MAGELLAN ADAPTIVE OPTICS FIRST-LIGHT OBSERVATIONS OF THE EXOPLANET β PIC b. I. DIRECT IMAGING IN THE FAR-RED OPTICAL WITH MagAO+VisAO AND IN THE NEAR-IR WITH NICI^*,†

Because this was the first attempt to conduct high-contrast observations with VisAO, we used our longest wavelength bandpass to maximize Strehl ratio (SR) and flux from the thermally self-luminous planet. We refer to this filter as "Y-short," or Y_S. For a complete characterization of this filter see Appendix A. In brief, it is defined by a long-pass dichroic at 950 μm and the CCD QE cutoff at ∼1.1 μm. Including a representative atmosphere in the profile, the central wavelength of Y_S is 0.985 μm and the width is 0.086 μm.

The VisAO camera contains a partially transmissive occulting mask, used to prevent saturation of the CCD when observing bright stars. The mask has a radius equivalent to 01 were it in the focal plane, but it is approximately 60 mm out of focus in an f/52 beam. This has two consequences of note here. The first is that the mask has an apodized attenuation profile that extends to ∼08 in radius, so at a separation of ∼046, β Pic b is under the mask. The second, and more challenging, consequence is that the mask attenuation will depend on wavefront quality. We did not fully characterize the mask using β Pic itself, so we bootstrapped an attenuation profile from other measurements at different levels of wavefront correction. We describe this process in detail in Appendix B. We estimate that the mask transmission at the separation of β Pic b was $0.60^{+0.05}_{-0.10}$.

In Close et al. (2013), we describe the calibration of plate-scale in several filters and North orientation of the VisAO camera. Here we describe our calibrations in Y_S and how we tied VisAO to the Clio2 astrometry. The primary stars used for VisAO calibration were θ¹ Ori B1 and B2 in the Trapezium. These stars were observed repeatedly and with a separation of ∼094 B2 are well within the isoplanatic patch when guiding on B1. Close et al. (2013) recently showed that all four stars in θ¹ Ori B are exhibiting orbital motion, so we measured their current astrometry using the wider field of view (FOV) Clio2 camera. A complete description of these measurements is provided in Paper II. In brief, we used combinations of Trapezium stars other than B1 and B2 to measure the distortion, plate-scale, and orientation of Clio2. This was done using the recent astrometry given in Close et al. (2012b), which used LBT AO/Pisces referenced to Hubble Space Telescope (HST) astrometry from Ricci et al. (2008). We then compared measurements of B1 and B2 with Clio2 to those with VisAO. This was done in 2012 December in the Y_S filter with the occulting mask out of the beam. The extra glass added by the mask substrate changes the focus position slightly, decreasing the plate-scale. We measured this change in 2013 May also using θ¹ Ori B1 and B2. The ratio of plate-scales with and without the mask is 0.9972 ± 0.0003. This was applied to the Y_S-open plate-scale to determine the Y_S-mask plate-scale.

We also determined the orientation of the CCD with respect to north, which we denote by NORTH_VisAO. Our images are derotated counterclockwise using the equation DEROT_VisAO = ROTOFF + 90^o + NORTH_VisAO, where ROTOFF is the rotator offset, equal to rotator angle plus parallactic angle. The astrometric calibration of VisAO is summarized in Table 1.

By dithering θ¹ Ori B around the detector we diagnosed a slight focal plane tilt, which causes a small change in plate-scale, <1%, from top to bottom predominantly in the y-direction (Close et al. 2013). At the ∼047 separation of β Pic b this change in plate-scale amounts to less than 1 mas, so we neglect it.

We observed β Pic with VisAO on the night of 2012 December 4 UT in the Y_S filter using the 50/50 beam splitter, sending half the λ < 1 μm light to the PWFS. The image rotator was fixed to facilitate angular differential imaging (ADI, Liu 2004; Marois et al. 2006). Conditions were photometric. V-band seeing, as measured by a colocated differential image motion monitor (DIMM), varied from ∼045 ∼075 during the 4.17 hr of elapsed time included in these observations.

3.1.1. VisAO Point-spread Function and Strehl Ratio

Toward the end of the observation we took off-mask calibration data to assess AO performance and calibrate our photometry. We took 1061 0.283 s frames off the occulting mask, at airmass 1.14. V-band seeing as measured by the DIMM was ∼065 during these measurements. To avoid saturation this data was taken in our fastest full-frame mode (1024 × 1024 pixels at 3.51 frames per second) and in the lowest gain setting. Even with these settings, we saturated the peak pixel in roughly a third of the exposures. To compensate we selected frames with peak pixel between 8000 and 9000 ADU, where the detector is linear, such that we are using data between approximately the 75th and 25th percentiles.

VisAO and Clio2 are operated simultaneously. The dichroic entrance window of Clio2 transmits light with λ ≳ 1.05 μm while reflecting shorter wavelengths to the PWFS and VisAO camera. When working in the thermal IR with Clio2, we perform small pointing offsets (called "nods") to facilitate background subtraction. These nods occur at intervals ranging from ∼2 to ∼5 minutes depending on wavelength and star brightness. The consequence for VisAO observations is occasionally short (5–15 s) periods of unusable data while the AO loop is paused during a nod. Pausing the loop causes wavefront error (WFE) to become much worse. To automatically reject these periods during postprocessing we apply a WFE cut using AO telemetry (Males et al. 2012). For all of these observations we used a 130 nm rms phase. For the point-spread function (PSF)measurement this rejected 84 frames. We then registered and median-combined the remaining 491 images, with the result shown in Figure 1.

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The unsaturated unocculted PSF core has a FWHM of 4.73 pixels (37 mas), compared to the 6.5 m diffraction limit at Y_S of 3.87 pixels (31 mas). We have identified two sources of broadening: ∼7 mas of residual jitter, most likely due to 60 Hz primary mirror cell fans, and the CCD charge diffusion pixel response function (PRF). For a near-Nyquist sampled CCD, charge diffusion causes a blurring effect, which was well documented for the HST Advanced Camera for Surveys (ACS) and WFPC cameras. See Krist (2003), Anderson & King (2006), and the ACS handbook.¹¹ We measured the PRF in the lab and found that it broadens our PSF by ∼0.4 pixels and lowers the peak such that SR due to PRF alone is 80%. The SR was measured using WFS telemetry, and the unsaturated PSF was 32 ± 2%. Because this includes PRF, we can divide by 0.8 to estimate that the true Y_S SR was 40%.

3.1.2. High-contrast Observations

The observations intended to detect β Pic b were conducted in full-frame mode (1024 × 1024 pixels, 8'' × 8''), in the camera's highest sensitivity gain setting, with an individual exposure time of 2.27 s. The star was behind the occulting mask, so no dithers were conducted. The individual images were bias- and dark-subtracted, using shutter-closed darks taken at 15 minute intervals throughout the observation. We did not flat field. The CCD-47 has very low pixel-to-pixel variation, and with an 8'' × 8'' FOV we expect only small illumination changes across an image. Clio2 nods were rejected using WFE telemetry as described above. We then examined each image by eye, rejecting those with apparent poor mask alignment or poor AO correction. Finally, to reduce the number of images to process, we median coadded the remaining 3399 dark-subtracted exposures until either 30 s had elapsed or 05 of rotation had occurred. This process resulted in 317 images corresponding to 2.5 hr of open-shutter data, with an elapsed clock-time of 4.17 hr and 116° of sky rotation from start to finish. Airmass was 1.12 at the beginning, reached 1.08 at transit, and was at a maximum of 1.29 at the end of the observations.

The coadded images were first coarsely registered and centered using a beam splitter ghost. The mask is partially transmissive (ND ≈2.8) in the core. To more finely register the images we located the center of rotational symmetry of the attenuated star using cross correlation with a tolerance of 0.05 pixels. We median-combined the registered images, forming our master PSF. This is shown in Figure 1.

We employed a reduction technique based on principal component analysis, using the Karhunen-Loéve Image Processing (KLIP) algorithm of Soummer et al. (2012) (see also Amara & Quanz 2012). We applied KLIP in search regions, as suggested by Soummer et al. (2012), dividing the image in both radius and azimuth in "optimization regions" using the strategy developed by Lafrenière et al. (2007) for the locally optimized combination of images (LOCI) algorithm. In each optimization region we conducted the complete KLIP procedure. Only a subsection of the optimization region, a "subtraction region,was kept. We used the parameters specifying the regions given by Lafrenière et al. (2007), except that instead of having the same azimuthal width, our subtraction regions were one-third the width of the optimization regions in azimuth. This provided a noticeable (∼10%) improvement in signal-to-noise ratio (S/N) without significantly increasing the computational burden. The final image is formed by combining the individually reduced subtraction regions. Note that when we choose the number of KL modes, we apply this choice to all subtraction regions.

We compare the results of our KLIP reduction to the simultaneously obtained Clio2 M' image, shown in Figure 2 and described in Paper II. The Clio2 position is shown in both images as an ellipse corresponding to the 2σ uncertainty. Here we use the mean position and error using data taken with Clio2 in four filters on subsequent nights. See Paper II for further details.

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In Figure 3, we zoom in on the VisAO image of β Pic b and compare it to the PSF at that position under the occulting mask. This under-the-mask PSF was measured on-sky in closed loop by scanning a star across the mask. The mask radially elongates a point source, and the image produced by our KLIP analysis matches this expectation. We also show two representative fake planets, injected using the same PSF (the details of this procedure are given below). The signal recovered at the precisely known location of the planet closely matches the expected signal based on our PSF model.

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Other tests conducted included a basic ADI-only reduction, which yields a lower significance detection (S/N < 3). We also tried many other search region geometries. Though varying reduction parameters modulates various speckles throughout the image and changes algorithm throughput, the signal at the location of β Pic b is always detected. We also tested reducing half the data in alternating chunks (to preserve rotation), and even with ADI-only we detected β Pic b using only half the data (albeit with much lower S/N). Along with our PSF comparisons, these results give confidence that our detection of β Pic b is valid. We quantify the significance of this detection next.

3.1.3. Detection Significance

To assess the statistical significance of the VisAO detection, we next calculated an S/N map. For this analysis we used 150 KL modes (we discuss choosing the number of modes in Section 3.1.4). The final image was Gaussian smoothed with a kernel of width 3 pixels. Each pixel was divided by the standard deviation calculated in an annulus 1 pixel in width. Pixels within 1 FWHM radius of the location of the planet were excluded from the standard deviation calculation. The S/N map is shown on the left in Figure 4. Within the 2σ uncertainty of the Clio2 detection β Pic b is detected by VisAO with S/N =4.1. Other choices of smoothing kernels, different numbers of modes, and different techniques for calculating the noise can change this value by ±∼25% (see Figure 5). Regardless, this is the maximum S/N pixel at or near the separation of β Pic b, so these choices have minimal impact on the following analysis.

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As a starting point we first calculated the histogram of all pixels within the annulus of width ±2σ (Clio2 uncertainty) centered on the location of the planet, excluding the planet location. We restrict ourselves to this annulus to ensure that the statistics are representative. The histogram is shown in Figure 4, where we also overplot a Gaussian distribution with σ = 1 for comparison. There are 2628 pixels included in the histogram, all with S/N <4.1. We note that these pixels will tend to be correlated across the PSF width and by the smoothing kernel, so we do not estimate a false alarm probability (FAP) from the histogram of individual pixels. However, this does show that the S/N = 4.1 peak at the location of β Pic b is not expected from the distribution of pixels in the image.

In truth, we would have considered any signal close to the location determined by Clio2 as a VisAO detection. We next analyze the 101 unique apertures with a radius of 2σ (Clio2 radial uncertainty) that fit in the same annulus, choosing the highest S/N pixel in each. These apertures have a diameter of ∼7 VisAO pixels, larger than the 4.7 pixel FWHM, so they are uncorrelated with respect to both the PSF and the smoothing kernel. The histogram for these trials is shown at lower right in Figure 4. The probability of having the aperture with the highest S/N pixel occur at the Clio2 position by chance is 1/102 = 1.0% (adding one aperture at the location of the planet). This then sets an empirical upper limit on FAP.

3.1.4. Photometry with Simulated Planets

3.1.5. VisAO Astrometry

We present observations of β Pic b taken during the course of the Gemini NICI (Chun et al. 2008) campaign (Liu et al. 2010b; Wahhaj et al. 2013b; Biller et al. 2013; Nielsen et al. 2013). We observed β Pic on 2010 December 25 UT, in K_S, and again on 2011 October 20 UT in $CH_{4S,1\%}$ and K_cont. The K_S data was independently analyzed by Boccaletti et al. (2013) but with an extrapolated calibration of mask transmission, and hence large photometric uncertainties. Here we provide photometry based on a direct measurement of the focal plane mask transmission. We reduced the NICI data using the well-tested tools developed for the NICI campaign (see references above), with some differences as noted next. The VisAO reduction techniques described above were developed independently.

The images were reduced as described in Wahhaj et al. (2013a) but with the addition of smart frame selection for PSF building similar to Marois et al. (2006) and Lafrenière et al. (2007). The standard ADI reduction procedure median combines all of the science images in the pupil-aligned orientations to make a sourceless PSF and thereby subtract the star from each individual image. In our method, we median-combine only the frames that are similar to the image that is to undergo PSF subtraction. This similarity is measured in the difference of the target image and the candidate reference image using the RMS of pixel values at radii between 03 and 06 separation. Only the best 20 images are used to make the reference PSF. We differ from Lafrenière et al. (2007) and Marois et al. (2006) in that we do not reject frames because they have too little rotation relative to the target image. Instead, we require that the range of reference frames selected have total rotation >2 times the NICI FWHM. These parameters were optimized by comparing the S/N maps resulting from the reductions, and we found that this algorithm performed better than either basic ADI or LOCI for data taken with NICI.

The NICI detections of β Pic b are presented in Figure 6. To estimate the S/N of these detections, each pixel was divided by the standard deviation of the pixels in an annulus of width 5 pixels centered on the same separation. No smoothing was applied. A robust standard deviation algorithm was used, so the much higher pixels at the location of the planet were not included in the estimated noise. The peak S/N in $CH_{4S,1\%}$ was 10.4, in K_S it was 6.8, and in the K_cont filter it was 27.6.

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NICI photometry was calibrated by injecting simulated planets. The simulated planet signals were scaled from the star PSF and were injected into the data at the same separation as the real planet. The star was nonlinear in the $CH_{4S,1\%}$ and K_cont science exposures, so we instead used short-acquisition exposures appropriately scaled. The simulated planets were injected into the data at 20 position angles opposite the planet, one at a time, and a complete reduction was carried out. The stellar PSF halo was occasionally saturated near the radius of the planet in the K_S observations, and such frames were removed from the reduction process.

We used aperture photometry with an aperture radius of 3 pixels. ADI self-subtraction was corrected using the difference between the injected and recovered flux of the simulated planets. We estimated the uncertainty in the measured flux as the standard deviation of the recovered fluxes. For $CH_{4S,1\%}$ and K_cont we estimated an additional uncertainty of 8% due to variability of the star peak.

These observations were made using a 022 radius coronagraphic focal plane mask. The 022 mask opacity falls to zero at 04 from the center of the mask, so we have to correct for the mask opacity at the location of β Pic b. As described in Wahhaj et al. (2011) for the 032 mask, we measured the 022 mask opacities using a pair of Two Micron Sky Survey (2MASS) stars, both off the mask, and then one under the mask at different separations from the center. The mask opacities in the K_S, K_cont, and $CH_{4S,1\%}$ bands were 5.03 ± 0.03, 5.05 ± 0.03, and 5.47 ± 0.09 mag, respectively. Typically, more than five measurements were taken at each position of the target under the mask, so our opacity measurement uncertainties should be well-estimated (see Wahhaj et al. 2011). The sampling of separations are sparse (in steps of 01), and any discontinuities could introduce systematics into our estimates, which are based on fitting a smooth curve through the opacities as a function of separation. However, we have no evidence that such discontinuities exist, and the uncertainties are estimated with this assumption.

Contrasts were calculated as −2.5log (star counts/planet counts) + mask opacity. The uncertainties described above were added in quadrature. We measured contrasts of $\Delta CH_{4S,1\%} = 9.65 \pm 0.14$ mag, ΔK_S = 8.92 ± 0.13 mag, and ΔK_cont = 8.23 ± 0.14 mag.

We used archival photometry of β Pictoris A to find its brightness in the filters used here and also to investigate whether there is any reddening, which could affect our λ < 1 μm photometry. We used V, R_C, and I_C photometry from Cousins (1980b) and Cousins (1980a). Especially useful was photometry in the 13 color system, which spans 0.33 μm to 1.10 μm in somewhat narrow passbands, from Mitchell & Johnson (1969) and Johnson & Mitchell (1975). In the infrared, we used Johnson–Glass J, H, and K from Glass (1974), and ESO broadband J, H, and K and narrow-band H₀, Br_γ, K₀, and CO photometry from van der Bliek et al. (1996). Finally, following Bonnefoy et al. (2013), we synthesize a A6V spectrum by averaging the A5V and A7V spectra in the Pickles Spectral Atlas (Pickles 1998). We then normalized this spectrum to Cousins V. We compare this spectrum to the photometry in Figure 7. Based on the good agreement we conclude that reddening is not significant for β Pic A, and we assume that this will also be true for the planet (though there could be circumplanetary reddening that this analysis would miss). This exercise also demonstrates that variability of the primary star is not a concern when using it as a photometric reference for AO observations.

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The central wavelength of the 99 filter of Mitchell & Johnson (1969) is nearly identical to VisAO Y_S, so we adopt their measurement of Y_S = 3.561 ± 0.035 mag for β Pic A. Using the interpolated A6V spectrum we find that $CH_{4S,1\%} - H_{{\rm ESO}} = 0.024 \pm 0.05$, so we have $CH_{4S,1\%} = 3.526 \pm 0.05$ mag for β Pic A (Bonnefoy et al. 2013). We find K_{S, NICI} − K_ESO = −0.026 ± 0.05, so we use K_{S, NICI} = 3.468 ± 0.05 mag. We find K_cont − K_ESO = 0.068 ± 0.05 mag for a A6V, so for β Pic A we have K_cont = 3.563 ± 0.05 mag. We combine these with our contrast measurements, adding uncertainties in quadrature. We present our new photometry of β Pic b in Table 3, along with prior measurements in J, H, and K. Measurements at longer wavelengths are considered in Paper II.

Table 3. YJHK Photometry of β Pictoris b

Filter	Instrument	Date	Apparent	Absolute	Notes
			Magnitude	Magnitude
YS	VisAO	2012 Dec 4	$15.53^{+0.34}_{-0.33}$	$14.09^{+0.34}_{-0.33}$	1
J	NACO	2011 Dec 16	14.0 ± 0.3	12.6 ± 0.3	2
	⋅⋅⋅	⋅⋅⋅	14.11 ± 0.21	12.68 ± 0.21	3
$CH_{4S,1\%}$	NICI	2011 Oct 20	13.18 ± 0.15	11.74 ± 0.15	1
H	NACO	2012 Jan 11	13.5 ± 0.2	12.0 ± 0.2	2
	⋅⋅⋅	⋅⋅⋅	13.32 ± 0.14	11.89 ± 0.14	3
	NICI	2013Jan 9	13.25 ± 0.18	11.82 ± 0.18	3
KS	NACO	2010 Apr 10	12.6 ± 0.1	11.2 ± 0.1	4
	NICI	2010 Dec 25	12.39 ± 0.14	10.94 ± 0.14	1
	NICI	2013 Jan 9	12.47 ± 0.13	11.04 ± 0.13	3
Kcont	NICI	2011 Oct 20	11.79 ± 0.15	10.34 ± 0.15	1

Notes. (1) this work; (2) Bonnefoy et al. 2014; (3) Currie et al. 2013; (4) Bonnefoy et al. 2011.

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In Figure 8, we compare β Pic b to field BDs and other low-mass companions in color-color plots. We show J − K_S versus H − K_S colors, where nearly all of the companions have photometry (HR 8799 e is the notable exception in J). The Y band is relatively unexplored territory for low-mass companions, so we present three different permutations of Y_S colors. The field objects are plotted in the NICI system using synthetic photometry as described in Appendix A. We found that conversions between photometric systems are typically <0.1 mag, especially for spectral type L (see also Stephens & Leggett 2004), so in Figure 8 the companion objects are plotted in the J, H, and K_S photometric system in which they were observed. We used available spectra to estimate Y_S photometry for the companions shown. For β Pic b we plot our new K_S point from NICI and the NICI H point from Currie et al. (2013). In all cases β Pic b has colors consistent with early- to mid-L dwarfs. It is also consistent with an early-T, a consequence of the blueward progression at the L/T transition.

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The color degeneracy of the L/T transition is broken by absolute magnitude. In Figure 9, we show Y_S and K_S color–magnitude diagrams. These plots firmly place β Pic b in the early-L dwarfs. As noted by Bonnefoy et al. (2013) and Currie et al. (2013) it is somewhat redder than the L dwarfs in K_S versus H − K_S. This is consistent with other low surface-gravity L dwarfs such as AB Pic B, 2M0122B, and PSO318.5, though within 1σ β Pic b is consistent with the field.

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We next fit each of 499 BD spectra collected from various sources to the Y_S through K_cont photometry of β Pic b (treating each measurement independently). We did this by computing the flux of each spectrum in each of the bandpasses then finding the single scaling factor that minimized χ². Only spectra with a complete Y-band measurement were used, which tends to select for high S/N. We adopted an error of 0.05 mag for our synthetic photometry in each bandpass based on the findings of Liu et al. (2013b). This was added in quadrature to the β Pic b measurement errors. The results are presented in Figure 10, where we show $\chi ^2_{\nu }$ versus SpT for each of the field objects as well as the median in each SpT. The error bars indicate the standard deviation in each SpT. There is a minimum in the early- to mid-L dwarfs, giving a range of L2–L5.

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In Figure 11, we show the five best-fitting spectra, which range from L3 to L5.5. Our new Y_S photometry is well fit by these spectra, and our new $CH_{4S,1\%}$ and K_S points are consistent with the prior measurements. The K_cont point is only consistent with prior measurements at the 2σ level, though. A possible culprit is the noted nonlinearity of the star, which may have biased the result. However, the same procedure was applied to the $CH_{4S,1\%}$ measurement from the same night. Based on the many measurements of β Pic A we discount the primary as a source of variability at this level. BDs are known to be variable (e.g., Buenzli et al. 2012) but typically with low amplitude for early-L dwarfs (Goldman et al. 2008). We do not have enough evidence to speculate other than to note variability in β Pic b as a possible explanation.

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Though it established that the Y through K photometry of β Pic b does not appear to be atypical compared to the field, this exercise ultimately does not yield a well-determined SpT.

Having established that the photometry of β Pic b places it in the early- to mid-L dwarfs, we next attempt to estimate its SpT. Spectral typing is usually done by comparing the spectral morphology of the object to spectral standards. Because there is not yet a measurement of the Y through K spectrum of β Pic b, we instead compare its broadband photometry to field objects. We first plot color versus SpT for the 499 spectra in our library, shown in Figure 12. For each color we fit a polynomial to the sequence and then find the root(s) of this polynomial corresponding to the photometry of β Pic b. A consequence of the L/T transition is that the BD SpT sequence is dual-valued in each permutation of the YJHK colors, hence the double values in most of the panels of Figure 12 (and the broad minimum in Figure 10). The H − K_S color measurements do not intersect the polynomial, though they are consistent with field dwarfs. For these H − K_S measurements we assign the SpT of the turnover in color versus SpT.

The bluer colors of β Pic b (e.g., Y_S − J, J−H) indicate an SpT of early-L or mid-T. The redder colorsespecially H − K_Sfavor mid-L. To break the degeneracy from colors we turn to absolute magnitudes. In similar fashion, we fit polynomials to the objects in our library with parallaxes. These fits, shown on the right in Figure 12, are single-valued and all favor an SpT of early-L. This paints a picture of β Pic b as having the luminosity of an early-L dwarf but being somewhat redder than typical for the field, much like many well-studied low-gravity field BDs and companions.

We next compared all of these SpT determinations. It has been shown that low-g BDs do not follow the field BD sequence in near-IR absolute magnitudes (Faherty et al. 2013; Liu et al. 2013a), so we must be cautious about using the absolute magnitudes of β Pic b to directly estimate SpT. However, according to (Liu et al. 2013a) in the SpT range of roughly L0–L3 the absolute J-band magnitudes of low-g objects do match the field. We also note that for spectral types later than L3, the absolute J-band magnitudes tend to be fainter than the field for low-g objects, which does not appear to be true for β Pic b. The absolute magnitudes of β Pic b all correspond to the early-L dwarf SpTs, and the weighted mean using just the absolute magnitudes is L2.1 ± 0.8. Turning to the colors next, we reject the T classifications based on the absolute photometry. We form a best estimate of SpT by averaging all of the L values, finding 3.6 ± 2.2 using only the colors, as expected from the range we derived from using Figure 10.

Based on the consistency and the findings of Liu et al. (2013a), we give somewhat more weight to the type estimate derived from absolute magnitudes than the color-derived estimate. We also take into account that low-g objects tend to be red compared to the field for their spectral types. Based on all of these considerations, we adopt L2.5 ± 1.5 as the near-IR spectral type of β Pic b. This is consistent with Quanz et al. (2010), who found an approximate spectral type of L4, with a range of L0–L7, using L' and narrow-band 4.05 μm color. Our estimate is also consistent with the spectral type of L2γ ± 2 estimated by Bonnefoy et al. (2013) and the range of L2–L5 given by Currie et al. (2013).

Armed with our SpT estimate, we next estimated the bolometric luminosity of β Pic b. We first convert to the MKO photometric system, using the relationships we derive in Appendix A. We converted each measurement independently, then calculated the uncertainty-weighted mean for each bandpass. The results are presented in Table 4. From there, we determined the BC for each of J, H, and K using the polynomials given in Liu et al. (2010a). We then took the uncertainty-weighted mean value of the bolometric magnitude and its uncertainty, also given in Table 4. The resulting uncertainty in M_bol is a relatively small 0.11 mag. There are likely additional systematic errors, for example from using the field relationships on a low-g object.

Converting to luminosity gives us log (L_bol/L_☉) = −3.86 ± 0.04 dex. This is very close to the value of −3.87 ± 0.08 dex by Bonnefoy et al. (2013). They used a somewhat different method, determining only the K-band-based M_bol by using the mean BC of two similar field dwarfs. They also reported −3.83 ± 0.24 dex based on model atmosphere fitting, including longer wavelengths. Our value is modestly fainter than the estimate of Currie et al. (2013), −3.80 ± 0.02 dex, which was also inferred from model fitting including longer wavelength measurements.

We next calculated estimates of mass, temperature, and radius with Monte Carlo trials based on the hot-start evolutionary models (Chabrier et al. 2000; Baraffe et al. 2003). We adopt the lithium depletion boundary age of 21 ± 4 Myr for the β Pic moving group from Binks & Jeffries (2013). We treated our estimate for log (L_bol) and this age estimate as Gaussian distributions and drew 10⁴ trial values. For each random pair of log (L_bol) and age we calculated the hot-start model prediction of mass, temperature, and radius by linear interpolation on the model grid. The resulting distributions are shown in Figure 13 and summarized in Table 5. The mass distribution has mean and standard deviation 11.9 ± 0.7 M_Jup and median 12.0 M_Jup. The mass distribution has negative skewness, and there appears to be an upper limit at M ≈ 13 M_Jup. For temperature we find T_eff = 1, 643 ± 32 K. For radius we find R = 1.43 ± 0.02 R_Jup with a small positive skewness. These very small uncertainties are the formal errors from our Monte Carlo analysis of the model grid, and they do not include any additional terms such as the uncertainties in the models themselves.

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Table 5. Estimated Physical Properties of β Pic b

Near-IR	log(Lbol/L☉)	Age	Mass	Teff	Radius
Sp. Type		(Myr)	(MJup)	(K)	(RJup)
L2.5 ± 1.5	−3.86 ± 0.04	21 ± 4	11.9 ± 0.7	1643 ± 32	1.43 ± 0.02
		$12^{+8}_{-4}$	10.5 ± 1.5	1623 ± 38	1.47 ± 0.04

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Repeating the Monte Carlo experiment with the prior age estimate of $12^{+8}_{-4}$ Myr from Zuckerman et al. (2001), we found M = 10.5 ± 1.5 M_Jup, T_eff = 1623 ± 38 K, and R = 1.47 ± 0.04 R_Jup. To account for the asymmetric uncertainty we used the skew-normal distribution for age, choosing its parameters such that the mode was 12 Myr, the left-half width was 4 Myr, and the right-half width was 8 Myr. The resulting 12 Myr distributions are also shown in 13 and Table 5. There is again an upper limit on mass at roughly 13 M_Jup. We surmise that this is due to our luminosity estimate being too faint to allow deuterium burning at these ages according to the models, hence the mass is strongly constrained to be below 13 M_Jup regardless of age. Note that we consider additional models, using the complete 1–5 μm photometry of β Pic b in Paper II.

Bonnefoy et al. (2013) arrive at an estimate T_eff = 1, 700 ± 100 K from fitting PHOENIX-based atmosphere models coupled with various cloud models (Chabrier et al. 2000; Allard et al. 2001; Baraffe et al. 2003) and found R = 1.4 ± 0.2 R_Jup. Currie et al. (2013) estimated a range of 1575–1650 K using the various cloud plus atmosphere models of Burrows et al. (2006), Madhusudhan et al. (2011), and Currie et al. (2011b) and estimated R = 1.65 ± 0.06 R_Jup. Both of these efforts assumed the previous age estimate of $12^{+8}_{-4}$ Myr.

We obtained a transmission profile and atmospheric transmission profile appropriate for each site. Table 6 summarizes the atmosphere assumptions and models used. We converted to photon-weighted "relative spectral response" (RSR) curves, using the following equation (Bessell 2000):

$$T(\lambda) = \frac{1}{hc}\lambda T_0(\lambda),$$

where T₀ is the raw energy-weighted profile. We calculate the central wavelength as

$$\lambda _0 = \frac{\int _0^\infty \lambda T(\lambda)d\lambda }{ \int _0^\infty T(\lambda)d\lambda }.$$

We calculate the effective width Δλ, such that

$$F_{\lambda }(\lambda _0)\Delta \lambda = \int _0^\infty F_{\lambda }(\lambda)T(\lambda)d\lambda.$$

To calculate the magnitude of some object with a spectrum given by F_λ, obj we used

$$m = -2.5\log \left[ \frac{\int _0^\infty R(\lambda)F_{\lambda,\: {\rm obj}}d\lambda }{\int _0^\infty R(\lambda)F_{\lambda,\: {\rm vega}}d\lambda }\right]$$

using the Vega spectrum of Bohlin (2007), which has an uncertainty of 1.5%. These calculations are summarized in Table 7. We next describe details particular to the different photometric systems.

Table 7. Synthetic Photometric System Characteristics

Filter	λ0	Δλ	0 mag Fλ
	(μm)	(μm)	(10−6 erg s−1 cm−2 μm−1)
Y Band
PAN-STARRS1 yp1	0.9633	0.0615	7.17
VisAO YS	0.9847	0.0855	6.75
MKO Y	1.032	0.101	5.82
IRCS z1.1	1.039	0.049	5.73
J Band
2MASS J	1.241	0.163	3.14
MKO J	1.249	0.145	3.03
NACO J	1.256	0.192	3.02
H Band
NICI $CH_{4S,1\%}$	1.584	0.0167	1.28
MKO H	1.634	0.277	1.19
2MASS H	1.651	0.251	1.14
NACO H	1.656	0.308	1.14
NICI H	1.658	0.27	1.15
K Band
MKO KS	2.156	0.272	0.438
NACO KS	2.16	0.323	0.438
2MASS KS	2.166	0.262	0.431
NICI KS	2.176	0.268	0.424
MKO K	2.206	0.293	0.403
NICI Kcont	2.272	0.0375	0.356

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The Y Band. The Y band was first defined in Hillenbrand et al. (2002). We follow Liu et al. (2012) and assume that the UKIDSS Y filter defines the MKO system passband because the largest number of published observations in this passband are from there (see Burningham et al. 2013). This is a slightly narrow version of the filter. The UKIDSS Y RSR curve is provided in Hewett et al. (2006), which is already photonormalized and includes an atmosphere appropriate for Mauna Kea.

We also consider the unfortunately named Z filter used at Subaru/IRCS and Keck/NIRC2, which is actually in the Y window rather than in the traditionally optical Z/z band. To add to the confusion the filter has been labeled with a lower-case z, but the scanned filter curves and Alan Tokunaga's Web site¹⁵ indicate that it was meant to be capital Z. In any case, it is a narrow version of the Y passband. Here we follow Liu et al. (2012) and refer to it as z_1.1 to emphasize its location in the Y window and that it is not related to the optical bandpasses of the same name. We used the same atmospheric assumptions as for the MKO system (see below).

VisAO Y_S. The VisAO Y-short (Y_S) filter is defined by a Melles-Griot long wavepass filter (LPF-950), which passes λ ≳ 0.95 μm, and the quantum efficiency (QE) limit of our near-IR coated EEV CCD47-20 detector. We convolved the transmission curve with the QE for our EEV CCD47-20 (both provided by the respective manufacturers) and included the effects of three Al reflections. We also include the Clio2 entrance window dichroic that reflects visible light to the WFS and VisAO, cutting on at 1.05 μm. We next multiply the profile by a model of atmospheric transmission, using the 2.3 mm of precipitable water vapor (PWV), airmass (AM) 1.0 ATRAN model for Cerro Pachon provided by Gemini Observatory¹⁶ (Lord 1992). Cerro Pachon, ∼2700 m, is slightly higher than the Magellan site at Cerro Manqui, ∼2380 m (D. Osip 2013, private communication), so this will slightly underestimate atmospheric absorption. We finally determine the photon-weighted RSR. We refer to this filter as "Y-short" or Y_S. This is similar to the y_p1 bandpass of the PAN-STARRS optical survey (Tonry et al. 2012). Y_S is ∼22nm redder than y_p1, and we prefer to emphasize that we are working in the Y atmospheric window. Y-band filter profiles are compared in Figure 15.

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The Y_S filter is slightly affected by telluric water vapor. Using the ATRAN models we assessed the impact of changes in both AM and PWV. The mean transmission changes by ±3% over the ranges 1.0 ⩽  AM  ⩽ 1.5 and 2.3 ⩽  PWV  ⩽ 10.0 mm. This change in transmission has little impact on differential photometry so long as PWV does not change significantly between measurements. The AM has almost no effect on λ₀, but changes in PWV do change it by 2 to 4 nm as expected given the H₂O absorption band at ∼0.94 μm. This is relatively small, and because we have no contemporaneous PWV measurements for the observations reported here, we ignore this effect.

The 2MASS System. The 2MASS J, H, and K_S transmission and RSR profiles were collected from the 2MASS Web site.¹⁷ The RSR profiles are from Cohen et al. (2003). They used an atmosphere based on the PLEXUS model for AM 1.0. This model does not use a parameterization corresponding directly to PWV, but according to the Web site it is equivalent to 5.0 mm of PWV.

The MKO System. We used the Mauna Kea filter profiles provided by the IRTF/NSFCam Web site¹⁸ for the MKO J, H, K_S, and K passbands that correspond to the 1998 production run of these filters. We again used the ATRAN model atmosphere from Gemini Observatory, now for Mauna Kea with 1.6 mm precipitable water vapor (PWV) at AM 1.0.

The NACO System. We obtained transmission profiles for NACO from the instrument Web site.¹⁹ We used the "Paranal-like" atmosphere provided by ESO,²⁰ which is for AM 1.0 and 2.3 mm of PWV. The NACO filters are close to the 2MASS system, but there are subtle differences, which are somewhat more pronounced once the atmosphere appropriate for each site is included.

The NICI System. Profiles for the NICI filters were obtained from the instrument Web sites for NICI²¹ and NIRI.²² The Cerro Pachon ATRAN atmosphere was used, with AM 1.0 and 2.3 mm of PWV. The NICI J, H, and K_S bandpasses are intended to be in the MKO system and so should be insensitive to atmospheric conditions, but there are subtle differences between the filter profiles.

To quantify the differences between these systems and to accurately compare results for objects measured in the different systems, we used the library of BD spectra we compiled from various sources (described in Appendix A.3). We calculated the magnitudes in each of the various filters and then fit a fourth- or fifth-order polynomial to the results. Our notation is

$$\begin{equation} m_1-m_2 = c_0 + c_1 \hbox{SpT}+ c_2 \hbox{SpT}^2+ c_3 \hbox{SpT}^3+ c_4 \hbox{SpT}^4 + c_5 \hbox{SpT}^5, \end{equation} \tag{ A1 }$$

where SpT is the near-IR spectral type given by

$$\begin{eqnarray*} \hbox{SpT} &=& 0... 9, \hbox{ for } \hbox{M0}... \hbox{M9}\\ \hbox{SpT} &=& 10... 19, \hbox{ for } \hbox{L0}... \hbox{L9}\\ \hbox{SpT} &=& 20... 29, \hbox{ for } \hbox{T0}... \hbox{T9.} \end{eqnarray*}$$

We provide the coefficients determined in this manner for a variety of transformations in Table 8.

Table 8. Photometric Conversion Coefficients

Filters	c0	c1	c2	c3	c4	c5	σ (mag)
YS − YMKO	0.00904	0.0247	0.00411	−0.000633	2.89 × 10−5	−3.96 × 10−7	0.038
z1.1 − YMKO	0.00424	−0.00911	0.000823	−2.85 × 10−5	1.23 × 10−7	0.0	0.011
J2M − JMKO	−0.0308	0.0208	−0.00165	6.4 × 10−5	−5.83 × 10−7	0.0	0.012
JNACO − JMKO	−0.0895	0.0343	−0.00331	0.000145	−1.87 × 10−6	0.0	0.015
H2M − HMKO	0.00358	−0.00903	0.000435	−1.14 × 10−5	1.82 × 10−7	0.0	0.008
HNACO − HMKO	−0.0521	0.0152	−0.00182	8.61 × 10−5	−1.25 × 10−6	0.0	0.011
HNICI − HMKO	−0.0138	−0.000532	−0.000303	1.92 × 10−5	−2.69 × 10−7	0.0	0.008
HNACO − HNICI	−0.0383	0.0157	−0.00151	6.69 × 10−5	−9.76 × 10−7	0.0	0.007
$H_{{\rm NICI}}-CH_{4S,1\%}$	−1.28	0.695	−0.152	0.0164	−9.31 × 10−4	0.0	0.037
KS, 2M − KMKO	−0.324	0.149	−0.0233	0.00171	−5.91 × 10−5	7.54 × 10−7	0.014
KS, 2M − KS, MKO	0.0272	−0.0155	0.00227	−1.71 × 10−4	6.12 × 10−6	−7.8 × 10−8	0.006
KS, NACO − KS, MKO	0.0428	−0.0209	0.00422	−3.39 × 10−4	1.22 × 10−5	−1.59 × 10−7	0.007
KS, NICI − KMKO	−0.154	0.0828	−0.0142	0.00112	−4.06 × 10−5	5.35 × 10−7	0.011
KS, NACO − KS, NICI	0.00554	0.000497	0.00128	−1.24 × 10−4	4.59 × 10−6	−6 × 10−8	0.007
KS, NICI − Kcont	1.07	−0.524	0.108	−0.00999	0.000428	−6.96 × 10−6	0.058

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As a check on our calculations, consider the conversions from 2MASS to MKO. There are many objects with measurements in both systems, which allows us to directly compare our synthetic photometry to actual measurements. We here use the compilation of Dupuy & Liu (2012). This also allows a comparison to the previous work of Stephens & Leggett (2004), who employed a methodology similar to ours but with fewer objects. The results are shown graphically in Figure 16. In all three bands, our synthetic photometry and fit appear to be a good match to the measurements. In J our results appear to be an improvement over Stephens & Leggett (2004), and in H and K either fit appears to be reasonable. These results give confidence that our synthetic photometry reproduces the variations in these systems reasonably well.

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Y_S − K_S Spectral Library. We analyzed the Y_SJHK_S photometry of β Pic b by comparison with a library consisting of 499 BD spectra. Of these, 441 are from the SpeX Prism Spectral libraries maintained by Adam Burgasser²³ (from various sources), 23 are WISE BDs from Kirkpatrick et al. (2011), and 35 are young field BDs from Allers & Liu (2013). We correlated 115 of these with parallax measurements, either listed in the SpeX Library (from various sources) or from Dupuy & Liu (2012). We conducted synthetic photometry on these spectra as described above. For the objects with parallaxes we normalized the spectra to available photometry. In most cases, there is a near-IR SpT assigned that we use here. In the few cases where there is no near-IR SpT, we use the optical SpT.

We also compiled very late-T and early-Y dwarf photometry from Liu et al. (2012) and Leggett et al. (2013). Here we lack spectra, so instead we use the above transformations from the MKO system determined using our compiled spectra.

Y-band Photometry of EGPs. The other young planetary mass companions with Y-band photometry are HR 8799 b and 2M 1207 b. Currie et al. (2011b) detected HR 8799 b at 1.04 μm in the z_1.1 filter with Subaru/IRCS. Oppenheimer et al. (2013) also have the ability to work in the Y band with Project 1640 and reported low S/N detections of HR 8799 b and HR 8799 c at 1.05 μm. 2M 1207 b was observed with the HST by Song et al. (2006). To compare our results we must convert these measurements into our Y_S bandpass. The SEDs of these two objects do not correspond to those of field BDs of comparable temperature, so we turn to published best-fit model spectra: for 2M 1207 b we use the model of Barman et al. (2011b) and for HR 8799 b we use the best-fit model from Madhusudhan et al. (2011). We use the models to calculate color between bandpasses. We illustrate this in Figure 17 and summarize the results in Table 9.

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Other Comparison Objects. We also collected a number of low-temperature, low-mass objects from the literature to compare to β Pic b, which are listed in Table 10. Most of these are companions. Of particular interest are the low-surface-gravity objects. This includes the four HR 8799 planets and the planetary mass BD companion 2M1207b. Two other companions with photometric properties similar to these faint red companions are AB Pic b (Chauvin et al. 2005b) and 2MASS 0122-2439B (Bowler et al. 2013).

Table 10. Comparison Objects

Name	Near-IR	Distance	Group	Age	log(Lbol/L☉)	Teff	Mass	Ref.
	Sp. Type	(pc)		(MYr)		(K)	(MJup)
Companions
HR 8799 b	late-L/early-T	39.4 ± 1	Col	30–60	−5.1 ± 0.1	850	7	1, 2, 3, 4
HR 8799 c	⋅⋅⋅	39.4 ± 1	Col	30–60	−4.7 ± 0.1	1100 ± 100	10	1, 2, 5
HR 8799 d	⋅⋅⋅	39.4 ± 1	Col	30–60	−4.7 ± 0.1	900	10	1, 2
HR 8799 e	⋅⋅⋅	39.4 ± 1	Col	30–60	−4.7 ± 0.2	1000	7–10	6, 7
2MASS 1207-3932 b	M8.5-L4, L3	52.4 ± 1.1	TWA	8	−4.73 ± 0.12	1000	5	8, 9, 10, 11, 12
1RXS 1609 b	L4$^{+1}_{-2}$	145 ± 20	USco	5–11	−3.55 ± 0.2	1800 ± 200	6–15	13, 14
HD 106906 b	L2.5±1	92 ± 6	LCC	13 ± 2	−3.64 ± 0.08b	1800 ± 100	11 ± 2	15
GJ 504 b	late-T/Y	17.56 ± 0.08	⋅⋅⋅	$105^{+30}_{-20}$	−6.09 ± 0.08		$4.0^{+4.5}_{-1.0}$	16
AB Pic B	L0 VL-G	46.1 ± 1.4	Tuc-Hor	30	−3.7 ± 0.2	$2000^{+100}_{-300}$	13–14	8, 17, 18, 19, 20
κ And B	L1 ± 1	51.6 ± 0.5	⋅⋅⋅	220 ± 100	−3.76 ± 0.06	2040 ± 60	$50^{+16}_{-13}$	21, 22, 23
CD-35 2722 B	L3±1 INT-G	22.7 ± 1.0	AB Dor	125 ± 25	−3.51 ± 0.12b	1700–1900	31 ± 8	8, 24, 25
G 196-3 B	L3 VL-G	14.9 ± 2.7a	⋅⋅⋅	≈100	−4.15 ± 0.16	1800 ± 200	$25^{+15}_{-10}$	8, 26, 27, 28
2MASS 0122-2439 B	L4-L6	36 ± 4a	AB Dor (?)	120 ± 10	−4.19 ± 0.1	1300–1500	12-14 / 23-27	29
LP 261-75 B	L4.5± 1.0	$32.95^{+2.80}_{-2.40}$	⋅⋅⋅	100–200	−4.43 ± 0.09	∼1400	13 / 22	29, 30
Gl 417 BC	L4.5 ± 1 + L6 ± 1	21.93 ± 0.21	⋅⋅⋅	80–300	−3.80 ± 0.04b	1600–1800	35 ± 15	8, 31, 32, 17, 33
HN Peg B	T2.5 ± 0.5	17.99 ± 0.14	⋅⋅⋅	237 ± 33	−4.77 ± 0.03	1115	28	17, 34, 35, 33, 36
Ross 458 C	T8.5p±0.5	11.69 ± 0.21	⋅⋅⋅	⩽1000	−5.61 ± 0.20	695 ± 60	5–20	17, 37, 38
Field Objects
2MASS 0608-2753	M8.5γ, L0 VL-G	30 ± 10	β Pic	21 ± 4	−3.43 ± 0.29b	2529	15–35	39, 40, 8
2MASS 0032-4405	L0γ, VL-G	26 ± 3.3	Field	⋅⋅⋅	−3.93 ± 0.14b	⋅⋅⋅	⋅⋅⋅	8, 41
2MASS 0355+1133	L5γ, VL-G	9.1 ± 0.1	AB Dor	125 ± 25	−4.23 ± 0.11	$1420^{+80}_{-130}$	$24^{+3}_{-6}$	42, 43, 44, 45
PSO318.5-22	L7±1 VL-G	24.6 ± 1.4	β Pic	21 ± 4	−4.42 ± 0.06	$1160^{+30}_{-40}$	$6.5^{+1.3}_{-1.0}$	43
CFBDSIR2149-0403	T7	40 ± 3a	AB Dor	125 ± 25	−5.57 ± 0.24b	650–750	4–7	46

Notes. ^aPhotometric distance. Trigonometric parallax otherwise. ^bQuantity estimated from field relations, either in this work or in references. References. (1) Marois et al. 2008; (2) Madhusudhan et al. 2011; (3) Bowler et al. 2010; (4) Barman et al. 2011a; (5) Konopacky et al. 2013; (6) Marois et al. 2010; (7) Skemer et al. 2012; (8) Allers & Liu 2013; (9) Chauvin et al. 2005a; (10) Ducourant et al. 2008; (11) Barman et al. 2011b; (12) Patience et al. 2010; (13) Lafrenière et al. 2010; (14) Pecaut et al. 2012; (15) Bailey et al. 2014; (16) Kuzuhara et al. 2013; (17) van Leeuwen 2007; (18) Chauvin et al. 2005b; (19) Bonnefoy et al. 2010; (20) Song et al. 2003; (21) Bonnefoy et al. 2014; (22) Hinkley et al. 2013; (23) Carson et al. 2013; (24) Wahhaj et al. 2011; (25) Shkolnik et al. 2012; (26) Rebolo et al. 1998; (27) Shkolnik et al. 2009; (28) Zapatero Osorio et al. 2010; (29) Bowler et al. 2013; (30) Reid & Walkowicz 2006; (31) Kirkpatrick et al. 2001; (32) Burgasser et al. 2010; (33) Dupuy & Liu 2012; (34) Luhman et al. 2007; (35) Leggett et al. 2008; (36) Barnes 2007; (37) Burningham et al. 2011; (38) Goldman et al. 2010; (39) Rice et al. 2010b; (40) Rice et al. 2010a; (41) Faherty et al. 2012; (42) Faherty et al. 2013; (43) Liu et al. 2013b; (44) Liu et al. 2013a; (45) Barenfeld et al. 2013; (46) Delorme et al. 2012.

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Both Bonnefoy et al. (2013) and Currie et al. (2013) noted that the near-IR SED of β Pic b resembled that of an early- to mid-L dwarf. For comparison then, we use companions such as κ And B (L1 ± 1; Bonnefoy et al. 2014; Hinkley et al. 2013) and CD-35 2722 B (L4±1; Wahhaj et al. 2011). We used the Project 1640 spectrum of κ And B from Hinkley et al. (2013) to estimate its Y-band photometry. We also highlight several field dwarfs. The L0γ object 2MASS 0608-2753 is believed to be a member of the β Pic moving group (Rice et al. 2010b), giving us a potentially co-eval object to compare with β Pic b. We include two field objects that appear to have low surface gravity and dusty photospheres and are young moving group members: 2MASS 0355+1133 (Faherty et al. 2013; Liu et al. 2013b) and PSO318.5 (Liu et al. 2013b). PSO318.5 is also a possible member of the β Pic moving group. 2MASS 0032-4405, an L0γ, was discussed as a possible proxy for both β Pic b and κ And B by Bonnefoy et al. (2013).