The Hawaii Infrared Parallax Program. III. 2MASS J0249–0557 c: A Wide Planetary-mass Companion to a Low-mass Binary in the β Pic Moving Group^{* †}

As part of our ongoing Hawaii Infrared Parallax Program at CFHT, we have been using the facility infrared camera WIRCam (Puget et al. 2004) to monitor 2MASS J0249−0557 in order to confirm the β Pic membership of the latest-type objects identified by Shkolnik et al. (2017). Because our observations were designed to measure the parallax of this relatively bright M6 dwarf, we used a narrow-band filter (0.032 μm bandwidth) in the K band. We refer to this filter as the ${K}_{{\rm{H}}2}$ band because it is centered at 2.122 μm, the wavelength of the H₂ 1–0 S(1) line. Figure 1 shows a portion of one of our WIRCam images.

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Our observing strategy and reduction pipeline are described in detail in our previous work (Dupuy & Liu 2012; Liu et al. 2016). Briefly, we measure relative astrometry of all stars above a threshold signal-to-noise ratio (S/N > 5 for this analysis), first using SExtractor (Bertin & Arnouts 1996) to compute (x, y) positions and fluxes and then our custom pipeline for the following steps. The astrometric uncertainty for a given object at a given epoch is the standard error on the mean, computed using the internal astrometric scatter across the dithered images at a single epoch. The accuracy of these error estimates is later verified by examining the χ² of our final five-parameter parallax and proper motion fits to our relative astrometry. The absolute calibration of our astrometry (e.g., the pixel scale) is determined by matching low-proper-motion sources (<30 $\mathrm{mas}\,{\mathrm{yr}}^{-1}$) that also appear in an external reference catalog. In this case, all 24 of our low-proper-motion reference stars were in DR12 of the Sloan Digital Sky Survey (SDSS; Alam et al. 2015), and the rms of our astrometry compared to SDSS after performing a linear transformation was 0031, which we expect is dominated by the uncertainty in the SDSS relative astrometry.

Unexpectedly, we found that one of the stars in the field had a proper motion and parallax very similar to our intended target 2MASS J0249−0557 (Figure 2). This other source has the Two-Micron All-Sky Survey (2MASS) designation 2MASS J02495436−0558015, and its 2MASS photometry indicates a very red color (J − K_S = 1.66 ± 0.17 mag) that would be consistent with being a later-type companion. Table 1 presents our measurements for both objects. The median relative astrometric error per epoch is 4.2 mas for 2MASS J0249−0557 (median S/N = 240) and 6.0 mas for the much fainter companion (median S/N = 15), indicating that the uncertainty in the reference grid is setting the astrometric noise floor, not the centroiding errors that scale as ∝FWHM/(S/N). The parallax and proper motion solutions for 2MASS J0249−0557 and the companion are given in Table 2. The relative proper motions of the two objects are consistent within the errors (1.4σ), as are the relative parallaxes (0.1σ). We show in Section 3.1 that the companion is a young L dwarf, making it very improbable that it is an unrelated object in the volume probed by our CFHT/WIRCam field of view (1.0 pc³ within a distance limit of <70 pc). According to the 25 pc sample from W. M. J. Best et al. (2018, in preparation), the space density of L0 and later dwarfs of all ages is ≈1 × 10⁻² pc⁻³, while for young objects in the same spectral type range it is ≈6 × 10⁻⁴ pc⁻³. Thus, the probability of the companion being a chance alignment is ≪1% even before considering that it has consistent parallax and proper motion. Therefore, we find the two sources are physically associated.

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Table 1.  Integrated-light ${K}_{{\rm{H}}2}$-band Astrometry from CFHT/WIRCam

		2MASS J02495639−0557352				2MASS J02495436−0558015
Observation date		R.A.	Decl.	σR.A.	σDecl.	R.A.	Decl.	σR.A.	σDecl.	Mean	Seeing	Δ${K}_{{\rm{H}}2}$
(UT)	(MJD)	(degree)	(degree)	(mas)	(mas)	(degree)	(degree)	(mas)	(mas)	airmass	(arcsec)	(mag)
2011 Aug 6	55779.6419	042.48532936	−05.95995963	4.9	4.1	042.47695124	−05.96729310	8.8	6.4	1.137	0.54	3.796 ± 0.026
2011 Sep 11	55815.5725	042.48533240	−05.95996130	6.7	4.3	042.47695026	−05.96729258	12.1	5.2	1.111	0.58	3.748 ± 0.051
2011 Oct 16	55850.4559	042.48533009	−05.95996196	3.7	3.1	042.47695126	−05.96729288	5.0	5.9	1.126	0.50	3.780 ± 0.031
2012 Aug 12	56151.6387	042.48534333	−05.95996614	2.0	4.2	042.47696454	−05.96729865	4.6	6.0	1.118	0.60	3.851 ± 0.022
2012 Oct 5	56205.5070	042.48534321	−05.95996834	3.3	3.4	042.47696800	−05.96730269	5.4	6.0	1.110	0.58	3.764 ± 0.021
2013 Oct 14	56579.5098	042.48535363	−05.95997709	2.4	3.1	042.47697513	−05.96731035	4.0	4.0	1.123	0.48	3.742 ± 0.030
2014 Jul 30	56868.6432	042.48536427	−05.95998217	2.7	5.1	042.47698636	−05.96731379	6.1	5.3	1.172	0.50	3.776 ± 0.022
2014 Oct 3	56933.5614	042.48536358	−05.95998275	6.1	7.2	042.47698706	−05.96731761	7.8	6.3	1.157	0.53	3.795 ± 0.030
2014 Oct 13	56943.4851	042.48536301	−05.95998551	10.4	5.6	042.47699064	−05.96731977	5.5	7.5	1.110	0.63	3.743 ± 0.041
2014 Oct 16	56946.4721	042.48536565	−05.95998450	5.6	4.8	042.47698737	−05.96731859	7.3	4.6	1.112	0.51	3.779 ± 0.056
2015 Jan 21	57043.2480	042.48535865	−05.95998794	3.5	2.8	042.47698235	−05.96732283	5.9	8.2	1.133	0.57	3.801 ± 0.032

Note. The quoted uncertainties correspond to relative, not absolute, astrometric errors.

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Table 2.  Parallax and Proper Motion from CFHT/WIRCam Astrometry

Parameter	2MASS J02495639−0557352	2MASS J02495436−0558015
R.A. at first epocha (degree)	42.4853267	42.4769477
Decl. at first epocha (degree)	−05.9599598	−05.9672920
Relative parallax πrel (mas)	19.2 ± 2.1	18.8 ± 3.5
Relative proper motion in R.A. ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	39.4 ± 1.0	42.5 ± 1.6
Relative proper motion in Decl. ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	−27.1 ± 0.9	−28.7 ± 1.4
Absolute parallax πabs (mas)	20.5 ± 2.1	20.1 ± 3.5
Absolute proper motion in R.A. ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	42.9 ± 2.0	46.0 ± 2.3
Absolute proper motion in Decl. ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	−30.2 ± 1.8	−32.0 ± 2.1
χ2 (17 dof)	17.4	19.2
p(χ2)	0.43	0.32

Note.

^aFirst observation epoch: 55779.64 MJD, 2011 August 6 UT.

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We used the flux measurements reported by SExtractor (FLUX_AUTO) to compute relative photometry between 2MASS J0249−0557 and the companion at each epoch. In order to examine photometric variations in each object separately, we first computed the flux of each component relative to a well-detected nearby reference star (2MASS J02495396−0557594, K_S = 13.28 ± 0.04 mag). In our ${K}_{{\rm{H}}2}$-band data, this reference star is 1.600 ± 0.027 mag brighter than the companion and 2.179 ± 0.027 mag fainter than 2MASS J0249−0557 itself. These quoted flux ratio errors are the rms across all epochs, so neither source appears to be more variable relative to the reference star than the other. Computing the magnitude difference relative to each other instead of the reference star gives Δ${K}_{{\rm{H}}2}$ = 3.780 ± 0.032 mag, with χ² = 14.6 (10 dof) using the standard error at each epoch as quoted in Table 1, which again is consistent with no variability above 0.03 mag in the ${K}_{{\rm{H}}2}$ band for either object.

We first observed the M6 dwarf 2MASS J0249−0557 on 2012 January 28 UT using the LGS AO system at the Keck II telescope (Bouchez et al. 2004; van Dam et al. 2006; Wizinowich et al. 2006). We obtained several dithered K-band images with the facility near-infrared camera NIRC2 and noted an elongation in the point-spread function (PSF), but it was not clear if this was due to unstable AO correction or a marginally resolved binary. On 2012 September 7 UT, we obtained data using the nine-hole nonredundant aperture mask installed in the filter wheel of NIRC2 (Tuthill et al. 2006), in addition to more imaging in which the PSF was elongated in a fashion similar to the previous epoch. We analyzed our masking data using the same pipeline as in our previous papers (e.g., Ireland & Kraus 2008; Dupuy et al. 2009b, 2015b; Dupuy & Liu 2017). The analysis indicated a significant detection of a nearly equal-flux binary with the same PA as the PSF elongation. In order to confirm the physical association of this binary, we obtained more masking data on 2013 January 17 UT and recovered a detection at a similar separation, PA, and flux ratio. Figure 3 shows examples of all of our imaging and masking data. In computing astrometry from our NIRC2 data, we adopt the calibration from Yelda et al. (2010), as appropriate for our data taken during 2012–2013, which has a pixel scale of 9.952 ± 0.002 mas ${\mathrm{pixel}}^{-1}$ and an orientation for the detector's +y axis of −0252 ± 0009 east of north.¹²

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At discovery, the separation of the binary was 44.4 ± 0.2 mas, and after 0.36 year it had moved inward to 40.1 ± 0.2 mas. The total motion of the secondary relative to the primary between the two epochs was $({\rm{\Delta }}\alpha \cos \delta ,{\rm{\Delta }}\delta )=(+1.8\pm 0.3,+5.0\pm 0.4)$ mas. According to our CFHT parallax solution for 2MASS J0249−0557, if the object in our Keck data were an unbound background object with zero proper motion and parallax, it would have moved $({\rm{\Delta }}\alpha \cos \delta ,{\rm{\Delta }}\delta )=(+19.6\pm 3.5,+19.5\pm 1.1)$ mas with respect to the primary. Therefore, we conclude that the observed motion is consistent with orbital motion as a physically bound binary system, since a background object would require a finely tuned and high-amplitude proper motion (≈20 $\mathrm{mas}\,{\mathrm{yr}}^{-1}$) to match our Keck LGS AO astrometry. Table 3 summarizes our measured astrometry and flux ratios for this new binary 2MASS J0249−0557AB. We note that ΔK is consistent within ≈0.01 mag and within the quoted uncertainties between the two epochs.

Table 3.  Keck LGS AO Astrometry of 2MASS J0249−0557AB

Observation date		Separation	PA	ΔK
(UT)	(MJD)	(mas)	(degree)	(mag)
2012 Sep 7	56177.60	44.4 ± 0.2	2331 ± 03	0.123 ± 0.005
2013 Jan 17	56309.27	40.1 ± 0.2	2373 ± 05	0.111 ± 0.017

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We obtained low-resolution near-IR (0.8–2.5 μm) spectra of 2MASS J0249−0557 c on 2018 February 17 UT from IRTF located on Maunakea, Hawaii. Conditions were lightly cloudy with 09 seeing. We used the facility near-IR spectrograph SpeX (Rayner et al. 1998) in prism mode with the 08 slit. The wavelength-dependent resolution with this slit ranges from R ≈ 50 in the J band to R ≈ 120 in the K band. We oriented the field to prevent other stars from landing on the slit. This fixed PA did not correspond to the parallactic angle, but as we discuss in Section 3.1, synthetic colors derived from our spectrum agree well with 2MASS photometry, indicating that wavelength-dependent slit losses were negligible. We nodded the object along the slit in an ABBA pattern with individual exposure times of 180 s, observed over an average airmass of 1.30. We observed the A0V star HD 18571 contemporaneously for telluric calibration. The total on-source integration time was 60 minutes. All spectra were reduced using version 4.1 of the SpeXtool software (Vacca et al. 2003; Cushing et al. 2004).

On 2018 February 27 UT, we obtained a moderate-resolution (R ≈ 3500) near-IR spectrum of 2MASS J0249−0557 c using TripleSpec on Apache Point Observatory's ARC 3.5 m telescope. TripleSpec (Wilson et al. 2004) is a cross-dispersed spectrograph that provides simultaneous wavelength coverage from 1.0 to 2.4 μm. Conditions during our observations were clear with ≈14 seeing, which was well matched to TripleSpec's 11 slit. We observed 2MASS J0249−0557 c for a total on-source integration time of 80 minutes at an average airmass of 1.83. Over the course of our observations, the orientation of the slit was continuously updated to the parallactic angle to minimize atmospheric dispersion. Immediately following our observation, we observed the A0V star HD 25792 at an airmass of 1.86 to correct for telluric absorption. All spectra were reduced using a modified version of SpeXtool 4.1 (Vacca et al. 2003; Cushing et al. 2004).

Figures 4–6 show the spectrum of 2MASS J0249−0557 c compared to objects of similar near-IR spectral type. The low-gravity nature of the object is seen clearly in the H-band continuum shape (triangular compared to field objects), K-band continuum shape (redder continuum peak and different curvature of the blueward continuum), VO 1.08 μm absorption (stronger), and FeH 0.99 μm absorption (weaker), as discussed, for example, in Allers & Liu (2013, hereinafter AL13). To assign a spectral type and to assess the gravity for 2MASS J0249−0557 c, we follow the near-IR classification methods of AL13. This approach uses a combination of qualitative visual typing with quantitative measurement of flux indices to determine a spectral type. The AL13 approach then determines a gravity classification using flux indices and equivalent widths of gravity-sensitive features.

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For visual typing, we compare our SpeX J- and K-band spectra to near-IR spectroscopic standards for field (high-gravity [fld-g]) objects from Kirkpatrick et al. (2010) and for young (low-gravity [vl-g]) objects from AL13. Following the prescription of AL13, in each bandpass we normalize the fluxes of 2MASS J0249−0557 c and the spectroscopic standards prior to visual comparison.¹³ The near-IR spectrum of 2MASS J0249−0557 c matches the L3 vl-g standard 2MASSW J2208136+292121 (hereinafter 2MASS J2208+2921) very well, even for the H-band spectrum, though this was not used for typing.

For index-based analysis, we use the approach of Aller et al. (2016), which calculates the AL13 indices and includes a Monte Carlo estimation of the measurement errors. Combining spectral types calculated from AL13's four gravity-sensitive indices (L2.4 ± 1.2, L2.1 ± 1.0, L0.5 ± 1.2, and L2.0 ± 1.0) with our visual classification of the SpeX J- and K-band spectra (L3 ± 1 and L3 ± 1, respectively), we assign a spectral type of L2 ± 1.

From the low-resolution SpeX spectrum, we find an AL13 gravity score of 1222, which represents the gravity inferred from four spectral features, leading to a gravity classification of vl-g. We also used our moderate-resolution TripleSpec spectrum to calculate the AL13 low-resolution gravity-sensitive indices as well as the additional AL13 indices and equivalent widths available at moderate resolution. We find an AL13 gravity score of 2222 for our TripleSpec spectrum, confirming the vl-g classification determined from our lower resolution SpeX spectrum. We assign a final classification of L2 ± 1 vl-g.

We also use our spectrum of 2MASS J0249−0557 c along with the published integrated-light SpeX spectrum of 2MASS J0249−0557AB from Shkolnik et al. (2017) to synthesize photometry on the MKO system. We first synthesize offsets for both objects between the MKO and 2MASS photometric systems in each bandpass, as well as the offset between broadband K and the narrow ${K}_{{\rm{H}}2}$ bandpass used in our CFHT/WIRCam imaging. We used 2MASS photometry (Cutri et al. 2003) to flux calibrate the spectrum of 2MASS J0249−0557AB, and then we used our CFHT flux ratio (Δ${K}_{{\rm{H}}2}$ = 3.780 ± 0.032 mag) to flux calibrate the spectrum of 2MASS J0249−0557 c. In this process, we checked our synthesized 2MASS JHK_S magnitudes against the 2MASS photometry of 2MASS J0249−0557 c and found good agreement, p(χ²) = 0.35, but with our synthesized photometry having much smaller errors. The resulting synthesized JHK photometry on the MKO system for both objects is given in Table 4. As in our previous work with synthesized photometry (Dupuy & Liu 2012), we consider the errors on photometric system offsets negligible compared to the uncertainties in 2MASS photometry, and we adopt 0.05 mag errors on synthesized magnitudes when no direct photometry is available.

Table 4.  Properties of the 2MASS J0249−0557 System

Property	2MASS J0249−0557A	2MASS J0249−0557B	2MASS J0249−0557 c	Notes
Distance (pc)		${48.9}_{-5.4}^{+4.4}$		1
m − M (mag)	${3.44}_{-0.23}^{+0.21}$			1
Age (Myr)	22 ± 6			2
Spectral type	M6 vl-g		L2 vl-g	3
J (mag)	11.885 ± 0.027		16.64 ± 0.06	4
H (mag)	11.410 ± 0.026		15.61 ± 0.06	4
K (mag)	11.73 ± 0.03	11.85 ± 0.03	14.78 ± 0.03	4
J − K (mag)	0.852 ± 0.034		1.86 ± 0.05	4
H − K (mag)	0.376 ± 0.033		0.83 ± 0.05	4
W1 (mag)	10.844 ± 0.023		14.125 ± 0.034	5
W2 (mag)	10.597 ± 0.020		13.588 ± 0.036	5
W1 − W2 (mag)	0.247 ± 0.030		0.54 ± 0.05	5
mbol (mag)	14.65 ± 0.05	14.77 ± 0.05	18.18 ± 0.06	6
log (${L}_{\mathrm{bol}}$) [${L}_{\odot }$]	−2.59 ± 0.09	−2.64 ± 0.09	−4.00 ± 0.09	6
Mass (${M}_{\mathrm{Jup}}$)	${48}_{-12}^{+13}$	${44}_{-11}^{+14}$	${11.6}_{-1.0}^{+1.3}$	7
	Relative properties of AB–c
Separation (au)	1950 ± 200			8
Separation (arcsec)	39959 ± 0005			8
PA (degree)	228649 ± 0013			8
Δ${K}_{{\rm{H}}2}$ (mag)	3.780 ± 0.032			8
	Relative properties of A–B
Separation (au)	2.17 ± 0.22		⋯	9
Separation (arcsec)	00444 ± 00002		⋯	9
PA (degree)	2331 ± 03		⋯	9
ΔK (mag)	0.123 ± 0.005		⋯	9

Note. (1) Computed directly from our measured parallax; (2) lithium-depletion boundary age from Shkolnik et al. (2017); (3) infrared types on the Allers & Liu (2013) system; (4) MKO photometry synthesized from SpeX spectra, where the integrated-light spectrum of 2MASS J0249−0557AB was flux calibrated using its 2MASS photometry and 2MASS J0249−0557 c was flux calibrated from our CFHT/WIRCam ${K}_{{\rm{H}}2}$-band photometry; (5) AllWISE photometry (Cutri et al. 2014); (6) for 2MASS J0249−0557AB, we used its integrated-light ${m}_{\mathrm{bol}}$ and observed K-band flux ratio, and we assumed that the difference in K-band bolometric corrections for A and B is negligible; (7) estimated from Baraffe et al. (2015) models for 2MASS J0249−0557AB and Saumon & Marley (2008) hybrid models for 2MASS J0249−0557 c; (8) from CFHT/WIRCam imaging; (9) Keck/NIRC2 masking detection at discovery epoch 2012 September 7 UT.

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In order to ultimately derive physical properties for the components of the 2MASS J0249−0557 system, we must first estimate their bolometric fluxes. We use the procedure from Mann et al. (2015), which we briefly summarize here. For both 2MASS J0249−0557AB (in integrated light) and 2MASS J0249−0557 c, we compiled optical and IR photometry from SDSS-DR14 (Abolfathi et al. 2017), 2MASS, and the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010). We also used the MKO K-band photometry of 2MASS J0249−0557 c from Section 3.1 that is based on our CFHT/WIRCam imaging. For each object, we compared all available photometry to synthetic magnitudes computed from either observed, template, or model spectra. For 2MASS J0249−0557AB, we used our IRTF/SpeX spectrum and a template optical spectrum of the M6 vl-g object 2MASS J03363144−2619578 obtained with SNIFS (A. W. Mann et al. 2018, in preparation). For 2MASS J0249−0557 c, we used the combination of our IRTF/SpeX spectrum, an optical spectrum from SDSS, and a BT-Settl model (Allard et al. 2011) in regions not covered by the empirical spectra. To compute synthetic magnitudes from each spectrum, we used appropriate filter profiles and zero points (e.g., Cohen et al. 2003; Jarrett et al. 2011). Spectra were then scaled to match all available photometry, using the overlapping wavelengths of the IR and optical spectra (0.75–0.85 μm) as an additional constraint.

Figure 7 shows final calibrated spectra. To compute bolometric fluxes (${f}_{\mathrm{bol}}$), we integrated over these joined and absolutely calibrated spectra. We derived ${f}_{\mathrm{bol}}$ errors accounting for uncertainties in the spectral flux calibration, filter zero points, and Poisson errors in the observed photometry and spectra, yielding final values of (1.35 ± 0.07) × 10⁻¹² erg cm⁻² s⁻¹ for 2MASS J0249−0557 c and (6.56 ± 0.29) × 10⁻¹¹ erg cm⁻² s⁻¹ for 2MASS J0249−0557AB in integrated light. Table 4 summarizes these results in terms of apparent bolometric magnitudes (${m}_{\mathrm{bol}}$) so that future improvements in distance measurements can be readily applied. Our integrated-light magnitude for 2MASS J0249−0557AB of ${m}_{\mathrm{bol}}$ = 13.96 ± 0.05 mag is in good agreement with the value of 13.92 ± 0.02 mas determined from photometry alone by Shkolnik et al. (2017).

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Our new parallax and independently measured proper motion allow us to reexamine the membership of 2MASS J0249−0557AB in the β Pic moving group, as the original analysis by Shkolnik et al. (2017) used a less precise proper motion, did not have a parallax, and did not know it was an unresolved binary. In fact, even our proper motion measurement could be influenced by photocenter motion due to the binary orbit of 2MASS J0249−0557AB. Over short time baselines, long-term orbital motion can cause systematic offsets in measured proper motions (e.g., see Section 2.4.1 of Dupuy & Liu 2012), while parallaxes are not commonly affected systematically. Fortunately, the companion has proper-motion precision similar to 2MASS J0249−0557AB but is less likely to harbor unknown systematic errors due to orbital motion, as it is not known to be a binary and is marginally fainter than average for its spectral type (Section 3.5). Therefore, in the following kinematic analysis, we use the proper motion of 2MASS J0249−0557 c but the more precise parallax of 2MASS J0249−0557AB.

3.3.1. Binary Influence on the RV

We consider the possibility that the unresolved binarity of 2MASS J0249−0557AB may have influenced the Shkolnik et al. RV measured in optical integrated light. The velocity difference of the two components was not large enough relative to $v\sin (i)$ to appear as a double-lined spectroscopic binary, but the line centroids could have been shifted by the binary orbit. If this were an exactly equal-flux, equal-mass binary, then the spectral lines would broaden slightly while remaining centered at the system velocity. But for an arbitrary flux ratio and mass ratio, the flux-weighted centroid shift of the spectral lines away from the system velocity is

$$\begin{eqnarray*}&&{\rm{\Delta }}{\mathrm{RV}}_{\mathrm{orb}}\left(\displaystyle \frac{{F}_{{\rm{A}}}}{{F}_{\mathrm{tot}}}\displaystyle \frac{{M}_{{\rm{B}}}}{{M}_{\mathrm{tot}}}-\displaystyle \frac{{F}_{{\rm{B}}}}{{F}_{\mathrm{tot}}}\displaystyle \frac{{M}_{{\rm{A}}}}{{M}_{\mathrm{tot}}}\right),\end{eqnarray*}$$

where ΔRV_orb is the RV difference between the two components at a given epoch. As described in Section 3.6, we estimate a mass ratio of M_B/M_A = 0.9 from evolutionary models at the age of the β Pic moving group. (The mass ratio would be negligibly different at older field ages.) Using our Keck infrared flux ratio of ΔK = 0.123 ± 0.005 mag with the BT-Settl evolutionary model magnitudes (Allard et al. 2011), we estimate an r-band flux ratio of F_B/F_A = 0.75 (0.31 mag), and this is also essentially the same for young and old ages. Thus, the factor by which ΔRV_orb must be multiplied to compute the expected shift in the integrated-light RV (i.e., the term in parentheses in the equation above) is 0.045 assuming β Pic membership.¹⁴

We consider the possibilities of low- and high-eccentricity orbits and conservatively assume an edge-on orbit, which would produce maximal RVs. As described below, the detection of lithium implies that the system must be younger than ≈100 Myr, corresponding to masses of 0.08–0.11 ${M}_{\odot }$ for the components of 2MASS J0249−0557AB, depending on the age, so we assume a system mass of 0.2 ${M}_{\odot }$ to convert semimajor axis to orbital period. To estimate the semimajor axis from the observed projected separation, we use the conversion factors calculated by Dupuy & Liu (2011) for very low-mass binaries. Because this binary was discovered near the resolution limit of our Keck imaging, we use the value of a/ρ = 0.85 corresponding to severe discovery bias. Thus our measured separation of 2.17 ± 0.22 au implies a semimajor axis of 1.8 ± 0.3 au and orbital period of 5.4 years for a system mass of 0.2 ${M}_{\odot }$. In this case, the median ΔRV_orb is 6.6 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for low eccentricity (e = 0.2) and 2.9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for high eccentricity (e = 0.8). The maximum possible ΔRV_orb values for these orbits are 12 $\mathrm{km}\,{{\rm{s}}}^{-1}$ and 30 $\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively. A fractional shift of 0.045 × ΔRV_orb implies typical deviations from systemic velocity in the integrated-light spectral lines of 0.30 $\mathrm{km}\,{{\rm{s}}}^{-1}$ (up to 0.55 $\mathrm{km}\,{{\rm{s}}}^{-1}$) for low eccentricity and 0.13 $\mathrm{km}\,{{\rm{s}}}^{-1}$ (up to 1.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$) for high eccentricity, depending on orbital phase. The integrated-light RV of 14.42 ± 0.44 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from Shkolnik et al. (2017) was measured on 2010 December 31 UT, 1.69 years prior to our first Keck LGS AO astrometry. Thus we cannot rule out a scenario in which 2MASS J0249−0557AB is an eccentric binary that would have been going through periastron passage (i.e., maximum ΔRV_orb) at the RV measurement epoch. We therefore conservatively assume an uncertainty of 1.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ on the system velocity as measured by the integrated-light RV.¹⁵

3.3.2. Reaffirming ACRONYM Membership

Combining the RV from the Shkolnik et al. (2017) ACRONYM survey with our absolute parallax and proper motion, we find (U, V, W) = (−10.7 ± 0.9, −12.8 ± 1.4, −9.8 ± 1.1) $\mathrm{km}\,{{\rm{s}}}^{-1}$ and (X, Y, Z) = (−28 ± 3, −0.68 ± 0.07, −40 ± 4) pc. Despite our parallax distance (${48.9}_{-5.4}^{+4.4}$ pc) being somewhat smaller than the kinematic distance of 60 pc used in the analysis of Shkolnik et al., our XYZ values agree within 0.7–1.0σ of their values (X, Y, Z) = (−35 ± 4, −0.80 ± 0.08, −49 ± 5) pc. Here we assume that the XYZ uncertainties of Shkolnik et al. are dominated by kinematic distance uncertainty, which we estimate to be 10% based on the fractional error in the proper motion they used: (44.6 ± 4.1, −35.0 ± 4.1) $\mathrm{mas}\,{\mathrm{yr}}^{-1}$. Compared to their (U, V, W) = (−10.6, −16.2, −10.0) $\mathrm{km}\,{{\rm{s}}}^{-1}$, only the V component is more than 0.2σ different from our own measurements. Examining the covariance between our input measurements and output velocities indicates that this discrepancy in V is almost entirely due to the difference in the decl. component of our CFHT proper motion μ_δ = − 32.0 ± 2.1 $\mathrm{mas}\,{\mathrm{yr}}^{-1}$ for 2MASS J0249−0557 c compared to −35.0 ± 4.1 $\mathrm{mas}\,{\mathrm{yr}}^{-1}$ for 2MASS J0249−0557AB in Shkolnik et al. (2017). These two independent measurements are consistent within 0.7σ; therefore, we conclude that our updated UVW velocity is consistent within the 1σ uncertainties of the kinematic data used by Shkolnik et al. (2017). By extension, we expect that their assessment of 2MASS J0249−0557 as a likely member of the β Pic moving group would remain unchanged using our new proper motion, but we now consider membership in more detail given our addition of a parallax.

Because the β Pic moving group is spread over thousands of square degrees, both the directly observable kinematics of members (proper motion and RV) and contamination due to the field population will vary widely over the sky. Achieving a highly complete group census requires casting a wide net in kinematic space, but not so wide as to become unacceptably contaminated by field objects. We consider these two competing effects in the following.

First, to estimate the completeness of selecting β Pic group members using various kinematic criteria, we created a Monte Carlo population of simulated members at the sky position and distance of 2MASS J0249−0557. For the kinematics of the β Pic moving group, we consider two velocity ellipsoids derived from slightly different membership lists. One is the Gaussian ellipsoid derived by Mamajek & Bell (2014), which has a mean velocity of (U, V, W) = (−10.9, −16.0, −9.2) $\mathrm{km}\,{{\rm{s}}}^{-1}$ and intrinsic velocity dispersions along these axes of (1.5, 1.4, 1.8) $\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively. This is based on the classic membership list of 26 stars from Zuckerman & Song (2004) plus four additional high-probability members from Malo et al. (2013). We also consider an ellipsoid based on a somewhat larger membership list of 57 stars from Lee & Song (2018) that was derived from a uniform assessment of all potential β Pic candidates in the literature at the time, selecting only the highest-probability members. The mean velocity of the Lee & Song (2018) ellipsoid, (U, V, W) = (−10.5, −15.9, −9.1) $\mathrm{km}\,{{\rm{s}}}^{-1}$, is nearly identical to that of Mamajek & Bell (2014) but with dispersion axes that are rotated to match the covariances in the data as fit by three Euler angles. Our UVW for 2MASS J0249−0557AB places it 3.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$ away from the mean velocity of the β Pic moving group using either the Mamajek & Bell (2014) or Lee & Song (2018) results.

To properly account for all covariances, we project the UVW velocities of the simulated β Pic population into proper motions and RVs using the sky coordinates, parallax, and corresponding measurement uncertainties of the 2MASS J0249−0557 system. In proper motion–RV space, we can more clearly investigate observational selection effects. Figure 8 shows the projection of the 3D velocity ellipsoids into 2D proper motion space. For display purposes, Figure 8 also shows contours corresponding to the young field population (<150 Myr) as simulated in the Besançon model of the Galaxy (Robin et al. 2003). As expected, the field population spans a large amount of parameter space, encompassing the entirety of the β Pic moving group and 2MASS J0249−0557.

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For every simulated β Pic group member and 2MASS J0249−0557 itself, we compute the 3D distance in (μ_α cos δ, μ_δ, RV) space from the mean velocity. In general, we quote 3D distances in units of σ, that is, normalized along each principal component axis by the standard deviation in that direction (a.k.a., the Mahalanobis distance). In 3D space, the usual Gaussian confidence intervals do not correspond to integer units of σ, but rather 68.3% of the distribution is contained within 1.88σ, 95.4% within 2.83σ, and so on. 2MASS J0249−0557 is fairly close to the mean velocity of the β Pic moving group, only 1.46σ and 1.32σ away from the ellipsoids of Mamajek & Bell (2014) and Lee & Song (2018), respectively. Among simulated β Pic group members, most of them (54% and 63%, respectively) are more distant than 2MASS J0249−0557 from the ellipsoid means. Thus, 2MASS J0249−0557 would pass any reasonably inclusive kinematic criteria for membership in the β Pic moving group using this approach.

To estimate the probability that 2MASS J0249−0557 could be a field interloper that happens to share the kinematics of the β Pic moving group, we consider the ACRONYM search in which it was originally identified (Shkolnik et al. 2017). The first step in this search was to select candidates based on astrometry and photometry, using proper motions to estimate a kinematic distance (the distance required to minimize the difference between the measured and expected proper motion of a β Pic member at the given R.A. and decl.) and spectral energy distributions (SEDs) to estimate spectral types. Of the 4.5 × 10³ objects with proper motions consistent with β Pic kinematics, only 104 objects with estimated spectral types of K7–M9 were consistent with being young on the H-R diagram and thus selected for spectroscopic follow-up. The latest-type sources were first screened for signs of low gravity using low-resolution IR spectra. High-resolution optical spectroscopy was obtained for all remaining objects to measure RVs and look for Hα emission and Li i absorption. This resulted in 91 objects with RV measurements, including both β Pic members and field contaminants. For each object, Shkolnik et al. (2017) computed the expected RV for β Pic motion, and the difference from the measured value (ΔRV_BPMG) was used, along with other youth indicators, in assigning final memberships. Here we use the ΔRV_BPMG distribution of the objects that Shkolnik et al. (2017) classified as nonmembers to estimate the fraction of field interlopers that would pass both the initial proper motion and final RV selection.

We assume that both populations (members and nonmembers) found in the ACRONYM search can be approximated as Gaussians in ΔRV_BPMG. The nonmembers should be distributed widely in ΔRV_BPMG while members cluster tightly around zero. Shkolnik et al. (2017) used a threshold in ΔRV_BPMG of 5.4 $\mathrm{km}\,{{\rm{s}}}^{-1}$ to select members, corresponding to a 3σ cut given the velocity dispersion of 1.8 $\mathrm{km}\,{{\rm{s}}}^{-1}$ used in their analysis for the β Pic moving group. We assume that the subset of 32 objects that did not pass their ΔRV_BPMG cut or lacked Hα emission (as expected at the age of β Pic) represent the contaminant population, and these objects have a mean and standard deviation in ΔRV_BPMG of 13 ± 46 $\mathrm{km}\,{{\rm{s}}}^{-1}$. In contrast, the 52 objects identified as members have a ΔRV_BPMG mean and standard deviation of 0.3 ± 2.4 $\mathrm{km}\,{{\rm{s}}}^{-1}$. (Here we have excluded seven objects with ambiguous status, mostly spectroscopic binaries where the RV likely has a systematic orbital offset.) To compute a false alarm rate, we combine these two Gaussians into a single probability distribution, normalized according to 52/84 = 62% members (centered at ΔRV_BPMG = 0) and 32/84 = 38% contaminants.

For a given ΔRV_BPMG selection criterion, the false-alarm rate is the integral of the nonmember distribution divided by the integral of the combined distribution over the same ΔRV_BPMG range (Figure 9). Using the original ACRONYM criterion of $| {\rm{\Delta }}{\mathrm{RV}}_{\mathrm{BPMG}}| \lt 5.4$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, we compute a false-alarm rate of 4%. Even if we consider an extremely restrictive criterion of $| {\rm{\Delta }}{\mathrm{RV}}_{\mathrm{BPMG}}| \lt 0.8$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, which would let past just 2MASS J0249−0557 and 11 other members, the false-alarm rate would only be reduced to 3.1%. Therefore, contamination does not strongly depend on the ΔRV_BPMG cut, as long as the cut is relatively restrictive.

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According to the binomial distribution, a false alarm rate of 4% implies a 90% probability of at least one contaminant among the 52 objects that Shkolnik et al. (2017) identified as members meeting this criterion and a <1% probability of ≥7 contaminants. However, the appropriate sample to consider here is the set of 12 latest-type ACRONYM members accessible from CFHT that we have been following up to obtain parallaxes. Among all 12, only 0.5 contaminants are expected for a 4% false alarm rate, and ≤3 should be present at 99% confidence. 2MASS J0249−0557 is the first object for which we are reporting a parallax, so it is not yet possible to determine if the parallaxes and improved proper motions for the other objects are consistent with β Pic membership or not.

The false alarm rate of 4% derived for the ACRONYM sample should be considered a conservative upper limit in the case of 2MASS J0249−0557. First, parallaxes were not available in the ACRONYM sample selection. If they were, then they would have reduced the number of interlopers that made it to the spectroscopic follow-up stage of the ACRONYM search and thereby reduced the nonmember component of the probability distribution used above. Our addition of a parallax for 2MASS J0249−0557 could have ruled out membership by being inconsistent with the β Pic group kinematic distance, but it did not. Second, spectroscopic binaries that are true members may have been excluded from the ACRONYM member sample due to orbital RV deviations. If such objects had not been excluded, that would have increased the relative number of members to nonmembers adopted in our analysis. Third, we used both young and old stars in our analysis to improve statistics and because stars from ACRONYM do not have homogeneous constraints on their ages. The detection of Li i absorption in 2MASS J0249−0557 provides a much stronger constraint than Hα in an earlier-type ACRONYM star lying above the lithium-depletion boundary. To determine an age constraint for 2MASS J0249−0557, we examined other associations with measured lithium-depletion boundaries. The components of 2MASS J0249−0557AB have bolometric magnitudes of ${M}_{\mathrm{bol}}={11.21}_{-0.22}^{+0.24}$ mag and ${11.33}_{-0.22}^{+0.24}$ mag (Section 3.2) that are both consistent within their errors with the boundary of ${M}_{\mathrm{bol}}$ = 11.31 mag for α Persei (85 ± 10 Myr; Barrado y Navascués et al. 2004), implying a system age ≲100 Myr. This is somewhat stronger than the age constraint implied by the gravity classifications of vl-g for both 2MASS J0249−0557AB and 2MASS J0249−0557 c (≲150 Myr; e.g., Liu et al. 2016). If we were able to restrict the field interloper population used in our false-alarm analysis to such young stars, the false-alarm probability of 4% would be reduced by a factor roughly equal to the number of >100 Myr old stars divided by the number of <100 Myr old stars, which is likely at least an order of magnitude.

We conclude that the 2MASS J0249−0557 system is a very likely member of the β Pic moving group given its excellent kinematic agreement, low false-alarm probability, and independent constraints on youth (lithium and low-gravity classification) that are consistent with the age of the group. Although we have chosen not to use the spatial XYZ position of 2MASS J0249−0557 in our membership probability analysis, because the current census of the β Pic moving group has not been established to be complete, 2MASS J0249−0557 seems to be well within the spatial range of other β Pic members (Figure 10). It is also within the minimum volume enclosing ellipsoid of the "exclusive" (smallest) list of members shown in Figure 4 of Lee & Song (2018).

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3.3.3. Comparison to Membership Tools

In our previous work, Liu et al. (2016) identified the L3 vl-g dwarf 2MASS J2208+2921 as a promising candidate member of the β Pic moving group based on our parallax and proper motion but in need of RV confirmation. Since then, Vos et al. (2017) measured an RV of −15.7^+0.8_−0.9 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Combining all these measurements gives (U, V, W) = (−11.7 ± 0.7, −18.9 ± 0.9, −7.6 ± 0.9) $\mathrm{km}\,{{\rm{s}}}^{-1}$, which is 3.6 $\mathrm{km}\,{{\rm{s}}}^{-1}$ away from the mean β Pic group velocity of Mamajek & Bell (2014) and 3.8 $\mathrm{km}\,{{\rm{s}}}^{-1}$ away from the mean velocity of Lee & Song (2018). Projecting the β Pic ellipsoids into proper motion–RV space, as in our analysis of 2MASS J0249−0557 in the previous section, we find 3D distances for 2MASS J2208+2921 that are 2.0σ using the Mamajek & Bell (2014) group parameters and 2.2σ using Lee & Song (2018). (Even though 2MASS J2208+2921 has similar distances in $\mathrm{km}\,{{\rm{s}}}^{-1}$ from the β Pic ellipsoids as 2MASS J0249−0557, it has slightly larger 3D distances in σ because its parallax, proper motion, and RV are more precise.) The fraction of simulated β Pic members that are closer than 2MASS J2208+2921 in 3D space are 73% and 82%, respectively. Thus, even a >90% completeness criterion would require 2MASS J2208+2921 to be considered a candidate member. Unlike 2MASS J0249−0557, most of the 3D distance is in the RV axis, but with ΔRV_BPMG = − 3.3 ± 1.7 $\mathrm{km}\,{{\rm{s}}}^{-1}$, 2MASS J2208+2921 is still within <2σ of the expected velocity for a member and would easily pass the RV criterion used for the ACRONYM sample (Figure 9).Therefore, based on kinematics alone, 2MASS J2208+2921 appears to be a likely member of the β Pic moving group.

Spatially, 2MASS J2208+2921 coincides with other published members of the β Pic moving group given its position of (X, Y, Z) = (3.1 ± 0.2,37.0 ± 2.4, −14.5 ± 0.9) pc (Figure 10). Compared only to stars belonging to the most restrictive member lists, it is somewhat discrepant in the Y axis; for example, it lies just outside the minimum volume enclosing ellipsoid of Lee & Song (2018). This may not be a major cause for concern, as it has been suggested that the spatial distribution of members may be larger than is currently known, especially for widely dispersed groups like β Pic and AB Dor (e.g., Liu et al. 2016; Bowler et al. 2017; Desrochers et al. 2018).

BANYAN Σ reports a surprisingly low probability of 0.8% for β Pic membership (99.2% for field) for 2MASS J2208+2921. This in contrast with the previous β Pic probability of 18% computed by Liu et al. (2016) using BANYAN II (Gagné et al. 2014) with the same proper motion and parallax, as well as a membership probability of 96.5% using BANYAN I (Malo et al. 2013) with both a parallax and RV. The only change in the observations since Liu et al. (2016) is the addition of an RV from Vos et al. (2017), which is consistent with the expected value for β Pic within 2σ even according to BANYAN Σ (optimal RV of −13.6 ± 0.7 $\mathrm{km}\,{{\rm{s}}}^{-1}$). As for other membership tools, they also give a higher membership probability for the β Pic moving group than any other young association, with 94% from the convergent point tool (Rodriguez et al. 2013) and 19% from LACEwING (Riedel et al. 2017).

The discrepancy between 2MASS J2208+2921 passing the same kinematic selection criteria as 2MASS J0249−0557 and the >10× lower membership probability from BANYAN Σ may be related to the fact that BANYAN Σ does not account for evidence of youth that would reduce the fraction of field interlopers. Given the vl-g gravity classification, 2MASS J2208+2921 is quite young. Among parallax-confirmed members of young moving groups, Liu et al. (2016) found that the vl-g classification becomes less prevalent by an age of ≈150 Myr compared to the intermediate-gravity classification int-g. This trend is less clear among (less definitive) candidate lists for moving groups using objects that lack parallaxes or RVs (e.g., Gagné et al. 2015c; Faherty et al. 2016). Still, all previously known parallax- and RV-confirmed ultracool dwarf members of the β Pic moving group are classified as vl-g. Therefore, 2MASS J2208+2921 is independently known to be consistent with the age of the β Pic group, which reduces the probability that it is a field interloper.

We conclude that 2MASS J2208+2921 is a possible member of the β Pic moving group, but given the discord with BANYAN Σ, we consider its status ambiguous. Unlike 2MASS J0249−0557, there is little room for improving the observations of 2MASS J2208+2921 (system RV, distance, proper motion), so a more robust look at its membership will need a more complete census of β Pic members. Gaia will not map the spatial distribution of young L dwarfs out to the necessary distances for such work, due to their faintness (e.g., 2MASS J2208+2921 itself does not have an entry in Gaia DR2). However, it should be possible to use the higher mass M dwarfs to better determine the spatial distribution of the β Pic moving group.

Combining our photometry with the distance modulus derived from our parallax ($m-M={3.44}_{-0.23}^{+0.21}$ mag) allows us to compute absolute magnitudes and compare them to the polynomial relations of magnitude versus spectral type from Liu et al. (2016). For a spectral type of L2 ± 1 vl-g, the polynomials give M_J = 12.4 ± 1.0 mag and M_K = 10.6 ± 0.9 mag, where the uncertainties are a quadrature sum of the rms of objects used in the fit about the polynomial curve (±0.6 mag and ±0.4 mag, respectively) and the propagation of the spectral type uncertainty (±0.8 mag). The absolute magnitudes of 2MASS J0249−0557 c are M_J = 13.20^+0.22_−0.24 mag and ${M}_{K}={11.34}_{-0.24}^{+0.22}$ mag, which are 0.8σ and 0.9σ fainter than the polynomial and thus consistent with being a normal object for its spectral type and gravity classification. Its faintness also suggests that 2MASS J0249−0557 c is not likely to be an unresolved, near-equal-flux binary. For the M6 vl-g integrated-light spectral type of 2MASS J0249−0557AB, the Liu et al. (2016) polynomial gives M_K = 7.2 ± 0.4 mag. (The polynomial is only valid for types M6 and later, so we cannot reliably estimate the additional error due to a ±1 subtype uncertainty.) Our resolved K-band magnitudes of the primary (${M}_{K}={8.29}_{-0.23}^{+0.21}$ mag) and secondary (${M}_{K}={8.41}_{-0.23}^{+0.21}$ mag) are 1.1 mag and 1.2 mag fainter, respectively, than the polynomial but again not overly discrepant within the scatter about the polynomials. For context, there are other examples of low-gravity M6 dwarfs with similar or fainter absolute magnitudes, such as HD 1160B (M_K = 8.83 ± 0.16 mag; Nielsen et al. 2012).

Figure 11 shows the components of the 2MASS J0249−0557 triple system alongside members of the β Pic moving group on an IR color–magnitude diagram. 2MASS J0249−0557AB has a color similar to other late-M members of β Pic, like PZ Tel B (M7) and 2MASS J0335+2342 (M7 vl-g), and each component has a comparable or somewhat brighter absolute magnitude, if we assume the two components have similar infrared colors. Likewise, 2MASS J0249−0557 c lies near the other β Pic objects with L1–L3 spectral types: β Pic b and 2MASS J2208+2921.

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In order to derive physical properties, we rely on the predicted luminosity (${L}_{\mathrm{bol}}$) as a function of mass and age from evolutionary models. We compute luminosities by combining the bolometric fluxes derived in Section 3.2 with our parallax measurement of 20.5 ± 2.1 mas. For 2MASS J0249−0557 c, we find log (${L}_{\mathrm{bol}}$/${L}_{\odot }$) = − 4.00 ± 0.09 dex. For 2MASS J0249−0557AB, we divide its integrated-light luminosity assuming that the nearly equal-flux components (ΔK = 0.123 ± 0.005 mag) have a negligible difference in their K-band bolometric corrections compared to the uncertainty in the distance modulus (${3.44}_{-0.23}^{+0.21}$ mag). Thus, adopting our K-band flux ratio as the bolometric flux ratio results in component luminosities of log (${L}_{\mathrm{bol}}$/${L}_{\odot }$) = − 2.59 ± 0.09 dex and −2.64 ± 0.09 dex.

No single model grid completely covers the luminosities of all three components, so we use the Baraffe et al. (2015) tracks for 2MASS J0249−0557AB and Saumon & Marley (2008) hybrid tracks for 2MASS J0249−0557 c. In a fashion similar to that of Dupuy & Liu (2017), we use Monte Carlo rejection sampling with uniformly distributed masses and ages as the initial input. For each trial mass and age, we compute

$$\begin{eqnarray*}&&{\chi }^{2}={\left(\displaystyle \frac{\mathrm{log}({L}_{\mathrm{bol},\mathrm{model}})-\mathrm{log}({L}_{\mathrm{bol}})}{{\sigma }_{\mathrm{log}({L}_{\mathrm{bol}})}}\right)}^{2}+{\left(\displaystyle \frac{t-22\mathrm{Myr}}{6\mathrm{Myr}}\right)}^{2},\end{eqnarray*}$$

from which we compute a rejection probability $p={e}^{-({\chi }^{2}-\min ({\chi }^{2}))/2}$. We then draw random, uniformly distributed variates u and reject samples where p < u. This method allows us to properly account for the possibility that objects of different masses and ages have the same luminosity due to deuterium fusion, which can be important at such young ages. The age prior of 22 ± 6 Myr is based on the most recent measurement of the lithium-depletion boundary in the β Pic moving group from Shkolnik et al. (2017), which is consistent with the previous lithium-depletion age of 23 ± 3 Myr from Binks & Jeffries (2014) and the isochronal age of 24 ± 3 Myr from Bell et al. (2015).

Table 4 gives the resulting masses of the three components. As expected given its M6 vl-g spectral type, the tight binary 2MASS J0249−0557AB is estimated to be a pair of brown dwarfs, while the L2 vl-g companion's mass of ${11.6}_{-1.0}^{+1.3}$ ${M}_{\mathrm{Jup}}$ is likely below the deuterium fusion boundary (≈13 ${M}_{\mathrm{Jup}}$; e.g., Spiegel et al. 2011). For comparison, we also derived masses for other late-type members of β Pic using the Saumon & Marley (2008) models and the same rejection sampling method. For the free-floating objects, we computed our own bolometric fluxes using the same method described in Section 3.2, except that in these cases we simply used published IRTF/SpeX spectra combined with BT-Settl models at other wavelengths. This included 2MASS J0335+2342, SDSS J0443+0002, 2MASS J1935−2846, 2MASS J2013−2806, PSO J318.5−22, and 2MASS J2208+2921. For companions, we used published values from the literature for β Pic b and 51 Eri b, and K_S-band photometry combined with the spectral type–${\mathrm{BC}}_{{K}_{s}}$ relation for young objects from Filippazzo et al. (2015) for PZ Tel B and HR 7329B. All of the luminosities and derived masses are given in Table 5. We emphasize that none of our quoted mass errors attempt to account for unknown systematic uncertainties in the evolutionary models, which are likely larger than the random errors in cases where luminosity is measured very precisely. We also note that formal mass errors are larger for the higher mass components 2MASS J0249−0557AB than for the wide companion 2MASS J0249−0557 c because the evolutionary models predict that such young, massive brown dwarfs have similar masses at a fixed age. In other words, isomass tracks pile up on an ${L}_{\mathrm{bol}}$–age diagram due to deuterium fusion; for example, see Figure 1 in Burrows et al. (2001).

Table 5.  Late-type Members of the β Pic Moving Group

Name	Spectral Type	π	${m}_{\mathrm{bol}}$	log (${L}_{\mathrm{bol}}$/${L}_{\odot }$)	Mass	References
		(mas)	(mag)	(dex)	(${M}_{\mathrm{Jup}}$)
PZ Tel B	M7	19.4 ± 1.0	14.44 ± 0.15	−2.45 ± 0.07	61 ± 12	F15, M16, v07
2MASSI J0335020+234235	M7 vl-g	21.8 ± 1.8	14.29 ± 0.05	−2.50 ± 0.08	${56}_{-12}^{+13}$	AL13, D18, L16, S17
HR 7329B	M7.5	20.74 ± 0.21	14.60 ± 0.16	−2.58 ± 0.07	${49}_{-10}^{+12}$	L00, v07, F15
2MASS J0249−0557A	M6 vl-g	20.5 ± 2.1	14.65 ± 0.05	−2.59 ± 0.09	${48}_{-12}^{+13}$	D18
2MASS J0249−0557B	M6 vl-g	20.5 ± 2.1	14.77 ± 0.05	−2.64 ± 0.09	${44}_{-11}^{+14}$	D18
SDSS J044337.60+000205.2	L0 vl-g	47.3 ± 1.0	14.43 ± 0.06	−3.23 ± 0.03	${20}_{-5}^{+4}$	AL13, D18, L16, RB09
β Pic b	L2a	51.44 ± 0.12	15.63 ± 0.08	−3.78 ± 0.03	${13.0}_{-0.3}^{+0.4}$	D18, v07, M15
2MASS J0249−0557 c	L2 vl-g	20.5 ± 2.1	18.18 ± 0.06	−4.00 ± 0.09	${11.6}_{-1.0}^{+1.3}$	D18
PSO J318.5338−22.8603	L7 vl-g	45.1 ± 1.7	17.85 ± 0.12	−4.55 ± 0.06	${6.5}_{-0.8}^{+1.2}$	D18, L13, L16, A16
51 Eri b	T6.5 ± 1.5	33.98 ± 0.34	21.8 ± 0.4	−5.87 ± 0.15	2–12b	R17, v07
Possible Members (π or RV unavailable, or ambiguous membership)
2MASS J02241739+2031513	M6 int-g	⋯	⋯	⋯	⋯	S17
2MASS J03363144−2619578	M6 vl-g	⋯	⋯	⋯	⋯	S17
2MASS J03370343−3042318	M6 fld-g	⋯	⋯	⋯	⋯	S17
2MASS J19082195−1603249	M6 vl-g	⋯	⋯	⋯	⋯	S17
2MASS J23355015−3401477	M6 vl-g	⋯	⋯	⋯	⋯	S17
2MASS J22334687−2950101	M7 vl-g	⋯	⋯	⋯	⋯	S17
2MASS J23010610+4002360	M7 vl-g	⋯	⋯	⋯	⋯	S17
DENIS J004135.3−562112AB	M7.5 vl-g	⋯	⋯	⋯	⋯	G15
2MASS J03550477−1032415	M8 int-g	⋯	⋯	⋯	⋯	S17
2MASS J19355595−2846343	M9 vl-g	14.2 ± 1.2	15.9 ± 0.2	−2.76 ± 0.11	${35}_{-15}^{+7}$	AL13, D18, L16
2MASS J20004841−7523070	M9 vl-g	⋯	⋯	⋯	⋯	G15
2MASS J00464841+0715177c	L0 vl-g	⋯	⋯	⋯	⋯	G15, F16
2MASS J20135152−2806020	L0 vl-g	21.0 ± 1.3	16.18 ± 0.05	−3.22 ± 0.06	${20}_{-6}^{+4}$	AL13, D18, L16
EROS-MP J0032−4405d	L0 int-g	⋯	⋯	⋯	⋯	AL13, G14, G15b
2MASSW J2208136+292121e	L3 vl-g	25.1 ± 1.6	17.41 ± 0.08	−3.87 ± 0.07	${12.6}_{-0.5}^{+0.7}$	AL13, D18, L16, V17
Candidates (proper motion only)
2MASS J20334670−3733443	M6 int-g	⋯	⋯	⋯	⋯	G15
2MASS J01294256−0823580	M7 vl-g	⋯	⋯	⋯	⋯	G15
2MASS J02501167−0151295	M7 vl-g	⋯	⋯	⋯	⋯	G15
2MASS J05120636−2949540	L5 int-g	⋯	⋯	⋯	⋯	G15
2MASS J23542220−0811289	L5 vl-g	⋯	⋯	⋯	⋯	Sc17
2MASS J00440332+0228112	L7 vl-g	⋯	⋯	⋯	⋯	Sc17

Notes. This table does not include nine new candidates identified by Gagné & Faherty (2018) using parallaxes and proper motions from the Gaia DR2 catalog because the objects have not been spectroscopically confirmed (photometrically estimated spectral types of M6–L3).

^aSpectral resolution insufficient for gravity classification. ^bThe luminosity of 51 Eri b is low enough to be consistent with both hot-start and cold-start models, so its mass is correspondingly very uncertain. ^cGagné et al. (2015c) reported this as a β Pic moving group candidate, but Faherty et al. (2016) classify it as an ambiguous member after measuring an RV. ^dThere are two published parallaxes for EROS-MP J0032−4405. The value of 38.4 ± 4.8 mas from Faherty et al. (2012) used to determine β Pic membership by Gagné et al. (2014, 2015c) is 1.8× larger than the value of 21.6 ± 7.2 mas from Marocco et al. (2013) used by Faherty et al. (2016) to determine high-likelihood AB Dor membership. ^eOur kinematic analysis indicates likely membership for 2MASS J2208+2921 based on proper motion, parallax, and RV. But this is discordant with the results of BANYAN Σ, so we consider the membership status ambiguous.

References. (A16) Allers et al. (2016), (AL13) Allers & Liu (2013), (D18) this work, (F15) Filippazzo et al. (2015), (F16) Faherty et al. (2016), (G14) Gagné et al. (2014), (G15) Gagné et al. (2015c), (G15b) Gagné et al. (2015b), (L00) Lowrance et al. (2000), (L13) Liu et al. (2013), (L16) Liu et al. (2016), (M15) Morzinski et al. (2015), (M16) Maire et al. (2016), (R17) Rajan et al. (2017), (RB09) Reiners & Basri (2009), (S17) Shkolnik et al. (2017), (Sc17) Schneider et al. (2017), (v07) van Leeuwen (2007), (V17) Vos et al. (2017).

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A parallax and proper motion for 2MASS J0249−0557AB (in integrated light) are available from Gaia DR2 (Gaia Collaboration et al. 2016, 2018). Binary orbital motion can impact the parallax and proper motion in an unpredictable, systematic way, especially when there are relatively few independent observation epochs (DR2 reports visibility_periods_used = 10 for this system). Indeed, the excess source noise (_i) reported in DR2 for 2MASS J0249−0557AB is 0.70 mas at a significance of 37σ, suggesting that systematic, correlated noise from orbital motion impacts the five-parameter DR2 solution. There is evidence from hierarchical M dwarf triple systems, where one component is single and the other is unresolved in Gaia (e.g., GJ 1245 and GJ 2069), that parallax systematics for unresolved binaries can be up to at least 2 mas (≈20σ) with even larger proper motion systematics. Therefore, we have chosen not to use the DR2 astrometry for 2MASS J0249−0557AB in our analysis until the accuracy of DR2 parallaxes for close binaries like this can be more carefully vetted. However, we briefly consider here what the difference in our analysis would be if we used the DR2 parallax and proper motion.

The Gaia DR2 parallax of 15.11 ± 0.10 mas is 2.6σ lower than our value for 2MASS J0249−0557AB and 1.4σ lower than for 2MASS J0249−0557 c. The Gaia DR2 proper motions are 1.2σ higher in R.A. and 2.0σ lower in decl. Using the Gaia DR2 parallax and proper motion with the RV from Shkolnik et al. (2017) gives (U, V, W) = (−11.4 ± 0.8, −18.81 ± 0.14, −9.3 ± 1.1) $\mathrm{km}\,{{\rm{s}}}^{-1}$ and (X, Y, Z) = (−38.2 ± 0.3, −0.924 ± 0.006, −54.1 ± 0.4) pc. The most significant difference with our kinematics is in V, which our CFHT astrometry shows is 3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ higher than the mean β Pic group motion but Gaia DR2 indicates is 3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ lower. Rerunning our kinematic analysis using Gaia DR2 gives a 3D distance from β Pic in proper motion–RV space of 2.0σ, still closer to the mean than 25% of simulated members. Our false-alarm analysis is unchanged because it is based on the selection criteria of the ACRONYM search, which 2MASS J0249−0557AB would still pass.

We also note that the smaller Gaia DR2 parallax implies brighter absolute magnitudes for all three components. For 2MASS J0249−0557AB, this would mean bolometric magnitudes of ${M}_{\mathrm{bol}}$ = 10.51 ± 0.03 mag and 10.63 ± 0.03 mag, which in turn would imply a younger age upper limit from the detection of lithium. 2MASS J0249−0557AB would be younger than α Persei (85 ± 10 Myr), where the lithium depletion boundary is at ${M}_{\mathrm{bol}}$ = 11.31 ± 0.15 mag. It would instead be consistent with the next youngest measured lithium depletion boundary in IC 2391 (45 Myr, ${M}_{\mathrm{bol}}$ = 10.24 ± 0.15 mag; Barrado y Navascués et al. 2004). An even younger upper limit on the age would make it correspondingly less likely that the 2MASS J0249−0557 system is a field contaminant rather than a member of the very young β Pic moving group (22 ± 6 Myr). We therefore conclude that the Gaia DR2 results are generally consistent with our membership assessment based on our CFHT astrometry. The 0.66 mag brighter J- and K-band absolute magnitudes would also bring all three components of 2MASS J0249−0557ABc closer to the Liu et al. (2016) polynomial relations. 2MASS J0249−0557 c would also lie much closer to β Pic b on the color–magnitude diagram.

The DR2 parallax also implies higher luminosities. The components of 2MASS J0249−0557AB would have log (${L}_{\mathrm{bol}}$/${L}_{\odot }$) = −2.32 ± 0.02 dex and −2.37 ± 0.02 dex, which would make them more luminous than other known ultracool dwarfs in the β Pic moving group but still normal for a spectral type of M6. Their estimated masses would be somewhat higher, at ${75}_{-11}^{+12}$ ${M}_{\mathrm{Jup}}$ and ${69}_{-9}^{+13}$ ${M}_{\mathrm{Jup}}$, but still consistent with being brown dwarfs. 2MASS J0249−0557 c would have log (${L}_{\mathrm{bol}}$/${L}_{\odot }$) = −3.73 ± 0.02 dex, that is, 0.05 dex (1.4σ) more luminous than β Pic b, and a mass of ${13.2}_{-0.2}^{+0.4}$ ${M}_{\mathrm{Jup}}$ (1.2σ higher than the mass derived using our CFHT parallax).

The 2MASS J0249−0557ABc system increases the total number of ultracool (≥M6) members of the β Pic moving group from seven to ten. Table 5 summarizes these members, as well as other possible members that are lacking either parallax or RV for confirmation, and also those based on proper motion alone. Gaia will soon enable a reassessment of all these objects, either directly via high-precision parallaxes and proper motions for the brightest ones or indirectly via an improved census of local moving groups. In the meantime, it is noteworthy that current methods of assessing group membership can still disagree significantly. The 2MASS J0249−0557 system is one such example, as it is not classified as a high-probability (P ≥ 90%) β Pic member from BANYAN Σ, even though we reaffirm its membership as originally determined by Shkolnik et al. (2017). 2MASS J2208+2921 is a more puzzling case of an object with kinematics that would make it a likely β Pic member according to our analysis but with widely varying probabilities from generalized membership tools, as low as 0.8% from BANYAN Σ (Gagné et al. 2018), so we must conclude that its membership is ambiguous.

2MASS J0249−0557ABc is the first ultracool triple system found in the β Pic moving group. The only other β Pic system containing more than one late-type component is the possible member DENIS J0041−5621AB (integrated-light type M7.5 vl-g; Gagné et al. 2015c; Shkolnik et al. 2017), a 7 au binary with an estimated orbital period of 126 years (Reiners et al. 2010). To our knowledge, no other ultracool triple systems are known in any other young moving groups. The only known binaries are 2MASS J1119−1137AB (Best et al. 2017), which is a likely TWA member, and DENIS J0357−4417AB (Bouy et al. 2003), which is a candidate Tuc-Hor member (Gagné et al. 2014, 2015b). 2MASS J0249−0557ABc is the sixth known substellar triple system, that is, composed entirely of likely brown dwarfs (Bouy et al. 2005; Radigan et al. 2013; Stone et al. 2016; Dupuy & Liu 2017). Compared to the 1950 au separation for 2MASS J0249−0557 c, the other known substellar triples are more compact, with the widest of them (VHS J1256−1257; Stone et al. 2016) having an outer pair separation of 100 au, and the rest having outer separations of 2–27 au.

In contrast to other known young ultracool binaries, 2MASS J0249−0557AB is much tighter (projected separation 2.17 ± 0.22 au at discovery). Its estimated orbital period of ≈8 years makes it likely to yield the first dynamical mass measurement in the β Pic moving group in the substellar regime. In addition to the usual strong tests of substellar models enabled by dynamical masses (e.g., Liu et al. 2008; Dupuy et al. 2010, 2016a; Crepp et al. 2012), this binary will yield the first substellar cooling age (i.e., using luminosity and mass) for a young moving group. Thus, 2MASS J0249−0557AB will enable a unique cross-calibration of substellar evolutionary model tracks by comparing to ages from the lithium-depletion boundary and stellar isochrone methods. The cooling rate of brown dwarfs predicted by evolutionary models has only been independently tested where brown dwarf binaries orbit young stars with gyrochronology-derived ages (Dupuy et al. 2009a, 2014) or where a brown dwarf orbits an older star with a (less precise) isochronal or kinematic age (e.g., Ireland et al. 2008; Bowler et al. 2018). Tests of substellar evolutionary models are especially needed at the young age of β Pic as they are frequently used to infer the physical properties of planetary-mass companions.

2MASS J0249−0557 c (${11.6}_{-1.0}^{+1.3}$ ${M}_{\mathrm{Jup}}$) is unique among companions at or below the deuterium-fusion boundary given its wide separation (1950 ± 200 au) and the fact that it orbits a very low-mass binary (${48}_{-12}^{+13}$ ${M}_{\mathrm{Jup}}$ and ${44}_{-11}^{+14}$ ${M}_{\mathrm{Jup}}$). Figure 12 shows the mass ratios of all known directly imaged planetary-mass companions (≲13 ${M}_{\mathrm{Jup}}$) as a function of their projected separation. There are only five other companions with similarly wide separations (≳10³ au): the AB Dor member GU Psc b (11 ± 2 ${M}_{\mathrm{Jup}}$ at 2000 au; Naud et al. 2014), the Ophiuchus member SR 12 c (13 ± 2 ${M}_{\mathrm{Jup}}$ at 1100 au; Kuzuhara et al. 2011), the young field objects Ross 458 c (9 ± 3 ${M}_{\mathrm{Jup}}$ at 1190 au; Goldman et al. 2010) and TYC 9486-927-1B (12–15 ${M}_{\mathrm{Jup}}$ at 6900 au; Deacon et al. 2016), and the old field object WD 0806−661 b (7.5 ± 1.5 ${M}_{\mathrm{Jup}}$ at 6900 au; Luhman et al. 2012).¹⁹ These host stars range from 0.3 to 2 ${M}_{\odot }$ (adopting the progenitor mass for WD 0806−661) and thus represent companion mass ratios of ∼0.03 or much lower, in contrast to the ∼0.1 mass ratio of 2MASS J0249−0557 c. (We adopt the combined mass of 2MASS J0249−0557AB as the host mass for the system.)

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Among planetary-mass companions at all separations, few have hosts with such low masses as 2MASS J0249−0557AB, even using its combined mass (50–150 ${M}_{\mathrm{Jup}}$ at 2σ). The two clearest examples are 2MASS J1207−3932 b (5 ± 2 ${M}_{\mathrm{Jup}}$), which orbits a 25 ${M}_{\mathrm{Jup}}$ TWA member (Chauvin et al. 2004), and 2MASS J0441+2301Bb (10 ± 2 ${M}_{\mathrm{Jup}}$), which orbits the 19 ± 3 ${M}_{\mathrm{Jup}}$ tertiary component of a quadruple system in Taurus (Todorov et al. 2010; Kraus et al. 2011; Bowler & Hillenbrand 2015).²⁰ The slightly higher-mass companions FU Tau B (≈16 ${M}_{\mathrm{Jup}}$; Luhman et al. 2009) and 2MASS J0219−3925B (14 ± 1 ${M}_{\mathrm{Jup}}$; Artigau et al. 2015) orbit a 50 ${M}_{\mathrm{Jup}}$ brown dwarf in Taurus and a 110 ${M}_{\mathrm{Jup}}$ star in Tuc-Hor, respectively.²¹ These systems' mass ratios range from 0.13 to 0.5, comparable to but somewhat higher than 2MASS J0249−0557 c. In addition, there are a number of potentially planetary-mass brown dwarfs on close-in orbits of other brown dwarfs with similar or only slightly higher masses that resemble scaled-down binary star systems: SDSS J2249+0044AB (L3+L5; Allers et al. 2010), CFBDSIR J1458+1013AB (T9+Y; Liu et al. 2011), WISE J1217+1626AB (T9+Y0; Liu et al. 2012), WISE J0146+4234AB (T9+Y0; Dupuy et al. 2015a), and 2MASS J1119−1137AB (L7+L7; Best et al. 2017). In short, 2MASS J0249−0557 c is the only planetary-mass companion with both a very wide separation (>10³ au) and relatively high mass ratio (M_comp/M_host ≳ 0.1), suggesting that it is more binary-like than planet-like.

The mass ratio of 2MASS J0249−0557 c to its host binary is consistent with typical stellar triple systems (e.g., Moe & Di Stefano 2017). But even viewed as a very low-mass analog of stellar systems, 2MASS J0249−0557 c is still unusual for the large separation of its tertiary orbit. At a projected separation of 1950 au, it is only weakly bound to 2MASS J0249−0557AB. Although theoretical work suggests that such wide systems can form via the dissolution of the parent cluster (Kouwenhoven et al. 2010), this route is less likely at low component masses, and the progenitor β Pic cluster may never have been dense enough to facilitate capture. Alternatively, turbulent fragmentation models of star formation do predict that objects can form at wide separations (e.g., Offner et al. 2009; Bate 2012). In this scenario, the 2MASS J0249−0557 system would represent the low-mass tail of the star formation process, drawn from an initial mass function that sharply drops toward very low masses (Chabrier 2003). This is consistent with previous surveys for wide-orbit planetary-mass companions that find such systems are rare in young moving groups (e.g., Aller et al. 2016; Naud et al. 2017).

An alternative hypothesis for the origin of 2MASS J0249−0557 c is that it formed in a disk around the binary brown dwarf pair and was scattered outward via dynamical interactions. For the masses and separations involved, this scenario is disfavored for several reasons. First, formation via the bottom-up core accretion process is strongly disfavored based on simple mass requirements. Given the combined mass of the brown dwarf binary host (∼100 ${M}_{\mathrm{Jup}}$), even a disk with a total gas mass equal to the central masses would contain only ∼1 ${M}_{\mathrm{Jup}}$ of solids. This mass is insufficient to trigger runaway gas accretion, even under favorable conditions (Bodenheimer & Pollack 1986; Piso & Youdin 2014). Formation of a tertiary in the disk by gravitational instability instead would also require very high disk masses, which have yet to be observed around brown dwarfs (e.g., Testi et al. 2016). To achieve the current system architecture in this scenario, one must also invoke dynamical interactions between the three objects. While binaries are efficient ejectors of planetary-mass objects (Smullen et al. 2016), the architecture of the 2MASS J0249−0557 system is somewhat disfavored based on energetic arguments. The Keplerian velocity of the tertiary is roughly 3% of the Keplerian velocity of the host binary. Typical scattering encounters would send the tertiary outward at velocities 10× higher than this (Valtonen & Karttunen 2006). Fine-tuning of the interaction would be required to achieve something so marginally bound.

In both scenarios, the fact that the PA of the tertiary companion (228649 ± 0013) is very close to that of the inner binary (2331 ± 03) is most likely a coincidence. Orbit monitoring of the inner binary is needed to determine the actual PA of the orbital node of 2MASS J0249−0557AB, but even if it is aligned with the companion PA, it would be difficult to physically explain orbital alignment over three orders of magnitude in separation.

2MASS J0249−0557 c is the first wide-orbit companion (≳10³ au) to have properties so similar to a close-in planet from the same moving group, in this case β Pic b (9 au). The existence of a third nearly identical, but free-floating, possible member of the β Pic group 2MASS J2208+2921 would make for a unique trio of planetary-mass objects. There are other well-known analogs; for example, the HR 8799 planets have spectra, colors, and magnitudes similar to that of free-floating objects like PSO J318.5338−22.8603 (Liu et al. 2013) and WISEP J004701.06+680352.1 (Gizis et al. 2015), but no such objects are kinematically associated with the HR 8799 system. 2MASS J0249−0557 c (and possibly 2MASS J2208+2921) are therefore "twins," not merely analogs, of β Pic b because they all formed from the same natal material. Figure 11 illustrates that the colors and magnitudes of these three objects are comparable within the uncertainties, as expected for having similar spectral types and the same age. Similarly, Table 5 shows that they have estimated masses that are consistent within the uncertainties.

If different formation mechanisms produced these objects, then their spectra could contain evidence of their divergent pasts. As noted above, we suspect that 2MASS J0249−0557 c arose from a star-formation-like process of global, top-down gravitational collapse in the same way as the free-floating object 2MASS J2208+2921. On the other hand, β Pic b bears architectural resemblance to planetary systems and thus may have formed via core accretion. Core accretion models and observations of solar system gas giants show substantial metal enrichment (e.g., Stevenson 1982; Bolton et al. 2017). Thus, if β Pic b is a scaled-up gas giant (≈13 ${M}_{\mathrm{Jup}}$), then we may expect to see substantial metal enrichment in its atmosphere. Thorngren et al. (2016) have shown that transiting planets over a wide range of masses (∼0.1–10 ${M}_{\mathrm{Jup}}$) have enhanced metal content with respect to their host stars, with ${Z}_{\mathrm{pl}}/{Z}_{\star }\,\approx 10\times {({M}_{\mathrm{pl}}/{M}_{\mathrm{Jup}})}^{-0.5}$. While this correlation was derived from bulk density measurements, the amount of heavy elements is so large that it implies a significant amount of the metals are likely present in planetary atmospheres as well as their cores.

Some have proposed that planets like β Pic b could form via gravitational instability in a disk (e.g., Boss 2011), though most models suggest that it is unlikely (e.g., Kratter et al. 2010; Rameau et al. 2013). In principle, metallicity enhancement is also possible in this case (Helled et al. 2014), either from dust trapping in spiral arms (Clarke & Lodato 2009) or from accretion of dust and planetesimals (Boley & Durisen 2010). However, in the modern paradigm in which most planetesimals are formed via the streaming instability (Youdin & Goodman 2005), such enhancement may be suppressed. Thus, if β Pic b showed metal enhancement compared to 2MASS J0249−0557 c, this could be a convincing signature of core accretion operating at very high planetary masses. Measuring elemental abundances via molecules in ultracool atmospheres is challenging, but significant progress has already been made on a number of directly imaged planets (e.g., Konopacky et al. 2013; Barman et al. 2015; Skemer et al. 2016; Lavie et al. 2017). The very wide separation of 2MASS J0249−0557 c (40'') and its nearly equatorial decl. will make it amenable to such follow-up observations from nearly any ground-based telescope without needing high-contrast AO.

Formation may also affect the typical rotation rates of planetary-mass objects. The relatively slow rotation of solar system planets is a well-known problem requiring some mechanism to shed angular momentum (e.g., Takata & Stevenson 1996). The equatorial velocity of β Pic b was measured to be 25 $\mathrm{km}\,{{\rm{s}}}^{-1}$ by Snellen et al. (2014), consistent with an extrapolation of the trend among solar system planets for faster rotation to higher masses. The free-floating β Pic moving group member PSO J318.5−22 (${6.5}_{-0.8}^{+1.2}$ ${M}_{\mathrm{Jup}}$) is lower in mass than β Pic b and shows a slower equatorial velocity (17.5 ± 1.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$), as would be expected if it followed the same rotation–mass relation (Allers et al. 2016). The results of Zhou et al. (2016) and Bryan et al. (2018) are also consistent with a single relationship between companions and free-floating objects at planetary masses. However, studies to date have been unable to hold both mass and age constant when testing for differences between the rotation of free-floating objects and companions. Fortunately, 2MASS J2208+2921 already has a published rotation period of 3.5 ± 0.2 hr (Metchev et al. 2015) and $v\sin (i)={40.6}_{-1.4}^{+1.3}$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ (Vos et al. 2017), both of which imply significantly more rapid rotation than β Pic b. This is suggestive of the split in behavior that is expected from the slowly rotating solar system planets: objects like β Pic b that spend their early evolution embedded in a disk experience some amount of angular momentum braking, while free-floating objects are more free to spin up. 2MASS J0249−0557 c likely did not form in a disk, so measuring its rotation from variability or $v\sin (i)$ would allow a direct test of this idea.

As directly imaged objects, β Pic b and 2MASS J0249−0557 c provide a new opportunity to test atmospheric compositions and angular momentum evolution for a close-in planet and a very wide companion that share a common mass and age and that formed from the same material.