Characterizing 51 Eri b from 1 to 5 μm: A Partly Cloudy Exoplanet

51 Eri b was observed with the Integral Field Spectrograph (IFS) of GPI through the K1 filter on 2015 November 06 UT and 2016 January 28 and through the K2 filter on 2015 December 18 UT (see Table 1). Standard procedures, namely using an argon arc lamp, were used to correct the data for instrumental flexure. To maximize the parallactic rotation for angular differential imaging (ADI; Marois et al. 2006), the observations were centered on the meridian passage. All of the GPI data sets underwent the same initial data processing steps using the GPI Data Reduction Pipeline v1.3.0 (DRP; Perrin et al. 2014). The processing steps included dark-current subtraction and bad-pixel identification and interpolation; this is followed by compensating for instrument flexure using the argon arc spectrum (Wolff et al. 2014). Following this step, the microspectra are extracted to generate the IFS data cubes (Maire et al. 2014). During the process of generating the 3D (x, y, λ) cubes, the microspectra data are resampled to $\lambda /\delta \lambda =65$ and 75 at K1 and K2, respectively, after which they are interpolated to a common wavelength scale and corrected for geometric distortion (Konopacky et al. 2014). The data cubes are then aligned to a common center calculated using the four satellite spots (Wang et al. 2014). The satellite spots are copies of the occulted central star, generated by the use of a regular square grid printed on the apodizer in the pupil plane (Marois et al. 2006; Sivaramakrishnan & Oppenheimer 2006; Macintosh et al. 2014). The satellite spots also help convert the photometry from contrast units to flux units. No background subtraction was performed since the following steps of high-pass filtering and point-spread function (PSF) subtraction efficiently remove this low-frequency component.

Table 1.  Observations of 51 Eri b

Date	Instrument	Filter	Total Int.	Field	Averaged	Averaged	Averaged
			time (minutes)	Rot. (°)	air mass	DIMM seeing (as)	MASS ${\tau }_{0}$ (ms)
2015 Jan 30	GS/GPI	Ja	70	23.8	1.15	0.52	3.26
2014 Dec 18	GS/GPI	Ha	38	37.7	1.14	⋯	⋯
2015 Nov 06	GS/GPI	K1b	55	30.5	1.17	0.38	1.56
2015 Dec 18	GS/GPI	K2b	103	71.7	1.22	0.69	0.94
2016 Jan 28	GS/GPI	K1b	97	55.5	1.15	0.86	4.40
2015 Oct 27	Keck/NIRC2	LPb	100	74.2	1.10	⋯	⋯
2016 Jan 02	Keck/NIRC2	MSb	139	115.7	1.18	⋯	⋯
2016 Jan 21	Keck/NIRC2	MSb	174	116.0	1.21	⋯	⋯
2016 Feb 04	Keck/NIRC2	MSb	148	101.4	1.21	⋯	⋯
2016 Feb 05	Keck/NIRC2	MSb	142	102.1	1.21	⋯	⋯

Notes.

^aMacintosh et al. (2015). ^bThis work.

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Further steps to remove quasi-static speckles and large-scale structures were executed outside the DRP. Each data cube was filtered using an unsharp mask with a box width of 11 pixels. The four satellite spots were then extracted from each wavelength slice and averaged over time to obtain templates of the star PSF. The Linear Optimized Combination of Images algorithm (LOCI; Lafrenière et al. 2007) was used to suppress the speckle field in each frame using a combination of aggressive parameters: dr = 5 px, N_A = 200 PSF FWHM, g = 0.5, and ${N}_{\delta }=0.5\mbox{--}0.75$ FWHM for the three data sets, where dr is the radial width of the optimization zone, N_A is the number of PSF FWHM that can be included in the zone, g is the ratio of the azimuthal and radial widths of the optimization zone, and N_δ defines the maximum separation of a potential astrophysical source in FWHM between the target and the reference PSF. The residual image of each wavelength slice was built from a trimmed (10%) temporal average of the sequence.

Final K1 and K2 broadband images were created using a weighted mean of the residual wavelength frames according to the spectrum of the planet, examples of which can be found in Figure 1. These broadband images were used to extract the astrometry of the planet in each data set thanks to a higher signal-to-noise ratio (S/N) than in individual frames. To do so, a negative template PSF was injected into the raw data at the estimated position and flux of the planet before applying LOCI and reduced using the same matrix coefficients as the original reduction (Marois et al. 2010). The process was iterated over these three parameters (x position, y position, flux) with the amoeba simplex optimization (Nelder & Mead 1965) until the integration squared pixel noise in a wedge of 2 × 2 FWHM was minimized. The best-fit position was then used to extract the contrast of the planet in each data set. The same procedure was executed in the noncollapsed wavelength residual images, varying only the flux of the negative template PSF and keeping the position fixed to prevent the algorithm from catching nearby brighter residual speckles in the lower S/N spectral slices. To measure uncertainties, we injected the template PSF with the measured planet contrast into each data cube at the same separation and 20 different position angles. We measured the fake signal with the same extraction procedure. The contrasts measured in the 2015 November 06 and 2016 January 28 K1 data sets agreed within the uncertainties, the latter having significantly better S/N, and were combined with the weighted mean to provide the final planet contrasts.

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2.1.1. Spectral Covariances

We observed the 51 Eri system on 2015 October 27 in the L_P filter with the NIRC2 camera (McLean & Sprayberry 2003) at the Keck II observatory (Program ID U055N2). The observations were taken in ADI mode, starting ∼1 hr prior to meridian crossing to maximize the field-of-view rotation. The target was observed for ∼3 hr total, with 100 minutes of on-source integration. The observations were acquired using the 400 mas focal plane mask and the circular undersized "in-circle" cold stop. To calibrate the planet brightness, unsaturated observations of the star were taken at the end of the observing sequence. The images were dark and flat-field corrected. We used the K_S-band lamp flats to build the flat-field and masked hot and bad pixels. As these observations were taken after the 2015 April servicing of NIRC2, the geometric distortion was corrected using the solution presented in Service et al. (2016, updating the original Yelda et al. 2010 solution), with an updated plate scale of 9.971 ± 0.004 mas pixel⁻¹ and the offset angle β (0.262 ± 0.020) that is required when calculating the position angle prior to rotating the images to put north up (Yelda et al. 2010). Postprocessing of the data was carried out using the Python version of the Karhunen–Loève (KL) Image Projection algorithm (KLIP; Amara & Quanz 2012; Soummer et al. 2012), pyKLIP (Wang et al. 2015). As part of this study, we included an NIRC2 module in the pyKLIP code base that is publicly available for users.³⁶ The algorithm accepts aligned images and performs PSF subtraction using KLIP where the image can be divided into sections both radially and azimuthally. Aside from the choice of zones, two main parameters were adjusted, the number of modes used in the KL transform and an exclusion criterion for reference PSFs, similar to N_δ mentioned above, that determine the number of pixels an astrophysical source would move due to the rotation of the reference stack. We carried out a parameter search where the four parameters mentioned were varied to optimize the S/N in the planet signal. The planet photometry was estimated using the method described above for the K1 and K2 filters, using a negative template PSF. The L_P magnitude contrast for the star/planet is 11.58 ± 0.15 mag, which agrees very well with the photometry in the original epoch, 11.62 ± 0.17 mag. The weighted mean of both measurements is used in the rest of the analysis.

Observations of 51 Eri b were taken in the M_S-band filter over four separate half nights on 2016 January 02 and 21 and 2016 February 04 and 05 with the Keck/NIRC2 Narrow camera. The details of the observations are presented in Table 1. Each night the target was observed for a period of ∼6 hr, as part of two separate NASA and UC Keck observing programs (Program IDs N179N2, U117N2). The data were obtained in ADI mode, with the field of view rotating at the sidereal rate. To reduce the effects of persistence and enable accurate thermal background correction, the star was nodded across the detector in four large dithers centered in each quadrant of the detector. Furthermore, to prevent saturation of the detector by the thermal background, the exposures were limited to 0.3 s with 200 coadds, without using an occulting spot. The images were dark and flat-field corrected with twilight sky flats, followed by hot and bad pixel correction. As with the L_P data, the solution provided by Service et al. (2016) was used to correct the NIRC2 Narrow camera geometric distortion. Finally, all of the images were rotated to put north up.

An additional step required for the M_S-band data that is not as critical for the other data sets is the background subtraction. Since the thermal background at 5 μm is large and highly time variable, rather than median combine or high-pass filter to remove the background, we adopted the least-squares sky-subtraction algorithm proposed in Galicher et al. (2011). For each point in the dither pattern, the algorithm uses the images where the star is in one of the other three positions to construct a reference library. We used a ring centered on the star to estimate the thermal background in each image, with an inner annulus of 24 pixels and an outer annulus of 240 pixels. The final calibration step involved aligning the background-corrected PSFs. Since the core of the PSF is saturated in the data, we aligned the data using two different methods: (1) fitting a 2D Gaussian to the wings of the stellar PSF to estimate the center of the star and then shifting the PSF to a predetermined pixel value to align all the images and (2) using the rotation symmetry of the PSF using the method described in Morzinski et al. (2015). To compare the two methods, we calculated the residuals between images aligned using the methods and compared the noise in the residuals and found them to be similar, so we chose to go with the 2D Gaussian, which is computationally faster.

The procedure used for the PSF subtraction for the M_S data was similar to that for the L_P data. The planet is not detected in each of the individual half-night data sets, requiring a combination of all four half nights to increase the S/N to detect the planet flux. To correctly combine the planet flux across the multiple epochs, we adjusted the PA to account for the astrophysical motion of the planet around the star, for which we used the best-fitting orbit presented in De Rosa et al. (2015). In the month between the first and last data sets, the planet rotated ∼048 or ∼0.4 pixel, which is a sufficiently large correction that it must be included in the data reduction. Each night's data were reduced individually to generate 603 PSF-subtracted images. These images were then combined by dividing each image into 13 annuli, which were combined using a weighted mean, where the weights are the inverse variance in each annulus. As seen in Figure 1, we detect the planet signal at ∼2–3σ. To confirm that we are detecting the planet, we rotated the data to match the PA value of the L_P epoch to find that the flux peak in the M_S band matches the location of the planet in L_P. We measured a star-to-planet contrast of 11.5 mag using the same procedure as described for the L_P data. We injected 25 fake PSFs that were scaled to match the contrast measured for the planet and detected the fakes at the same contrast as the planet. The final magnitude of the star-to-planet contrast in the M_S is 11.5 ± 0.5 mag.

The 2MASS near-IR colors of 51 Eri A were compared to empirical colors for young F0 stars taken from Kenyon & Hartmann (1995), where an F0IV star should have J − H = 0.13 mag and H − K = 0.03 mag. The colors of 51 Eri A estimated using the 2MASS photometry are however discrepant, with J − H = −0.03 ± 0.08 and H − K = 0.23 ± 0.08 mag. The discrepant near-IR colors combined with poor-quality flags suggest that the published photometry is potentially incorrect.

We observed the star 51 Eri A using the 6.5 m MMT on Mt. Hopkins with the ARIES instrument (McCarthy et al. 1998) on 2016 February 28 UT under photometric conditions. We obtained data in the MKO JHK_S broadband filters (Tokunaga et al. 2002), for a total of 3.4 minutes in each filter. To flux calibrate these observations, we observed a photometric standard star at a similar air mass as 51 Eri A, HR 1552 (Carter 1990). The raw images for both targets were processed through a standard near-IR reduction pipeline, performing dark-current subtraction, flat-field calibration, and bad-pixel correction. Aperture photometry was performed on both targets, with the curve of growth used to select an aperture that minimized the error on the measured flux. The measured brightness of 51 Eri A is presented in Table 2.

Table 2.  System Properties

Property	51 Eri A	51 Eri b
Distance (pc)	⋯	29.43 ± 0.29a
Age (Myr)	⋯	26 ± 3b
Spectral Type	F0IV	T6.5 ± 1.5
$\mathrm{log}(L/{L}_{\odot }$)	${0.85}_{-0.07}^{+0.06}$ c	$-{5.83}_{-0.12}^{+0.15}$ to $-{5.93}_{-0.14}^{+0.19}$ d
${T}_{\mathrm{eff}}$	7331±30 Ke	605–737 Kd
$\mathrm{log}g$	3.95 ± 0.04e	3.5–4.0d
${J}_{\mathrm{MKO}}$	4.690 ± 0.020d	19.04 ± 0.40d,f
${H}_{\mathrm{MKO}}$	4.562 ± 0.031d	18.99 ± 0.21d
${K}_{S,{MKO}}$	4.546 ± 0.024d	18.49 ± 0.19d
${K}_{\mathrm{MKO}}$	4.600 ± 0.024e	18.67 ± 0.19d
LP	4.604 ± 0.014e	16.20 ± 0.11d,g
MS	4.602 ± 0.014e	16.1 ± 0.5d

Notes.

^aHipparcos catalog (van Leeuwen 2007). ^bNielsen et al. (2016). ^cMacintosh et al. (2015) using hot-start predictions. ^dThis work. ^eStellar photometry estimated using SED fit. ^fDistance modulus = 2.34 ± 0.02 mag. ^gWeighted mean of the two L_P observations.

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Converting the MKO K_S-band measurement into the 2MASS system using empirical relations³⁷ yields ${K}_{S,2\mathrm{MASS}}=4.551\,\pm 0.032$ mag, which is within 1σ of the published 2MASS photometry. Furthermore, the J − H and H − K colors estimated from the revised photometry are 0.128 ± 0.037 mag and 0.016 ± 0.039 mag, which are consistent with the empirical expectations.

The published 51 Eri b spectrum in Macintosh et al. (2015) was calibrated using the Pickles stellar models (Pickles 1998) to estimate the spectrum of the primary, where each band was scaled using the published 2MASS photometry. In Figure 2 we present a comparison between the published spectrum and one scaled using the new MKO photometry, using the same stellar models. The revised photometry scales the planet spectrum higher by ∼10% in the J band and ∼15% in the H band, which is significant given the high S/N of the H-band data.

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To mitigate the effects of incorrect photometry, rather than scale the spectrum in pieces using the relevant broadband photometry, we decided to fit the full SED of 51 Eri A using literature photometry and colors, including Geneva $U,{B}_{1},B,{B}_{2},{V}_{1},V,G$ (Rufener & Nicolet 1988), Tycho2 ${B}_{T},{V}_{T}$/Hipparcos H_P (ESA 1997; Høg et al. 2000), MKO JHK_S (this work), and WISE $W1,W2$ (Cutri et al. 2013) measurements. We made use of the Geneva color relations as constraints to the full SED fit since the published Geneva V magnitude, which anchors the colors to estimate the remaining photometry, appears to be offset by ∼5% when compared to the Tycho2 photometry. The WISE W2 photometry was corrected using the Cotten & Song (2016) relation for bright stars. We combine the photometry with model stellar atmospheres from the BT-NextGen grid³⁸ (Allard et al. 2012), and we estimated the stellar spectrum using a five-parameter Markov chain Monte Carlo (MCMC) grid search. The best-fit atmosphere was found with ${T}_{\mathrm{eff}}=7331\pm 30$ K, $\mathrm{log}g=3.95\pm 0.04$, $[{\rm{M}}/{\rm{H}}]=-0.12\pm 0.06$, and a stellar radius $R=1.45\pm 0.02$ ${R}_{\odot }$ (assuming a parallax of 33.98 ± 0.34 mas; van Leeuwen 2007). No correction for extinction is performed as the extinction in the direction of 51 Eri is negligible (${A}_{V}=0.00;$ Guarinos 1992). These values are consistent with previous literature estimates (e.g., Koleva & Vazdekis 2012). The final SED of 51 Eri A is shown in Figure 3, which highlights the significantly discrepant 2MASS JH-band photometry that was used previously to calibrate the spectrum of 51 Eri b. We extracted MKO K and NIRC2 L_P and M_S photometry from the SED fit using the filter response functions presented in Tokunaga et al. (2002); see Table 2.

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3.2.1. Confirming the Stellar L_P Photometry

We present the final SED of the planet 51 Eri b in Figure 4 and use it to analyze the system properties in the following sections. Using the stellar SED estimated earlier, we have updated the J and H spectra that were published in Macintosh et al. (2015). In Table 2, we present the properties of the system, including updated MKO JHK and NIRC2 ${L}_{P}{M}_{S}$ photometry for both the star and the planet. A future study will refine the orbital solution presented in De Rosa et al. (2015).

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We plot a series of CMDs for ultracool objects in Figure 5 and compare the photometry of field M, L, and T dwarfs and young brown dwarfs and imaged companions to that of 51 Eri b (red star). The colors of 51 Eri b seem to match the phase space of the late-T dwarfs. To classify the spectral type of 51 Eri b, we do a chi-squared comparison of the GPI ${JHK}1K2$ spectrum of 51 Eri b to a library of brown dwarf spectra compiled from the IRTF (Cushing et al. 2005), SpeX (Burgasser 2014), and Montreal (e.g., Gagné et al. 2015; Robert et al. 2016) spectral libraries. Only a small subsample of the brown dwarfs have corresponding mid-IR photometry, so we choose to restrict our comparison to the near-IR. The spectra within the library were convolved with a Gaussian kernel to match the spectral resolution of GPI.

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To compute the chi-squared between the spectrum of 51 Eri b and the objects within the library, we use two different equations. The first method permits each individual filter spectrum to vary freely (unrestricted fit). In the unrestricted fit, we compute the ${\chi }^{2}$ statistic for the $j\mathrm{th}$ object within the library as

$$\begin{eqnarray}&&{\chi }_{j}^{2}=\displaystyle \sum _{i=1}^{4}{({{\boldsymbol{S}}}_{i}-{\alpha }_{i,j}{{\boldsymbol{F}}}_{i,j})}^{T}{{\boldsymbol{C}}}_{i}^{-1}({{\boldsymbol{S}}}_{i}-{\alpha }_{i,j}{{\boldsymbol{F}}}_{i,j}),\end{eqnarray} \tag{ 1 }$$

where ${{\boldsymbol{S}}}_{i}$ is the spectrum of the planet, ${{\boldsymbol{C}}}_{i}$ is the covariance matrix calculated in Section 6, and ${{\boldsymbol{F}}}_{i,j}$ is the spectrum of the $j\mathrm{th}$ comparison brown dwarf, all for the $i\mathrm{th}$ filter. For each object, the scale factor ${\alpha }_{i,j}$ that minimizes ${\chi }^{2}$ is found using a downhill simplex minimization algorithm. In this method, the scale factor for each object, ${\alpha }_{i,j}$, is allowed to vary between the four filters (${JHK}1K2$). This is equivalent to allowing the near-IR colors to vary freely up and down in order to better fit the object (e.g., Burningham et al. 2011).

In the second method, the individual filter spectra are still allowed to vary, only within the satellite spot brightness ratio uncertainty (restricted fit), thereby restricting the scale factor for each filter. For the restricted fit, the scale factor is split into two components. The first, ${\alpha }_{j}$, is independent of the filter and accounts for the bulk of the difference in flux between 51 Eri b and the comparison object due to differing distances and radii. The second, ${\beta }_{i,j}$, is a filter-dependent factor that accounts for uncertainties in the satellite spot ratios given in Maire et al. (2014). Equation (1) is modified to include an additional cost term restricting the possible values of ${\beta }_{i,j}$:

$$\begin{eqnarray}{\chi }_{j}^{2} & = & \displaystyle \sum _{i=1}^{4}[{({{\boldsymbol{S}}}_{i}-{\alpha }_{j}{\beta }_{i,j}{{\boldsymbol{F}}}_{i,j})}^{T}{{\boldsymbol{C}}}_{i}^{-1}({{\boldsymbol{S}}}_{i}-{\alpha }_{j}{\beta }_{i,j}{{\boldsymbol{F}}}_{i,j})\\ & & +\left.{N}_{i}{\left(\displaystyle \frac{{\beta }_{i,j}-1}{{\sigma }_{i}}\right)}^{2}\right]\end{eqnarray} \tag{ 2 }$$

where N_i is the number of spectral channels in the 51 Eri b spectrum for the $i\mathrm{th}$ filter, and ${\sigma }_{i}$ is the uncertainty in the satellite spot flux ratio given in Maire et al. (2014) for the same filter. The second term in Equation (2) penalizes values of the scale factor, ${\beta }_{i,j}$, that are very different from the satellite spot uncertainty and thus increases the chi-squared for objects significantly different from 51 Eri b.

The spectral type of 51 Eri b was estimated for both fits from the ${\chi }^{2}$ of the L5–T9 near-IR spectral standards (Burgasser et al. 2006; Kirkpatrick et al. 2010; Cushing et al. 2011). To compute the weighted mean and standard deviation of 51 Eri b, we converted the spectral type to a numerical value for the standard brown dwarfs, that is, L5 = 75, T5 = 85. Each numerical spectral type when compared to 51 Eri b is weighted according to the ratio of its ${\chi }^{2}$ to the minimum ${\chi }^{2}$ for all standards (e.g., Burgasser et al. 2010), and the lowest value was adopted as the spectral type of 51 Eri b. A systematic uncertainty of one-half subtype was assumed for the standards. We find that the two estimates are consistent with one another, that is, T6.3±1.3 and 6.1±1.4 for unrestricted and restricted fits, respectively; see Figure 6. We adopt a spectral type for 51 Eri b of T6.5±1.5 from the unrestricted fit, rounded to the nearest half subtype.

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The best-fit object for both the unrestricted and restricted fits was G 204-39 B (SDSS J175805.46+463311.9; ${\chi }_{\nu }^{2}=1.033$ and 1.209), a T6.5 brown dwarf common proper motion companion to the nearby M3 star G 204-39 A (Faherty et al. 2010). G 204-39 B has marginally low surface gravity based on photometric ($\mathrm{log}g\approx 4.5;$ Knapp et al. 2004) and spectroscopic measurements ($\mathrm{log}g=4.7$–4.9; Burgasser et al. 2006), indicative of it being younger than the field population. While the binary system is not thought to be a member of any known young moving group (Gagné et al. 2014), the stellar primary can be used to provide a constraint on the age of the system. Combining the X-ray and chromospheric activity indicators for the M-dwarf primary and a comparison of the luminosity of the secondary with evolutionary models, Faherty et al. (2010) adopt an age of 0.5–1.5 Gyr for the system. 51 Eri b is redder than the spectrum of G 204-39 B (Figure 7), especially in terms of the H − K color, which is a photometric diagnostic of low surface gravity among T-dwarfs (e.g., Knapp et al. 2004). This is consistent with the younger age of 51 Eri b, and the most likely cause for this is that it has lower surface gravity than does G 204-39 B.

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Additional good matches to the 51 Eri b spectrum include 2MASS J22282889–4310262 (2M 2228–43, ${\chi }_{\nu }^{2}=1.07$ and 1.26 for the two fits) and 2MASS J10073369–4555147 (2M 1007–45, ${\chi }_{\nu }^{2}=1.07$ and 1.33). 2M 2228–43 is a well-studied T6 brown dwarf that exhibits a spectrophotometric variability in multiple wavelengths that is indicative of patchy clouds in the photosphere (Buenzli et al. 2012; Yang et al. 2016). 2M 1007–45 is a T5 brown dwarf at a distance of 17 ± 2 pc (Smart et al. 2013). It was identified by Looper et al. (2007) as a low surface gravity object based on its H₂O $-J$ versus K/H spectral ratios defined in Burgasser et al. (2006); comparisons against solar-metallicity models imply an age of between 200 and 400 Myr (Looper et al. 2007).

The best-fit objects for each spectral type between spectral types T4.5 and T7.5 using the restricted fit are plotted in Figure 7. While the quality of the fits were generally good, none of the objects were able to provide a good match across all of the bands simultaneously, being too luminous in either the J or K bands. Differences in surface gravity, effective temperature, or metallicity could be the cause (e.g., Knapp et al. 2004). The poor fit to the color of 51 Eri b is especially apparent in the CMDs plotted in Figure 5, with 51 Eri b having unusually red near-IR colors relative to similar spectral type objects.

Searches for young companions and moving group objects have resulted in detections of several tens to hundreds of million year old L-type brown dwarf and planetary-mass companions as well as the identification of L-dwarf subclasses based on youth (e.g., Allers & Liu 2013; Filippazzo et al. 2015; Faherty et al. 2016; Liu et al. 2016). In comparison, there exist relatively few known (or suspected) young T-dwarf brown dwarfs. In Figure 8, we plot the known young T-dwarfs and compare them in a manner similar to what was done above for field brown dwarfs. The chi-squared for the fits is not much better than what is seen for the field dwarfs, which is likely due to the absence of young T-dwarfs of spectral type similar to 51 Eri b.

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The brown dwarf SDSS J1110+0116 with a spectral type of T5/T5.5 is the best-fitting young comparison object. It has been identified as a bona fide member of the AB Doradus moving group and is thus young (110–130 Myr) and low in mass (10–12 ${M}_{\mathrm{Jup}}$; Gagné et al. 2015). The other young field object that closely matches the near-IR spectrum of 51 Eri b is the T7 peculiar brown dwarf, CFBDSIR J2149−0403 (Delorme et al. 2012). CFBDSIR J2149−0403 was originally suggested to be a member of the AB Doradus moving group, but Delorme et al. (2017) find that the parallax and kinematics of the free-floating object rule out its membership in any known young moving group. However, despite the lack of proof of youth, medium-resolution spectroscopy examining the equivalent width of the KI doublet at 1.25 μm suggests that the object has low surface gravity and is most likely a young planetary-mass object (2–13 $M\mathrm{Jup}$). An alternative solution is that it is a higher mass, 2–40 $M\mathrm{Jup}$, brown dwarf with high metallicity. CFBDSIR J2149−0403 shows stronger methane absorption features in the red end of the H-band spectrum as compared to 51 Eri b. However, it is worth pointing out that while both young objects, SDSS J1110+0116 and CFBDSIR J2149−0403, are reasonable matches across the J and H spectra of 51 Eri b, they appear to be underluminous in the K band. A likely reason for this is that 51 Eri b is much younger than both of the comparison companions and thus has the lowest surface gravity among the three objects (Burgasser et al. 2006).

Based on the position of 51 Eri b in Figure 5, it appears that the trend of planetary-mass objects having redder colors compared to the field, seen in young L-type brown dwarfs and planetary-mass companions (Faherty et al. 2016; Liu et al. 2016), possibly continues for the T-type companions. Note that the $K-{L}_{P}$ CMD shows little reddening, which is natural if clouds are causing the effect. The effect of clouds is negligible in the K and L_P bands. Across both the near- and mid-IR CMDs, 51 Eri b is one of the reddest T-type objects, and within its spectral classification it has the reddest colors. This trend in the 51 Eri b colors was originally noted in Macintosh et al. (2015), where they compared the L_P versus $H-{L}_{P}$ color for the planet and noted that it was clearly redder than the field. Rather than simply being redder than the field T-dwarfs because of the presence of clouds, we present a second possible interpretation for the red colors of 51 Eri b, of the planet still undergoing the process of transitioning from L-type to T-type. This hypothesis assumes that the evolutionary track followed is gravity dependent, with examples for higher mass objects shown in Figure 9. In this scenario, 51 Eri b transitions at fainter magnitudes than that seen for field L–T transition brown dwarfs, and it has not yet completed its evolutionary transition to reach the blue colors typical of field mid-T dwarfs.

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In Figure 9, we replot the J vs. J − H panel from the series of CMDs shown in Figure 5. In addition to the photometry of 51 Eri b and the field and young brown dwarfs, we also overplot two low-mass, 5 and 14 ${M}_{\mathrm{Jup}}$, evolutionary model tracks (assuming hot-start conditions) from Saumon & Marley (2008) and Marley et al. (2012). If the L–T transition is gravity dependent, as multiple lines of evidence now suggest (Leggett et al. 2008; Dupuy et al. 2009; Stephens et al. 2009), then lower mass objects may turn blue at fainter absolute magnitudes than field objects. In Figure 9, we show a simple model in which the L-to-T transition begins at 900 K at $\mathrm{log}g=4$ (solid red line) instead of 1200 K at $\mathrm{log}g=5.3$ (dashed black line). In the case of a $5{M}_{\mathrm{Jup}}$ planet, the L-to-T transition begins and ends about one magnitude fainter in the J band than is observed for the field population. Furthermore, the congruence of the spectrum of SDSS J1110+0116 with 51 Eri b (Figure 8) is interesting as SDSS J1110+0116 lies just short of the blue end of the field L-to-T transition, although it does so at an absolute magnitude just slightly fainter than the field transition magnitude. While these simple models explain the fainter absolute magnitudes of the transition, their colors are too blue and appear to miss the younger brown dwarf and free-floating planets. Similarly, the models are too blue to match the T-dwarf sequence. Clearly, more sophisticated modeling of evolution through the L-to-T transition, accounting for inhomogeneous cloud cover and a gravity-dependent transition mechanism as well as a range of initial conditions, is required. Testing this hypothesis is difficult and would require knowledge of the true mass of the companion as well as the formation mechanism. If this hypothesis is true, then the only objects that are brighter on the CMD should be higher mass objects. There should not be any lower mass objects above and to the left of 51 Eri b on the J vs. J − H CMD shown in Figure 9.

In Section 4.3, we suggested that 51 Eri b, rather than having completely evolved to T-type, could be transitioning from L to T. In this scenario, the cloud composition of the planetary atmosphere might still be influenced by the deep iron and silicate condensate grains and patchy cloud atmosphere. Therefore, we compared the planet SED to a grid of models with a fixed low surface gravity and solar metallicity, where the key variable is the cloud hole fraction, and the unique aspect of this grid is the presence of iron or silicate clouds in an atmosphere with clear indications of methane absorption. The clouds are modeled using the prescription presented in Ackerman & Marley (2001), where cloud thickness is parameterized via an efficiency factor (${f}_{\mathrm{sed}}$). Small values of ${f}_{\mathrm{sed}}$ indicate atmospheres with thick clouds, whereas large values of ${f}_{\mathrm{sed}}$ are for atmospheres with large particles that rain out of the atmosphere, leaving optically thinner clouds. As mentioned earlier, the primary condensate species in this grid are iron, silicate, and corundum clouds, molecules that are expected to dominate clouds in L-dwarfs (Saumon & Marley 2008; Stephens et al. 2009). At the L–T transition, clouds are expected to be patchy, so for each ${T}_{\mathrm{eff}}$, the models went from fully cloudy, with ${f}_{\mathrm{sed}}=2$ and 0% holes, to an atmosphere with ${f}_{\mathrm{sed}}=2$ and 75% holes (patchy clouds). The methodology used to calculate the flux emitted from the patchy cloud atmosphere includes both cloud and cloud-free regions simultaneously in the atmosphere using a single global temperature–pressure profile and is not created via a linear combination of two models, as is sometimes done in the literature (Marley et al. 2010). The iron and silicate cloud grid models use solar metallicity (Lodders 2003). The opacity database used for the absorbers are described in Freedman et al. (2008), including updated molecular line lists for ammonia and methane (Yurchenko et al. 2011; Yurchenko & Tennyson 2014). The models span effective temperatures from 600 to 1000 K for solar metallicity ([M/H] = 0.0) and low surface gravity ($\mathrm{log}g=3.25,3.50$; see Table 3).

Presented in Figure 10 is the best-fitting model to the SED of 51 Eri b. Stated in the figure are the model parameters along with the radius of the planet required to scale the model spectrum to match the planet SED. This scaling factor is required since the model spectra are typically computed to be the emission at the photosphere or at 10 pc from the object. One of the free parameters in most model fitting codes is the term R²/d² to scale the model flux to match the SED, where R is the radius of the planet and d is the distance to the object. For 51 Eri, the distance is known to better than 2% (see Table 2), so we only fit the radius term. Shown in Figure 11 is the posterior distribution for the radius, where we find that the best-fitting radii are significantly smaller than that predicted by evolutionary models, for example, 1.33–1.14 ${R}_{\mathrm{Jup}}$ for a 2–10 ${M}_{\mathrm{Jup}}$ hot/cold-start planet at the age of 51 Eri (Marley et al. 2007; Fortney et al. 2008). This discrepancy has been noted previously as well for the HR8799 planets (Marois et al. 2008; Bowler et al. 2010; Barman et al. 2011; Currie et al. 2011; Marley et al. 2012), β Pic b (Morzinski et al. 2015), and for 51 Eri b itself in the discovery paper (Macintosh et al. 2015). In an attempt to circumvent this issue, while modeling the SED we adopted a Bayesian prior probability density function for the radius in the form of a Gaussian centered on the expected radius from evolutionary models (green line in Figure 12), with the width chosen to include the radius of Jupiter. Without the prior (i.e., using a uniform prior), the median radius is 0.68 ${R}_{\mathrm{Jup}}$ and ${T}_{\mathrm{eff}}\sim 740$ K; with the prior, the median radius value is forced closer to the predictions of evolutionary models (red line in Figure 12) at 0.98 ${R}_{\mathrm{Jup}}$ and ${T}_{\mathrm{eff}}$ ∼ 690 K, biasing the luminosity of the planet to larger values. When fitting the SED, the term that is conserved is the luminosity rather than the effective temperature or the radius. Adopting the evolutionary radius and marginalizing over the uncertainty in radius raises the luminosity ($\mathrm{log}L/{L}_{\odot }$) from −5.83 to −5.65. Since observational constraints on the radius for young planets are unavailable, we chose to use an uninformative prior.

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Plotted in Figure 11 are the normalized posterior distributions for each of the model parameters varied in the model fit, along with the covariances to show how each of the parameters are affected. Since the grid only had a few models with $\mathrm{log}g=3.5$, with the majority being 3.25, we marginalized over the surface gravity. The irregular shape of the effective temperature posterior is caused by the missing models in the grid. The median effective temperature, 737 K, estimated from the grid falls right in between the range of best-fitting temperatures from the models in the Macintosh et al. (2015) paper (700–750 K). However, based on the shape of the posterior and the covariances, the peak of the effective temperature distribution extends to cooler temperatures. Since the L-to-T transition has been suggested to arise from holes or low-opacity patches appearing in an initially more uniform cloud deck (Ackerman & Marley 2001; Burgasser et al. 2002; Marley et al. 2010), our finding here that partly cloudy models best fit the 51 Eri b spectrum is consistent with this interpretation. In general, however, the models struggled to fit the entire planet SED, typically being able to fit either the near- or mid-IR portions of the SED. The inability to fit mid-IR photometry suggests that chemical equilibrium models are not appropriate. Disequilibrium chemistry predicts less CH₄ in the atmosphere and could explain the higher flux at 1.6 μm and in the L_P band. It would also introduce CO, accounting for the lower flux in the M_S band.

In Section 4.1, we showed that the best-fitting spectral type of 51 Eri b is a mid-to-late-T dwarf. At the effective temperatures of mid-to-late-T dwarfs, Cr, MnS, Na₂S, ZnS, and KCl are expected to condense and form clouds high in the photosphere. The second grid we tested the planet SED against made use of a model grid that includes salt and sulfide clouds to test additional parameters such as the surface gravity and metallicity (which were varied, unlike the iron/silicate grid) and the properties of clouds typically associated with T-dwarfs. The grid was designed specifically for lower temperature objects ($450\sim 900$ K; Morley et al. 2012, 2014) and has been used successfully to reproduce the SED of GJ 504 b (Skemer et al. 2016), a cool low-mass companion with a similar spectral type (late-T) that is comparable to 51 Eri b (Kuzuhara et al. 2013). Note that the use of this cloud grid does not preclude the possibility of the planet transitioning from L to T.

Also included as part of this grid are the clear atmosphere models from Saumon & Marley (2008), the ranges for which are presented in Table 3. The ranges of parameters varied are presented in Table 3, including temperatures, surface gravities, metallicities, and sedimentation factor (${f}_{\mathrm{sed}}$) ranging from cloudy (${f}_{\mathrm{sed}}$ = 1) to cloud-free. The cloud model used in the sulfide/salt grid is the same as the one described above. In addition to the opacity updates mentioned above, opacity effects due to alkali metals (Li, Na, K) have been included using the results from Allard et al. (2005). For effective temperatures between 450 and 775 K, the grid is complete with models available for every step of the varied parameters. For effective temperatures between 800 and 900 K, the temperature steps switch from increments of 25–50 K, and there are no models with ${f}_{\mathrm{sed}}$ values of 1 and 2. This grid does not include the opacity effect that is due to iron and silicate condensates. A future series of papers describing an extended atmosphere model grid will describe the updates, but the present grid extends the models to greater than solar metallicities.

In Figure 13, we present the four best-fitting model atmospheres for 51 Eri b. Presented in each panel are the atmosphere with the lowest reduced chi-squared in one of four cases, namely, solar and cloudless (top left), solar and cloudy (top right), nonsolar and cloudless (bottom left), and nonsolar and cloudy (bottom right). Both cloudless model atmospheres are warmer and thus fit the near-IR spectrum of the planet while completely missing the L_P photometry. The cloudy atmosphere model fits are cooler and do a much better job of fitting the overall SED of 51 Eri b, and the best-fitting atmospheres for both solar and nonsolar metallicity have very similar reduced chi-squared values.

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The normalized posterior distributions for the different parameters varied as part of the model fitting are shown in Figure 14. The best-fitting ${T}_{\mathrm{eff}}$ (${605}_{-66}^{+61}$ K) is much cooler in comparison to the iron/silicate grid, but the values are within 2σ of each other. We also note that the median might not be the best estimate for the effective temperature PDF in the iron/silicate grid where the peak extended to cooler temperatures. For the surface gravity and metallicity posterior distributions, we present the median values and error bar assuming a Gaussian distribution, though they may not be Gaussian. The surface gravity PDF suggests that the planet has high surface gravity. However, 51 Eri b is clearly a low-mass companion, indicating that the data do not constrain the gravity. A prior might help constrain the distribution, but there are currently no physically motivated priors available for the surface gravity of young planets. Similarly, the PDF for the metallicity is also unconstrained, and higher resolution spectra in the K band might help provide greater constraints on the metallicity of 51 Eri b (Konopacky et al. 2013).

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A difference between the iron/silicate and salt/sulfide atmosphere grids is in the planet radius, where the best-fit radii for the cloudy models and the median radius of the PDF for the salt/sulfide models are much closer to evolutionary model predictions. A possible explanation for this discrepancy is that fitting the lower effective temperatures while still matching the bolometric luminosity requires a larger radius. If the iron/silicate models extended to lower temperatures, assuming the continued presence of these clouds at these colder temperatures, it is likely that the radius discrepancy would not be as apparent. The sedimentation factor was fixed (at ${f}_{\mathrm{sed}}=2$) in the iron/silicate grids but had varying hole fractions (${h}_{\mathrm{frac}}$). In the sulfide/salt grid, ${f}_{\mathrm{sed}}$ was varied, and the median value for the distribution is ${f}_{\mathrm{sed}}=2.48$. If we equate the ${h}_{\mathrm{frac}}$ from the iron/silicate model with the ${f}_{\mathrm{sed}}$ as the physics controlling the emission of flux from the photosphere, then for both model grids the best-fitting models tend to favor the presence of clouds over cloud-free atmospheres. Furthermore, in both cases, the best-fitting models were not the fully cloudy atmospheres, with the smallest ${h}_{\mathrm{frac}}$/${f}_{\mathrm{sed}}$. While the cloud compositions in both models are different, fitting either grid requires the cloud opacity. This can be achieved in one of two ways: either make the deep iron/silicate clouds be very vertically extended (small ${f}_{\mathrm{sed}}$) or introduce a new cloud layer in the form of the sulfide/salt clouds.

The cloudy model atmosphere fits presented in Figure 13 match the H through K spectrum while being slightly underluminous in the J and overluminous M_S bands. Given the large photometric errors in the M_S data, the model photometry lies within 2σ of the data. JWST and other future low-background mid-IR instruments will better constrain the 3–24 μm SED, a further test of current models. In Figure 15, we show 10 of the best-fitting models assuming cloudy (sulfide/salt clouds) or cloudless atmospheres extended out to 20 μm. It is clear from these models that observations with the coronagraph on the Near InfraRed Camera, spanning the 3–5 μm wavelengths, will add significant constraints on the atmosphere of the planet. If the planet can be studied with the Mid Infrared Instrument, it could be used to apply constraints on the chemical disequilibrium in the atmosphere through observations of NH₃ in the 10–11 μm range.

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The two different grids used in this study have produced similar luminosity predictions for the planet despite the different cloud compositions. From the iron/silicate grid we infer a bolometric luminosity of $\mathrm{log}L/{L}_{\odot }=-{5.83}_{-0.12}^{+0.15}$, and $\mathrm{log}L/{L}_{\odot }=-{5.93}_{-0.14}^{+0.19}$ from the sulfide/salt model atmospheres. We compare these luminosity estimates to predictions of evolutionary models to infer the planet mass and discuss its initial formation conditions.

5.3.1. Standard Cold- and Hot-start Models

In Figure 16 we compare the bolometric luminosity to evolutionary models for planets formed via the two extreme scenarios, namely, the hot-start and cold-start models (Burrows et al. 1997; Marley et al. 2007). In the hot-start scenario, planets are formed with high initial entropy and are very luminous at birth. This scenario is usually associated with rapid formation in the circumstellar disk through disk instabilities. Alternatively, in the cold-start scenario, which is often associated with current 1D models of the core-accretion mechanism, planets start with a solid core that accretes gas from the stellar disk. The accreting gas loses energy via a radiatively efficient accretion shock and form with low initial entropy and thereby lower postformation luminosity.

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The other directly imaged companions plotted in Figure 16 can all be considered as having formed via the hot-start scenario. Despite the older age assessment for the companion in this study, 26 ± 3 Myr (Nielsen et al. 2016) compared to 20 ± 6 Myr (Macintosh et al. 2015), the revised luminosity when compared to the system age places 51 Eri b in a location where either cold or hot initial conditions are possible. Based on the hot-start tracks, it would have an inferred mass between 1 and 2 ${M}_{\mathrm{Jup}}$. However, for the cold-start case, the planet mass could lie anywhere between 2 and 12 ${M}_{\mathrm{Jup}}$, since the model luminosity is largely independent of mass at the age of 51 Eri b. Dynamical mass estimates for the planet could help clarify the formation mechanism, especially if the planet mass $\gt 2$ ${M}_{\mathrm{Jup}}$.

5.3.2. Warm-start Models

Spiegel & Burrows (2012) proposed a complete family of solutions existing between the hot- and cold-start extreme cases. Warm-start models³⁹ explore a wide range of initial entropies aimed at covering the possible range of initial parameters that govern the formation of planets. In Figure 17, we compare the inferred bolometric luminosity and the planet SED to models from Spiegel & Burrows (2012). The Spiegel & Burrows (2012) models are evolutionary tracks calculated assuming different initial entropies for the planet, between 8 and 13 ${k}_{{\rm{B}}}$/baryon, where ${k}_{{\rm{B}}}$ is Boltzmann's constant, with steps of 0.25 ${k}_{{\rm{B}}}$/baryon and masses between 1 and 15 ${M}_{\mathrm{Jup}}$ with steps of 1 ${M}_{\mathrm{Jup}}$. Four different model atmospheres are considered in combination with the evolutionary model: cloud-free and solar metallicity to fully cloudy with 3× solar metallicity (Burrows et al. 2011). The bolometric luminosity of each point in the grid for each of the four atmosphere scenarios was computed by integrating the SED over the wavelength range. Because of the sparse sampling of the grid, we linearly interpolate the evolutionary tracks with steps of 0.06 ${k}_{{\rm{B}}}$/baryon and 0.2 ${M}_{\mathrm{Jup}}$.

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In the top row of Figure 17, we plot the probabilities for each grid point measured by comparing the average of the inferred bolometric luminosities from the SED fit ($\mathrm{log}L/{L}_{\odot }$ = −5.87 ± 0.15) to the predictions of the Spiegel & Burrows (2012) models with the four atmosphere conditions. For the bottom row in Figure 17, the surface is calculated by fitting the planet SED to the Spiegel & Burrows (2012) model atmosphere grid, using Equation (2). For both comparisons, luminosity and SED, we chose the age of the evolutionary grid best matching the age of 51 Eri (25 Myr), to minimize the number of interpolations, and only varied the mass of the planet and initial entropy for the models.

Mordasini (2013) find that the luminosity of a planet that underwent accretion through a supercritical shock (the standard cold-start core accretion hypothesis) is highly dependent on the mass of the core, ${M}_{\mathrm{core}}^{2-3}$. Therefore, the continuum of warm-start models can also be explained by similar bulk-mass planets with increasing core mass. These models suggest that the entropy of 51 Eri b can be explained via core accretion, with a core mass ranging between 15 and 127 ${M}_{\oplus }$, which can reproduce the planet luminosity with various initial entropies.

The four panels generated by fitting the inferred luminosity (upper four panels) appear highly consistent and in agreement with the results from Figure 16. The 1σ contour encompasses the entire available entropy space, where for intermediate and high entropies the most likely mass for the planet is between 2 and 3 ${M}_{\mathrm{Jup}}$ and for low initial entropy the most likely mass for the planet increases, making distinguishing between cold, warm, and hot starts difficult.

When we compare the model spectra directly to the planet SED, the surface is qualitatively similar to that made with the luminosity but shifted to higher mass and with the 1σ contours and best-fit models favoring lower entropy. According to the Mordasini (2013) models, the fits presented here would be consistent with a planet having core masses ranging from 15 to 127 ${M}_{\oplus }$.

Compared to other directly imaged companions (see figures in Marleau & Cumming 2014), 51 Eri b is the only planet compatible with very low initial entropy and the cold-start case. Tighter constraints on the bolometric luminosity or higher S/N data will help to reduce the width of the two branches, and independent mass constraints from dynamical measurements will enable us to infer the initial entropy and possible formation route. Atmospheric retrievals or higher resolution spectra aimed at exploring and characterizing the planet's chemical composition might also help us understand whether the planet has higher C/O ratios than the star, since planetary C/O can be used to understand planet formation (Öberg et al. 2011; Konopacky et al. 2013).