Investigating Possible Binarity for GJ 229B

GJ 229B is noted for being the first type-T brown dwarf to be discovered (Nakajima et al. 1995), ⁵ with a measured effective temperature well below the L/T transition, ∼1200 K. Yet its atmospheric structure and composition have been less thoroughly studied than now-more-standard benchmark objects such as the similar GJ 570D (e.g., Line et al. 2015). This may be owing to its peculiar spectrum, which shows unusually weak H₂O and CH₄ features for its spectral type (Burgasser et al. 2006) and elevated levels of CO (Oppenheimer et al. 1998).

Dynamical measurements of the mass of GJ 229B have also yielded surprising results, with the most precise recent analysis finding a value of 71.4 ± 0.6 M_J (Brandt et al. 2021). This measurement was based on Gaia EDR3 data combined with several other astrometric and radial velocity data sets, resulting in an uncertainty significantly less than previous results. Yet it is incompatible with evolutionary models, as an object of that mass could not cool to the observed temperature of GJ 229B within a Hubble time. Meanwhile, an independent analysis of radial velocities alone found a minimum mass of only 1.62 M_J (Feng et al. 2020). Reconciling such a small minimum mass with the astrometric results requires fine-tuning the orbit solution with an orientation within ∼2° of face-on.

A newer analysis of the combined astrometric and radial velocity (RV) data set was undertaken with the addition of the Gaia–Hipparcos positional difference by Feng et al. (2022). This analysis found a dynamical mass for GJ 229B of . This mass is somewhat more plausible in terms of fitting evolutionary models. However, it still strongly precludes fitting the observed dynamical mass, effective temperature, and luminosity (and by proxy radius) simultaneously.

Recently, we undertook a spectroscopic retrieval study of GJ 229B’s atmosphere with our APOLLO atmospheric retrieval framework (Howe et al. 2022), supplemented by an analysis incorporating the Sonora–Bobcat (S-B) grid of brown dwarf evolutionary models by Marley et al. (2017). This study showed that both spectroscopic retrieval measurements and evolutionary model fits return dramatically lower masses than the dynamical fits, with a retrieved mass estimate of 41.6 ± 3.3 M_J . We also obtained an unexpectedly large radius estimate 1.105 ± 0.025 R_J (which is also implied by the luminosity and effective temperature of the object), which is inconsistent with evolutionary models of either mass, both of which predict a more compact object.

With such a large disparity in mass measurements, the most natural explanation would appear to be that GJ 229B is in fact a binary brown dwarf of unequal mass, with one component contributing most of the total flux to the spectrum, while the other contributes just enough flux to boost the apparent radius. This sort of discrepancy has been observed before for other objects, with binarity suggested as a solution to anomalously large retrieved radii (Line et al. 2017) and overall flux (Burgasser et al. 2008), so a similar solution seems likely for GJ 229B. In this Letter, we explore the possible parameter space for a binary GJ 229B using two different grid-fitting methods based on the S-B evolutionary models (Marley et al. 2017) and the APOLLO retrieval code, extending our analysis from Howe et al. (2022). First, we fit the observed spectrum of GJ 229B (Geballe et al. 1996; Noll et al. 1997; Schultz et al. 1998; Oppenheimer et al. 1998) to binary spectra derived from the S-B model grid directly. These atmosphere models are self-consistent, but do not account for the peculiar chemistry of GJ 229B or the supersolar C/O ratio found by Howe et al. (2022). Second, we generate a grid of APOLLO forward models for a binary object based on values for radius, gravity, and temperature structure from the S-B evolutionary tracks, but using our retrieved molecular abundances from Howe et al. (2022). For completeness, we consider fits using both the M_tot = 71 M_J and M_tot = 60 M_J dynamical mass measurements.

For each of these grids, we compute goodness-of-fit statistics for comparison to the observed spectrum of GJ 229B, and we find that both grid fits return qualitatively similar results. In the M_tot = 71 M_J case, we find a primary mass of 51 M_J (q = 0.39) using both methods. The M_tot = 60 M_J case shows modest differences, with M₁ = 46 M_J (q = 0.30) for S-B and M₁ = 49 M_J (q = 0.22) for APOLLO. Given this consistency between our two methods and the physical arguments against a single-object solution, we consider this to be significant evidence for a binary solution for this object.

The results from the two model grid fits are shown in Section 2, with an explanation of the limitations of our model in Section 3. We discuss the implications of our results in Section 4 and summarize our conclusions in Section 5. A full description of the data set we use in this paper is included in Howe et al. (2022).

We constructed two grids of spectra for binary brown dwarfs based on the solar-metallicity evolutionary tracks of the S-B model set (Marley et al. 2017). To create these spectra, we linearly interpolated the S-B tracks to a grid of 1 M_J in mass and 10 K in primary effective temperature. For each grid point in the resulting “S-B grid,” we computed a primary spectrum and two secondary spectra by interpolating the nearest S-B spectra provided in the parameter space for two brown dwarfs of equal age and masses summing to 60 and 71 M_J . Likewise, for each grid point in the “APOLLO grid,” we computed forward models using APOLLO for the same radii, surface gravities, and temperature profiles from the S-B models combined with our retrieved molecular abundances from Howe et al. (2022). Thus, we used the same evolutionary tracks for both grids, but two different, incomplete, but complementary chemistry models.

For each grid and each case (60 and 71 M_J ), we summed the primary and secondary spectra together to create a grid of model binary spectra. We then computed the goodness of fit to the observed spectrum of GJ 229B using a reduced chi-squared statistic. We chose the reduced chi-squared statistic for this analysis for its relative simplicity. However, most other measures of goodness of fit such as the Bayesian likelihood, Bayesian information criterion, and APOLLO’s own likelihood function produce virtually identical results because all of these measures are dominated by the error in the large number of spectral data points (which comprise nearly all of the >3200 degrees of freedom) rather than other statistical factors.

Heat maps of the reduced chi-squared results for both grids are shown in Figure 1 for the M_tot = 71 M_J case and Figure 2 for the M_tot = 60 M_J case, plotting primary effective temperature versus mass and age, as well as secondary effective temperature versus mass. All of the fits were found to have , but this is not an unexpected result given that we are not performing full retrievals (such as Markov Chain Monte Carlo retrievals) on the spectrum. To assess the uncertainties in these fits, we adopt 1σ errors of based on an analysis of chi-squared statistics by Beringer et al. (2012; see their Figure 36.2 and associated chapter). We mark reduced chi-squared contours on the plots of . Based on our definition, the outer contour is roughly equivalent to our 1σ uncertainties, although they are slightly different for each local minimum.

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All four grid fits result in a relatively broad minimum in spanning a width of ∼15 M_J . For example, for the S-B model grid, our 1σ uncertainties in primary mass span 44–63 M_J in the 71 M_J case and 39–54 M_J in the 60 M_J case. In all cases, the primary effective temperature falls in a significantly narrower range of ∼900–1000 K, which is consistent between the two total mass cases. Within each case, the S-B and APOLLO fits are qualitatively similar. However, the distribution for APOLLO forward models is broader in effective temperature and occurs at slightly lower temperatures overall. This is likely due to the chemistry model used for the APOLLO model grid, which assumes a constant atmospheric composition with respect to temperature, muting the effect of changing T_eff on the spectrum shape. Meanwhile, the realistic changes in chemistry in the S-B grid are likely to produce worse spectral fits at nonoptimal temperatures, as would be expected.

The parameters of the best fits from our model grids are listed in Tables 1 and 2 for the 71 and 60 M_J cases, respectively. We note that while the S-B grid has a single global minimum in reduced chi-squared, in both of our cases, the APOLLO grid produces three local minima along a line of increasing mass and temperature. For completeness, we list all three of the APOLLO minima for each case in Tables 1 and 2. These are compared with our best single-object free retrieval from Howe et al. (2022), and reduced chi-squared values are listed for all of the fits. Including the three APOLLO fits is also useful in that they are representative of our 1σ uncertainty distributions as a whole.

Table 1. The Best-fit Binary Models from the Sonora–Bobcat (S-B) Model Set and Our APOLLO Forward Model Grid with a Total Mass of 71 M_J

	Binary				Single
	S-B	APOLLO 1a	APOLLO 2a	APOLLO 3	S-B	APOLLO	Free Retrieval
Primary Mass (MJ )					No Solution	No Solution	41.6 ± 3.3
Primary Teff (K)		910 ± 60		960 ± 30
Primary Radius (RJ )							1.105 ± 0.025
Primary
Secondary Mass (MJ )
Secondary Teff (K)
Secondary Radius (RJ )
Secondary
Mass Ratio (M2/M1)
Flux Ratio (F2/F1)
Age (Gyr)							>1.0
	10.37	11.81	11.14	11.54			8.15

Note. Bolometric flux ratios are calculated from the Stephan–Boltzmann law. The retrieved parameters are compared with our best-fit free retrieval for a single object (Howe et al. 2022). No solutions for a single object with a global minimum lie within either of the model grids, which we interpret as having no solution with physically plausible parameters. Uncertainties are defined by based on an analysis by Beringer et al. 2012.

^a The APOLLO 1 and APOLLO 2 models are two peaks of a shared 1σ distribution.

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Table 2. Same As Table 1, Except with a Total Mass of 60 M_J

	Binary				Single
	S-B	APOLLO 1	APOLLO 2	APOLLO 3	S-B	APOLLO	Free Retrieval
Primary Mass (MJ )					60	60	41.6 ± 3.3
Primary Teff (K)				950 ± 30		970 ± 20
Primary Radius (RJ )							1.105 ± 0.025
Primary					5.412 ± 0.002	5.416 ± 0.003
Secondary Mass (MJ )
Secondary Teff (K)
Secondary Radius (RJ )
Secondary
Mass Ratio (M2/M1)
Flux Ratio (F2/F1)
Age (Gyr)		2.6 ± 0.3					>1.0
	9.97	11.22	10.92	10.25	11.25	24.56	8.15

Note. Single-object solutions for both grid fits are listed alongside the free retrieval from Howe et al. (2022).

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In Table 2, we also include single-object fits to both of our grids, subject to the same dynamical mass constraint of 60 M_J . These fits have higher reduced chi-squared values than the binary fits, so the binary solution is still favored in this case. For the 71 M_J case, the global minimum in falls outside the distribution of allowed evolutionary models (and all models within the grid have very large ), so we consider it to have no single-object solutions.

The most notable differences between the 60 and 71 M_J cases are in the mass ratio of the binary and the inferred age of the system. The 9 M_J difference in mass between the two cases is partitioned roughly equally between the primary and secondary mass, with the overall effect being a significantly more extreme mass ratio in the 60 M_J case. The S-B best fit (which in both cases is also representative of the APOLLO best fits) in the 71 M_J case has a mass partition of 51 and 20 M_J for a mass ratio of q = 0.392. In the 60 M_J case, the mass partition is 46 and 14 M_J , with q = 0.304. Given a smaller total mass, a smaller primary mass with nearly the same T_eff has a larger radius and thus produces a larger fraction of the total flux of the binary, so a cooler and lower-mass secondary is needed to make up the difference.

Likewise, a lower-mass primary would need a shorter time to cool to the same T_eff, resulting in a younger inferred age of the system. For the S-B best fit, the difference is about 1 Gyr, reducing from 4.5 Gyr in the 71 M_J case to 3.5 Gyr in the 60 M_J case. All of the fits listed in Tables 1 and 2 fall in the range of 2.6–6.1 Gyr, somewhat older than previous estimates (e.g., Nakajima et al. 2015).

As a representative example of the spectra resulting from our grid fits, Figure 3 compares the best-fit spectra from each grid (blue and gold) and their residuals (green and red) with the observed spectrum of GJ 229B in the 71 M_J case. Both grid fits match the observed spectrum at many wavelengths; however, they both show errors in different wavelength ranges. The S-B fit shows significant residuals in the J and M bands, while the APOLLO fit shows significant residuals mainly in the Y and K bands. Note that features in the residual spectra are exaggerated in regions of low observational uncertainties, so their magnitude is more indicative of the observational precision than actual absorption features.

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The S-B model set provides a complete grid of spectra only for brown dwarf models of solar metallicity and C/O ratio. Therefore, a detailed grid fit to an observed spectrum must make compromises with regard to the chemistry. Our S-B grid fit to GJ 229B assumes an essentially solar composition, which is inconsistent with both the peculiar spectrum of this object and the retrieved molecular abundances from Howe et al. (2022). Our measured supersolar C/O ratio of 1.13 is consistent with other retrievals of T dwarfs (e.g., Line et al. 2015), but is well outside the a priori parameters of generic brown dwarf model sets such as S-B.

Additionally, the temperature–pressure (T-P) profiles in both forward model grids are interpolated from the S-B models. They are not informed by our retrieved T-P profile from Howe et al. (2022), and in the context of the grid, it is de facto a two-parameter model controlled only by T_eff and log g. This is analogous to the parametric T-P profile used in Howe et al. (2022), which we found to return relatively poor goodness-of-fit statistics, even in a full ensemble retrieval.

Meanwhile, our APOLLO grid assumes a constant molecular composition for brown dwarfs of different temperatures, as a full thermochemical model of the atmosphere is beyond the scope of APOLLO, which is designed around a free retrieval philosophy for a single object. Therefore, neither of the model grids used in this analysis fully simulate the atmospheric chemistry of GJ 229B. A fully self-consistent chemical model with supersolar C/O would be needed to model the spectrum of a binary brown dwarf to a greater accuracy than we have done in this paper.

The limitations of the chemical model for the APOLLO grid are especially significant for the secondary spectrum, which is much cooler than the effective temperature retrieved for a single-object fit. Thus, the atmospheric chemistry is expected to be quite different from our assumed abundances. In performing the fits with the APOLLO grid, we assume that the relatively smaller flux from the secondary means that it will produce a proportionately smaller error in the overall spectrum.

An additional limitation of the APOLLO-based grid was the inability of APOLLO to model atmospheres of very cold (old and low-mass) secondaries due to the low-temperature limits of our molecular optical cross-section tables. This prevented us from fully exploring the parameter space at ages ≳10 Gyr in the 71 M_J case and ≳6 Gyr in the 60 M_J . However, the contour plots in Figures 1 and 2 indicate that the best-fit models are clustered at younger ages in the region of the parameter space we did explore.

The reduced chi-squared values for our grid fits in this work are consistently significantly larger than that of our free retrieval of the single-object solution for GJ 229B in Howe et al. (2022). We attribute this to our less accurate treatment of the chemistry in both model grids, as described above, and to the simplified T-P profiles. The goodness of fit when performing a free retrieval using a parametric T-P profile was comparable to that of our grid fits in this work, which may be a result of both models being underdetermined to fully fit the observed spectrum.

We do not attempt a full retrieval of the prospective binary spectrum in this work, as would be required to make an accurate comparison of the goodness of fit between the single and binary models. The number of variables involved in retrieving properties of two independent objects from a blended spectrum is prohibitive and beyond the scope of the current version of APOLLO, and a free retrieval on a blended spectrum would likely have too many degeneracies to produce unambiguous results. Again, a full chemical model for a binary object would be needed to constrain the parameter space.

Nonetheless, we see that both of our grid fits produce similar results for best fits in M–T_eff space, and they also fit complementary wavelength regimes of the observed spectrum. The consistency of this result across two methods emphasizing different chemistry increases our confidence in the viability of our method to infer the properties of a binary brown dwarf in this context.

4.1. Physical Argument for a Binary Solution

4.2. Inferred Mass Ratio of GJ 229B in the Context of Other Brown Dwarf Binaries

4.3. Detectability of a Binary

Both spectroscopic retrievals and spectral energy distribution considerations combined with evolutionary models consistently suggest a smaller mass for the late T dwarf GJ 229B than the dynamical mass of 71.4 ± 0.6 M_J (Brandt et al. 2021), or (Feng et al. 2022), suggesting that it may be a binary object. We have employed grid-based methods using the S-B evolutionary models (Marley et al. 2017) and the APOLLO retrieval code (Howe et al. 2022) to estimate the mass ratio of a prospective binary GJ 229Ba and Bb. Our best-fit solutions for the S-B grid fits (which have the smallest reduced chi-squared values) give a mass ratio of for the 71 M_J case and for the 60 M_J case. While these ratios are fairly unequal, they do overlap with the ranges inferred for resolved brown dwarf binaries from some population studies. These fits are also consistent with an intermediate age range for the system of 2–6 Gyr.

There is a significant probability that precise astrometric and/or radial velocity measurements will be able to confirm the binarity of GJ 229B. In the absence of such measurements, a blended spectrum retrieval incorporating an equilibrium chemistry model may be able to significantly refine the mass ratio estimated in this work.

A.R.H. was supported by an appointment to the NASA Postdoctoral Program at NASA Goddard Space Flight Center, administered by Oak Ridge Associated Universities under contract with NASA. A.R.H. also acknowledges support by NASA under award No. 80GSFC21M0002 through the CRESST II cooperative agreement. A.M.M. acknowledges support from GSFC Sellers Exoplanet Environments Collaboration (SEEC), which is funded in part by the NASA Planetary Science Divisions Internal Scientist Funding Model. This work was partially supported by the GSFC Exoplanets Spectroscopy Technologies (ExoSpec), which is part of the NASA Astrophysics Science Division’s Internal Scientist Funding Model. We thank Beth Biller and Robert Haring-Kaye for helpful conversations. We also thank the anonymous referee, whose commentary has signficantly improved the thoroughness and clarity of this paper.