 of Zhang et al. 2021b).

CONCLUSION
We have reported the third discovery from our COol Companions ON Ultrawide oribiTS (COCONUTS) program. The COCONUTS-3 system is composed of a young M-dwarf primary star with strong Hα and X-ray emis-sion, as well as an unusually red L-dwarf companion which was previously identified as the free-floating object WISEA J081322.19−152203.2 by Schneider et al. (2017). Given the consistency in proper motions and distances, we confirm the physical association between A and B components and compute a projected separation of 61 (1891 au). Based on the primary star's optical and near-infrared spectrophotometry, we derive its physical properties (e.g., T eff, = 3291 ± 49 K and M = 0.123 ± 0.006 M ) and a slightly super-solar metallicity of [Fe/H] = 0.21 ± 0.07 dex. We note this [Fe/H] is derived using empirical calibrations established by older and higher-gravity M dwarfs, and could be under-estimated by 0.2 − 0.3 dex according to PHOENIX stellar models given COCONUTS-3A's younger age and lower surface gravity. Combining the host star's stellar activity, kinematics, HR diagram position, lithium absorption, and surface gravity-sensitive spectroscopic features, we estimate an age of 100 Myr to 1 Gyr for the COCONUTS-3 system.
We also study the near-infrared spectra of COCONUTS-3B and derive a spectral type of L6 with an intermediate surface gravity classification (INT-G). Based on the companion's observed bolometric luminosity and its host star's age, we use the hot-start  hybrid evolution models to infer the physical properties of COCONUTS-3B to be T eff = 1362 +48 −73 K, log(g)= 4.96 +0.15 −0.34 dex, R = 1.03 +0.12 −0.06 R Jup , and M = 39 +11 −18 M Jup . It has been recently suggested that the ultracool evolution models tend to overpredict the mass at a given L bol and age by ∼ 25% for moderately young brown dwarfs (< 1 Gyr) based on two substellar binary systems with directly measured dynamical masses, meaning that the true mass of COCONUTS-3B might be as low as ∼ 30 M Jup .
We construct the  atmospheric model spectra at our derived evolution-based physical properties of COCONUTS-3B and compare them with the observed spectra. We find models with f sed = 1 match the companion's spectrophotometry, although these models predict slightly brighter fluxes in the red optical, shallower depths for alkali resonance lines, bluer K-band spectral slope, and fainter fluxes near 3.3 µm. These data-model differences are very likely due to the older version of the opacity database used by  and new sets of cloudy models that incorporate the theoretical advances over the past decade will likely improve the consistency between data and model predictions.
Compared to field-age, high-gravity L6 dwarfs, COCONUTS-3B has much fainter absolute magnitudes, similar bolometric luminosity, and a 120 K cooler effective temperature. This companion's J − K color is among the reddest of ultracool benchmarks with ages older than a few 100 Myr. These anomalous spectrophotometric and physical properties are in accord with its intermediate surface gravity, dusty atmosphere, and moderately young age, given the surface gravity dependence of the L/T transition.
Similar to stellar binaries, the COCONUTS-3 system likely formed via fragmentation processes of the collapsing proto-stellar clouds, given the companion's mass and the large companion-to-host mass ratio (0.29 ± 0.10). Under this formation scenario, COCONUTS-3B is expected to share the bulk metallicity and elemental abundances (e.g., C/O) as its host star. Modeling spectroscopy of COCONUTS-3B and comparing the resulting chemical properties to those of COCONUTS-3A can directly quantify the systematic errors of substellar and exoplanet model atmospheres. Expanding such calibration to a large ensemble of wide-orbit companions will enable thorough examination of model atmospheres over a wide parameter space, and these empirically calibrated models will lead to robust characterization of the atmospheric properties and formation of directly imaged exoplanets.
Z.Z. thanks Didier Saumon for sharing the  atmospheric model spectra; Andre-Nicolas Chene and Bin Yang for helpful discussions about the Gemini/GMOS data reduction; Eric Mamajek for discussions about typical photometric properties of dwarf stars; Andrew Mann for discussions about the empirical metallicity calibrations of young low-mass stars; Eunkyu Han for discussions about the magnetic fields in M dwarfs; Adam Kraus and Brendan Bowler for helpful comments on the manuscript. Z.P.V. acknowledges the Heising-Simons Foundation for postdoctoral scholar support at Caltech. This work has benefited from The UltracoolSheet at http://bit.ly/UltracoolSheet, maintained by Will Best, Trent Dupuy, Michael Liu, Rob Siverd, and Zhoujian Zhang, and developed from compilations by Dupuy & Liu (2012), Dupuy & Kraus (2013), Liu et al. (2016), Best et al. (2018), andBest et al. (2021). This research has benefitted from the Ultracool RIZzo Spectral Library (http://dx.doi. org/10.5281/zenodo.11313), maintained by Jonathan Gagné and Kelle Cruz. This research has benefitted from the Montreal Brown Dwarf and Exoplanet Spectral Library, maintained by Jonathan Gagné. This work is based in part on observations obtained at the international Gemini Observatory, a program of NSF's NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). This research has made use of the NASA/IPAC Infrared Science Archive, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. 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.  (Riedel et al. 2017), TOPCAT (Taylor 2005), Astropy (Astropy Collaboration et al. 2013, 2018, IPython (Pérez & Granger 2007), Numpy (Oliphant 2006), Scipy (Jones et al. 2001), Matplotlib (Hunter 2007). We highlight a few equal-Teff tracks in each panel, with a sequence of 3000 K (blue), 2800 K (orange), 2600 K (purple), and 2400 K (green) for the Mann et al. (2014) calibration, and 3600 K (blue), 3400 K (orange), 3200 K (purple), and 3000 K (green) for the Newton et al. (2014) calibration. In each panel, we also label the mean and standard deviation (inside the parenthesis) of the computed empirical [Fe/H] at each log (g).
COCONUTS-3A. The metal-sensitive lines (e.g., Na I doublet at 2.2µm) adopted by these calibrations are also sensitive to the surface gravity, meaning that our derived [Fe/H] may be unreliable. Here we use stellar model atmospheres to explore the surface-gravity dependence of the empirical calibrations of low-mass stellar metallicity as developed by Mann et al. (2013;M13), Mann et al. (2014;M14), and Newton et al. (2014;N14).
We base our analysis on the PHOENIX synthetic model spectra (Husser et al. 2013) over a parameter space of [2300, 4500] K in T eff , [3.5, 5.5] dex in log (g), and [−1.0, +0.5] dex in [Fe/H] with intervals of 100 K, 0.5 dex, and 0.5 dex, respectively. We choose the range of T eff to cover the applicable spectral types (K5-M9.5) of all empirical calibrations considered here. The log (g) is also a proxy of stellar age, with log (g) = 5.5 dex corresponding to field ages (> 1 Gyr), 5.0 dex for moderately young ages of 100 Myr to 1 Gyr, and 4.5 dex and 4.0 dex for very young ages of 5 − 100 Myr over the aforementioned parameter space (based on the evolution models of Baraffe et al. 2015). We downgrade the spectral resolution of these models to match that of SpeX SXD and put the model wavelengths in vacuum following Ciddor (1996). We then apply each calibration method to compute the empirical [Fe/H] emp for all model spectra that satisfy the method's applicable range in spectral type and metallicity. Specifically, we apply (1) the J/H/K-band calibration of M13 to PHOENIX models with 4500 K T eff 3000 K (i.e., K5-M5) and −1.04 dex [Fe/H] +0.56 dex; (2) the M14 calibration to models with 3100 K T eff 2300 K (i.e., M4.5-M9.5) and −0.58 dex [Fe/H] +0.56 dex; (3) the N14 calibration to models with 3700 K T eff 3000 K (i.e., M1-M5) and −1.00 dex [Fe/H] +0.35 dex. The conversion between stellar effective temperatures and spectral types is based on the mean stellar properties compiled by E. Mamajek 6 (also see Pecaut & Mamajek 2013).
In Figures 13 and 14 Veyette et al. 2017). These mismatches are likely due to the systematic uncertainties of stellar model atmospheres and the adopted opacity line lists (e.g., Figure 11 of Czekala et al. 2015) and that the calibrations considered here are all tied to the SpeX SXD instrument rather than PHOENIX models. In other words, our analysis re-affirms the value of empirical metallicity calibrations as opposed to a purely model-based characterization.
Here we only focus on the trend (instead of the absolute values) of [Fe/H] emp with respect to log (g). We first discuss the surface-gravity effect on the N14 and M14 calibrations (Figure 13), which we use to derive [Fe/H] of COCONUTS-3A. For models with [Fe/H]= 0 dex and +0.5 dex, the M14 calibration (applied to 3100-2300 K) tends to derive a smaller [Fe/H] emp toward lower surface gravities or younger ages. Specifically, compared to the case with log (g) = 5.5 dex (i.e., field age), the M14-based [Fe/H] emp is smaller by 0.2-0.3 dex for the lower log (g) of 5.0 dex and by 0.5-0.6 dex for log (g) of 4.0 dex or 4.5 dex. The N14 calibration (applied to 3700-3000 K) exhibits a similar trend with surface gravities for models with [Fe/H]= −1.0 dex (except for ones with T eff = 3000 K), −0.5 dex, and 0 dex. COCONUTS-3A has T eff ≈ 3000 K and log (g) ≈ 5.0 dex (Section 4.4), so our derived [Fe/H] emp might be under-estimated by 0.2 − 0.3 dex according to these PHOENIX models. Qualitatively, this underestimate is expected since a lower surface gravity can cause weaker strengths of the Na I doublet for early-to-mid M stars (e.g., Luhman et al. 1998;Newton et al. 2014) and the [Fe/H] values by both M14 and N14 calibrations monotonically decrease with decreasing equivalent widths of Na I (as long as this equivalent width is below 7.5 Å when applying the N14 calibration).
Interestingly, surface gravity imposes an opposite effect on the M14 calibration for models with [Fe/H]= −0.5 dex as compared to ones at higher metallicity (i.e., 0 dex and +0.5 dex), where the M14-based [Fe/H] emp tends to be larger with decreasing surface gravities. This means that the gravity dependence of the Na I doublet strengths at [Fe/H]= −0.5 dex and T eff < 3000 K is different from the case with higher [Fe/H] and/or hotter T eff , according to the PHOENIX models.
The M13 calibrations ( Figure 14) also tend to derive smaller [Fe/H] emp toward lower surface gravities for models with cool T eff ( 3600 K) and solar or super-solar [Fe/H]. For hot, sub-solar models with T eff of 4000 K and [Fe/H] of −0.5 dex and −1 dex, the M13-based [Fe/H] emp can be comparable or even larger toward lower log (g) compared to the case with log (g) = 5.5 dex.
Our analysis aims to provide a qualitative perspective about the surface-gravity dependence of the empirical metallicity calibrations. We caution that the quantitative log (g) dependence revealed by our work should not be directly used as correction factors to the computed [Fe/H] emp , given that the systematics of the stellar model atmospheres likely change with surface gravities and effective temperatures as well. Also, compared to field-age low-mass stars, younger lower-gravity stars tend to be more active and possess stronger magnetic fields, which can alter the metal-sensitive line profiles and enhance the equivalent widths (and thus the resulting [Fe/H]) via Zeimann broadening and intensification (e.g., Basri et al. 1992;Basri & Marcy 1994;Kochukhov 2021;López-Valdivia et al. 2021). Estimation of the bulk metallicity for low-gravity low-mass stars would benefit from an empirical calibration customized for young stars, which is unfortunately not available to date. We note this calibration is difficult to construct with the existing sample of nearby young stars, which lacks sufficiently large variations in [Fe/H] and mostly has solar metallicity.

B. ESTIMATED X-RAY EMISSION FROM BACKGROUND STARS NEAR COCONUTS-3A
Searching around COCONUTS-3A, we find a source 2RXS J081318.4−152252 (2RXS J0813−1522) in the Second ROSAT All-Sky Survey and its counterpart 1RXS J081318.4−152250 (1RXS J0813−1522) in the ROSAT All-Sky Survey Faint Source Catalog (Voges et al. 2000), with the latter catalog reporting a position error of 15 . COCONUTS-3A is the closest match to both X-ray detections, with an angular separation of 13.8 and 12.2 , respectively. Seven background sources are also within 30 of 2RXS J0813−1522 but six are outside the 15 position error. Here we quantify the potential X-ray fluxes of all these background stars to assess whether the ROSAT detection comes from COCONUTS-3A. Figure 5 and Table 5 present coordinates and photometry of the background sources (with distances of 2 − 12 kpc from Gaia EDR3), including six FGK dwarfs and one K-type giant star based on their HR diagram positions. For the dwarf stars, we convert BP−RP into spectral types and then obtain typical B−V and bolometric luminosities, by using the mean stellar colors and properties compiled by E. Mamajek (see footnote 6 and Pecaut & Mamajek 2013). We estimate the maximum possible X-ray fluxes of these objects by assuming their X-ray emission are in the saturated regime. We obtain the saturated log (L X /L bol ) for each star based on Jackson et al. (2012) using the objects' B−V colors. We then compute the X-ray flux from each background dwarf star, with uncertainties in log(L bol /L ), log (L X /L bol ), and distances propagated accordingly. The remaining giant star (BG2, TYC 5996−1259−1) falls in the asymptotic giant branch, evolving across the X-ray dividing line, and thereby has faint intrinsic X-ray emission. According to Maggio et al. (1990), K giants have an X-ray-to-V -band flux ratio of log (F X /F V )< −6.2, where log (F X /F V )= log ( f X ) + 0.4V + 5.47. We use this object's observed V = 11.57 ± 0.14 mag to compute its maximum possible X-ray flux.