Y Dwarf Trigonometric Parallaxes from the Spitzer Space Telescope

Near-infrared images of WISE 0336−0143, WISE 0550−1950, WISE 0615+1526, WISE 0642+0423, WISE 1055−1652, WISE 1220+5407, and WISE 2203+4619 were obtained using the WIRC (Wilson et al. 2003) on the 200 inch Hale Telescope at Palomar Observatory on 2012 January 4 (WISE 0336−0143, WISE 1055−1652), 2014 March 7 (WISE 2203+4619) and 2016 February 26 (WISE 0550−1950, WISE 0615+1526, WISE 0642+0423, WISE 1220+5407). WIRC has a pixel scale of 02487/pixel providing a total field of view of 87. For each object, fifteen 2-minute images were obtained in the J filter (30 minutes total exposure time). The sky was clear during the observations on all nights.

Images obtained in 2012 and 2014 were reduced using a suite of IRAF scripts and FORTRAN programs provided by T. Jarrett. These scripts first linearize and dark subtract the images. From the list of input images, a sky frame and flat field image are created and subtracted from and divided into (respectively) each input image. At this stage, WIRC images still contain a significant bias that is not removed by the flat field. Comparison of Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and WIRC photometric differences across the array shows that this flux bias has a level of ≈10% and the pattern is roughly the same for all filters. Using these 2MASS-WIRC differences for many fields, we can create a flux bias correction image that can be applied to each of the "reduced" images.

In 2014 April, the primary science-grade detector experienced a catastrophic failure and was replaced with a lower quality engineering-grade detector (there are more cosmetic defects, for example). The previous reduction scripts were fine-tuned for the original detector and produced sub-optimal results with the new chip. A WIRC reduction package written in IDL by J. Surace was used for the 2016 data as it was able to better handle the nonuniformity in one of the quadrants. In addition to the quadrant cleaning, the Surace package differed from the Jarrett package in that the reduced data from the former did not exhibit, and thus did not require, a flux bias correction. The other data reduction steps were essentially the same. The processed frames were mosaicked together using a median and had their astrometry and photometry calibrated using 2MASS stars in the field.¹²

Table 1 lists the photometry, using Vega system magnitudes. Additional photometry for the remaining targets in this sample was taken from the literature. The majority of the near-infrared photometry listed in Table 1 is on the MKO system, though some of the Y dwarfs have synthetic photometry measured with HST and corrected to match MKO filter profiles (see Schneider et al. 2015 for further details). We caution the reader that the photometric filter system can significantly change the near-infrared photometry of Y dwarfs.

Using the NIRSPEC instrument at the W. M. Keck Observatory (McLean et al. 1998), we made J-band spectroscopic observations of four targets from the original Spitzer Parallax Program with unknown or uncertain spectral types: WISE 0336−0143, WISE 1051−2138, WISE 1055−1652, and WISE 1318−1758. We observed an additional five targets that were likely late-type T or Y dwarfs based on their W1 − W2 colors from the AllWISE processing (Kirkpatrick et al. 2014). Spectral types and observation information for these targets are listed in Table 2. All targets were observed using AB nod pairs along the 057 (3-pixel) slit, producing a spectral resolution of R = λ/Δλ ∼1500 per resolution element.

Spectroscopic reductions were made using a modified version of the REDSPEC package,¹³ following a similar procedure to Mace et al. (2013a). Frames were spatially and spectrally rectified to remove the instrumental distortion on the image plane of the detector. Frames were then background-subtracted and divided by a flat field. Spectra from each nod pair were extracted by summing over 9–11 pixels before combining the nods. The extracted spectrum was then divided by an A0V calibrator spectrum to remove telluric features and lastly, corrected for barycentric velocity. Observations made of the same target on separate nights were combined into a single spectrum after being reduced separately. Raw spectra in this paper are available in the Keck Observatory Archive¹⁴ and reduced spectra are available on the NIRSPEC Brown Dwarf Spectroscopic Survey website.¹⁵

Here we present new and updated spectral types for nine objects in our sample that we observed with NIRSPEC. J band spectra for these objects, and the spectral standards used to classify them are shown in Figure 1.

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WISE 0336−0143 was originally classified as T8: by Mace et al. (2013a). In 2016, we sought to re-observe WISE 0336−0143 for two reasons. First, the spectrum published in Mace et al. (2013a) had a low S/N and we wished to obtain a higher S/N spectrum. Second, we hypothesized based on its [3.6]–[4.5] color of 2.57 mag that WISE 0336−0143 should be much colder than a T8 to explain its extreme redness. Typical [3.6]–[4.5] colors for T8 objects are ∼1.5–2 mag (see Figure 7 in Mace et al. 2013b; WISE 0336−0143 is the obvious T8 outlier in that plot.) In Figure 2, we plot the normalized NIRSPEC spectra of the 2011 and 2016 observations. The 2016 observations match much better to a Y dwarf (see also Figure 1), so we will henceforth classify this object as a Y0:. We have only been able to obtain limits on the near-infrared photometry for this object. With J > 21, WISE 0336−0143 will require additional observations with an 8 or 10 m class ground-based telescope, or observations with HST or JWST to further characterize its spectrum.

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WISE 0550−1950, WISE 0615+1526, WISE 0642+0423, WISE 1220+5407, and WISE 2203+4619 are new T dwarfs found using the AllWISE color cuts discussed in Section 2. We find spectral types of T6.5, T8.5, T8, T9.5, and T8, respectively, based on comparison of their J-band spectra to spectral standards.

WISE 1051−2138 was given a spectral type of T9: in Mace et al. (2013a). Our re-observed spectrum, shown in Figure 1, indicates that this object should be classified as T8.5.

WISE 1055−1652 was placed on our parallax program without having an observed spectrum to confirm its substellar nature. We present the discovery of this new T9.5: dwarf.

WISE 1318−1758 was classified as a T9: in Mace et al. (2013b) based on a noisy Palomar/TripleSpec spectrum and we re-classify it here as a T8. As shown in Figure 1, the T8 spectral standard is a very good match for WISE 1318−1758.

Spitzer IRAC [4.5] images have a field of view of 52 on a side, over 256 × 256 pixels, producing a pixel scale of 12 pix⁻¹. The full-width at half-maximum for a centered point response function (PRF) is 18, for the warm mission. The raw images have a maximum optical distortion of 1.6 pixels, on the edge of the array. During Spitzer cryogenic operations, [3.6] was more sensitive than [4.5]. After cryogen depletion, however, the deep image noise¹⁶ was found to be 12% worse in [3.6] and 10% better in [4.5], making the channels more comparable in sensitivity for average field stars ([3.6]–[4.5] ∼ 0 mag) during warm operations (Carey et al. 2010). The behavior of latent images from bright objects was also found to change during warm operations; whereas latents in [4.5] decay rapidly—typically within 10 minutes—[3.6] latents decay on timescales of hours. Moreover, the [4.5] intrapixel sensitivity variation (also known as the pixel phase effect) is about half that of [3.6]. Given these points, the fact that the PRF is better sampled in [4.5] than in [3.6], and the fact that our cold brown dwarfs are also much brighter in [4.5] than in [3.6] (1.0 < [3.6]–[4.5] < 3.0 mag; Figure 11 of Kirkpatrick et al. 2011), we chose to do our imaging in [4.5]. All [4.5] Spitzer/IRAC observations of the targets, the MJD range of usable data for each source, and the number of epochs available in each program, are given in Table 3.

Our primary program, Program 90007, used a total integration time of 270 s per epoch so that all targets would have S/N > 100 in [4.5]. To smear out the effects of intrapixel sensitivity variation, which can bias the astrometry in a frame, we chose a 9-point random dither pattern with 30 s exposures per dither. Dither sizes vary for this setup, but are on the order of ∼5''–30''.¹⁷ To keep the number of common reference stars between individual exposures high, we chose a dither pattern of medium scale. Timing constraints were imposed so that there was one sample within a few days of maximum parallax factor with (usually) evenly spaced samples throughout the rest of the target's visibility period.

We also used [4.5] data taken as part of earlier programs 551, 70062, and 80109 as well the later program 11059 (PI: Kirkpatrick) to increase the time baseline to help disentangle proper motion from parallax. Program 11059 used the same observing setup as program 90007, described above. All the other programs from which we utilized data (except 551; PI: Mainzer) used a frame time of 30 s and a 5-point cycling dither pattern with medium scale, and observations were obtained in both [3.6] and [4.5]. In anticipation of parallax program 90007, we used the same [4.5] setup to re-observe our most promising targets during programs 70062 and 80109 after the original [3.6]+[4.5] Astronomical Observation Request (AOR) was completed.

Program 551, which targeted only WISE 1828+2650, used a frame time of 100 s and a 36-point Reuleaux with medium dither in [3.6] and a frame time of 12 s and a 12-point Reuleaux pattern of medium dither in [4.5]. Program 10135 (PI: Pinfield), which targeted only WISE 2203+4619, used a frame time of 30 s and a 16-point spiral dither pattern of medium step in both channels; in this case, two exposures were taken at each dithered position.

We used the Spitzer Heritage Archive¹⁸ to download all of the basic calibrated data (BCD) at [4.5] for the programs listed in Table 3. Data were reduced using the Mosaicker and Point Source Extractor (MOPEX¹⁹ ) with customized scripts created following instructions in the MOPEX handbook. These scripts use the individually dithered BCD files to create a coadded image at each epoch (i.e., for each AOR) and to detect and characterize sources on the resulting coadd.

The data and scripts have been modified in two ways to utilize new knowledge gained during the Spitzer warm mission. First, the headers of the BCD files available at the Spitzer Heritage Archive have been updated to include a new Spitzer-produced fifth-order distortion correction for the IRAC camera, which is an improvement over the third-order correction included previously (Lowrance et al. 2014). Second, the PRF employed by the code is one created specifically for use on Spitzer warm data,²⁰ sampled onto a 5 × 5 grid to account for small changes in shape across the array. The MOPEX code performs a simultaneous chi-squared minimization²¹ using fits of the PRF to the stack of individual frames to measure the photometry and position of the source in that AOR. It should be noted that the random dithers will help to zero out the astrometric bias caused by the intrapixel distortion in each individual frame (Ingalls et al. 2012), so this effect did not have to be specifically addressed in our reduction methodology.

Our [3.6] observations were run identically to the [4.5] data discussed above. We divided the resulting PRF-fit fluxes by the appropriate [3.6] and [4.5] correction factors (1.021 and 1.012, respectively) indicated in Table C.1 of the IRAC Instrument Handbook²² and converted these fluxes to magnitudes using the [3.6] and [4.5] zero points of 280.9 ± 4.1 Jy and 179.7 ± 2.6 Jy, respectively, as given in Table 4.1 of the same document. The final [3.6] and [4.5] photometry is listed in columns 9–10 of Table 1.

Prior studies have shown that the amplitude of [3.6] and/or [4.5] variability in T0–T8 dwarfs can can reach the 10% level, with some objects varying more in one band than the other (Metchev et al. 2015). This amplitude increases at later spectral types. In fact, one Y dwarf, WISE 1405+5534, has already been observed to vary at levels as high as 3.5% in [3.6] and [4.5] based on a limited data set (Cushing et al. 2016). Another Y dwarf observed for variability, WISE 1738+2732, showed peak-to-peak variability of ∼3%, at [4.5] with potentially up to 30% variability in the near-infrared (Leggett et al. 2016). Therefore, our tabulated values list photometry only for the one AOR having concurrent [3.6] and [4.5] observations so that the resulting [3.6]–[4.5] value represents a physical snapshot of the color at a specific time rather than a possibly non-physical color created from disparate epochs of [3.6] and [4.5] observations. The AORs from which the [3.6] and [4.5] photometry is measured are listed in Column 4 of Table 3.

The centroid locations determined by the MOPEX routine on each of the epochal coadds (average positions across multiple dithers) were then used as the fundamental source of our astrometric measurements. Our resulting inputs to our astrometric fitting routine at each epoch were the source location, time of observation of the middle frame, and geometric coordinates of Spitzer during the observations.

Prior to fitting our astrometric solutions for each target, we re-registered the coordinates of our targets in each epoch onto a single reference frame. We chose to align our coordinates to those provided by the Gaia Mission in Data Release 1 (DR1; Gaia Collaboration et al. 2016a, 2016b). These positions are the best that are currently available across the whole sky. 2MASS positions, which provide the basis for the WCS coordinates given by MOPEX/APEX, have positional uncertainties on the order of ∼70 mas (McCallon et al. 2007), while Gaia DR1 positions for the brightest, unsaturated reference stars have positional uncertainties on the order of ≲1 mas.

We selected reference background sources for the reregistration process by requiring that the sources be detected in all epochal coadds, have a S/N > 100, and have positional uncertainties within 2σ of the median positional uncertainty of the field. Requiring a detection in every coadded frame cut sources on the extreme edge of the field, while the positional uncertainty cut removed any sources with any significant proper motion. We then evaluated each reference target by eye to discard any non-pointlike sources. We obtained Gaia coordinates for each reference star, where available, and excluded any with exceptionally high uncertainties (≳1 mas) in the Gaia DR1, as well as reference sources that were lacking Gaia coordinates. The resulting set of reference stars varied from 7–96, depending on the stellar density in the field. Thumbnail images of three example fields with the target and reference sources highlighted can be found in Figure 3, showcasing fields with low, moderate, and high numbers of reference stars.

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We found that the positional uncertainties output by the MOPEX/APEX centroid extractions were overestimated by a factor of ≳2 compared to the uncertainties on background stars with similar S/N. Instead of using these inflated uncertainties, we determined empirical positional uncertainties for each target by comparison to the positional uncertainties of the presumably non-moving field reference stars. For each field, we re-registered the locations of all stars in the field using the correction determined by the reference field stars as detailed above. We then calculated the positional uncertainty of every source in both R.A. and decl. as the standard deviation of the centroid location across all epochs, post-reregistration. As expected, positional uncertainty drops with increasing S/N until it reaches a systematic floor of ∼15–40 mas, depending on the field. Figure 4 shows three examples of positional uncertainty versus source S/N, given a low, medium, or high number of reference stars. Our target S/Ns are typically high enough that their positional uncertainties can be determined from the asymptotic portion of the graph. We measure the median positional uncertainty above a cutoff S/N > 100 after performing a 2σ clipping to remove significant outliers. These outliers could be non-pointlike sources, e.g., galaxies, or they could have significant proper motion. The median value rounded to the nearest 5 mas is then the positional uncertainty that we use in each epoch to determine the astrometric fits for each of our targets, with a floor of 15 mas. Positional uncertainties for each target are listed in Column 10 of Table 5.

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After determining our target uncertainties, the selected reference stars that likewise met the sigma clipping requirement were then used to perform a final reregistration. We performed a least-squares affine transformation to adjust each frame onto the Gaia reference frame. To do this, we projected both the Gaia and MOPEX coordinates onto a tangent plane (ξ, η) and then solved for the best-fit generalized six-term solution, allowing for offsets, rotation, and scaling between the two planes.

After reregistering each source onto a common reference frame, we then solved simultaneously for five parameters: trigonometric parallax π, proper motion in both R.A. and decl. (μ_α, μ_δ), and initial position (α₀, δ₀) at a fiducial time of T₀ = 2014.0, which falls roughly in the middle of our time baseline for each object. We used the standard astrometric equations (Smart & Green 1977; Green 1985), inputting epochal coordinates, time of observation, and rectangular observatory coordinates obtained from the image headers. We then used Pythons' Scipy least-squares minimization module²³ to solve for the best fit. Our best-fit astrometric solutions are listed in Table 5 and plotted in Figure 5. Three examples are printed here. The complete figure set (22 objects) is available in the online journal. We show both the overall astrometric fit, as well as the parallactic ellipse, after removing the best-fit proper motion component. The best-fit model shown makes use of the Spitzer ephemerides from JPL's Horizons²⁴ to calculate the heliocentric rectangular coordinates of Spitzer over a longer time baseline and with higher cadence than our observations. These measurements are for relative parallaxes, not absolute. We estimate that the correction for the systematic offset of the average parallax of the background stars is ∼1 mas, well within the random errors of our solutions.

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View figure set (22 panels)

Tarball of figure set images

One caveat for the targets at high declination ($| \delta | \gtrsim 70^\circ$) is that an unidentifiable problem in the MOPEX mosaicking code leads to much more uncertain astrometry. This is reflected in the larger uncertainties we adopt for their epochal positions and the generally larger reduced chi-squared (${\chi }_{\nu }^{2}$) values we measure. This issue will be further discussed in our forthcoming paper presenting parallaxes for all of the T6 and later brown dwarfs in our parallax program (Kirkpatrick et al. 2018).

We used our measured distances to calculate the absolute magnitudes for all objects in J_MKO, H_MKO, [3.6], [4.5], W1, and W2, when available, listed in Table 6. In Figure 6, we plot four different CMDs, showing M_J versus $J-W2$, M_H versus H − W2, M_W2 versus $J-W2$, and M_[4.5] versus [3.6]–[4.5]. Data from this paper are plotted as filled circles and data from the literature are open symbols (Tinney et al. 2014: circles; Dupuy & Kraus 2013: diamonds). Every object is colored according to its spectral type, as shown in the legend. The CMDs show a tight trend, particularly in M_J versus $J-W2$ and M_H versus H − W2, in which the trends previously seen for earlier spectral types are continued, showing decreasing absolute magnitudes in the near-infrared as $J-W2$ colors redden.

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Table 6.  Absolute Magnitudes

Object	${\pi }_{\mathrm{trig}}$	Distance	MJ	MH	${M}_{[3.6]}$	${M}_{[4.5]}$	MW1	MW2
Name	(mas)	(pc)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
WISE 0146+4234	45.575 ± 5.74	${21.94}_{-2.45}^{+3.16}$	17.69 ± 0.37	17.00 ± 0.36	15.65 ± 0.29	13.36 ± 0.27	>17.43	13.38 ± 0.28
WISE 0336−0143	100.90 ± 5.86	${9.91}_{-0.54}^{+0.61}$	>21.12	>20.22	17.22 ± 0.15	14.65 ± 0.13	18.47 ± 0.49	14.58 ± 0.14
WISE 0350−5658	168.84 ± 8.53	${5.92}_{-0.28}^{+0.32}$	23.32 ± 0.13	23.40 ± 0.17	18.97 ± 0.17	15.85 ± 0.11	>19.84	15.88 ± 0.12
WISE 0359−5401	75.36 ± 6.62	${13.27}_{-1.07}^{+1.28}$	20.95 ± 0.20	21.41 ± 0.22	16.95 ± 0.22	14.74 ± 0.19	>18.42	14.77 ± 0.20
WISE 0410+1502	153.42 ± 4.05	${6.52}_{-0.17}^{+0.18}$	20.25 ± 0.06	20.83 ± 0.07	17.51 ± 0.07	15.08 ± 0.06	>19.10	15.04 ± 0.07
WISE 0535−7500	79.51 ± 8.79	${12.58}_{-1.25}^{+1.56}$	21.63 ± 0.25	22.84 ± 0.42	17.15 ± 0.26	14.62 ± 0.24	17.44 ± 0.28	14.41 ± 0.24
WISE 0647−6232	83.73 ± 5.68	${11.94}_{-0.76}^{+0.87}$	22.47 ± 0.16	22.92 ± 0.22	17.44 ± 0.20	14.77 ± 0.15	>19.15	14.84 ± 0.16
WISE 0713−2917	100.73 ± 4.74	${9.93}_{-0.45}^{+0.49}$	20.00 ± 0.11	20.21 ± 0.13	16.66 ± 0.11	14.22 ± 0.10	>18.79	14.48 ± 0.11
WISE 0734−7157	67.63 ± 8.68	${14.79}_{-1.68}^{+2.18}$	19.50 ± 0.28	20.22 ± 0.29	16.76 ± 0.30	14.42 ± 0.28	17.90 ± 0.40	14.34 ± 0.28
WISE 0825+2805	139.02 ± 4.33	${7.19}_{-0.22}^{+0.23}$	23.12 ± 0.08	23.68 ± 0.15	18.14 ± 0.12	15.36 ± 0.07	>19.16	15.29 ± 0.09
WISE 1051−2138	49.27 ± 6.47	${20.3}_{-2.4}^{+3.1}$	17.40 ± 0.30	17.65 ± 0.48	14.93 ± 0.29	13.10 ± 0.29	15.76 ± 6.84	13.06 ± 0.29
WISE 1055−1652	71.21 ± 6.82	${14.04}_{-1.2}^{+1.5}$	19.97 ± 0.30	>19.36	16.61 ± 0.22	14.27 ± 0.21	>17.37	14.33 ± 0.22
WISE 1206+8401	85.12 ± 9.27	${11.75}_{-1.15}^{+1.44}$	20.12 ± 0.24	20.71 ± 0.24	16.91 ± 0.25	14.97 ± 0.24	>18.38	14.71 ± 0.24
WISE 1318−1758	48.06 ± 7.33	${20.81}_{-2.75}^{+3.74}$	16.84 ± 0.38	16.12 ± 0.40	15.20 ± 0.34	13.12 ± 0.33	15.92 ± 0.37	13.07 ± 0.34
WISE 1405+5534	144.35 ± 8.60	6.93 ${}_{-0.39}^{+0.44}$	21.86 ± 0.13	22.30 ± 0.15	17.65 ± 0.14	14.87 ± 0.13	19.56 ± 0.42	14.89 ± 0.13
WISE 1541−2250	167.05 ± 4.19	5.99 ${}_{-0.147}^{+0.154}$	22.75 ± 0.08	23.20 ± 0.18	17.63 ± 0.07	15.34 ± 0.06	17.85 ± 0.17	15.36 ± 0.08
WISE 1639−6847	228.05 ± 8.93	${4.39}_{-0.17}^{+0.18}$	22.42 ± 0.09	22.54 ± 0.09	18.08 ± 0.09	15.47 ± 0.09	19.06 ± 0.21	15.33 ± 0.10
WISE 1738+2732	136.26 ± 4.27	${7.34}_{-0.22}^{+0.24}$	20.22 ± 0.07	20.92 ± 0.07	17.64 ± 0.09	15.15 ± 0.07	18.38 ± 0.17	15.17 ± 0.08
WISE 1828+2650	100.21 ± 4.23	${9.98}_{-0.40}^{+0.44}$	23.48 ± 0.25	22.85 ± 0.26	16.91 ± 0.09	14.33 ± 0.09	>18.25	14.36 ± 0.10
WISE 2056+1459	138.32 ± 3.86	${7.23}_{-0.20}^{+0.21}$	19.83 ± 0.06	20.35 ± 0.07	16.77 ± 0.07	14.61 ± 0.06	17.18 ± 0.10	14.54 ± 0.07
WISE 2209+2711	154.41 ± 5.67	${6.48}_{-0.23}^{+0.25}$	23.80 ± 0.15	23.33 ± 0.17	18.68 ± 0.14	15.68 ± 0.08	>19.77	15.71 ± 0.10
WISE 2220−3628	84.10 ± 5.90	${11.89}_{-0.78}^{+0.90}$	20.07 ± 0.15	20.48 ± 0.16	16.80 ± 0.17	14.37 ± 0.15	>18.40	14.34 ± 0.16

A machine-readable version of the table is available.

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We determined a weighted linear fit to both M_J versus $J-W2$ and M_H versus H − W2 and tabulate the coefficients in Table 7. Although these relations require two photometric observations to obtain a photometric distance estimate, we find that this relationship is much tighter than if we were to determine fits to the absolute magnitude versus spectral type.

Table 7.  Coefficients for Linear Fits to Color–Magnitude Relations

Color	c0	c1	rms
(1)	(2)	(3)	(4)
MJ versus $J-W2$	12.186	1.386	0.475
MH versus H − W2	11.935	1.401	0.544

Note. These coefficients fit a line such that ${M}_{X}=c0+c1\times ({M}_{X}-W2)$, where X is the J or H photometry on the MKO system.

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M_W2 versus $J-W2$ shows more scatter than the near-infrared CMDs. Interestingly, M_W2 versus $J-W2$ appears to plateau in M_W2 across the T/Y transition. It is unclear if this feature is real, or due to a bias (systematic or otherwise). It is possible that this represents a T/Y transition, perhaps due to the rainout of an opacity source or the appearance of the salt/sulfide clouds (Morley et al. 2012).

The M_[4.5] versus [3.6]–[4.5] plot shows significantly more cosmic scatter than the other panels in Figure 6. This is likely due to [3.6] being a nonideal band for observing objects with significant CH₄ absorption. The blue tail of the 4.5 μm  bandpass falls into the [3.6] filter transmission, giving late-T and Y an overall very red slope in [3.6]. It is possible that variations in gravity and/or metallicity cause this slope to shift, producing the observed scatter. It is likely that the W2 versus W1 − W2 CMD would show a much tighter correlation, because the W1 and W2 bandpasses were designed specifically for cold brown dwarfs; however, many targets only have limits on their W1 magnitudes.

Figure 7 shows absolute magnitude in various near and mid-infrared bands as a function of spectral type, for this sample as well as other values taken from the literature. Studying the relationship of the absolute magnitude emitted at each bandpass as a function of spectral type provides us with insight on the evolution of the brown dwarf spectral energy distribution as it cools over time. Earlier-type brown dwarfs tend to follow a narrow trend in absolute magnitude, with flux decreasing in each of the bands monotonically as a function of spectral type. Because spectral typing historically sorts objects by effective temperatures, we expected the Y dwarf sample to continue this trend. However, instead of a tight correlation between spectral type and absolute magnitude, we see a large amount of scatter, spanning as much as ∼5 mag within the Y0 spectral class alone.

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Such a large spread in absolute properties cannot be explained by typical levels of variability (Cushing et al. 2016; Leggett et al. 2016) and must be indicative of a different physical mechanism. In Figure 7, each of the objects is colored according to $J-W2$ color cutoffs, as detailed in the legend. Here, we are using $J-W2$ as a proxy for temperature, based on Figure 18 from Schneider et al. (2015), which in turn utilizes the atmospheric models of Saumon et al. (2012), and Morley et al. (2012, 2014). Regardless of the type of clouds used in the atmospheric models, they all show a monotonic reddening of $J-W2$ as temperature decreases. When we separate objects by their $J-W2$ color, new trends appear in Figure 7. In particular, the Y0 dwarfs appear to cover a very broad range in effective temperatures, likely accounting for the ∼5 orders of absolute magnitudes observed in the J band.

In Section 6.1 we determine photometric distance relationships based on linear fits to M_J versus $J-W2$ and M_H versus H − W2. These fits are valid for objects with 2 < J − W2 < 9 and 3 < H − W2 < 9. Below, we use this photometric distance relationship to estimate distances to the new ≥ T8 objects presented here. For objects <T8, we use the spectrophotometric distance relations from Filippazzo et al. (2015).

WISE 0550−1950: We do not have an adequate baseline to measure the parallax of this new T6.5 dwarf, but using the spectrophotometric distance estimates from Filippazzo et al. (2015), we estimate a distance of 32.9 pc to this object.

WISE 0615+1526: We estimate a photometric distance of 22.3 pc for this object.

WISE 0642+0423: We estimate its photometric distance to be 29.6 pc.

WISE 1220+5407: Our photometric distance estimate puts it at 22.5 pc.

WISE 2203+4619 is estimated to be 18.9 pc away, based on our photometric distance relationships in Section 6.1.

In Table 8 and Figure 8 we compare our results to previously published astrometric fits for all of our targets with previous parallax measurements. We find that our results are mostly consistent with previously published values in the literature, with a few notable exceptions.

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Table 8.  Comparison to Published Parallaxes and Proper Motions

Object	Measurement	This Paper	Smart et al. (2017)	Beichman et al. (2014)	Tinney et al. (2014)	Dupuy & Kraus (2013)	Leggett et al. (2017) a
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	${\pi }_{\mathrm{trig}}$ (mas)	45.6 ± 5.7	⋯	94 ± 14	⋯	⋯	54 ± 5
WISE 0146+4234	${\mu }_{\alpha }$ (mas yr−1)	−450.67 ± 6.3	⋯	−441 ± 13	⋯	⋯	−455 ± 4
	${\mu }_{\delta }$ (mas yr−1)	−27.9 ± 6.3	⋯	−26 ± 16	⋯	⋯	−24 ± 4
	${\pi }_{\mathrm{trig}}$ (mas)	168.8 ± 8.5	⋯	⋯	⋯	⋯	184 ± 10
WISE 0350−5658	${\mu }_{\alpha }$ (mas yr−1)	−206.9 ± 6.5	⋯	⋯	⋯	⋯	−206 ± 7
	${\mu }_{\delta }$ (mas yr−1)	−577.7 ± 6.7	⋯	⋯	⋯	⋯	−578 ± 8
	${\pi }_{\mathrm{trig}}$ (mas)	75.4 ± 6.62	⋯	⋯	63.2 ± 6.0	⋯	⋯
WISE 0359−5401	${\mu }_{\alpha }$ (mas yr−1)	−152.7 ± 4.8	⋯	⋯	−176.0 ± 10.8	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	−783.7 ± 4.9	⋯	⋯	−744.5 ± 11.9	⋯	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	153.4 ± 4.0	144.3 ± 9.9	160 ± 9	⋯	132 ± 15	⋯
WISE 0410+1502	${\mu }_{\alpha }$ (mas yr−1)	959.9 ± 3.6	956.8 ± 5.6	966 ± 13	⋯	958 ± 37	⋯
	${\mu }_{\delta }$ (mas yr−1)	−2218.6 ± 3.5	−2221.2 ± 5.5	−2218 ± 13	⋯	−2229 ± 29	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	79.5 ± 8.8	⋯	⋯	74 ± 14	⋯	70 ± 5
WISE 0535−7500	${\mu }_{\alpha }$ (mas yr−1)	−113.2 ± 7.7	⋯	⋯	−113.4 ± 15.4	⋯	−127 ± 4
	${\mu }_{\delta }$ (mas yr−1)	23.7 ± 7.5	⋯	⋯	36.2 ± 8.8	⋯	13 ± 4
	${\pi }_{\mathrm{trig}}$ (mas)	83.7 ± 5.7	⋯	⋯	93 ± 13	⋯	⋯
WISE 0647−6232	${\mu }_{\alpha }$ (mas yr−1)	1.0 ± 5.1	⋯	⋯	0.6 ± 16.1	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	391.0 ± 4.6	⋯	⋯	368.0 ± 18.0	⋯	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	100.7 ± 4.7	⋯	106 ± 13	08.7 ± 4.0	⋯	⋯
WISE 0713−2917	${\mu }_{\alpha }$ (mas yr−1)	341.1 ± 6.6	⋯	388 ± 20	350.1 ± 4.8	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	−411.1 ± 6.0	⋯	−419 ± 22	−411.4 ± 5.6	⋯	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	67.6 ± 8.7	⋯	⋯	73.7 ± 6.6	⋯	⋯
WISE 0734−7157	${\mu }_{\alpha }$ (mas yr−1)	−566.2 ± 8.8	⋯	⋯	−565.8 ± 7.7	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	−77.5 ± 8.8	⋯	⋯	−81.5 ± 8.0	⋯	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	139.0 ± 4.3	⋯	⋯	⋯	⋯	158 ± 7
WISE 0825+2805	${\mu }_{\alpha }$ (mas yr−1)	−64.4 ± 5.6	⋯	⋯	⋯	⋯	−66 ± 8
	${\mu }_{\delta }$ (mas yr−1)	−234.7 ± 5.4	⋯	⋯	⋯	⋯	−247 ± 10
	${\pi }_{\mathrm{trig}}$ (mas)	85.1 ± 9.3	⋯	⋯	⋯	⋯	85 ± 7
WISE 1206+8401	${\mu }_{\alpha }$ (mas yr−1)	−557.7 ± 6.5	⋯	⋯	⋯	⋯	−585 ± 4
	${\mu }_{\delta }$ (mas yr−1)	−241.3 ± 6.5	⋯	⋯	⋯	⋯	−253 ± 5
	${\pi }_{\mathrm{trig}}$ (mas)	144.3 ± 8.6	⋯	⋯	⋯	129 ± 19	155 ± 6
WISE 1405+5534	${\mu }_{\alpha }$ (mas yr−1)	−2336.0 ± 6.9	⋯	⋯	⋯	−2263 ± 47	−2334 ± 5
	${\mu }_{\delta }$ (mas yr−1)	238.0 ± 7.40	⋯	⋯	⋯	288 ± 41	232 ± 5
	${\pi }_{\mathrm{trig}}$ (mas)	167.1 ± 4.2	⋯	176 ± 9	175.1 ± 4.4	74 ± 31	⋯
WISE 1541−2250	${\mu }_{\alpha }$ (mas yr−1)	−895.0 ± 4.7	⋯	−857 ± 12	−894.7 ± 4.2	−870 ± 130	⋯
	${\mu }_{\delta }$ (mas yr−1)	−94.7 ± 4.7	⋯	−87 ± 13	−87.7 ± 4.7	−13 ± 58	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	228.1 ± 8.9	⋯	⋯	202.3 ± 3.1	⋯	⋯
WISE 1639−6847	${\mu }_{\alpha }$ (mas yr−1)	579.1 ± 12.5	⋯	⋯	586.0 ± 5.5	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	−3104.5 ± 12.2	⋯	⋯	−3101.1 ± 3.6	⋯	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	136.3 ± 4.3	128.5 ± 6.3	128 ± 10	⋯	102 ± 18	⋯
WISE 1738+2732	${\mu }_{\alpha }$ (mas yr−1)	343.3 ± 3.5	345.0 ± 5.7	317 ± 9	⋯	292 ± 63	⋯
	${\mu }_{\delta }$ (mas yr−1)	−340.6 ± 3.4	−340.1 ± 5.1	−321 ± 11	⋯	−396 ± 22	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	100.2 ± 4.2	⋯	106 ± 7	⋯	70 ± 14	⋯
WISE 1828+2650	${\mu }_{\alpha }$ (mas yr−1)	1021.0 ± 3.2	⋯	1024 ± 7	⋯	1020 ± 15	⋯
	${\mu }_{\delta }$ (mas yr−1)	175.6 ± 3.1	⋯	⋯	⋯	173 ± 16	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	138.3 ± 3.9	148.9 ± 8.2	140 ± 9	⋯	144 ± 23	⋯
WISE 2056+1459	${\mu }_{\alpha }$ (mas yr−1)	823.0 ± 3.3	826.4 ± 5.5	812 ± 9	⋯	761 ± 46	⋯
	${\mu }_{\delta }$ (mas yr−1)	535.7 ± 3.4	530.7 ± 8.5	34 ± 8	⋯	500 ± 21	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	154.4 ± 5.7	⋯	147 ± 11	⋯	⋯	⋯
WISE 2209+2711	${\mu }_{\alpha }$ (mas yr−1)	1199.6 ± 4.9	⋯	c1217 ± 13	⋯	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	−1359.0 ± 4.8	⋯	−1372 ± 15	⋯	⋯	⋯
	${\pi }_{\mathrm{trig}}$ (mas)	84.1 ± 5.9	⋯	136 ± 17	87.2 ± 3.7	⋯	⋯
WISE 2220−3628	${\mu }_{\alpha }$ (mas yr−1)	292.9 ± 7.4	⋯	283 ± 13	282.7 ± 5.0	⋯	⋯
	${\mu }_{\delta }$ (mas yr−1)	−61.5 ± 7.0	⋯	−97 ± 17	−94.0 ± 3.0	⋯	⋯

Notes.

^aThe data presented in Leggett et al. (2017) include astrometric data first published in Luhman & Esplin (2016).

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6.4.1. Comparison to Tinney et al. (2014) and Beichman et al. (2014)

6.4.2. Comparison to Dupuy & Kraus (2013)

We also measure significant offsets in parallax values from Dupuy & Kraus (2013). We find systematically larger parallax values (closer distances) than they do for 5 out of the 6 targets we have in common. Each object has at least one other measurement in the literature and we find that we are consistently in agreement with the other reference. Tinney et al. (2014) and Smart et al. (2017) also note systematic offsets between their parallax measurements and those of Dupuy & Kraus (2013), concluding that these are likely due to the smaller number of measurements and thus a degeneracy between the parallax and proper motion parameters. For the extreme case of 1541−2250 (not plotted in comparison figures), we note, as did Beichman et al. (2014) and Tinney et al. (2014) that this object has several epochs skewed by a blend with a background star that throw off the fit in the [3.6] data, which explains the >3-σ difference between the Dupuy & Kraus (2013) results and others in the literature.

We explored several hypotheses to explain the discrepancies between the Dupuy & Kraus (2013) measurements and those presented here. Similar to our parallax measurements, Dupuy & Kraus (2013) uses the IRAC instrument on Spitzer to measure the positions of each target. However, they observed in [3.6], whereas the measurements presented here were made using [4.5] data.

Our first hypothesis is that the use of [3.6] data causes a chromatic distortion on the image plane that is different for the target than the background stars, and which would cause a systematic offset in the positions of the targets in the Dupuy & Kraus (2013) data set. The IRAC instrument design utilizes beam splitters in each of its two fields of view to refract shorter wavelength light ([3.6] and [4.5]) to separate focal planes from the longer wavelength light (ch3 and ch4). Both [3.6] and [4.5] have similar background characteristics during the warm mission (Carey et al. 2010). The brown dwarf targets are significantly fainter in [3.6] compared to [4.5], requiring longer integration times (thus providing more background stars in each field). Late-T and Y dwarfs exhibit extreme methane absorption near the methane fundamental bandhead at 3.3 μm, which produces a dramatic upward slope in the spectral energy distribution within the [3.6] bandpass. Thus the targets have significantly redder effective central wavelengths compared to the relatively flat spectral energy distributions of the background stars. This reddening effect in [3.6] would lead to a slightly different average angle of refraction, compared to the background stars' average angles of refraction. The target spectral energy distributions in the [4.5] bandpass peak much closer to the center of the bandpass and should not have significantly different effective wavelengths from the background stars, so they should be immune to this effect. We thus expect that this effect would be evident by comparing the offset parallax measurement to the [3.6]–[4.5] color (Figure 9). We see a slight correlation between [3.6]–[4.5] color and parallax offset, but there is not enough data to draw a firm conclusion.

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Our second hypothesis is that there is a fundamental difference between our fitting analysis and that of Dupuy & Kraus (2013). In Section 2.4 of Dupuy & Liu (2012), they describe their methodology for determining astrometric fits: "We fitted three parameters to the combined (α, δ) data: proper motion in right ascension (μ_α), proper motion in declination (μ_δ ), and parallax (π). This is notably different from one standard approach taken in the literature of fitting two separate values of the parallax in α and δ (...) MPFIT minimized the residuals in (α, δ) after subtracting the relative parallax and proper motion offsets (three parameters) and the mean (α, δ) position (effectively removing 2 additional degrees of freedom)."

We interpret this to meant that the subtraction of the average (α, δ) position requires the parallax solution to fit through one point located at the center of the parallactic ellipse. The effect would be averaged out over long time baselines, but we believe this method to be ineffectual for limited epochs. The sense of the bias that we see is in the expected direction; that is, their ellipse fits are artificially smaller because of their choice of data analysis method. To test this, we performed a reduction of the same [3.6] data used in their paper but employing our methodology described above. In this case, we used the [3.6] PRF appropriate for Warm Spitzer data. The resulting astrometric fits are compared to our [4.5] parallax measurements in Figure 10. In Figure 10, the original measurements from Dupuy & Kraus (2013) are shown in yellow, and the recalculation using our fitting analysis and the Dupuy & Kraus (2013) data are in blue. In most cases, our calculations measure parallax solutions that are closer to those measured with our [4.5] data, though consistent with the original Dupuy & Kraus (2013) values within the uncertainties.

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Our third hypothesis to explain the discrepant measurements is that the shorter time baseline of the Dupuy & Kraus (2013) data set made it difficult to disentangle the effects of proper motion when calculating the parallax. We explored this effect by reducing later epochs of [3.6] data, available on the Spitzer archive. The addition of 9–10 epochs for each target cannot fully account for the earlier difference seen between the [3.6] and [4.5] parallax measurements. These differences are plotted in Figure 10 in red. All targets except for 0410+1502 show an improved comparison, though the systematic offset remains.

We believe that some combination of the three effects contributed to the systematically offset parallaxes published in Dupuy & Kraus (2013). After re-reducing the Dupuy & Kraus (2013) data and adding additional epochs, we were unable to fully account for the discrepancy, but the offset as a function of color also appears to only have a slight trend.

6.4.3. Comparison to Leggett et al. 2017

Y0 dwarfs span several magnitudes in M_J, and nearly two in W2, based on the near-infrared classification of Y0 dwarfs. As previously mentioned, we used $J-W2$ as a proxy for temperature to separate populations in Figure 7. The color cuts show that the Y0 class spans >4 mag in $J-W2$ and also overlaps the $J-W2$ color space occupied by the Y1 and later-typed objects. These findings indicate that the classical near-infrared spectral typing method of sorting M, L, and T dwarfs by their J band spectral morphologies does not efficiently separate Y dwarfs by their respective temperatures. Y dwarfs, with ${T}_{\mathrm{eff}}$ ≲ 500 K, emit only a small fraction of their light in the near-infrared and would be best-characterized based on their mid-infrared spectra. This was noted in the Y dwarf discovery paper, Cushing et al. (2011); however, until the launch of JWST, observers have little hope of obtaining high S/N mid-infrared spectra of Y dwarfs- though some have tried (e.g., Skemer et al. 2016). The peak emission of a ≲500 K brown dwarf falls in the ∼3–10 μm  range, causing the J band to lie on the Wien tail of the blackbody spectrum. Considering the above, we recommend that mid-infrared spectra (i.e., from JWST) be used to more fully characterize the physical properties of these extremely cold objects. Below we examine some of the more interesting targets in our sample.

WISE 0146+4234 AB: This object has discrepant near-infrared photometry in the literature due to its blended binary nature. For this reason, we have excluded it from our color cuts and plot it in gray in Figures 6 and 7.

WISE 0336−0143: This exhibits absolute magnitude and colors much more similar to Y dwarfs, than late-T dwarfs, as seen in Figures 6 and 7. We currently only have a limit on its near-infrared magnitudes, but our photometry agree with the later epoch of spectroscopy that this object is indeed a Y dwarf.

WISE 0734−7157: This particular dwarf is likely one of the warmest Y0's, based on its color and M_J. The best-fit temperature from Schneider et al. (2015) is 450 K, and Leggett et al. (2017) estimate its ${T}_{\mathrm{eff}}$ to be 435–465 K.

WISE 1639−6847: This is the second coldest Y0, based on $J-W2$ color. It is location in color–magnitude space is much more similar to the Y1 objects. Leggett et al. (2017) estimate its ${T}_{\mathrm{eff}}$ ∼ 360–390 K, coinciding with our findings.

WISE 2209+2711: This is the faintest Y0 dwarf in every absolute magnitude band we measure. It is also the reddest in Y0 in J − W2. From Schneider et al. (2015), the best fit model gives ${T}_{\mathrm{eff}}$ = 500–550 K, $\mathrm{log}g$ = 4–4.5, 0.2–1.5 Gyr old. Leggett et al. (2017) estimate ${T}_{\mathrm{eff}}$ = 310–340 K, which agrees better with our estimates that this object is colder than most Y0's. Even if we re-classify this as a Y1, this would still be the faintest and reddest Y1. This object is also the reddest Y0 in J − H and H − W2. It is mildly blue but not unusual in Y − J (Schneider et al. 2015). If we use the $J-W2$ versus Temperature plot from Schneider et al. (2015) to determine an effective temperature, this object should be only ∼300 K. At such cold temperatures, the near-infrared flux is solely coming from the Wien tail. Our observations are thus not able to fully sample the peak of the Planck function, and thus a small shift in ${T}_{\mathrm{eff}}$ can cause a significant change in absolute magnitudes and colors. This particular target would be excellent for follow-up with JWST spectroscopy and imaging.

WISE 0825+2805: This target is the third-reddest object in this sample in J − W2 after WISE 1828+2650 and WISE 2209+2711, likely indicating its extremely cold nature.

WISE 0350−5658 is the reddest in [3.6]–[4.5] in this sample, also the faintest in M_[3.6] and M_[4.5], and the faintest Y1 in M_J. It is likely extremely cold, probably matching the predicted ∼300 K from Schneider et al. (2015) and the 310–340 K from Leggett et al. (2017).

WISE 0535−7500 is the brightest Y1-classified object and yet it was classified as ≥Y1 in Kirkpatrick et al. (2012). WISE 0535 is located on the outskirts of the Large Magellanic Cloud and is in a highly crowded field that partially contaminated the HST spectrum. This object would also benefit from follow-up observations in the mid-infrared.

WISE 1828+2650 is a known outlier that has thus far evaded a satisfactory explanation. Leggett et al. (2017) propose that the peculiar near- and mid-infrared colors could be due to an unseen or equal-mass binary, however there are a couple of problems with the binarity hypothesis. First, extreme redness cannot be explained with binarity. Based on evolutionary models, extremely cold Y dwarfs effectively cannot be young, and so a protoplanetary or debris disk makes an unlikely culprit for the enhanced [3.6] and [4.5]. Second, the amount by which this object is over-luminous is at least one mag (depending on the band) and the maximum over-brightness observed from an equal-mass binary is 0.75 mag.