The Field Substellar Mass Function Based on the Full-sky 20 pc Census of 525 L, T, and Y Dwarfs

We now find ourselves at a moment in history where selecting parallax-based censuses of nearby objects from the hottest O stars to the coldest Y dwarfs is almost a reality. With the release of Gaia Data Release 2 (DR2; Gaia Collaboration et al. 2018) and Data Release 3 (scheduled for the first half of 2022), the astronomical community can begin extracting complete, volume-limited samples out to distances that provide exquisite statistics on the distribution of stellar types. As a result of operating at wavelengths <1 μm and selecting a conservative detection threshold, Gaia provides complete astrometry only for L5 dwarfs out to ∼24 pc (Smart et al. 2017). Extending this census to colder types, though, is more easily accomplished by ground-based or space-based astrometric monitoring at longer wavelengths, where late-L, T, and Y dwarfs are brightest. A complete, volume-limited census across all stellar and substellar types is extremely useful in a variety of investigations, including: (1) analysis of the mass function, (2) determining the frequency of binaries across all types, (3) providing a catalog of host stars around which the nearest habitable planets to our own solar system can be searched, and (4) establishing correlations among colors, absolute magnitudes, spectral types, effective temperatures, etc., that can be applied to other samples whose parallaxes are unknown or not so easily measured.

In this paper, we provide the cold dwarf complement to the complete, nearby samples being extracted from Gaia. Our contribution is twofold. One, we present analysis of a flurry of new discoveries by the Backyard Worlds: Planet 9 (hereafter, "Backyard Worlds") and CatWISE teams that in the last several months have helped to identify even more previously hidden members of the 20 pc census. Two, we present a set of 361 parallaxes measured by the Spitzer Space Telescope (hereafter, Spitzer) that, when combined with astrometric monitoring of other objects by the astronomical community, establishes a complete, full-sky, volume-limited census of L, T, and Y dwarfs out to 20 pc. We use this census to establish the shape and functional form of the mass function in the substellar regime.

This paper is organized as follows. In Section 2, we provide motivation for studying the mass function and describe what can be learned from the results. In Section 3, we build the seed list of targets for the 20 pc L, T, and Y census and describe how this parallels historical efforts to catalog nearby stars of types M and earlier. In Section 4, we discuss our Spitzer data acquisition and the subsequent astrometric reductions, and we compare our results to other published parallaxes for objects with independent measurements. In Section 5, we discuss photometric and spectroscopic follow-up in support of the 20 pc seed list. In Section 6, we construct the final 20 pc census. In Section 7, we examine outliers on various color–color and color–magnitude diagrams in order to more carefully characterize objects in the census. In Section 8, we assign values of T_eff to each object, then calculate space densities as a function of T_eff, once we have determined completeness limits and completeness corrections. In Section 9, we provide the best fits of these measured space densities to predictions. These predictions simulate space densities for various forms of the mass function passed through two different sets of evolutionary models. We also discuss the value of the low-mass cutoff and ponder why so few brown dwarfs with T_eff < 400 K have been uncovered to date. We conclude with future avenues of exploration in Section 10.

What does an analysis of the mass function tell us? The astronomical literature is replete with arguments about the functional form of the overall mass function, but what knowledge do we gain from its determination?

The two main, competing forms for the stellar mass function are the power law and the log-normal. At a fundamental level, a power law would inform us that the physical process is scale-free, meaning that the mass of the natal cloud has no bearing on the final stellar mass distribution, only on the total number of objects formed. That is, the relative distribution of masses formed from a small cloud will be the same as that from a much more massive cloud. A power-law functional form would therefore imply a single physical process reigning over all of star production. If a universal power law is the correct form, then averaging results over many different star formation sites—as we do when looking at an older, well-mixed, volume-limited sample near the Sun—should still result in a mass distribution with a power-law form.

Even if a power-law form describes the observed data, it is common in nature to find that it applies only above some minimum value. For example, in investigations such as the peak intensity of solar flares or the magnitudes of earthquakes, a power law fits the data well only if a minimum value is imposed (Clauset et al. 2009). To employ a reductio ad absurdum of our own, there must be a minimum value for the cutoff mass of star formation because nature cannot create a star containing only one atom.

The log-normal form, on the other hand, is the result expected when there are many processes that contribute multiplicatively to the result. (Contrast this with a normal distribution, which is the result of processes that contribute additively.) As Kapteyn (1903) elegantly argued, even if some physical processes, like the swelling in diameter of a growing blueberry (or a stellar embryo), appear to be normally distributed—i.e., a symmetric distribution centered on some mean value—other quantities, such as the growing volumes of those blueberries (or stars), would necessarily have skewed distributions. He argued that skewed forms are, in fact, favored over symmetrical ones. Many of nature's skewed distributions are well-characterized by a log-normal form (Limpert et al. 2001), again implying that several independent processes are working together to produce the final outcome (Miller & Scalo 1979).

If a single functional form fails to describe the observed distribution over the entire mass range from O stars to Y dwarfs—and it is well-known that there is a break in the shape of the mass function below 1 M_⊙ (see Figure 2 of Bastian et al. (2010), who give an overview of the stellar initial mass function)—then the inflection in the shape of the mass function roughly corresponds to the mass at which a new set of physical processes is becoming dominant. In fact, the mass function may have several inflection points, indicating that separate sets dominate in different mass regimes.

Even with solid knowledge of the mass function's shape across the entire mass spectrum of interest—in our case, over the entirety of the brown dwarf masses—divining the physical causes responsible for that shape will be difficult. Nonetheless, knowing the shape enables a semi-empirical determination of the low-mass cutoff and allows us to build simulations that better reflect true space densities across all spectral types.

Since the 1988 discovery of GD 165B (Becklin & Zuckerman 1988), large swaths of the astronomical community have contributed to uncovering hidden L, T, and Y dwarfs in the immediate solar vicinity. New members of the 20 pc census have been announced not only by brown dwarf researchers specifically looking for examples (e.g., Kendall et al. 2004) but also by researchers in unassociated fields who have serendipitously found others (e.g., Hall 2002; Thorstensen & Kirkpatrick 2003). New additions to the sample have been published as single-object papers (e.g., Ruiz et al. 1997; Folkes et al. 2007); as part of large photometric (e.g., Delfosse et al. 1997; Lucas et al. 2010), spectroscopic (e.g., Schmidt et al. 2010), proper motion (e.g., Smith et al. 2014; Meisner et al. 2020a, 2020b), or parallax surveys (e.g., from Gaia: Reylé 2018; Scholz 2020); or as the result of dedicated searches for companions around higher mass stars (e.g., Freed et al. 2003; Thalmann et al. 2009) or around other brown dwarfs (e.g., Volk et al. 2003; Gelino et al. 2011). Construction of the census of the closest L, T, and Y dwarfs has been the effort of many dozens of lead authors presenting results in hundreds of publications.

3.1. A Nearby Census in Its Historical Context

3.2. Building a List of Probable 20 pc L, T, and Y Dwarfs

The reduction of the Spitzer astrometry used the same methodology as that outlined in Section 5.2 of Kirkpatrick et al. (2019a), with the following exceptions. First, the list of possible re-registration stars was paired not against Gaia Data Release 1 (DR1) but instead with the newer Gaia DR2, as the latter contains five-parameter (α₀, δ₀, ϖ_abs, μ_α , and μ_δ ) solutions for ∼70% of cataloged objects. Second, we used these full astrometric solutions to predict the per-epoch positions of each re-registration star at the observation date of each AOR, thereby enabling us to measure absolute parallaxes and proper motions of the Spitzer targets directly. ⁴³ Third, to assure that we had a sufficient number of five-parameter Gaia DR2 re-registration stars per frame, we set the signal-to-noise ratio (S/N) requirement to S/N ≥ 30 per frame; ⁴⁴ in Kirkpatrick et al. (2019a), we used S/N ≥ 30 only when the field for that target was starved of S/N ≥ 100 background stars. As stated in that paper, however, the inclusion of re-registration stars with 30 < S/N < 100 does not generally degrade the χ² values of the final parallax and proper motion solution compared to solutions using S/N ≥ 100 stars only. Fourth, one small modification to the astrometric solution was included for these new reductions. In Kirkpatrick et al. (2019a), the mean epoch for all solutions was set to 2014.0 because the time span for each of the objects was similar. The time coverage of the new data set, however, varies greatly from object to object (see Table 2), so we have chosen to compute and report the mean epoch of each object separately.

For those AORs in Table 3 that came from the cryogenic portion ⁴⁵ of the Spitzer mission, we modified our reductions slightly. During the single-frame reduction step detailed in Section 5.2.2 of Kirkpatrick et al. (2019a), we ran the MOPEX/APEX software so that the Point Response Function (PRF) fitting made use of the PRF maps measured for cryogenic data. All data from the warm mission were, as before, reduced using PRF maps applicable to the warm phase.

As stated in Section 3.2, some of our Spitzer astrometry from Cycle 14 lacked a sufficient time baseline with which to disentangle proper motion and parallax, so we supplemented the Spitzer data with positions derived from the unWISE (Lang 2014) "time-resolved" coadds of Meisner et al. (2018a, 2018b). The methodology is the same as that described in Section 8.3 of Meisner et al. (2020a), which measures the positions of our sources on the time-resolved unWISE coadds whose astrometry has been re-registered to the Gaia DR2 reference frame. The unWISE measurements used here are the NEO5 version of the time-resolved coadds, covering early 2010 through late 2018. For this current work, however, the coadds were produced on an epochal basis; that is, because we needed a clearly defined time stamp, positions were not combined across differing time-resolved sets (usually spaced by six months), as was done in Meisner et al. (2020a) to increase the S/N of the final detection.

Because our planned observations between 2019 April 15 and June 16 never materialized (see Section 3.2), 13 of our 361 sources had Spitzer observations sampling only one side of the parallactic ellipse—and thus only a proper motion measurement was possible. The same fitting procedure as outlined above was used for these cases, except that the parallax term was set to zero.

For each target, a listing of all of the measured positions from our Spitzer reductions—and from the unWISE reductions, if applicable—is given in Table 4. Per the above discussion, all positions are re-registered to the Gaia DR2 reference frame and have uncertainties and time stamps attached. Additional information regarding registration of the unWISE astrometry can be found in Section 8.3 of Meisner et al. (2020a).

Because the two sets of astrometry are taken from different positions within our Solar System—one from the Earth-orbiting WISE spacecraft and the other from the Sun-orbiting Spitzer spacecraft—all observations were tagged with the XYZ positions within the Solar System corresponding to the Modified Julian Date (MJD) of the data. For Spitzer observations, these XYZ positions are tabulated by the Spitzer Science Center in the FITS image headers; for the unWISE epochs, we used the mean MJD of each epochal coadd and assigned to them the XYZ of the Earth at that time, using data available through the JPL Horizons website. ⁴⁶ Note that the use of the Earth's position is sufficient because the unWISE epochal data themselves are an average over a few days of WISE observations near that mean epoch. Even with the inclusion of non-Spitzer astrometry into the astrometric solutions, no special modifications to the fitting routine employed in Section 5.2.3 of Kirkpatrick et al. (2019a) were needed. It should be noted that, with the exception of a very small number of confused observations noted in Table 2, all astrometric data points were used in the fits, since no sigma clipping and refitting were performed.

In principle, the unWISE epochal astrometry was needed only for those Spitzer data sets that had observations covering fewer than three Spitzer visibility windows. In practice, however, we included unWISE data into the astrometric solutions for all objects in programs 14000, 14224, and 14326; the only exceptions were objects in common to program 13012, as these already had Spitzer observations spanning multiple years.

Plots of our astrometric measurements and their best fits are shown in the figure set for each of our 361 targets. Figures 1–3 show examples of the three types of plots found within the figure set.

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View figure set (361 panels)

Tarball of figure set images

Our astrometric results are summarized in Tables 5–7. For each object, the R.A. and decl. position (in deg) and their uncertainties (in mas) are quoted at the mean epoch, t₀, along with the absolute parallax (ϖ_abs) and absolute proper motions (μ_R.A. and μ_Decl.) and their uncertainties. Also listed are the chi-squared value of the best fit (χ²), the number of degrees of freedom in the fit (ν), and the reduced chi-squared value (${\chi }_{\nu }^{2}$), along with the number of Spitzer (#_Spitzer) and WISE (#_WISE) astrometric epochs and the number of Gaia DR2 five-parameter re-registration stars used (#_Gaia). The two values listed in the #_WISE column refer to the number of astrometric epochs in bands W1 (3.4 μm) and W2 (4.6 μm), respectively. We find that the median ${\chi }_{\nu }^{2}$ value across all of our solutions in Tables 5–7 is 1.03, indicating that our uncertainties are properly measured.

Given the wide range of parallax uncertainties found in our final astrometry, we should determine at what point the uncertainty is too large to give a credible result. Lutz & Kelker (1973) looked at populations of objects with differing parallax uncertainties to see at which values these uncertainties become so large that characterizing the true absolute magnitude of the population becomes impossible. For parallax uncertainties of 5%, the distribution of the ratio of the true parallax to the measured one resembles a Gaussian with a tight variance, but the central value is slightly less than one. This effect is predictable and thus correctable. When the astrometric uncertainty of the population reaches 15%, the effect is still correctable, but the distribution of true-to-measured parallaxes is broader and centered considerably further from unity than for the case of 5% uncertainties. Francis (2014) improves (and corrects) the formalism of Lutz & Kelker (1973), showing that the predicted absolute magnitude error is 0.1 mag for an astrometric uncertainty of ∼12.5%. (Lutz & Kelker (1973) state that, for a magnitude error this small, an astrometric uncertainty of <10% is required.) Francis (2014) further demonstrates that the effect becomes uncorrectable at astrometric uncertainties between 17.5% and 20.0%. With these values in mind, we have chosen "high-quality" parallaxes to be those with uncertainties ≤12.5%, "low-quality" to be those with 12.5%–17.5% uncertainties, and "poor-quality (suspect)" to be those with ≥17.5% uncertainties.

Table 5 lists 296 targets for which the uncertainty in the parallax is ≤12.5%. Results in this table can be considered robust. Table 6 lists 18 targets for which the parallax uncertainty falls between 12.5% and 17.5%. Results from this table should be used with caution, as additional monitoring is needed to drive these uncertainties lower. Finally, Table 7 lists 47 targets for which the parallax uncertainties are ≥17.5%. For most of these objects, the > 3σ detection of a parallax and/or proper motion proves that they are nearby, but derived distances and absolute magnitudes should be regarded as suspect. For these, additional astrometric observations from post-Spitzer resources are needed to establish credible values.

Table 5. Parallax and Motion Fits for Objects with High-quality Parallaxes

Object	R.A.	Decl.	t0	ϖabs	μR.A.	μDecl.	χ2	ν	${\chi }_{\nu }^{2}$	#Spitzer	#WISE	#Gaia
Name	at t0	at t0	MJD	(mas)	(mas yr−1)	(mas yr−1)
	(deg(mas))	(deg(mas))	(day)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
WISE J000517.48+373720.5	1.324667(2.0)	37.621951(2.0)	57226.89	126.9 ± 2.1	997.3 ± 1.0	−271.6 ± 1.0	24.63	45	0.54	25	0,0	45
WISE J001505.87−461517.6	3.775538(2.4)	−46.255813(2.2)	57210.91	75.2 ± 2.4	413.4 ± 1.1	−687.8 ± 1.0	42.76	47	0.91	26	0,0	18
PSO J007.9194+33.5961	7.919347(8.0)	33.596018(8.9)	57416.75	44.4 ± 3.9	−9.2 ± 2.5	−31.8 ± 2.7	131.81	65	2.02	9	13,13	19
WISE J003110.04+574936.3	7.793459(4.7)	57.826711(5.1)	57500.34	71.0 ± 3.2	521.8 ± 1.5	−18.3 ± 1.6	44.16	69	0.64	11	13,13	139
WISE J003231.09−494651.4	8.128639(2.4)	−49.782345(2.3)	57263.63	60.8 ± 2.5	−368.6 ± 1.2	−861.7 ± 1.1	60.03	45	1.33	25	0,0	16
2MASS J00345157+0523050	8.717679(2.6)	5.385476(2.9)	57179.27	118.8 ± 2.7	673.6 ± 1.3	178.2 ± 1.5	24.62	47	0.52	26	0,0	19
WISE J003829.05+275852.1	9.621131(1.9)	27.981211(1.9)	57166.13	88.2 ± 2.0	−12.0 ± 0.9	92.4 ± 1.0	47.60	51	0.93	28	0,0	27
CWISE J004143.77−401929.9	10.432378(7.5)	−40.324986(5.0)	57621.97	76.7 ± 9.6	1196.6 ± 1.7	−958.1 ± 1.3	26.84	37	0.72	9	0,12	14
WISE J004542.56+361139.1	11.427213(5.0)	36.193936(5.5)	57382.01	57.0 ± 3.7	−83.6 ± 1.5	−165.8 ± 1.6	83.88	67	1.25	10	13,13	35
WISE J004945.61+215120.0	12.439534(2.0)	21.855377(2.0)	57182.30	140.4 ± 2.1	−479.4 ± 1.0	−54.0 ± 1.0	32.72	47	0.69	26	0,0	20
WISEA J005811.69−565332.1	14.549325(7.7)	−56.892218(7.5)	57618.24	35.3 ± 4.1	206.4 ± 2.9	22.6 ± 2.8	51.56	61	0.84	9	12,12	10
CWISEP J010527.69−783419.3	16.368057(21.5)	−78.572398(21.1)	57873.04	87.2 ± 4.4	293.0 ± 8.8	−155.1 ± 8.6	112.25	37	3.03	9	0,12	45
WISE J011154.36−505343.2	17.975838(4.6)	−50.896048(4.2)	57515.54	57.3 ± 4.7	−274.7 ± 1.3	−416.1 ± 1.2	53.95	65	0.83	11	12,12	14
WISEPA J012333.21+414203.9	20.890166(2.8)	41.701448(2.8)	57797.45	45.5 ± 2.9	602.3 ± 1.6	90.3 ± 1.6	18.83	21	0.89	13	0,0	54
CFBDS J013302.27+023128.4	23.261157(2.6)	2.524501(2.2)	57231.44	53.1 ± 2.6	606.1 ± 1.4	−115.7 ± 1.1	33.69	45	0.74	25	0,0	9
WISE J014656.66+423410.0	26.735358(2.0)	42.569399(1.9)	57131.69	51.7 ± 2.0	−451.6 ± 0.9	−33.1 ± 0.9	78.47	49	1.60	27	0,0	55
WISEP J015010.86+382724.3	27.547226(4.1)	38.456577(4.0)	57409.89	44.6 ± 3.2	881.4 ± 1.2	−120.1 ± 1.2	128.88	69	1.86	11	13,13	44
2MASS J01550354+0950003	28.766272(6.6)	9.833050(6.9)	57420.03	35.5 ± 4.1	329.8 ± 2.1	−86.3 ± 2.1	47.95	65	0.73	9	13,13	17
WISEA J020047.29−510521.4	30.197466(6.0)	−51.089401(6.3)	57581.09	39.6 ± 4.3	167.3 ± 2.2	−63.5 ± 2.3	53.99	65	0.83	9	13,13	11
2MASSW J0205034+125142	31.266134(8.0)	12.861627(7.0)	57423.44	45.1 ± 3.4	364.5 ± 2.5	−32.0 ± 2.1	49.08	65	0.75	9	13,13	19
WISEP J022105.94+384202.9	35.275158(2.8)	38.700979(2.8)	57807.55	44.8 ± 2.9	139.6 ± 1.6	−24.9 ± 1.6	47.03	21	2.24	13	0,0	62
WISEPA J022623.98−021142.8	36.599419(2.5)	−2.195890(2.3)	57917.68	56.3 ± 2.5	−294.4 ± 1.4	−432.3 ± 1.2	487.05	43	11.32	24	0,0	14
WISE J023318.05+303030.5	38.324981(2.8)	30.508410(2.8)	57718.39	31.4 ± 2.8	−133.2 ± 1.7	−29.0 ± 1.5	22.84	23	0.99	14	0,0	34
WISE J024124.73−365328.0	40.353521(2.3)	−36.890949(2.5)	57121.52	53.1 ± 2.5	242.9 ± 1.1	141.8 ± 1.0	49.09	49	1.00	27	0,0	10
WISE J024512.62−345047.8	41.302353(3.8)	−34.846697(5.0)	57414.37	42.5 ± 4.2	−101.7 ± 1.0	−34.8 ± 1.4	51.53	59	0.87	12	7,13	13
WISE J024714.52+372523.5	41.810724(2.0)	37.422935(2.0)	57159.04	64.4 ± 2.1	30.0 ± 0.9	−88.3 ± 0.9	37.90	47	0.80	26	0,0	70
WISEA J030237.53−581740.3	45.656205(3.3)	−58.294736(3.1)	57901.80	59.9 ± 3.3	52.0 ± 3.5	−70.8 ± 3.5	40.68	21	1.93	13	0,0	18
WISE J030449.03−270508.3	46.204672(2.3)	−27.084538(3.6)	58206.80	73.1 ± 2.6	124.6 ± 1.8	494.3 ± 2.6	207.12	41	5.05	23	0,0	3
WISEA J030919.70−501614.2	47.333447(2.8)	−50.270279(2.7)	57553.58	62.2 ± 2.8	527.5 ± 1.4	207.3 ± 1.3	11.51	25	0.46	15	0,0	14
WISEPA J031325.96+780744.2	48.359149(2.6)	78.129087(2.7)	57460.71	135.6 ± 2.8	73.9 ± 0.9	53.8 ± 1.0	14.00	27	0.51	16	0,0	59
WISE J031614.68+382008.0	49.060978(3.8)	38.335022(3.8)	57592.96	44.2 ± 3.1	−96.1 ± 1.3	−308.9 ± 1.2	81.25	69	1.17	13	12,12	63
WISE J031624.35+430709.1	49.102455(2.0)	43.118689(2.0)	57225.83	74.7 ± 2.1	375.5 ± 0.9	−227.4 ± 0.9	50.80	45	1.12	25	0,0	87
2MASS J03185403−3421292	49.727431(7.5)	−34.357929(6.4)	57427.90	74.1 ± 4.6	397.1 ± 2.3	27.8 ± 1.9	53.12	65	0.81	9	13,13	15
CWISEP J032109.59+693204.5	50.292298(25.7)	69.534458(24.8)	57796.33	68.5 ± 4.0	923.9 ± 10.0	−365.3 ± 9.6	44.39	35	1.26	8	0,12	162
WISE J032301.86+562558.0	50.758879(5.3)	56.432280(5.4)	57653.23	51.9 ± 3.0	319.8 ± 1.9	−293.8 ± 1.9	121.11	67	1.80	12	12,12	135
WISEA J032309.12− 590751.0	50.789692(2.8)	−59.129991(3.0)	57643.18	72.1 ± 2.9	532.5 ± 1.3	507.5 ± 1.7	20.29	23	0.88	14	0,0	19
WISEPC J032337.53−602554.9	50.907945(2.2)	−60.432034(2.3)	57167.73	71.7 ± 2.3	517.2 ± 1.0	−165.3 ± 1.0	44.27	45	0.98	25	0,0	18
WISE J032517.69−385454.1	51.324332(2.8)	−38.915248(3.5)	57658.12	60.2 ± 3.5	287.9 ± 1.3	−110.6 ± 1.6	21.26	23	0.92	14	0,0	16
WISE J032504.33−504400.3	51.268534(2.0)	−50.733637(1.9)	57683.01	35.6 ± 2.0	97.5 ± 0.9	−159.3 ± 0.8	221.30	59	3.75	32	0,0	20
WISE J032547.72+083118.2	51.449089(2.7)	8.521631(2.9)	57210.59	76.3 ± 2.8	125.7 ± 1.3	−49.3 ± 1.5	22.61	45	0.50	25	0,0	16
SDSSp J033035.13−002534.5	52.648217(6.9)	−0.427999(7.0)	57640.16	38.7 ± 3.4	391.6 ± 2.6	−343.3 ± 2.6	40.40	67	0.60	12	12,12	21
PSO J052.7214−03.8409	52.721230(7.4)	−3.840830(6.6)	57639.59	59.2 ± 3.3	−135.5 ± 2.7	57.6 ± 2.5	62.92	67	0.93	12	12,12	16
WISEPC J033349.34−585618.7	53.455274(4.5)	−58.939391(4.8)	57555.55	46.2 ± 3.7	−121.0 ± 1.4	−604.6 ± 1.6	76.80	73	1.05	13	13,13	11
WISE J033515.01+431045.1	53.814680(1.6)	43.177782(1.6)	57631.01	84.8 ± 1.7	822.7 ± 0.6	−792.4 ± 0.6	185.62	71	2.61	38	0,0	157
WISE J033605.05−014350.4	54.020761(2.0)	−1.732628(2.0)	57159.47	99.8 ± 2.1	−251.5 ± 0.9	−1216.1 ± 0.9	58.58	47	1.24	26	0,0	27
WISE J033651.90+282628.8	54.216476(4.2)	28.441046(4.2)	57604.12	39.7 ± 3.1	107.7 ± 1.5	−173.2 ± 1.4	62.78	69	0.91	13	12,12	46
2MASSW J0337036−175807	54.265981(8.1)	−17.968319(7.3)	57529.21	33.9 ± 3.3	199.7 ± 2.7	108.0 ± 2.4	57.91	71	0.81	12	13,13	24
2MASS J03400942−6724051	55.034906(6.0)	−67.398884(5.4)	57727.97	109.4 ± 3.5	−326.5 ± 2.4	498.2 ± 2.0	46.26	67	0.69	12	12,12	21
WISE J035000.32−565830.2	57.500868(2.2)	−56.975831(2.4)	57097.72	176.4 ± 2.3	−208.7 ± 1.0	−575.4 ± 1.1	40.87	47	0.87	26	0,0	23
UGPS J03553200+4743588	58.884626(12.0)	47.732689(12.1)	57878.73	66.4 ± 3.2	505.8 ± 5.7	−184.9 ± 5.7	156.40	57	2.74	12	7,12	103
2MASS J03582255−4116060	59.594374(6.2)	−41.267913(7.0)	57505.01	39.4 ± 3.5	72.5 ± 2.0	89.3 ± 2.2	27.37	69	0.39	11	13,13	18
WISE J035934.06−540154.6	59.891664(1.9)	−54.033035(2.3)	57558.80	73.6 ± 2.0	−134.1 ± 0.7	−758.9 ± 0.9	101.78	73	1.39	39	0,0	18
WISE J040443.48−642029.9	61.181088(2.1)	−64.341755(2.2)	57306.84	44.8 ± 2.2	−38.3 ± 1.0	−54.6 ± 1.0	99.17	41	2.41	23	0,0	27
WISEPA J041022.71+150248.5	62.596159(1.9)	15.043733(1.9)	57064.58	151.3 ± 2.0	960.3 ± 0.8	−2219.4 ± 0.8	54.66	51	1.07	28	0,0	35
WISE J041358.14−475039.3	63.492600(3.0)	−47.843712(3.2)	57818.46	50.7 ± 3.3	110.9 ± 2.2	310.3 ± 2.6	38.58	21	1.83	13	0,0	22
2MASS J04210718−6306022	65.281624(5.3)	−63.099572(5.7)	57654.85	50.0 ± 3.3	148.7 ± 2.0	219.3 ± 2.1	42.33	69	0.61	11	13,13	21
WISE J043052.92+463331.6	67.723058(2.8)	46.559463(2.8)	57862.37	96.1 ± 2.9	882.5 ± 1.8	381.5 ± 1.8	16.02	21	0.76	13	0,0	184
2MASSI J0443058−320209	70.774218(4.1)	−32.034860(3.6)	57542.48	79.6 ± 3.8	−19.1 ± 1.4	198.8 ± 1.1	502.78	71	7.08	14	12,12	21
WISEPA J044853.29−193548.5	72.223712(3.1)	−19.595535(3.1)	57518.49	57.6 ± 3.0	901.1 ± 0.9	761.1 ± 0.9	75.61	73	1.03	15	12,12	20
WISE J045746.08−020719.2	74.442262(5.9)	−2.122197(6.1)	57661.10	95.2 ± 3.0	99.0 ± 2.1	−100.7 ± 2.2	49.35	67	0.73	12	12,12	40
WISEPA J045853.89+643452.9	74.725487(2.6)	64.581763(2.6)	57554.19	106.7 ± 2.8	210.4 ± 1.0	289.6 ± 1.0	10.18	25	0.40	15	0,0	78
WISEPA J050003.05−122343.2	75.011776(2.7)	−12.394492(2.7)	57548.43	95.2 ± 2.8	−531.6 ± 1.1	493.0 ± 1.1	13.57	25	0.54	15	0,0	28
WISEA J050238.28+100750.0	75.659189(27.0)	10.130089(23.3)	57852.84	42.7 ± 4.6	−131.1 ± 11.3	−200.6 ± 9.4	39.48	37	1.06	9	0,12	25
WISEU J050305.68−564834.0	75.776553(25.5)	−56.808684(27.5)	57714.91	98.3 ± 3.9	759.2 ± 9.3	288.2 ± 10.1	48.94	39	1.25	9	0,13	36
PSO J076.7092+52.6087	76.709335(10.8)	52.608376(11.0)	57669.04	61.3 ± 3.1	45.0 ± 4.0	−203.4 ± 4.1	166.51	67	2.48	12	12,12	199
2MASSI J0512063−294954	78.026512(4.5)	−29.831262(4.8)	57661.90	44.4 ± 3.1	1.6 ± 1.6	81.9 ± 1.8	41.82	67	0.62	12	12,12	29
WISE J051208.66−300404.4	78.037194(2.2)	−30.067444(2.3)	57115.04	47.0 ± 2.5	616.9 ± 1.0	188.2 ± 1.0	78.74	49	1.60	27	0,0	22
WISE J052126.29+102528.4	80.359997(6.7)	10.423818(6.9)	57668.72	150.2 ± 3.0	223.7 ± 2.5	−438.3 ± 2.5	579.09	67	8.64	12	12,12	86
WISE J053516.80−750024.9	83.819290(2.0)	−75.006729(2.0)	57174.27	68.7 ± 2.0	−120.1 ± 0.8	23.6 ± 0.8	72.16	45	1.60	25	0,0	179
CWISEP J053644.82−305539.3	84.186801(25.3)	−30.927585(24.2)	57806.18	78.1 ± 3.8	26.4 ± 10.0	−26.5 ± 9.3	32.35	35	0.92	8	0,12	55
CWISE J054025.89−180240.3	85.107885(28.6)	−18.044550(22.6)	57808.01	57.3 ± 4.7	−73.5 ± 10.9	−25.8 ± 8.8	20.97	35	0.59	8	0,12	40
WISE J054047.00+483232.4	85.196431(2.0)	48.541309(2.0)	57231.50	69.4 ± 2.1	249.0 ± 0.9	−631.5 ± 0.9	68.54	45	1.52	25	0,0	158
WISE J054601.19−095947.5	86.504968(6.1)	−9.996528(4.2)	57629.96	57.5 ± 3.9	−10.0 ± 2.1	−2.6 ± 1.4	47.54	69	0.68	13	12,12	12
2MASS J06020638+4043588	90.528061(4.2)	40.732000(4.2)	57599.94	76.4 ± 3.1	237.6 ± 1.5	−220.2 ± 1.4	53.72	67	0.80	12	12,12	148
CWISE J061348.70+480820.5	93.452894(28.0)	48.139133(23.6)	57805.24	49.7 ± 4.9	−47.4 ± 10.6	122.1 ± 9.3	46.74	35	1.33	8	0,12	87
WISE J061437.73+095135.0	93.657827(1.9)	9.859562(1.9)	57076.39	64.9 ± 2.0	387.2 ± 0.8	−153.2 ± 0.8	46.62	51	0.91	28	0,0	228
WISEA J061557.21+152626.1	93.988341(5.4)	15.439648(5.3)	57855.87	52.8 ± 3.1	−29.1 ± 2.6	−532.1 ± 2.5	61.06	43	1.42	12	0,12	250
WISE J062842.71−805725.0	97.179502(3.4)	−80.957735(3.5)	57553.74	48.5 ± 3.0	142.4 ± 1.0	−493.7 ± 1.0	130.87	67	1.95	13	11,12	49
WISE J062905.13+241804.9	97.271327(10.7)	24.300685(10.8)	57614.42	37.5 ± 3.3	−34.6 ± 3.8	−367.7 ± 3.9	92.46	63	1.46	10	12,12	193
CWISEP J063428.10+504925.9	98.617026(35.2)	50.823248(35.2)	57742.77	62.0 ± 4.2	285.9 ± 13.6	−1157.6 ± 13.6	37.93	33	1.14	7	0,12	67
WISE J064205.58+410155.5	100.523307(3.7)	41.031413(3.7)	57561.51	62.6 ± 3.1	−2.0 ± 1.2	−383.1 ± 1.2	77.62	65	1.19	11	12,12	74
WISEA J064503.72+524054.1	101.264364(29.5)	52.680156(30.0)	57744.20	53.5 ± 4.2	−298.5 ± 11.4	−935.6 ± 11.6	28.42	33	0.86	7	0,12	55
WISEA J064528.39−030247.9	101.368294(2.9)	−3.047350(2.8)	57884.01	54.1 ± 3.0	−1.4 ± 1.4	−322.2 ± 1.7	36.11	21	1.72	13	0,0	228
2MASS J06453153−6646120	101.371025(6.5)	−66.763941(6.5)	57216.69	53.8 ± 2.9	−885.2 ± 1.8	1311.5 ± 1.8	179.19	133	1.34	11	29,29	63
WISE J064723.23−623235.5	101.846799(1.7)	−62.542541(1.7)	57620.04	99.5 ± 1.7	2.2 ± 0.6	393.9 ± 0.6	134.49	67	2.00	36	0,0	58
WISEA J064750.85−154616.4	101.962110(6.2)	−15.771033(5.9)	57578.67	62.7 ± 3.3	119.6 ± 2.2	132.4 ± 2.1	222.59	61	3.64	9	12,12	220
PSO J103.0927+41.4601	103.092698(6.2)	41.459964(6.3)	57580.22	57.6 ± 3.3	1.7 ± 2.2	−41.0 ± 2.3	65.56	61	1.07	9	12,12	78
WISE J070159.79+632129.2	105.499114(3.2)	63.357673(3.3)	57542.77	52.6 ± 3.0	−23.3 ± 0.9	−262.0 ± 1.0	90.69	69	1.31	13	12,12	34
WISEA J071301.86−585445.2	108.258010(2.8)	−58.911799(2.8)	57971.79	82.1 ± 3.0	78.3 ± 1.7	364.0 ± 1.8	35.50	21	1.69	13	0,0	71
WISE J071322.55−291751.9	108.344602(2.0)	−29.298377(2.0)	57259.08	109.3 ± 2.1	354.1 ± 0.9	−410.3 ± 0.9	37.28	45	0.82	25	0,0	236
WISE J072312.44+340313.5	110.802002(2.1)	34.053026(2.1)	57966.21	60.8 ± 2.1	−3.2 ± 0.8	−348.1 ± 0.9	46.44	43	1.08	24	0,0	50
WISE J073444.02−715744.0	113.680052(1.7)	−71.962381(1.7)	57712.17	74.5 ± 1.7	−565.0 ± 0.6	−67.5 ± 0.6	132.38	65	2.03	35	0,0	72
2MASS J07414279-0506464	115.427625(5.3)	−5.112797(5.3)	57581.76	32.7 ± 3.2	−152.0 ± 2.0	74.6 ± 2.0	773.14	61	12.67	9	12,12	171
SDSS J074149.15+235127.5	115.453611(4.5)	23.856717(4.3)	57580.03	73.2 ± 3.4	−264.1 ± 1.6	−220.1 ± 1.5	62.85	59	1.06	10	11,11	48
SDSS J074201.41+205520.5	115.503627(3.0)	20.920997(2.9)	57417.17	63.5 ± 3.1	−327.3 ± 0.8	−230.4 ± 0.7	48.70	63	0.77	12	11,11	44
WISEPA J074457.15+562821.8	116.238936(1.9)	56.471453(2.0)	57145.12	65.3 ± 2.0	149.3 ± 0.8	−767.3 ± 0.8	69.28	49	1.41	27	0,0	32
2MASS J07555430−3259589	118.975554(6.0)	−32.998918(5.5)	57589.28	40.5 ± 3.5	−127.8 ± 2.2	162.2 ± 2.1	32.70	61	0.53	9	12,12	214
2MASSI J0755480+221218	118.949721(3.7)	22.203511(3.2)	57477.06	67.4 ± 3.2	−20.6 ± 1.1	−256.3 ± 0.8	65.02	61	1.06	11	11,11	45
SDSS J075840.33+324723.4	119.666932(3.9)	32.788510(3.7)	57436.19	101.3 ± 3.3	−227.4 ± 1.1	−330.2 ± 1.0	72.18	61	1.18	11	11,11	36
WISEPC J075946.98−490454.0	119.944966(2.0)	−49.081344(2.0)	57212.75	90.7 ± 2.1	−370.7 ± 0.8	250.0 ± 0.8	34.96	45	0.77	25	0,0	184
WISEA J080622.22−082046.5	121.593013(68.5)	−8.348917(46.5)	57809.47	82.2 ± 9.0	300.1 ± 30.7	−1296.8 ± 19.4	60.84	35	1.73	8	0,12	116
WISE J080700.23+413026.8	121.750978(3.9)	41.506828(3.8)	57571.40	50.7 ± 3.3	−5.1 ± 1.3	−346.6 ± 1.2	61.52	59	1.04	10	11,11	30
SDSS J080959.01+443422.2	122.494847(7.0)	44.571699(7.0)	57630.85	39.8 ± 3.4	−167.5 ± 2.7	−216.9 ± 2.8	72.79	57	1.27	9	11,11	24
WISE J081220.04+402106.2	123.084256(2.1)	40.351706(1.7)	57504.83	34.3 ± 2.1	253.0 ± 0.8	17.3 ± 0.7	119.96	67	1.79	36	0,0	27
WISE J082000.48−662211.9	125.001344(6.7)	−66.369487(6.4)	57396.81	56.1 ± 3.4	−161.6 ± 2.1	317.1 ± 2.0	82.16	65	1.26	9	13,13	131
WISE J082507.35+280548.5	126.280525(2.0)	28.096445(2.0)	57215.77	152.6 ± 2.0	−66.7 ± 0.9	−235.8 ± 0.9	46.42	47	0.98	26	0,0	28
WISEA J082640.45−164031.8	126.667106(7.2)	−16.674676(6.8)	57590.91	67.8 ± 3.5	−840.9 ± 2.7	514.5 ± 2.6	34.42	61	0.56	9	12,12	122
WISE J083337.83+005214.2	128.409249(2.8)	0.867492(2.8)	57937.66	79.7 ± 3.1	786.8 ± 2.1	−1593.7 ± 2.0	14.86	21	0.70	13	0,0	48
WISEPC J083641.12−185947.2	129.171411(2.0)	−18.996628(2.1)	57996.15	44.2 ± 2.2	−52.5 ± 0.8	−153.0 ± 0.8	161.56	43	3.75	24	0,0	103
SDSS J085234.90+472035.0	133.145121(7.5)	47.341299(8.1)	57631.30	52.5 ± 3.7	−48.3 ± 2.9	−384.7 ± 3.2	51.51	57	0.90	9	11,11	18
WISE J085510.83−071442.5	133.780984(2.3)	−7.243932(2.3)	57633.39	439.0 ± 2.4	−8123.7 ± 1.3	673.2 ± 1.3	19.56	33	0.59	19	0,0	46
WISEPA J085716.25+560407.6	134.315810(2.1)	56.068427(2.0)	57139.00	85.3 ± 2.1	−714.7 ± 0.9	−243.1 ± 0.9	43.31	49	0.88	27	0,0	14
SDSSp J085758.45+570851.4	134.490295(3.9)	57.145869(4.1)	57472.47	77.2 ± 3.5	−405.1 ± 1.2	−387.4 ± 1.2	43.32	63	0.68	10	12,12	18
SDSS J085834.42+325627.7	134.640739(3.8)	32.941248(3.4)	57425.54	50.3 ± 3.7	−626.0 ± 1.2	56.2 ± 0.9	42.64	65	0.65	11	12.12	26
2MASS J09054654+5623117	136.444051(6.0)	56.387076(6.6)	57629.62	47.9 ± 3.6	8.6 ± 2.3	103.2 ± 2.7	174.68	57	3.06	9	11,11	16
WISEPA J090649.36+473538.6	136.704326(2.8)	47.592884(2.6)	57504.05	47.0 ± 2.9	−550.7 ± 1.1	−713.8 ± 1.1	23.46	27	0.86	16	0,0	16
SDSS J090900.73+652527.2	137.251186(4.5)	65.423798(4.0)	57471.73	63.9 ± 3.9	−222.9 ± 1.3	−119.6 ± 1.2	53.50	61	0.87	11	11,11	27
WISE J091408.96−345941.5	138.537197(2.8)	−34.994618(2.9)	57946.67	48.0 ± 3.0	−23.6 ± 1.8	174.1 ± 1.8	29.58	21	1.40	13	0,0	170
WISE J092055.40+453856.3	140.230653(6.5)	45.647468(6.7)	57584.32	88.9 ± 4.7	−74.5 ± 2.5	−852.3 ± 2.6	96.79	61	1.58	9	12,12	18
WISEA J094020.09−220820.5	145.083479(2.8)	−22.138820(2.8)	57936.82	36.7 ± 3.1	−150.2 ± 1.8	172.6 ± 1.7	27.20	21	1.29	13	0,0	47
WISE J094305.98+360723.5	145.776141(2.8)	36.122541(3.0)	57155.77	97.1 ± 2.9	669.5 ± 1.2	−501.2 ± 1.4	35.00	49	0.71	27	0,0	12
WISEPC J095259.29+195507.3	148.246978(3.3)	19.918957(2.6)	57525.01	40.0 ± 3.0	−37.8 ± 1.6	−37.4 ± 1.1	23.06	27	0.85	16	0,0	15
PSO J149.0341−14.7857	149.034247(7.0)	−14.785896(7.3)	57613.53	69.2 ± 3.9	86.5 ± 2.6	−146.3 ± 2.8	58.02	61	0.95	9	12,12	30
2MASSI J1010148−040649	152.560123(6.7)	−4.113904(6.7)	57612.39	57.7 ± 3.6	−319.6 ± 2.5	−15.2 ± 2.6	35.96	61	0.59	9	12,12	18
ULAS J101243.54+102101.7	153.180361(5.3)	10.349085(6.0)	57528.95	59.7 ± 4.8	−400.2 ± 1.7	−538.0 ± 1.9	68.96	65	1.06	11	12,12	15
WISEPC J101808.05−244557.7	154.533610(2.6)	−24.767531(2.6)	57667.84	83.0 ± 2.8	49.6 ± 1.1	−821.0 ± 1.0	21.17	25	0.84	15	0,0	31
WISE J102557.72+030755.7	156.488602(2.2)	3.131989(2.1)	57323.51	83.6 ± 2.3	−1203.0 ± 1.0	−143.6 ± 1.0	28.23	43	0.65	24	0,0	21
CFBDS J102841.01+565401.9	157.171642(2.5)	56.900357(2.3)	57259.03	46.6 ± 2.6	197.1 ± 1.2	−17.9 ± 1.0	39.40	45	0.87	25	0,0	19
2MASSW J1036530−344138	159.220852(7.0)	−34.696057(6.0)	57523.09	75.4 ± 3.5	−41.0 ± 2.4	−461.1 ± 2.1	61.34	61	1.00	9	12,12	58
WISE J103907.73−160002.9	159.781943(2.1)	−16.000967(2.0)	57249.83	54.2 ± 2.2	−199.8 ± 1.0	−121.2 ± 0.9	45.12	47	0.96	26	0,0	17
2MASS J10430758+2225236	160.780878(8.0)	22.423127(9.6)	57610.48	55.7 ± 5.0	−114.9 ± 3.1	−13.1 ± 3.7	71.44	61	1.17	9	12,12	16
SDSS J104335.08+121314.1	160.896243(7.7)	12.219606(7.2)	57614.12	63.1 ± 5.7	7.7 ± 2.8	−250.4 ± 2.8	30.03	61	0.49	9	12,12	17
WISE J105047.90+505606.2	162.698098(2.7)	50.934797(2.4)	58219.40	42.2 ± 2.7	−434.9 ± 1.8	−71.5 ± 1.5	45.39	39	1.16	22	0,0	11
WISE J105130.01−213859.7	162.875304(2.1)	−21.650122(2.1)	57321.04	64.0 ± 2.3	130.0 ± 1.0	−154.9 ± 0.9	82.14	43	1.91	24	0,0	26
WISE J105257.95−194250.2	163.242099(2.8)	−19.714614(2.8)	57922.49	64.9 ± 3.1	320.6 ± 1.8	−315.7 ± 1.5	19.18	21	0.91	13	0,0	31
WISEA J105553.62−165216.5	163.971935(2.2)	−16.870689(2.1)	57427.85	71.7 ± 2.3	−1000.4 ± 1.0	417.7 ± 1.0	84.26	39	2.16	22	0,0	28
CWISE J105512.11+544328.3	163.799544(10.5)	54.724527(10.1)	57580.05	145.0 ± 14.7	−1518.7 ± 2.1	−222.7 ± 2.0	24.05	37	0.65	9	0,12	12
2MASSI J1104012+195921	166.005599(6.6)	19.989927(7.3)	57616.50	59.1 ± 5.7	54.9 ± 2.4	125.0 ± 2.8	63.77	61	1.04	9	12,12	13
WISE J111239.24−385700.7	168.164941(4.7)	−38.949060(4.2)	57687.51	102.6 ± 3.7	671.5 ± 1.6	674.0 ± 1.5	35.54	39	0.91	10	0,12	93
WISE J112438.12−042149.7	171.157926(2.9)	−4.363702(2.5)	57340.54	59.4 ± 2.9	−569.3 ± 1.4	64.1 ± 1.2	23.68	43	0.55	24	0,0	18
SIMP J11322058−3809562	173.086824(7.9)	−38.166327(8.0)	57404.35	59.0 ± 3.5	177.9 ± 2.4	−155.2 ± 2.4	60.36	65	0.92	9	13,13	61
CWISE J113717.27−532007.9	174.322097(4.6)	−53.335547(4.9)	57521.83	47.6 ± 4.9	238.7 ± 1.4	−124.0 ± 1.4	27.33	37	0.73	8	0,13	162
WISE J113949.24−332425.1	174.954892(2.8)	−33.407144(2.8)	57928.60	28.3 ± 3.0	−104.2 ± 1.9	−51.1 ± 1.9	29.79	21	1.41	13	0,0	142
WISEA J114156.67−332635.5	175.484176(2.8)	−33.443308(2.8)	57928.92	104.0 ± 2.9	−910.9 ± 1.9	−76.4 ± 1.8	27.76	21	1.32	13	0,0	151
WISE J114340.22+443123.8	175.917804(3.8)	44.523266(4.4)	57936.96	32.6 ± 4.0	81.1 ± 4.0	−88.9 ± 3.3	16.67	21	0.79	13	0,0	7
WISEP J115013.88+630240.7	177.558965(2.8)	63.044112(2.3)	57159.28	121.4 ± 2.7	407.2 ± 1.1	−540.4 ± 0.9	25.40	49	0.51	27	0,0	9
ULAS J115239.94+113407.6	178.165234(2.5)	11.568659(2.3)	58254.13	56.7 ± 2.7	−488.2 ± 1.7	−35.6 ± 1.5	59.73	39	1.53	22	0,0	16
SDSS J115553.86+055957.5	178.972562(7.4)	5.999079(4.0)	57350.10	54.7 ± 6.4	−454.1 ± 2.2	−66.0 ± 1.0	35.62	65	0.54	11	12,12	9
SDSSp J120358.19+001550.3	180.986678(7.1)	0.262636(8.9)	57527.77	71.4 ± 4.9	−1217.4 ± 2.4	−283.2 ± 3.2	19.91	61	0.32	9	12,12	20
WISE J120604.38+840110.6	181.510437(2.2)	84.019183(2.0)	57158.53	84.7 ± 2.1	−577.5 ± 1.0	−263.1 ± 0.8	65.17	49	1.33	27	0,0	19
2MASSI J1213033−043243	183.262300(4.7)	−4.545637(4.9)	57352.79	66.0 ± 5.2	−367.4 ± 1.3	−34.5 ± 1.4	31.94	65	0.49	11	12,12	10
SDSS J121440.95+631643.4	183.671853(6.0)	63.278779(4.8)	57419.99	55.8 ± 4.6	131.1 ± 1.8	22.0 ± 1.4	65.52	65	1.00	11	12,12	9
WISEPC J121756.91+162640.2	184.488710(3.8)	16.442057(2.7)	58058.35	107.4 ± 3.5	754.9 ± 1.2	−1249.8 ± 1.8	293.57	43	6.82	24	0,0	13
SDSS J121951.45+312849.4	184.963351(10.6)	31.480344(8.6)	57570.78	63.9 ± 7.2	−249.5 ± 3.8	−17.4 ± 3.2	52.03	65	0.80	9	13,13	7
WISEA J122036.38+540717.3	185.152201(5.2)	54.120783(3.6)	58017.58	47.6 ± 5.1	181.7 ± 4.5	−322.0 ± 4.5	32.40	21	1.54	13	0,0	14
WISE J122152.28−313600.8	185.468814(2.1)	−31.599679(2.1)	57282.08	76.8 ± 2.2	590.9 ± 1.1	403.0 ± 1.0	50.18	45	1.11	25	0,0	39
WISE J122558.86−101345.0	186.495053(2.3)	−10.229728(2.2)	57333.53	39.4 ± 2.3	−160.6 ± 1.1	−332.7 ± 1.0	47.57	45	1.05	25	0,0	15
2MASS J12314753+0847331	187.942429(4.4)	8.787544(3.7)	57862.84	70.6 ± 4.4	−1178.7 ± 2.4	−1044.0 ± 2.9	11.95	23	0.52	14	0,0	9
CWISEP J124138.41−820051.9	190.410770(20.5)	−82.014242(19.3)	57836.79	69.1 ± 3.8	280.0 ± 8.4	−20.8 ± 7.8	77.80	37	2.10	9	0,12	105
WISE J124309.61+844547.8	190.777710(2.8)	84.762231(2.8)	57877.19	54.5 ± 3.1	−531.9 ± 1.8	−524.0 ± 1.8	43.93	21	2.09	13	0,0	33
WISE J125015.56+262846.9	192.563971(30.1)	26.478708(24.1)	57526.91	61.1 ± 5.9	−480.4 ± 10.7	−570.6 ± 8.3	48.31	61	0.79	9	12,12	15
WISE J125448.52−072828.4	193.702040(3.9)	−7.474871(3.4)	57868.24	45.6 ± 3.9	2.9 ± 3.2	−129.6 ± 2.3	15.72	21	0.74	13	0,0	18
WISE J125715.90+400854.2	194.316970(8.3)	40.148605(3.4)	57921.99	53.8 ± 5.8	303.2 ± 5.6	170.3 ± 2.4	9.98	21	0.47	13	0,0	10
VHS J125804.89−441232.4	194.520761(2.8)	−44.209315(2.8)	57824.89	67.0 ± 2.9	135.8 ± 1.8	−151.7 ± 1.8	30.93	21	1.47	13	0,0	123
WISE J130141.62−030212.9	195.423723(4.5)	−3.037427(2.8)	57879.36	54.5 ± 4.5	229.2 ± 3.2	−299.3 ± 2.0	17.35	21	0.82	13	0,0	19
WISE J131833.98−175826.5	199.640853(2.2)	−17.973998(2.0)	57181.71	63.5 ± 2.2	−526.2 ± 1.0	0.9 ± 1.0	64.85	49	1.32	27	0,0	27
PSO J201.0320+19.1072	201.031798(14.8)	19.107064(16.6)	57405.04	42.5 ± 5.1	−107.8 ± 4.6	−99.9 ± 5.1	60.12	65	0.92	9	13,13	9
2MASS J13243559+6358284	201.144281(6.3)	63.974174(6.1)	57529.71	99.7 ± 5.6	−364.4 ± 2.2	−72.4 ± 2.1	48.89	63	0.77	10	12,12	15
SDSSp J132629.82−003831.5	201.623104(9.2)	−0.642599(8.9)	57413.04	49.4 ± 5.2	−232.5 ± 2.9	−100.3 ± 2.9	44.94	65	0.69	9	13,13	13
WISEA J133300.03−160754.4	203.249437(3.5)	−16.132061(2.9)	57836.32	52.8 ± 3.5	−329.0 ± 1.9	−131.9 ± 1.6	32.50	21	1.54	13	0,0	20
SDSS J135852.68+374711.9	209.719370(20.8)	37.784993(19.0)	57467.12	53.2 ± 5.6	−38.6 ± 6.7	−463.5 ± 6.1	80.95	63	1.28	9	12,13	18
WISE J140035.40−385013.5	210.147455(4.5)	−38.837516(4.6)	57503.23	61.7 ± 3.6	−15.2 ± 1.5	−231.0 ± 1.4	73.74	63	1.17	10	12,12	96
WISEPC J140518.40+553421.4	211.320620(2.7)	55.572896(2.2)	57249.47	158.2 ± 2.6	−2334.8 ± 1.2	226.8 ± 1.0	23.31	45	0.51	25	0,0	12
CWISE J141127.70−481153.4	212.865225(29.5)	−48.198347(28.)1	57737.84	58.2 ± 4.7	−354.5 ± 10.8	−336.8 ± 10.1	31.73	33	0.96	7	0,12	249
VHS J143311.46−083736.3	218.297149(2.7)	−8.627103(2.9)	57575.68	56.5 ± 2.8	−300.0 ± 1.2	−210.4 ± 1.5	25.44	25	1.01	15	0,0	34
WISEPA J143602.19−181421.8	219.009052(2.0)	−18.239562(1.9)	57150.28	50.9 ± 2.0	−71.4 ± 0.9	−92.1 ± 0.9	64.52	49	1.31	27	0,0	34
WISE J144806.48−253420.3	222.027156(2.0)	−25.573457(2.0)	57240.72	54.8 ± 2.1	132.2 ± 1.0	−745.5 ± 1.0	78.15	45	1.73	25	0,0	67
WISE J150115.92−400418.4	225.317599(2.1)	−40.072524(2.1)	58169.67	72.8 ± 2.3	366.7 ± 1.3	−342.7 ± 1.3	51.92	39	1.33	22	0,0	198
PSO J226.2599−28.8959	226.260163(4.1)	−28.896742(4.1)	57500.87	42.5 ± 3.5	101.3 ± 1.3	−432.8 ± 1.2	69.00	63	1.09	10	12,12	96
WISE J151721.13+052929.3	229.337830(2.9)	5.491797(2.9)	57833.97	47.9 ± 3.0	−60.3 ± 2.0	189.2 ± 2.3	22.30	21	1.06	13	0,0	33
WISEPC J151906.64+700931.5	229.778957(3.1)	70.157986(2.2)	57213.77	78.5 ± 2.6	318.3 ± 1.3	−501.5 ± 0.9	31.06	45	0.69	25	0,0	22
SDSS J152039.82+354619.8	230.167284(7.4)	35.770834(6.9)	57256.43	73.6 ± 5.7	314.9 ± 2.1	−377.9 ± 1.7	101.87	69	1.47	11	13,13	12
WISE J152305.10+312537.6	230.771434(3.3)	31.426212(3.3)	57577.50	65.0 ± 3.5	95.1 ± 1.8	−513.8 ± 1.7	15.66	25	0.62	15	0,0	19
2MASSI J1526140+204341	231.557286(7.4)	20.726269(8.0)	57545.73	56.3 ± 4.5	−210.9 ± 2.5	−370.0 ± 2.7	47.49	61	0.77	9	12,12	25
SDSS J153453.33+121949.2	233.722751(7.7)	12.330225(6.7)	57551.92	41.1 ± 4.0	174.1 ± 2.6	−37.3 ± 2.3	133.74	61	2.19	9	12,12	27
CWISEP J153859.39+482659.1	234.747797(37.9)	48.449285(38.)7	57652.17	48.3 ± 6.0	69.0 ± 13.0	−470.0 ± 13.2	59.03	37	1.59	8	0,13	17
WISEPA J154151.66−225025.2	235.463692(2.0)	−22.840586(1.9)	57153.85	166.9 ± 2.0	−902.8 ± 0.9	−91.4 ± 0.9	55.22	49	1.12	27	0,0	88
WISE J154214.00+223005.2	235.556133(2.7)	22.500649(2.9)	57975.26	84.3 ± 3.0	−977.3 ± 1.4	−392.5 ± 1.2	38.97	43	0.90	24	0,0	17
2MASS J15461461+4932114	236.562183(8.8)	49.533306(9.0)	57409.93	53.0 ± 4.4	163.2 ± 2.8	−713.1 ± 2.9	241.30	65	3.71	9	13,13	23
CWISEP J160835.01-244244.7	242.146147(24.5)	−24.712500(23.)0	57829.98	36.9 ± 3.7	295.5 ± 10.1	−45.9 ± 9.3	23.05	37	0.62	9	0,12	241
WISEPA J161215.94−342027.1	243.065771(2.6)	−34.342242(2.6)	57539.39	90.0 ± 2.7	−292.0 ± 1.0	−587.5 ± 1.0	38.18	25	1.52	15	0,0	319
WISEPA J161441.45+173936.7	243.673745(2.5)	17.659099(2.6)	57457.86	98.2 ± 2.7	550.6 ± 1.0	−477.1 ± 1.0	21.22	27	0.78	16	0,0	36
2MASS J16150413+1340079	243.768603(2.0)	13.667277(2.0)	57210.50	55.4 ± 2.1	285.9 ± 0.9	−329.9 ± 1.0	44.32	47	0.94	26	0,0	42
SIMP J1619275+031350	244.864949(8.6)	3.229433(9.0)	57589.50	44.9 ± 3.3	61.8 ± 3.0	−306.1 ± 3.1	457.05	63	7.25	10	12,12	52
WISEPA J162208.94−095934.6	245.537308(2.5)	−9.992965(2.5)	57465.57	37.3 ± 2.6	41.1 ± 0.9	−10.7 ± 0.9	35.30	27	1.30	16	0,0	67
WISEA J162341.27−740230.4	245.920961(7.4)	−74.042480(7.3)	57640.95	50.6 ± 3.1	−133.8 ± 2.6	−390.9 ± 2.6	207.84	65	3.19	11	12,12	194
PSO J247.3273+03.5932	247.327749(3.6)	3.592966(3.6)	57574.12	81.2 ± 3.0	233.9 ± 1.2	−147.0 ± 1.1	91.06	67	1.35	12	12,12	67
SDSS J163022.92+081822.0	247.595286(4.0)	8.305705(3.4)	57499.56	55.8 ± 3.4	−63.1 ± 1.0	−107.2 ± 0.9	62.13	69	0.90	13	12,12	52
WISEA J163932.75+184049.4	249.885376(25.1)	18.680308(18.)7	57824.18	61.9 ± 4.7	−542.8 ± 10.2	74.9 ± 7.7	35.88	37	0.97	9	0,12	52
WISE J163940.86−684744.6	249.922582(2.1)	−68.798903(2.1)	57346.60	219.6 ± 2.3	578.1 ± 1.1	−3107.5 ± 1.1	57.96	43	1.34	24	0,0	344
WISEPA J165311.05+444423.9	253.295757(3.7)	44.739088(3.7)	57198.24	79.1 ± 3.8	−74.7 ± 1.9	−395.2 ± 1.5	11.93	47	0.25	26	0,0	13
WISE J165842.56+510335.0	254.676516(4.2)	51.059207(5.2)	57565.02	33.4 ± 3.4	−282.8 ± 1.4	−289.9 ± 1.7	74.99	67	1.11	12	12,12	26
CWISE J170127.12+415805.3	255.362852(7.1)	41.968399(6.3)	57770.84	38.3 ± 4.0	−191.9 ± 2.7	428.0 ± 2.5	35.76	37	0.96	9	0,12	36
WISE J170745.85−174452.5	256.941368(2.9)	−17.747953(2.9)	57535.51	86.0 ± 2.8	173.3 ± 0.9	−8.9 ± 0.9	175.58	73	2.40	15	12,12	130
WISEPA J171104.60+350036.8	257.768816(1.7)	35.010103(1.8)	57584.13	43.3 ± 1.9	−157.6 ± 0.6	−76.3 ± 0.6	244.29	71	3.44	38	0,0	42
PSO J258.2413+06.7612	258.241013(7.2)	6.761001(7.7)	57659.56	36.2 ± 3.0	−196.5 ± 2.7	−108.4 ± 2.8	526.99	67	7.86	12	12,12	108
WISEPA J171717.02+612859.3	259.320958(2.7)	61.483116(3.2)	57520.68	43.9 ± 2.9	82.3 ± 1.1	−35.0 ± 1.6	46.49	25	1.86	15	0,0	19
WISE J172134.46+111739.4	260.393381(2.8)	11.294536(2.8)	57868.33	50.4 ± 2.9	−91.1 ± 1.8	132.2 ± 1.8	22.99	21	1.09	13	0,0	110
WISEA J173453.90−481357.9	263.724282(6.3)	−48.233188(6.4)	57667.51	37.9 ± 2.9	−126.5 ± 2.4	−230.0 ± 2.4	47.59	67	0.71	12	12,12	258
WISEA J173551.56−820900.3	263.961506(2.8)	−82.150644(3.1)	57851.28	76.1 ± 3.2	−253.9 ± 1.6	−266.4 ± 1.6	32.39	21	1.54	13	0,0	104
WISEPA J173835.53+273258.9	264.648568(1.9)	27.549203(2.0)	57094.49	130.9 ± 2.1	337.1 ± 0.8	−343.4 ± 0.8	89.46	51	1.75	28	0,0	53
WISE J173859.27+614242.1	264.746989(3.6)	61.712104(4.0)	57354.17	44.5 ± 3.0	23.0 ± 1.0	259.1 ± 1.2	97.32	119	0.81	12	25,25	28
WISE J174102.78−464225.5	265.261478(5.5)	−46.707769(5.7)	57669.00	50.5 ± 2.9	−29.2 ± 2.1	−356.5 ± 2.1	62.94	67	0.94	12	12,12	177
WISE J174303.71+421150.0	265.765531(4.0)	42.196246(4.0)	57593.30	59.2 ± 3.3	27.6 ± 1.2	−513.8 ± 1.3	91.95	67	1.37	12	12,12	44
2MASS J17461199+5034036	266.551996(5.3)	50.567706(5.2)	57643.41	50.9 ± 3.1	287.5 ± 1.9	19.7 ± 1.8	46.46	65	0.71	11	12,12	35
WISE J174640.78−033818.0	266.669743(3.5)	−3.638490(3.5)	57469.86	39.8 ± 3.6	−35.2 ± 1.0	−112.8 ± 0.9	39.85	37	1.07	9	0,12	111
WISEA J175328.55−590447.6	268.368270(24.3)	−59.080430(23.1)	57853.73	60.2 ± 3.7	−138.8 ± 10.0	−302.2 ± 9.4	27.48	37	0.74	9	0,12	161
2MASSJ17545447+1649196	268.727516(8.1)	16.821483(8.3)	57656.92	74.0 ± 3.1	120.1 ± 3.1	−147.4 ± 3.1	122.85	67	1.83	12	12,12	165
WISE J175510.28+180320.2	268.792128(3.8)	18.055655(3.8)	57603.96	53.6 ± 3.1	−421.2 ± 1.3	14.6 ± 1.2	386.17	69	5.59	13	12,12	135
WISEPA J180435.40+311706.1	271.146832(2.5)	31.285127(2.6)	57471.63	62.2 ± 2.7	−254.1 ± 0.9	2.9 ± 0.9	35.51	27	1.31	16	0,0	72
WISE J180952.53−044812.5	272.468799(7.2)	−4.804286(6.8)	57669.83	49.2 ± 2.9	−54.0 ± 2.7	−402.3 ± 2.5	131.10	67	1.95	12	12,12	176
WISE J181243.14+200746.4	273.179658(2.7)	20.128523(2.7)	57717.92	48.2 ± 2.8	2.9 ± 0.9	−539.6 ± 1.2	47.64	23	2.07	14	0,0	118
WISE J181329.40+283533.3	273.371944(2.0)	28.591529(2.1)	57265.69	76.6 ± 2.2	−207.5 ± 0.9	−469.4 ± 0.9	44.00	45	0.97	25	0,0	129
WISEA J181849.59−470146.9	274.706867(24.2)	−47.030658(22.5)	57858.73	94.6 ± 3.9	−36.9 ± 10.1	−510.6 ± 9.2	351.33	37	9.49	9	0,12	160
WISEPA J182831.08+265037.8	277.131096(1.9)	26.844069(2.0)	57094.09	100.3 ± 2.0	1016.5 ± 0.8	169.3 ± 0.8	54.25	51	1.06	28	0,0	156
CWISE J183207.94−540943.3	278.032942(28.8)	−54.162165(24.3)	57878.51	57.0 ± 4.3	−129.1 ± 11.6	−172.1 ± 9.7	54.25	37	1.46	9	0,12	171
WISEPA J184124.74+700038.0	280.352854(3.4)	70.011382(3.4)	57264.19	35.1 ± 3.5	−66.6 ± 0.8	537.1 ± 0.8	59.60	61	0.97	9	0,24	32
WISE J185101.83+593508.6	282.757707(3.0)	59.586404(3.0)	57434.90	54.3 ± 2.7	30.2 ± 0.9	426.5 ± 0.9	92.26	97	0.95	13	19,19	62
WISEA J190005.76-310810.9	285.024000(24.8)	−31.136980(21.5)	57922.90	42.5 ± 3.6	−43.5 ± 11.0	−312.5 ± 9.4	28.40	35	0.81	9	0,11	156
2MASS J19010601+4718136	285.276033(4.2)	47.305813(4.1)	57624.42	67.3 ± 3.4	122.9 ± 1.4	405.7 ± 1.4	67.59	67	1.00	12	12,12	96
WISE J191915.54+304558.4	289.815624(5.8)	30.767021(6.5)	57705.19	62.5 ± 3.3	384.6 ± 2.3	419.7 ± 2.5	91.74	61	1.50	11	11,11	164
2MASS J19251275+0700362	291.303371(7.2)	7.011096(7.0)	57700.93	94.5 ± 3.2	51.1 ± 2.8	206.2 ± 2.8	80.67	61	1.32	11	11,11	256
CWISE J192636.29−342955.7	291.651234(4.8)	−34.498916(4.3)	57799.88	51.6 ± 3.9	85.1 ± 1.5	−193.4 ± 1.4	35.82	35	1.02	9	0,11	157
WISE J192841.35+235604.9	292.171706(1.7)	23.935048(1.8)	57623.03	154.9 ± 1.8	−247.5 ± 0.7	239.0 ± 0.7	36.28	63	0.57	34	0,0	252
WISEA J193054.55−205949.4	292.725194(23.9)	−20.999130(18.2)	57916.15	106.3 ± 4.9	−1047.5 ± 10.2	−1075.9 ± 8.0	33.00	35	0.94	9	0,11	152
CWISEP J193518.59−154620.3	293.827684(25.2)	−15.772363(25.1)	57939.58	69.3 ± 3.8	290.2 ± 11.6	43.1 ± 11.5	18.33	33	0.55	9	0,10	157
WISENF J193656.08+040801.2	294.232524(19.9)	4.131561(20.1)	58108.70	113.9 ± 3.8	−428.6 ± 11.4	−1102.1 ± 11.5	81.99	19	4.31	8	0,4	202
WISE J195500.42−254013.9	298.752234(2.0)	−25.670878(2.0)	57265.27	37.4 ± 2.1	346.1 ± 0.9	−257.8 ± 0.9	72.19	43	1.67	24	0,0	136
WISEPA J195905.66−333833.7	299.773586(1.9)	−33.642980(1.9)	57103.36	83.9 ± 2.0	−4.7 ± 0.8	−200.7 ± 0.8	48.93	51	0.95	28	0,0	82
WISE J200050.19+362950.1	300.209094(2.0)	36.497796(2.1)	57255.66	133.4 ± 2.2	6.1 ± 0.9	372.8 ± 0.9	16.52	45	0.36	25	0,0	88
WISE J200520.38+542433.9	301.331665(2.6)	54.407888(2.6)	57552.67	53.9 ± 2.7	−1156.2 ± 1.0	−904.4 ± 1.0	27.33	25	1.09	15	0,0	144
WISE J200804.71−083428.5	302.020104(3.7)	−8.574862(3.6)	57500.44	57.8 ± 3.3	304.6 ± 1.2	−156.3 ± 1.2	82.18	65	1.26	11	12,12	132
CWISEP J201146.45−481259.7	302.943925(25.0)	−48.216745(23.7)	57926.22	71.0 ± 3.7	72.4 ± 11.0	−402.8 ± 10.5	49.91	35	1.42	9	0,11	96
CWISE J201221.32+701740.2	303.088893(5.0)	70.294501(5.1)	57496.33	46.6 ± 5.0	−11.3 ± 1.4	−86.4 ± 1.7	77.69	35	2.22	7	0,13	40
WISE J201546.27+664645.1	303.942916(2.1)	66.779662(2.0)	57226.81	39.6 ± 2.1	290.2 ± 0.9	429.7 ± 0.9	93.53	43	2.17	24	0,0	82
WISEA J201748.74−342102.6	304.453629(2.8)	−34.350314(2.8)	57881.14	47.2 ± 2.9	190.5 ± 1.5	284.4 ± 1.5	34.06	21	1.62	13	0,0	80
WISE J201920.76−114807.5	304.837075(2.6)	−11.802171(2.6)	57635.08	79.9 ± 2.7	354.0 ± 1.1	−55.7 ± 1.1	23.55	25	0.94	15	0,0	75
WISE J203042.79+074934.7	307.679459(6.6)	7.826090(6.0)	57591.67	103.3 ± 3.5	664.5 ± 2.4	−108.6 ± 2.2	60.30	61	0.98	9	12,12	148
WISE J204356.42+622048.9	310.986202(6.0)	62.347773(5.6)	57648.40	37.5 ± 3.2	295.4 ± 2.2	488.6 ± 2.0	189.75	69	2.75	11	13,13	160
WISEPC J205628.90+145953.3	314.121593(1.9)	14.998858(1.9)	57130.44	140.8 ± 2.0	825.8 ± 0.8	528.8 ± 0.8	63.14	51	1.23	28	0,0	123
PSO J319.3102−29.6682	319.310489(7.2)	−29.668453(8.5)	57591.37	76.1 ± 3.5	149.2 ± 2.7	−168.1 ± 3.2	51.00	61	0.83	9	12,12	35
WISE J212100.87−623921.6	320.255042(6.5)	−62.656435(6.6)	57651.88	74.9 ± 3.2	382.7 ± 2.4	−256.9 ± 2.5	192.42	65	2.96	11	12,12	41
WISE J212321.92−261405.1	320.841215(3.9)	−26.234684(3.6)	57514.57	40.5 ± 3.3	58.0 ± 1.3	−23.1 ± 1.2	52.08	65	0.80	11	12,12	34
2MASS J21265916+7617440	321.761234(5.3)	76.299213(4.8)	57651.96	63.7 ± 3.0	768.0 ± 1.8	802.1 ± 1.7	43.94	67	0.65	12	12,12	78
2MASS J21373742+0808463	324.409034(5.7)	8.146582(5.7)	57609.35	70.1 ± 3.5	689.9 ± 2.1	82.3 ± 2.1	56.40	61	0.92	9	12,12	41
WISE J214155.85−511853.1	325.484604(4.0)	−51.315248(3.8)	57476.93	68.4 ± 3.7	705.8 ± 1.2	−259.5 ± 1.2	82.59	65	1.27	11	12,12	28
WISE J214706.78−102924.0	326.778468(2.3)	−10.490353(2.5)	58092.19	51.8 ± 2.4	96.5 ± 1.3	−143.2 ± 1.6	61.45	41	1.49	23	0,0	33
2MASS J21512543−2441000	327.857487(4.9)	−24.683544(3.8)	57540.73	37.6 ± 4.1	269.9 ± 1.6	−49.9 ± 1.2	49.40	63	0.78	10	12,12	26
2MASS J21522609+0937575	328.109861(3.6)	9.633273(3.2)	57420.86	51.3 ± 3.4	265.4 ± 1.0	143.8 ± 0.8	54.38	65	0.83	11	12,12	39
2MASS J21543318+5942187	328.636752(2.1)	59.703156(2.2)	57375.95	71.0 ± 2.3	−164.9 ± 0.7	−465.0 ± 0.7	398.99	93	4.29	23	13,13	225
WISEPC J215751.38+265931.4	329.464069(1.9)	26.991887(1.9)	57131.54	61.2 ± 2.0	67.9 ± 0.8	−98.3 ± 0.8	43.07	51	0.84	28	0,0	89
WISEA J215949.54−480855.2	329.957007(2.5)	−48.150396(2.4)	57159.72	73.9 ± 2.6	322.0 ± 1.2	−1238.4 ± 1.1	45.93	49	0.93	27	0,0	20
PSO J330.3214+32.3686	330.321532(9.7)	32.368686(10.4)	57626.61	37.7 ± 3.7	117.3 ± 3.6	64.2 ± 3.9	49.39	61	0.81	9	12,12	104
WISEA J220304.18+461923.4	330.770876(2.8)	46.322691(3.0)	57861.39	75.1 ± 3.4	1289.1 ± 3.3	−271.1 ± 3.2	35.40	21	1.68	13	0,0	331
WISE J220905.73+271143.9	332.275805(1.9)	27.193641(1.9)	57170.94	161.7 ± 2.0	1202.2 ± 0.8	−1365.4 ± 0.8	63.67	49	1.29	27	0,0	58
2MASS J22092183−2711329	332.340931(9.6)	−27.193113(11.5)	57603.74	39.0 ± 4.8	−6.6 ± 4.2	−150.5 ± 4.4	74.77	61	1.22	9	12,12	27
WISEPC J220922.10−273439.5	332.340951(3.6)	−27.578300(3.3)	57136.13	75.5 ± 3.6	−762.5 ± 1.7	−435.7 ± 1.5	15.46	49	0.31	27	0,0	12
WISEA J221140.53−475826.7	332.918547(3.0)	−47.974212(2.9)	57909.45	53.0 ± 3.3	−116.1 ± 2.3	−55.0 ± 1.7	18.45	21	0.87	13	0,0	22
WISE J221216.33−693121.6	333.072046(1.8)	−69.522691(1.8)	57562.45	80.6 ± 1.9	789.2 ± 0.7	−62.7 ± 0.7	120.85	65	1.85	35	0,0	41
2MASS J22153705+2110554	333.904694(7.8)	21.181255(8.2)	57624.43	57.6 ± 3.6	50.3 ± 2.9	−190.6 ± 3.1	82.01	61	1.34	9	12,12	53
WISE J222055.31−362817.4	335.231035(2.0)	−36.471677(2.0)	57239.17	95.5 ± 2.1	290.1 ± 0.9	−97.1 ± 0.9	64.60	47	1.37	26	0,0	26
WISEA J223204.53−573010.4	338.020044(3.2)	−57.503112(3.2)	57725.29	51.7 ± 3.4	412.6 ± 1.8	−106.4 ± 1.6	29.14	23	1.26	14	0,0	20
WISE J223617.59+510551.9	339.075302(6.4)	51.098286(6.6)	57592.92	100.3 ± 3.6	729.3 ± 2.3	323.5 ± 2.3	308.11	65	4.74	9	13,13	157
WISE J223720.39+722833.8	339.334582(2.1)	72.475960(2.0)	57215.38	67.3 ± 2.2	−83.4 ± 0.9	−100.2 ± 0.9	42.42	43	0.98	24	0,0	98
WISEP J223937.55+161716.2	339.907080(3.8)	16.288118(4.1)	57515.62	39.9 ± 3.5	393.4 ± 1.1	232.7 ± 1.2	198.88	65	3.06	11	12,12	19
2MASS J22490917+3205489	342.292227(5.6)	32.096106(6.0)	57581.68	48.9 ± 3.4	695.5 ± 2.0	−173.8 ± 2.1	54.76	65	0.84	9	13,13	58
2MASS J22551861−5713056	343.825651(6.7)	−57.219544(5.7)	57596.48	81.8 ± 4.7	−216.7 ± 2.6	−270.8 ± 2.1	120.89	61	1.98	9	12,12	24
WISEPC J225540.74−311841.8	343.920315(3.4)	−31.312002(4.7)	57532.21	72.8 ± 3.5	301.9 ± 1.5	−173.0 ± 2.2	34.19	27	1.26	16	0,0	12
CWISEP J225628.97+400227.3	344.121593(70.3)	40.040903(50.6)	57718.07	101.8 ± 11.2	698.4 ± 26.0	−175.1 ± 18.8	32.76	33	0.99	6	0,13	71
WISE J230133.32+021635.0	345.388753(2.4)	2.276313(3.0)	57386.72	54.1 ± 2.5	−65.6 ± 1.2	−90.9 ± 1.5	38.23	41	0.93	23	0,0	14
WISEA J230228.66−713441.7	345.618905(3.1)	−71.578197(2.9)	57884.60	64.8 ± 3.3	−98.0 ± 2.0	24.0 ± 1.7	10.62	21	0.50	13	0,0	38
WISEPA J231336.40−803700.3	348.404285(2.2)	−80.617344(2.0)	57209.26	92.6 ± 2.2	282.4 ± 0.9	−405.9 ± 0.9	40.21	45	0.89	25	0,0	34
2MASS J23174712−4838501	349.448026(7.8)	−48.646994(5.5)	57606.70	53.3 ± 5.9	248.3 ± 2.9	66.3 ± 2.1	27.70	61	0.45	9	12,12	9
WISEPC J231939.13−184404.3	349.913218(2.6)	−18.734416(2.7)	57184.02	80.9 ± 2.7	76.7 ± 1.1	134.4 ± 1.1	44.00	49	0.89	27	0,0	8
ULAS J232035.28+144829.8	350.148046(4.7)	14.808563(4.6)	57508.54	42.0 ± 4.7	390.5 ± 1.5	118.0 ± 1.5	61.29	69	0.88	11	13,13	21
ULAS J232123.79+135454.9	350.349360(2.0)	13.914050(2.1)	57095.25	82.8 ± 2.1	77.5 ± 0.9	−570.0 ± 1.0	59.98	51	1.17	28	0,0	19
2MASS J23254530+4251488	351.438521(5.8)	42.862125(5.8)	57596.28	81.3 ± 3.5	−40.9 ± 2.0	−294.7 ± 2.1	138.00	65	2.12	9	13,13	24
ULAS J232600.40+020139.2	351.502301(2.9)	2.027614(2.9)	57895.55	45.6 ± 3.1	304.2 ± 1.9	71.3 ± 1.9	30.95	21	1.47	13	0,0	22
WISEPC J232728.75−273056.5	351.870343(5.8)	−27.515689(4.5)	57508.42	46.8 ± 5.5	292.5 ± 1.7	56.8 ± 1.3	55.42	65	0.85	11	12,12	9
WISE J233226.49−432510.6	353.110885(2.0)	−43.420058(2.0)	57172.43	61.1 ± 2.1	250.2 ± 0.8	−262.5 ± 0.9	54.63	49	1.11	27	0,0	25
2MASSI J2339101+135230	354.794443(15.3)	13.870292(14.9)	57584.47	51.2 ± 4.2	371.9 ± 5.6	−958.6 ± 5.4	315.39	65	4.85	9	13,13	33
WISEPA J234351.20−741847.0	355.965700(2.1)	−74.312765(2.1)	57217.16	60.9 ± 2.2	394.5 ± 0.9	186.7 ± 0.9	47.86	45	1.06	25	0,0	34
WISEPC J234446.25+103415.8	356.194542(2.7)	10.570929(2.1)	57971.07	68.0 ± 2.6	946.5 ± 1.3	−30.4 ± 1.0	45.14	43	1.05	24	0,0	21
PM J23492+3458B	357.312946(4.6)	34.981810(8.6)	57596.74	48.0 ± 3.9	0.7 ± 0.4	−110.4 ± 3.1	127.48	65	1.96	9	13,13	40
WISEA J235402.79+024014.1	358.512498(3.1)	2.669898(3.0)	57860.05	130.6 ± 3.3	503.5 ± 2.2	−399.5 ± 2.3	27.64	21	1.31	13	0,0	16
WISE J235716.49+122741.8	359.318824(2.9)	12.460512(2.8)	57865.41	61.9 ± 3.0	28.7 ± 2.3	−508.3 ± 2.0	26.51	21	1.26	13	0,0	28

Notes. The R.A. and decl. values are listed on the ICRS coordinate system, and the number in parentheses after each value is the uncertainty in milliarcseconds. The last three columns represent the number of Spitzer epochs (#_Spitzer) and the number of unWISE epochs (#_WISE; W1 is the first value and W2 is the second) used in the fits, along with the number of five-parameter Gaia DR2 stars used for the astrometric re-registration (#_Gaia).

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2 3 4 5 6 7

Table 6. Parallax and Motion Fits for Objects with Low-quality Parallaxes

Object	R.A.	Decl.	t0	ϖabs	μR.A.	μDecl.	χ2	ν	${\chi }_{\nu }^{2}$	#Spitzer	#WISE	#Gaia
Name	at t0	at t0	MJD	(mas)	(mas yr−1)	(mas yr−1)
	(deg(mas))	(deg(mas))	(day)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
CWISE J002727.44−012101.7	6.864471(5.6)	−1.350482(5.2)	57678.42	54.2 ± 7.9	449.3 ± 2.6	57.1 ± 2.1	31.37	37	0.84	8	0,13	21
2MASSI J0103320+193536	15.885101(9.0)	19.593484(9.1)	57418.12	35.9 ± 5.7	304.3 ± 2.9	18.7 ± 2.8	45.05	65	0.69	9	13,13	18
WISE J013525.64+171503.4	23.856286(5.4)	17.250637(5.4)	57370.55	65.3 ± 10.0	−366.9 ± 2.3	−244.3 ± 1.4	31.58	35	0.90	7	0,13	20
WISEPC J013836.59−032221.2	24.652649(8.9)	−3.373114(5.9)	57367.54	38.5 ± 6.4	116.5 ± 2.6	−311.8 ± 1.7	53.67	67	0.80	10	13,13	10
WISEPA J030533.54+395434.4	46.390408(3.5)	39.909622(3.5)	57459.66	28.9 ± 4.3	277.0 ± 1.1	6.5 ± 0.9	30.98	37	0.83	9	0,12	71
SDSS J032553.17+042540.1	51.470985(4.5)	4.427632(4.4)	57544.73	28.3 ± 4.8	−178.5 ± 1.2	−66.2 ± 1.2	33.15	35	0.94	8	0,12	13
WISEA J083011.95+283716.0	127.549578(114.9)	28.617508(74.3)	57762.10	90.6 ± 13.7	−233.3 ± 48.6	−2040.8 ± 29.9	20.37	29	0.70	6	0,11	18
SDSS J104409.43+042937.6	161.039137(9.8)	4.494191(9.4)	57617.81	39.7 ± 6.7	−41.8 ± 3.6	94.5 ± 3.7	32.68	61	0.53	9	12,12	17
CWISEP J104756.81+545741.6	161.985934(105.4)	54.961405(88.7)	57721.13	75.2 ± 12.8	−447.9 ± 41.7	−65.5 ± 35.2	55.75	31	1.79	6	0,12	14
CWISE J113833.47+721207.8	174.639190(4.7)	72.202187(5.5)	57430.40	40.7 ± 7.1	−484.2 ± 1.3	183.2 ± 1.3	29.14	37	0.78	9	0,12	12
2MASS J11582077+0435014	179.588998(9.7)	4.579811(10.7)	57523.92	39.2 ± 6.2	566.2 ± 3.4	−932.4 ± 3.8	58.80	61	0.96	9	12,12	16
2MASS J14075361+1241099	211.971842(7.9)	12.686334(9.1)	57417.99	48.7 ± 6.4	−340.2 ± 2.5	42.0 ± 2.8	39.38	65	0.60	9	13,13	14
CWISEP J144606.62−231717.8	221.526873(130.2)	−23.288846(67.6)	57750.21	95.6 ± 13.9	−796.1 ± 48.8	−913.0 ± 24.3	72.96	33	2.21	7	0,12	77
PSO J224.3820+47.4057	224.382315(9.7)	47.405506(11.1)	57361.31	49.4 ± 7.5	133.3 ± 3.0	−75.1 ± 3.4	43.07	67	0.64	10	13,13	10
CWISE J153347.50+175306.7	233.448007(6.0)	17.885094(4.7)	57657.10	51.3 ± 7.0	126.4 ± 2.0	−182.7 ± 1.5	30.78	35	0.88	8	0,12	19
WISE J154459.27+584204.5	236.246712(10.8)	58.700516(5.3)	57319.10	61.2 ± 8.2	−74.9 ± 2.8	−529.8 ± 1.6	30.25	39	0.77	9	0,13	10
WISEA J172907.10−753017.0	262.279884(51.0)	−75.505145(29.5)	57906.88	35.7 ± 5.7	58.5 ± 21.5	−159.8 ± 12.4	22.57	39	0.57	10	0,12	176
2MASS J23312378−4718274	352.849652(9.0)	−47.307957(6.7)	57322.69	56.5 ± 7.5	76.8 ± 2.3	−65.8 ± 1.8	55.75	67	0.83	12	12,12	9

Note. See the comments under Table 5 for additional information.

A machine-readable version of the table is available.

Download table as:  DataTypeset image

Table 7. Astrometry for Objects with Poor-quality (or Unmeasurable) Parallaxes that Need Improvement

Object	R.A.	Decl.	t0	ϖabs	μR.A.	μDecl.	χ2	ν	${\chi }_{\nu }^{2}$	#Spitzer	#WISE	#Gaia
Name	at t0	at t0	MJD	(mas)	(mas yr−1)	(mas yr−1)
	(deg(mas))	(deg(mas))	(day)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
CWISE J004311.24−382225.0	10.796964(13.5)	−38.373645(7.0)	57624.29	38.1 ± 15.7	388.0 ± 3.5	59.1 ± 2.0	20.30	37	0.54	9	0,12	22
WISEU J004851.21+250814.9	12.213738(44.3)	25.137174(41.5)	57334.28	⋯	997.2 ± 13.2	−721.7 ± 11.9	28.65	24	1.19	2	0,12	22
2MASSW J0051107−154417	12.795312(9.0)	−15.738187(9.6)	57588.15	34.0 ± 6.6	65.2 ± 3.4	−29.2 ± 3.6	28.17	65	0.43	9	13,13	7
WISEA J013217.78−581825.9	23.075584(23.1)	−58.307239(26.6)	57906.21	27.2 ± 7.3	437.7 ± 9.2	−62.7 ± 11.1	25.90	37	0.70	9	0,12	25
CWISE J014837.51−104805.6	27.156400(9.6)	−10.801706(5.6)	57406.74	5.4 ± 49.3	−22.5 ± 10.6	−251.9 ± 4.3	41.69	33	1.26	6	0,13	9
CWISEP J021243.55+053147.2	33.181364(135.1)	5.529890(87.0)	57610.86	24.7 ± 16.3	−59.8 ± 45.0	57.0 ± 27.4	32.28	33	0.97	7	0,12	17
CWISEP J023842.60−133210.7	39.677455(168.2)	−13.536971(140.2)	57653.49	85.8 ± 21.4	−62.0 ± 58.2	−768.5 ± 44.6	59.55	29	2.05	8	0,9	15
WISEA J025756.40−265528.8	44.486076(74.8)	−26.924653(54.3)	57226.22	⋯	520.7 ± 18.7	98.9 ± 14.0	29.28	24	1.22	2	0,12	22
2MASS J03101401−2756452	47.557763(8.7)	−27.946173(7.3)	57459.65	29.5 ± 5.2	−122.3 ± 2.8	−51.7 ± 2.3	32.05	67	0.47	10	13,13	17
CWISEP J040235.55−265145.4	60.649091(67.7)	−26.863288(63.4)	57817.31	116.4 ± 20.5	767.0 ± 25.6	−532.9 ± 23.1	101.52	35	2.90	8	0,12	20
CWISE J042335.38−401929.5	65.897495(8.1)	−40.324872(7.1)	57664.64	−11.7 ± 6.9	−3.4 ± 2.4	−1.7 ± 2.3	33.98	35	0.97	8	0,12	15
CWISEP J042455.68+000221.4	66.232184(81.0)	0.039289(48.5)	57776.16	37.4 ± 11.7	183.1 ± 30.6	−100.2 ± 16.9	31.63	33	0.95	7	0,12	39
CWISE J044214.20−385515.7	70.559212(5.4)	−38.921020(8.0)	57602.53	−12.4 ± 4.9	2.6 ± 1.3	2.5 ± 2.3	32.06	33	0.97	7	0,12	22
CWISE J064223.54+042342.2	100.598022(8.6)	4.395140(8.6)	57395.12	⋯	144.7 ± 3.0	−134.4 ± 3.0	44.78	26	1.72	3	0,12	341
ULAS J074502.79+233240.3	116.260603(13.4)	23.543864(13.4)	57629.28	−12.3 ± 3.4	99.9 ± 5.3	−85.9 ± 5.3	4401	57	77.20	9	11,11	48
CWISEP J085938.95+534908.7	134.911948(102.7)	53.818871(70.8)	57759.66	46.9 ± 11.5	−215.6 ± 43.2	−327.8 ± 29.4	25.37	29	0.87	6	0,11	11
CWISE J091105.02+214645.1	137.770876(6.6)	21.779183(6.2)	57353.74	⋯	−104.4 ± 1.8	−658.8 ± 1.7	27.79	26	1.06	3	0,12	15
CWISEP J093852.89+063440.6	144.720858(108.5)	6.577415(68.1)	57730.01	67.9 ± 13.8	435.3 ± 43.3	−662.7 ± 26.2	36.68	31	1.18	6	0,12	9
CWISEP J094005.50+523359.2	145.022593(102.4)	52.566241(84.8)	57711.66	66.4 ± 12.2	−342.0 ± 40.4	−352.6 ± 32.5	19.44	31	0.62	6	0,12	18
CWISEP J100854.84+203136.6	152.228362(104.6)	20.526656(81.2)	57731.81	37.1 ± 15.1	−118.2 ± 41.2	−180.0 ± 30.9	32.86	31	1.06	6	0,12	12
CWISEP J102201.27+145520.2	155.504822(125.5)	14.922147(101.0)	57789.82	76.0 ± 16.4	−567.0 ± 53.0	−109.8 ± 40.1	21.50	33	0.65	7	0,12	14
WISEA J104051.77+450329.3	160.215919(49.2)	45.058069(46.0)	57897.03	18.8 ± 9.8	50.9 ± 23.8	−76.3 ± 21.8	19.48	33	0.59	9	0,10	14
ULAS J104355.37+104803.4	160.980885(4.1)	10.800692(3.0)	57937.76	22.0 ± 4.3	91.3 ± 2.6	−108.3 ± 1.7	24.95	21	1.18	13	0,0	12
CFBDS J111807−064016	169.528249(8.2)	−6.669034(11.6)	57519.99	1.4 ± 5.2	−197.7 ± 2.8	−38.5 ± 4.1	47.00	61	0.77	9	12,12	23
CWISE J113019.19−115811.3	172.579934(6.8)	−11.969837(8.2)	57277.57	⋯	−559.0 ± 1.8	411.0 ± 2.2	14.65	26	0.56	3	0,12	17
CWISE J114120.42−211024.5	175.334822(15.0)	−21.173499(16.9)	57588.67	31.5 ± 52.5	−1001.0 ± 19.0	−113.8 ± 10.8	25.56	31	0.82	6	0,12	36
CWISE J120502.74−180215.5	181.261441(11.8)	−18.037635(7.0)	57287.56	⋯	−154.2 ± 3.0	56.8 ± 1.9	16.94	26	0.65	3	0,12	19
WISEA J125721.01+715349.3	194.333106(41.0)	71.896932(36.3)	57507.56	⋯	−928.1 ± 14.4	85.7 ± 12.5	28.08	26	1.08	3	0,12	15
ULAS J131943.77+120900.2	199.931750(7.7)	12.151928(10.1)	57406.20	7.8 ± 6.5	−129.1 ± 2.4	14.7 ± 3.2	54.98	65	0.84	9	13,13	14
CWISEP J135937.65−435226.9	209.906619(129.4)	−43.874321(74.1)	57747.85	45.3 ± 13.6	−369.5 ± 48.4	−230.9 ± 26.6	31.48	33	0.95	7	0,12	251
CWISEP J145837.91+173450.1	224.657708(56.5)	17.580592(46.5)	57705.35	1.3 ± 7.2	−476.5 ± 20.1	162.9 ± 16.6	59.67	35	1.70	8	0,12	27
WISEA J153429.75−104303.3	233.622084(174.9)	−10.721453(86.2)	57498.93	47.8 ± 14.3	−1324.4 ± 51.7	−2435.9 ± 24.8	37.40	17	2.20	5	0,6	56
WISEA J161940.51+134752.0	244.918914(31.2)	13.797778(24.7)	57881.70	−9.1 ± 4.3	28.8 ± 12.9	4.4 ± 10.5	55.61	39	1.42	10	0,12	34
WISE J201404.13+042408.5	303.516175(6.0)	4.402821(6.0)	57326.30	⋯	−611.3 ± 1.5	313.4 ± 1.5	26.43	26	1.01	3	0,12	122
WISEA J201833.67−141720.3	304.640375(55.1)	−14.288722(39.8)	57767.31	47.3 ± 11.0	75.9 ± 23.9	140.1 ± 15.8	41.70	33	1.26	7	0,12	119
CWISEP J203821.53−064930.9	309.589591(120.7)	−6.825620(53.2)	57720.91	57.3 ± 18.2	−221.8 ± 48.9	−266.2 ± 20.7	29.88	31	0.96	6	0,12	88
CWISE J205701.64−170407.3	314.257055(18.1)	−17.068676(8.3)	57699.57	49.5 ± 72.3	342.1 ± 29.8	41.1 ± 9.5	50.43	33	1.52	7	0,12	44
CWISEP J210007.87−293139.8	315.033221(118.9)	−29.527825(60.1)	57719.73	43.8 ± 18.0	414.8 ± 48.3	−96.1 ± 23.0	49.78	31	1.60	6	0,12	49
WISEA J211456.86−180519.0	318.736060(68.9)	−18.089522(44.4)	57780.13	59.0 ± 10.7	−470.9 ± 29.3	−454.0 ± 17.7	48.29	33	1.46	7	0,12	36
CWISEP J213249.05+690113.7	323.204777(41.6)	69.020622(41.3)	57226.61	⋯	223.4 ± 10.9	159.4 ± 10.8	41.15	26	1.58	2	0,13	75
CWISEP J213930.45+042721.6	324.877010(62.6)	4.455625(44.2)	57881.44	42.5 ± 11.4	51.5 ± 28.6	−514.8 ± 19.9	50.13	29	1.72	6	0,11	51
CWISEP J223022.60+254907.5	337.593652(106.1)	25.818347(56.5)	57753.28	71.3 ± 16.0	−570.3 ± 42.0	−464.4 ± 22.5	53.93	29	1.86	6	0,11	73
WISEA J224319.56−145857.3	340.831935(42.6)	−14.983549(55.1)	57537.45	⋯	329.9 ± 14.4	−532.1 ± 16.8	10.81	26	0.41	3	0,12	27
WISEA J225404.16−265257.5	343.518402(47.1)	−26.882706(59.4)	57534.90	⋯	614.5 ± 16.6	10.0 ± 19.7	29.89	26	1.15	3	0,12	21
2MASS J23440624−0733282	356.026048(10.5)	−7.558234(8.8)	57632.52	29.2 ± 9.5	10.5 ± 3.7	−85.4 ± 3.5	63.72	61	1.04	9	12,12	8
CWISEP J235547.99+380438.9	358.950395(49.9)	38.077557(47.0)	57281.54	⋯	722.8 ± 13.6	14.2 ± 12.7	12.28	22	0.55	2	0,11	65
CWISEP J235644.78−481456.3	359.187270(52.8)	−48.249206(57.3)	57537.20	⋯	886.4 ± 16.8	−35.0 ± 18.5	46.08	26	1.77	3	0,12	14

Note. See the comments under Table 5 for additional information.

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2

In previous papers—Kirkpatrick et al. (2019a) and Martin et al. (2018)—we compared our parallax results to those of other surveys and found excellent agreement with all of those except the Spitzer/IRAC ch1 results of Dupuy & Kraus (2013). Below, we perform additional checks to assure that our newly measured Spitzer astrometry is robust.

4.1. Comparison to the Results of Kirkpatrick et al. (2019a)

All 142 Spitzer targets from Kirkpatrick et al. (2019a) have new measurements in this paper. A comparison between the measured astrometry for these objects is shown in Figure 4. No bias in the measured parallaxes is seen between the two sets of results, as shown in the top panel of the figure.

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Biases are evident in the measured proper motions, however, in both R.A. (middle panel) and decl. (bottom panel). These differences are small; the offset (dotted red line) in the lower panel of Figure 4, for example, corresponds to a motion difference in decl. of −4.6 mas yr⁻¹. Other than the longer time baseline, the only difference between our new results and those of Kirkpatrick et al. (2019a) is the methodology for calculating absolute parallaxes. In Kirkpatrick et al. (2019a), a correction from relative to absolute was applied after the fact, whereas in this paper, the Gaia DR2 parallax and motion values of the re-registration stars were used to measure the absolute astrometry of target objects directly. In Kirkpatrick et al. (2019a), the post facto corrections were applied only to the parallaxes. Therefore, the differences in motion values between the two papers are just a reflection of the fact that the Kirkpatrick et al. (2019a) motions were deliberately reported as relative whereas the ones in this paper are absolute.

We can illustrate this as follows. By not correcting the proper motions to absolute, the solar motion is imprinted on the values reported in Kirkpatrick et al. (2019a), and this is reflected in the way the differences between the Kirkpatrick et al. (2019a) relative motions and this paper's absolute motions behave around the celestial sphere. If we were to invent a coordinate system having the solar apex and antapex as its poles, then the difference between relative and absolute motions would be smallest toward the poles and largest at locations on the sphere 90° away from the poles—i.e., along this coordinate system's equator, where the solar motion is reflected in an apparent "streaming" motion of the background stars. The solar apex is located toward (R.A., decl.) = (18^h28^m, +30°), meaning that this invented coordinate system is within 30° of orthogonal to the equatorial system.

This means that the differences between relative and absolute motions will be near zero at the apex (R.A. ≈ 277°) and antapex (R.A. ≈ 97°). Likewise, the relative proper motions will be maximally too high relative to the absolute ones near R.A. = 7° (where the true motion and reflex solar motion add constructively) and maximally too low near R.A. = 187° (where they add destructively). This is the same qualitative behavior exhibited in the middle panel of Figure 4. The uncorrected solar reflex motion itself will be a more constant offset along decl., and the difference between relative and absolute motions in decl. will be negative because the solar apex lies north of the celestial equator. The bottom panel in Figure 4 qualitatively shows this behavior, too.

4.2. Comparison to Gaia Results

At the time objects were chosen for Spitzer program 14000, Gaia DR2 had not yet been released and the magnitude limit at which Gaia astrometry could be reliably measured was still unclear. Making a conservative guess resulted in an overlap of 25 objects that, fortunately, now enables a direct comparison to Gaia (Figure 5). As all three panels of the figure illustrate, the differences between our measured absolute astrometry and that of Gaia are only marginally significant, those differences falling at the 0.8σ (where σ refers to the combined value; Δϖ_abs = 2.8 mas), 0.9σ (Δμ_α = 2.7 mas yr⁻¹), and 0.6σ (Δμ_δ = − 1.9 mas yr⁻¹) levels for the top, middle, and bottom panels, respectively. These values of the significance would shrink even further if, for example, it were found that the Gaia astrometric uncertainties for objects this faint were underestimated. For reference, these 25 targets have Gaia G-band values between 19.1 and 20.9 mag and quoted parallax uncertainties between 0.4 and 2.1 mas, the latter of which are typically only 3–4× smaller than those we measure with Spitzer.

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The objects whose Gaia parallaxes we are using for comparison in Figure 5 are among the reddest and faintest objects that Gaia can detect. We can test whether the offsets seen between Gaia and our Spitzer results are pointing to an issue with the Gaia parallaxes themselves by comparing other Gaia parallaxes to independent literature values. Figure 6 illustrates this using parallaxes from Dahn et al. (2002), Dieterich et al. (2014), Winters et al. (2015), and Bartlett et al. (2017). Most of these parallaxes were measured by ground-based CCD programs, with the exception of those from Winters et al. (2015), who presented weighted parallax results using ground-based astrometry measured from photographic plates, CCDs, and infrared arrays as well as astrometry from Hipparcos. ⁴⁷ In our figure, care was taken not to double-count results, so any data from Winters et al. (2015) that were included in the other references were removed.

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These astrometric offsets with respect to Gaia are plotted as a function of apparent G_RP magnitude in the top panel of Figure 6. As G_BP is known to be systematically underestimated for the reddest objects in Gaia (Smart et al. 2019)—which in turn affects the G_BP − G_RP color—we instead use absolute Gaia G-band magnitude in the bottom panel as a proxy for color. Colors like B − R directly correlate with M_G (or M_V ) magnitudes across M and L dwarf spectral types (Pecaut & Mamajek 2013; Dieterich et al. 2014). The two panels also show a small bias between these published parallax values and those of Gaia, and the bias has the same sign as that seen in the Spitzer-to-Gaia comparison in Figure 5. Moreover, the two panels in Figure 6 suggest that there is a tendency for this bias to increase with fainter apparent magnitude and/or redder color.

The cause for this bias, and whether it highlights an unknown issue with the faintest Gaia astrometry, is unknown. Smart et al. (2019) compared a larger list of previously published parallaxes to those of Gaia DR2 and also found a difference. They concluded that the discrepancy could be reconciled if either the uncertainties in the (heterogeneous) ground-based parallaxes or the Gaia uncertainties themselves were increased. Given that our new set of homogeneous Spitzer astrometry shows a discrepancy similar to that in previous ground-based measurements suggests that the Gaia uncertainties are underestimated.

4.3. Comparison of Spitzer+unWISE to Pure Spitzer Results

Above, we hypothesized that the small offset seen in the parallax differences with respect to Gaia would shrink if the Gaia uncertainties were found to be underestimated. Another possibility, which we will dispel here, is that our own measurement technique has introduced a small bias.

The Spitzer parallax measurements used in Figure 5 were supplemented with data from unWISE in order to extend the astrometric time baseline. These objects, although they are among the faintest that Gaia can measure, are the brightest objects in the Spitzer program. For this reason, their high-S/N Spitzer data alone are sufficient to obtain quality parallaxes, so we have performed a special "Spitzer only" reduction to ascertain whether or not the inclusion of the unWISE data has led to a bias. A comparison of the reductions with and without the unWISE data is shown in Figure 7. As expected, no significant difference is present, a bias having been detected only at the 0.2σ level.

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4.4. Comparison to Best et al. (2020)

As this paper was being written, the parallax compilation of Best et al. (2020) became available, allowing us to compare our Spitzer results to another independent set of astrometry. This comparison is shown in Figure 8. The offsets seen are at the 0.8σ (Δϖ_abs = 4.3 mas), 0.5σ (Δμ_α = 1.6 mas yr⁻¹), and 0.4σ (Δμ_δ = 1.1 mas yr⁻¹) levels for the top, middle, and bottom panels, respectively. Whereas our Spitzer parallaxes are slightly larger (by 0.8σ) than those of Gaia, Best et al. (2020) find that their UKIRT parallaxes are slightly smaller (by 1.6σ) than those of Gaia. Curiously, Best et al. (2020) also conclude that either their parallax uncertainties or those of Gaia are underestimated, at least the third such case in the recent literature to suggest that Gaia astrometric uncertainties may be too small for L and T dwarfs.

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Distance is only one of the important quantities needed when characterizing sources for the mass function analysis. Photometry across the optical through mid-infrared bands is needed to better assess the temperature of each source, which is needed when building a mass function that is tied to T_eff as the "observable" parameter. Spectroscopy is another powerful tool, and the most reliable one when assessing the small fraction of sources that have unusual features. These oddities complicate our ability to assign objects to the correct T_eff bins because their colors and spectral types follow relations that are different from the bulk of normal, single objects. For example, one oddity identifiable through spectroscopy is low metallicity, which may indicate an older subdwarf (e.g., Zhang et al. 2017). Another is low gravity, which may indicate that the object is unusually young because it has yet to contract to its final, equilibrium radius (e.g., Faherty et al. 2016). Yet another is unresolved binarity, particularly at the L/T transition where spectroscopic blending of features makes composite spectra easier to distinguish (e.g., Burgasser et al. 2010a). In the subsections that follow, we describe the data acquisition and reduction implemented for our photometric and spectroscopic follow-up campaigns. A compilation of our photometric, spectroscopic, and astrometric data is listed in Table A1, which is described in the Appendix.

5.1. Photometry