Preliminary Trigonometric Parallaxes of 184 Late-T and Y Dwarfs and an Analysis of the Field Substellar Mass Function into the "Planetary" Mass Regime

Understanding the creation mechanisms for brown dwarfs has long been a stumbling block of star formation theory. Simplified arguments predicting the minimum Jeans mass fragment forming from a molecular cloud suggest a value of ∼7 M_Jup (Low & Lynden-Bell 1976), although more complicated considerations such as the role of magnetic fields and rotation are thought to drive this value higher. Lower formation masses are possible via secondary mechanisms. For example, sites replete with high-mass stars can create lower-mass brown dwarfs through the ablation, via O star winds, of protostellar embryos that would otherwise have formed bona fide stars (e.g., Whitworth & Zinnecker 2004). Also, protostars in rich clusters with many high-mass members may, via dynamical interactions, be stripped from their repository of accreting material, thus artificially stunting their growth (e.g., Reipurth & Clarke 2001). Star-forming regions lacking higher mass stars will form objects via neither of these processes but still create low-mass objects down to at least ∼3 M_Jup, as discoveries of low-mass brown dwarfs in nearby, sparse moving groups suggest (Liu et al. 2013; Gagné et al. 2015a; Faherty et al. 2016; Best et al. 2017). Providing direct measurements on the frequency of low-mass formation and its low-mass limit are thus key parameters needed to inform modified predictions.

Field brown dwarfs—the well-mixed, low-mass byproducts of star formation—can be used to derive the field substellar mass function. This function averages over any site-to-site differences and allows us to study the global efficiency of substellar formation integrated over the history of the Galactic disk. Does this field function suggest that low-mass star formation can be characterized by a simple form (Chabrier 2001) or only by a more complicated one (Kroupa et al. 2013)? What is the low-mass cutoff (Andersen et al. 2008)? Have these field objects, scattered from their stellar nurseries, been joined by other low-mass objects that escaped their birthplaces within a proto-planetary disk (Sumi et al. 2011; Mróz et al. 2017)? Is the formation efficiency of low-mass objects higher today than it was in the distant past (Bate 2005)?

Our ability to measure the low-mass cutoff is critically dependent on measuring the space density of objects with temperatures below 500 K (Figure 12 of Burgasser 2004), which corresponds to late-T and Y dwarf spectral types believed to span a mass range of ∼3–20 M_Jup (Cushing et al. 2011; Luhman 2014a). The functional form of the mass function is also most easily discerned at these same temperatures (Figure 5 of Burgasser 2004). Both of these measurements can be accomplished by establishing a volume-limited sample of nearby brown dwarfs.

The recent spate of cold, field brown dwarf discoveries by the NASA Wide-field Infrared Survey Explorer (WISE) now makes these measurements possible. The all-sky nature of WISE enables the creation of a sample of the closest, brightest brown dwarfs that exist, and these are the easiest brown dwarfs to characterize in detail. In this paper, we aim to use these discoveries to deduce the functional form and low-mass cutoff of the substellar mass function.

In Section 2 we discuss the empirical sample needed to address our goals, and in Section 3 we build a preliminary version of the sample. In subsequent sections we describe astrometric measurements from Spitzer (Sections 4 and 5), the U.S. Naval Observatory (Section 6), and other telescopes (Section 7) needed to further characterize the sample. In Section 8 we examine the measured trends in spectral type, color, and absolute magnitude to identify hidden binaries. In Section 9 we build predictions of the space density as a function of T_eff using two different suites of evolutionary models and several different forms of the underlying mass function; these are compared to our empirical results to deduce the most likely functional form and to place constraints on the mass of the low-mass cutoff. We discuss these results in context with theoretical predictions in Section 10. In Section 11 we summarize our conclusions and discuss future plans for making the sample even more robust.

To reach the above goals, we define an empirical sample and a list of follow-up observations necessary to adequately characterize it. We consider the following four points:

• (1)  
  Accurate distances to these objects must be measured so that space densities can be calculated. These objects will have large parallactic signatures, but they are extremely faint in the optical and near-infrared wavelengths where ground-based astrometric monitoring takes place. For the faintest objects (J > 21 mag), the Earth's atmosphere and thermal environment preclude parallax measurements entirely. Gaia is unable to measure parallaxes for cold brown dwarfs because it observes only shortward of 1.05 μm, a wavelength regime in which these sources emit very little flux. Observations are more easily done at wavelengths near 5 μm where these objects are brightest. The InfraRed Array Camera (IRAC; Fazio et al. 2004) on board the Spitzer Space Telescope is therefore a natural choice, and accurate parallaxes can be measured using only a modest amount of Spitzer observing time.
• (2)  
  Objects must be characterized to the extent that unresolved binarity can be deduced. Unresolved binaries can lead to overestimates of the space density when spectrophotometric distance estimates are used, or underestimates if objects truly in the volume are not recognized as double. This is an inherent problem with any magnitude-limited sample. Although high-resolution imaging has been acquired for some of the nearest brown dwarfs (Gelino et al. 2011; Liu et al. 2012; Opitz et al. 2016), very tight binaries or those with unfavorable orientations as seen from the Earth will go undetected. Measuring the absolute magnitude directly for each object is an excellent means of detecting unresolved doubles with small magnitude differences.
• (3)  
  The number of sources as a function of T_eff (or other observable quantity) must be known with sufficient resolution in mass to determine the low-mass cutoff to a few M_Jup. As Table 9 of Kirkpatrick et al. (2012) shows, a volume-limited sample with a distance limit of 20 pc provides between one dozen and four dozen objects in each half-subclass spectral type bin from T6 through early Y, although the magnitude limits of WISE restrict the T9 and later bins to somewhat smaller distances. This binning provides sufficient resolution to determine the low-mass cut-off to the precision required. Including brown dwarfs as early as T6 allows us to properly measure the shape of the density distribution below ∼1100 K so that we can also place constraints on the overall functional form of the mass function, as Figure 14 of Kirkpatrick et al. (2012) illustrates.
• (4)  
  A sufficient sample size must be considered to robustly measure biases due to metallicity effects. At late-T and Y types, a higher percentage of old objects may be expected relative to field stars because the only young objects possible at these types are those that are exceedingly low in mass, although the percentage is critically dependent upon the low-mass cutoff of formation. (See, e.g., Figure 8 of Burgasser 2004). Several late-T subdwarfs, believed to be older objects with lower-than-average metal content, are already recognized in the nearby sample. These can serve as metallicity calibrators with which to calibrate the absolute magnitude versus spectral type relations as a function of metallicity and to provide the first evidence on the efficiency of low-mass formation at lower metallicities. These objects are relatively rare, and to measure the spread in age for each mass bin, sufficient statistics (i.e., a large sample size over a sizable volume) is needed.

In conclusion, a volume-limited sample out to 20 pc that covers spectral types of T6 and later would fulfill our research goals. In the next section, we describe how we tabulated sources belonging to the sample itself.

Using the compilation of known T and Y dwarfs at Dwarf Archives¹⁵ along with a listing of more recent additions that one of us (CRG) has compiled since the last Dwarf Archives update, we cataloged all published objects of type T6 and later (>350 total), regardless of distance. We then used spectral types and H- and/or W2-band magnitudes to compute spectrophotometric distance estimates (Kirkpatrick et al. 2012) for those not already having measured parallaxes. Objects were retained in our list if their spectrophotometric distance estimates placed them within 22 pc (to account for distance uncertainties) or if they had published parallaxes good to 10% accuracy that placed them, within the measurement uncertainties, inside the 20 pc volume. This list of 235 objects is presented in Table 1. This table gives the discovery designation and reference in columns 1 and 2, the AllWISE designation in column 3, the measured infrared spectral type and its reference in columns 4 and 5, and the measured parallax and its reference in columns 6 and 7. For previously published parallax values in column 6, measurements of absolute parallax are commented with "(abs)" and those of relative parallax with "(rel)." In some cases, it is not clear whether the published value is an absolute or relative value, so those are left uncommented.

Table 1.  Dwarfs with Type ≥T6 and Distance or Distance Estimate ≤20 pc

Discovery	Disc.	WISEA	Infrared	Type	Parallax	Parallax
Designation	Ref.	Designation	Sp. Type	Ref.	(mas)	Ref.
(1)	(2)	(3)	(4)	(5)	(6)	(7)
WISE J000517.48+373720.5	8	J000517.49+373720.4	T9	8	Table 4	1
WISE J001505.87−461517.6	2	J001505.88−461517.8	T8	2	Table 4	1
WISE J003231.09−494651.4	2	J003231.06−494651.9	T8.5	2	Table 4	1
ULAS J003402.77−005206.7	27	J003402.79−005208.2	T8.5	10	68.7 ± 1.4 (abs)	67
2MASS J00345157+0523050	3	J003452.03+052306.9	T6.5	61	Table 4	1
	⋯	⋯	⋯	⋯	105.4 ± 7.5 (abs)	66
WISE J003829.05+275852.1	8	J003829.06+275852.0	T9	8	Table 4	1
Gl 27B (0039+2115)a	28	source not extracted	T8	61	89.7891 ± 0.0581 (abs)	72
WISE J004024.88+090054.8	8	J004024.88+090054.4	T7	8	Table 6	1
WISE J004945.61+215120.0	8	J004945.65+215119.6	T8.5	8	Table 4	1
2MASS J00501994−3322402	29	J005021.05−332228.8	T7	61	94.6 ± 2.4 (abs)	67
CFBDS J005910.90−011401.3	30	J005911.10−011401.1	T8.5	10	103.2 ± 2.1 (abs)	67
WISEPA J012333.21+414203.9	4	J012333.25+414203.9	T7	4	Table 4	1
CFBDS J013302.27+023128.4	5	J013302.45+023128.8	T8.5	5	Table 4	1
WISE J014656.66+423410.0AB	2	J014656.66+423409.9	Y0	2	Table 4	1
WISEPC J014807.25−720258.7	4	J014807.34−720258.7	T9.5	4	91.1 ± 3.4 (rel)	21
ULAS J015024.37+135924.0	31	J015024.40+135923.6	T7.5	31	Table 6	1
WISEP J022105.94+384202.9	4	J022105.99+384203.0	T6.5	4	Table 4	1
WISEPC J022322.39−293258.1	4	J022322.38−293257.3	T7.5	4	Table 6	1
WISEPA J022623.98−021142.8AB	4	J022623.99−021142.7	T7	4	Table 4	1
WISE J023318.05+303030.5	8	J023318.06+303030.4	T6	8	Table 4	1
WISE J024124.73−365328.0	2	J024124.74−365328.0	T7	2	Table 4	1
2MASSI J0243137−245329	32	J024313.47−245332.1	T6	61	93.62 ± 3.63 (abs)	68
WISE J024512.62−345047.8	8	J024512.62−345047.8	T8	8	59	1
WISE J024714.52+372523.5	8	J024714.54+372523.4	T8	8	Table 4	1
WISEPA J025409.45+022359.1	4, 33	J025409.55+022358.5	T8	4	Table 5	1
WISEA J030237.53−581740.3	6	J030237.53−581740.3	Y0:	6	Table 4	1
WISE J030449.03−270508.3	7	J030449.04−270508.1	Y0pec	7	Table 4	1
WISEA J030919.70−501614.2	6	J030919.70−501614.2	[T7]b	6	Table 4	1
WISEPA J031325.96+780744.2	4	J031326.00+780744.3	T8.5	4	Table 4	1
WISE J031624.35+430709.1	8	J031624.40+430708.7	T8	8	Table 4	1
WISEA J032309.12−590751.0	1	J032309.12−590751.0	[T6]c	1	Table 4	1
WISEPC J032337.53−602554.9	4	J032337.57−602554.5	T8.5	4	Table 4	1
WISE J032504.33−504400.3	9	J032504.52−504403.0	T8	9	Table 4	1
WISE J032517.69−385454.1	8	J032517.68−385453.8	T9	8	Table 4	1
WISE J032547.72+083118.2	8	J032547.73+083118.2	T7	8	Table 4	1
WISE J033515.01+431045.1	8	J033515.07+431044.7	T9	8	Table 4	1
WISE J033605.05−014350.4	8	J033605.04−014351.0	Y0	22	Table 4	1
2MASS J03480772−6022270	34	J034807.33−602235.2	T7	61	Table 6	1
WISE J035000.32−565830.2	2	J035000.31−565830.5	Y1	2	Table 4	1
WISE J035934.06−540154.6	2	J035934.07−540154.8	Y0	2	Table 4	1
WISE J040443.48−642029.9	9	J040443.50−642030.0	T9	9	Table 4	1
WISEPA J041022.71+150248.5	10	J041022.75+150247.9	Y0	10	Table 4	1
WISE J041358.14−475039.3	8	J041358.14−475039.4	T9	8	Table 4	1
2MASSI J0415195−093506	32	J041521.26−093500.4	T8	61	175.2 ± 1.7 (abs)	67
WISE J043052.92+463331.6	8	J043052.96+463331.7	T8	8	Table 4	1
WISEPA J045853.89+643452.9AB	11	J045853.91+643452.6	T8.5	10	Table 4	1
WISEPA J050003.05−122343.2	4	J050003.03−122343.1	T8	4	Table 4	1
WISE J051208.66−300404.4	8	J051208.67−300404.2	T8.5	8	Table 4	1
WISEPA J051317.28+060814.7	4	J051317.27+060814.5	T6.5	4	Table 5	1
WISE J052126.29+102528.4	35	J052126.30+102528.3	T7.5	35	171	1
UGPS J052127.27+364048.6	46	J052127.42+364043.6	T8.5	46	Table 6	1
WISEPA J052844.51−330823.9	4	J052844.52−330824.0	T7pec	4	Table 6	1
WISE J053516.80−750024.9	2	J053516.87−750024.6	≥Y1:	2	Table 4	1
WISE J054047.00+483232.4	8	J054047.01+483232.2	T8.5	8	Table 4	1
WISEPA J054231.26−162829.1	4	J054231.27−162829.1	T6.5	4	Table 6	1
Gl 229B (0610−2152)	36	source not extracted	T7pec	61	173.6955 ± 0.0457 (abs)	72
WISEPA J061213.93−303612.7AB	4	J061213.88−303612.1	T6	4	Table 6	1
WISEPA J061407.49+391236.4	4	J061407.50+391235.7	T6	4	Table 5	1
WISE J061437.73+095135.0	8	J061437.75+095135.2	T7	8	Table 4	1
WISEA J061557.21+152626.1	22	J061557.21+152626.1	T8.5	22	64	1
WISEPA J062309.94−045624.6	4	J062309.92−045624.5	T8	4	Table 6	1
WISEPA J062542.21+564625.5	4	J062542.23+564625.4	T6	4	Table 5	1
WISEPA J062720.07−111428.8	4	J062720.07−111427.9	T6	4	Table 6	1
WISE J062842.71−805725.0	6	J062842.74−805725.0	[T9]d	6	50	1
WISEA J064528.39−030247.9	6	J064528.39–030247.9	T6	6	Table 4	1
WISE J064723.23−623235.5	12	J064723.24−623235.4	Y1	12	Table 4	1
WISEA J071301.86−585445.2	6	J071301.86−585445.2	T9	6	Table 4	1
WISE J071322.55−291751.9	2	J071322.55−291752.0	Y0	2	Table 4	1
UGPS J072227.51−054031.2	37	J072227.27−054029.8	T9	10	242.8 ± 2.4	40
WISE J072312.44+340313.5	8	J072312.47+340313.5	T9:	8	Table 4	1
2MASSI J0727182+171001	32	J072719.15+170951.3	T7	61	112.5 ± 0.9 (abs)	67
2MASS J07290002−3954043	24	J072859.49−395345.3	T8pec	24	126.3 ± 8.3 (abs)	66
WISE J073444.02−715744.0	2	J073444.03−715743.8	Y0	2	Table 4	1
WISEPA J074457.15+562821.8	4	J074457.24+562820.9	T8	4	Table 4	1
ULAS J074502.79+233240.3	19	source not extracted	T8.5	19	63	42
WISEPA J075003.84+272544.8	4	J075003.75+272545.0	T8.5	4	Table 6	1
WISEPA J075108.79−763449.6	4	J075108.80−763449.3	T9	4	Table 6	1
WISEPC J075946.98−490454.0	4	J075946.98−490454.0	T8	4	Table 4	1
WD 0806−661B (0807−6618)	65	source not detected	[Y1]e	1	52.17 ± 1.67 (abs)	69
WISE J081117.81−805141.3	8	J081117.95−805141.4	T9.5:	8	98.5 ± 7.7 (rel)	21
WISE J081220.04+402106.2	8	J081220.05+402106.2	T8	8	Table 4	1
DENIS J081730.0−615520	38	J081729.76−615503.8	T6	38	203 ± 13	38
WISE J082507.35+280548.5	9	J082507.37+280548.2	Y0.5	9	Table 4	1
WISE J083337.83+005214.2	13	J083337.81+005213.8	(sd)T9	13	Table 4	1
WISEPC J083641.12−185947.2	4	J083641.13−185947.1	T8pec	4	Table 4	1
WISE J085510.83−071442.5	14, 15, 16	J085510.74−071442.5	[≥Y4]f	1	Table 4	1
WISEPA J085716.25+560407.6	4	J085716.21+560407.5	T8	4	Table 4	1
ULAS J085910.69+101017.1	64	J085910.62+101014.8	T7	64	Table 6	1
ULAS J090116.23−030635.0	39	J090116.20−030636.0	T7.5	39	62.6 ± 2.6 (abs)	70
WISEPA J090649.36+473538.6	4	J090649.33+473538.2	T8	4	Table 4	1
WISE J091408.96−345941.5	17	J091408.99−345941.4	T8	6	Table 4	1
WISEPC J092906.77+040957.9	4	J092906.76+040957.6	T6.5	4	Table 6	1
2MASSI J0937347+293142	32	J093735.63+293127.2	T6pec	61	162.84 ± 3.88 (abs)	68
2MASS J09393548−2448279	29	J093935.93−244838.9	T8	61	187.3 ± 4.6 (abs)	71
WISEA J094020.09−220820.5	6	J094020.09−220820.5	T8	6	Table 4	1
WISE J094305.98+360723.5	18	J094306.00+360723.3	T9.5	18	Table 4	1
ULAS J095047.28+011734.3g	40, 41	J095047.31+011733.1	T8	19, 8	Table 6	1
	⋯	⋯	⋯	⋯	53.40 ± 3.51	19
WISEPC J095259.29+195507.3	4	J095259.29+195508.1	T6	4	Table 4	1
WISEPC J101808.05−244557.7	4	J101808.03−244558.1	T8	4	Table 4	1
WISEPA J101905.63+652954.2	4	J101905.61+652954.0	T6	4	Table 5	1
WISE J102557.72+030755.7	8	J102557.67+030755.8	T8.5	8	Table 4	1
CFBDS J102841.01+565401.9	5	source not extracted	T8	5	Table 4	1
ULAS J102940.52+093514.6	19	J102940.51+093514.1	T8	20	Table 6	1
WISE J103907.73−160002.9	8	J103907.74−160002.9	T7.5	8	Table 4	1
WISEPC J104245.23−384238.3	4	J104245.24−384238.1	T8.5	4	64.8 ± 3.4 (rel)	21
ULAS J104355.37+104803.4	19	J104355.40+104802.4	T8	19	Table 4	1
2MASSI J1047538+212423	43	J104752.35+212417.2	T6.5	61	94.73 ± 3.81 (abs)	68
WISE J105047.90+505606.2	8	J105047.89+505605.9	T8	8	Table 4	1
WISE J105130.01−213859.7	8	J105130.02−213859.9	T8.5	22	Table 4	1
WISE J105257.95−194250.2	20	J105257.95−194250.1	T7.5	20	Table 4	1
WISEA J105553.62−165216.5	6	J105553.62−165216.5	T9.5	22	Table 4	1
WISE J111239.24−385700.7	6	J111239.25−385700.5	T9	6	56	1
2MASS J11145133−2618235	29	J111448.74−261827.9	T7.5	61	179.2 ± 1.4 (abs)	67
WISE J111838.70+312537.9h	2, 44	J111838.69+312537.7	T8.5	44	113.2 ± 4.6 (abs)	75
WISEPC J112254.73+255021.5	4	J112254.70+255021.9	T6	4	Table 5	1
WISE J112438.12−042149.7	8	J112438.10−042149.6	T7	8	Table 4	1
WISE J113949.24−332425.1	20	J113949.23−332425.4	T7	20	Table 4	1
WISEA J114156.67−332635.5	21	J114156.67−332635.5	Y0	6	Table 4	1
WISE J114340.22+443123.8	8	J114340.22+443124.0	T8.5	8	Table 4	1
WISEP J115013.88+630240.7	4	J115013.85+630241.3	T8	4	Table 4	1
ULAS J115239.94+113407.6	19	J115239.94+113406.9	T8.5	19	Table 4	1
WISE J120604.38+840110.6	9	J120604.25+840110.5	Y0	9	Table 4	1
2MASSI J1217110−031113	43	J121710.27−031112.1	T7.5	61	90.8 ± 2.2 (rel)	76
WISEPC J121756.91+162640.2AB	4	J121756.92+162640.3	T9	4	Table 4	1
WISEA J122036.38+540717.3	22	J122036.38+540717.3	T9.5	22	Table 4	1
WISE J122152.28−313600.8	8	J122152.28−313600.7	T6.5	8	Table 4	1
2MASS J12255432−2739466AB	43	J122554.66−273954.1	T6	61	75.1 ± 2.5 (rel)	76
WISE J122558.86−101345.0	8	J122558.86−101345.2	T6	8	Table 4	1
2MASS J12314753+0847331	3	J123146.70+084722.1	T5.5i	61	Table 4	1
2MASS J12373919+6526148	43	J123737.33+652608.0	T6.5	61	96.07 ± 4.78 (abs)	68
ULAS J123828.51+095351.3	42	J123828.38+095352.0	T8	10	Table 6	1
WISE J124309.61+844547.8	20	J124309.40+844547.7	T9	20	Table 4	1
WISE J125015.56+262846.9	8	J125015.56+262846.8	T6.5	8	53	1
WISE J125448.52−072828.4	20	J125448.50−072828.3	T7	20	Table 4	1
WISE J125715.90+400854.2	8	J125715.91+400854.2	T7	8	Table 4	1
VHS J125804.89−441232.4	23	J125804.91−441232.6	T6	23	Table 4	1
Gl 494C (1300+1221)j	45	J130041.63+122114.5	T8	10	86.8570 ± 0.1515 (abs)	72
WISE J130141.62−030212.9	8	J130141.63−030212.9	T8.5	8	Table 4	1
ULAS J130217.21+130851.2	31	J130217.07+130851.1	T8	10	65 ± 5 (abs)	77
WISEPC J131106.24+012252.4	4	J131106.21+012253.9	T9:	4	Table 6	1
ULAS J131508.42+082627.4	64	J131508.40+082627.0	T7.5	64	Table 6	1
WISE J131833.98−175826.5	8	J131833.96−175826.3	T8	22	Table 4	1
WISEPC J132004.16+603426.2	4	J132004.16+603426.1	T6.5	4	Table 5	1
WISEPA J132233.66−234017.1	4	J132233.63−234017.0	T8	4	Table 5	1
WISEA J133300.03−160754.4	1	J133300.03−160754.4	[T7.5]k	1	Table 4	1
ULAS J133553.45+113005.2	42	J133553.41+113004.7	T8.5	10	99.9 ± 1.6 (abs)	67
SDSSp J134646.45−003150.4	47	J134646.05−003151.5	T6.5	61	68.3 ± 2.3 (rel)	76
WISEPC J140518.40+553421.4	10	J140518.32+553421.3	Y0.5(pec?)	9, 73	Table 4	1
ULAS J141623.94+134836.3	49	J141623.96+134836.0	(sd)T7.5	62	109.7 ± 1.3 (abs)l	67
Gl 547B (1423+0116)m	50	J142320.84+011637.5	sdT8, T8	50, 8	57.3445 ± 0.0362 (abs)	72
VHS J143311.46−083736.3	23	J143311.41−083736.6	T8	23	Table 4	1
WISEPA J143602.19−181421.8	4	J143602.19−181422.0	T8pec	4	Table 4	1
WISE J144806.48−253420.3	20	J144806.48−253420.5	T8	20	Table 4	1
Gl 570D (1457−2121)	51	J145715.83−212208.0	T7.5	61	170.0112 ± 0.0851 (abs)	72
WISEPC J145715.03+581510.2	4	J145715.01+581510.1	T7	4	Table 5	1
WISE J150115.92−400418.4	17	J150115.92−400418.2	T6	6	Table 4	1
2MASS J15031961+2525196	52	J150319.68+252525.7	T5	61	157.2 ± 2.2 (abs)	67
SDSS J150411.63+102718.4	53	J150411.81+102715.4	T7	53	46.1 ± 1.5 (abs)	67
Gl 576B (1504+0538)n	54	J150457.56+053759.8	T6pec	54	52.5873 ± 0.0668 (abs)	72
WISEPC J150649.97+702736.0	4	J150649.92+702736.1	T6	4	Table 5	1
WISE J151721.13+052929.3	8	J151721.12+052929.3	T8	8	Table 4	1
WISEPC J151906.64+700931.5	4	J151906.63+700931.3	T8	4	Table 4	1
WISE J152305.10+312537.6	8	J152305.09+312537.3	T6.5pec	8	Table 4	1
WISEPA J154151.66−225025.2	10	J154151.65−225024.9o	Y1	9	Table 4	1
WISE J154214.00+223005.2	8	J154214.00+223005.2	T9.5	8	Table 4	1
2MASSI J1553022+153236AB	32	J155301.93+153238.8	T7	61	75.1 ± 0.9 (abs)	67
WISEPA J161215.94−342027.1	4	J161215.92−342028.5	T6.5	4	Table 4	1
WISEPA J161441.45+173936.7	4	J161441.47+173935.4	T9	4	Table 4	1
2MASS J16150413+1340079	24	J161504.36+134004.0	T6	24	Table 4	1
	⋯	⋯	⋯	⋯	68.6 ± 6.4 (abs)	66
WISEPA J161705.75+180714.3	4	J161705.73+180714.1	T8	4	Table 6	1
WISEPA J162208.94−095934.6	4	J162208.93−095934.6	T6	4	Table 4	1
SDSSp J162414.37+002915.6	55	J162414.07+002915.6	T6	61	90.9 ± 1.2 (rel)	76
WISEPA J162725.64+325525.5	4	J162725.64+325524.5	T6	4	Table 5	1
SDSS J162838.77+230821.1	53	J162838.99+230817.9	T7	53	75.1 ± 0.9 (abs)	67
WISE J163940.86−684744.6	17	J163940.84−684739.4	Y0pec	9	Table 4	1
WISEPA J165311.05+444423.9	4	J165311.03+444422.7	T8	4	Table 4	1
WISEPA J171104.60+350036.8AB	4	J171104.59+350036.7	T8	4	Table 4	1
WISEPA J171717.02+612859.3	4	J171717.04+612859.2	T8	4, 8	Table 4	1
WISE J172134.46+111739.4	8	J172134.46+111739.5	T6	8	Table 4	1
WISEA J173551.56−820900.3	6	J173551.56−820900.3	T6	6	Table 4	1
WISEPA J173835.53+273258.9	10	J173835.52+273258.8	Y0	10	Table 4	1
WISEPA J174124.26+255319.5	4, 33, 56	J174124.22+255319.2	T9	4	Table 5	1
SDSS J175805.46+463311.9p	57	J175805.45+463316.9	T6.5	61	71.4754 ± 0.0354 (abs)	72
WISEPA J180435.40+311706.1	4	J180435.37+311706.2	T9.5:	4	Table 4	1
WISEPA J181210.85+272144.3	4	J181210.83+272144.2	T8.5:	10	Table 6	1
WISE J181243.14+200746.4	8	J181243.14+200746.2	T9	8	Table 4	1
WISE J181329.40+283533.3	8	J181329.40+283533.3	T8	8	Table 4	1
WISEPA J182831.08+265037.8	10	J182831.08+265037.6	≥Y2	2	Table 4	1
SCR J1845−6357B	58	source not extracted	T6	63	259.45 ± 1.11 (abs)	78
WISEPA J185215.78+353716.3	4	J185215.82+353716.2	T7	4	Table 5	1
WISEPA J190624.75+450808.2	4	J190624.73+450807.0	T6	4	Table 5	1
WISE J192841.35+235604.9	8	J192841.39+235604.5	T6	8	Table 4	1
WISE J195500.42−254013.9	8	J195500.42–254013.5	T8	8	Table 4	1
WISEPA J195905.66−333833.7	4	J195905.64−333833.8	T8	4	Table 4	1
WISE J200050.19+362950.1	18	J200050.19+362950.1	T8	18	Table 4	1
WISE J200520.38+542433.9	25	J200520.35+542433.6	sdT8	25	Table 4	1
WISE J201546.27+664645.1	8	J201546.45+664645.2	T8	8	Table 4	1
WISEA J201748.74−342102.6	6	J201748.74−342102.6	[T7.5]q	6	Table 4	1
WISEPA J201824.96−742325.9	4	J201824.99–742327.9	T7	4	Table 6	1
WISE J201920.76−114807.5	8	J201920.75−114807.5	T8:	8	Table 4	1
WISEPC J205628.90+145953.3	10	J205628.88+145953.6	Y0	10	Table 4	1
WISE J210200.15−442919.5	2	J210200.14−442919.9	T9	2	92.3 ± 1.9 (rel)	21
WISEPA J213456.73−713743.6	4	J213456.79−713744.7	T9pec	4	109.1 ± 3.7 (rel)	21
ULAS J214638.83−001038.7r	59	J214639.07−001039.3	T8.5	10	79.8 ± 4.5 (abs)	79
WISE J214706.78−102924.0	8	J214706.79−102923.7	T7.5	8	Table 4	1
WISEPC J215751.38+265931.4	4	J215751.35+265931.2	T7	4	Table 4	1
WISEA J215949.54−480855.2	6	J215949.54−480855.2	T9	6	Table 4	1
WISEA J220304.18+461923.4	22	J220304.18+461923.4	T8	22	Table 4	1
Gl 845C (2204−5646)s	60	source not extracted	T6	61	274.8048 ± 0.2494 (abs)	72
WISE J220905.73+271143.9	4	J220905.75+271143.6	Y0:	18	Table 4	1
WISEPC J220922.10−273439.5	4	J220922.09−273439.9	T7	4	Table 4	1
WISEA J221140.53−475826.7	6	J221140.53−475826.7	[T8]t	6	Table 4	1
WISE J221216.33−693121.6	9	J221216.27−693121.6	T9	9	Table 4	1
WISEPC J221354.69+091139.4	4	J221354.69+091139.3	T7	4	Table 5	1
WISE J222055.31−362817.4	2	J222055.34−362817.5	Y0	2	Table 4	1
WISEPC J222623.05+044003.9	4	J222623.06+044003.2	T8	4	Table 5	1
2MASS J22282889−4310262	34	J222829.01−431029.8	T6	61	92.1 ± 2.6 (abs)	74
WISEA J223204.53−573010.4	6	J223204.53−573010.4	T9	6	Table 4	1
WISE J223720.39+722833.8	8	J223720.39+722833.9	T6	8	Table 4	1
WISEPC J225540.74−311841.8	4	J225540.75−311842.0	T8	4	Table 4	1
WISE J230133.32+021635.0	8	J230133.32+021635.0	T6.5	8	Table 4	1
WISEA J230228.66−713441.7	6	J230228.66−713441.7	[T4.5]u	6	Table 4	1
WISEPA J231336.40−803700.3	4	J231336.47−803700.4	T8	4	Table 4	1
WISEPC J231939.13−184404.3	4	J231939.14−184404.4	T7.5	4	Table 4	1
ULAS J232123.79+135454.9	26	J232123.82+135453.3	T7.5	31	Table 4	1
	⋯	⋯	⋯	⋯	84 ± 4 (abs)	77
WISEPC J232519.54−410534.9	4	J232519.55−410535.1	T9pec	4	107.8 ± 3.7 (rel)	21
ULAS J232600.40+020139.2	19	J232600.44+020138.4	T8	19	Table 4	1
WISE J233226.49−432510.6	2	J233226.54−432510.9	T9:	2	Table 4	1
WISEPC J234026.62−074507.2	4	J234026.61−074508.4	T7	4	Table 5	1
ULAS J234228.96+085620.1	26	J234228.97+085619.9	T6.5	8	Table 6	1
WISEPA J234351.20−741847.0	4	J234351.28−741846.9	T6	4	Table 4	1
WISEPC J234446.25+103415.8	4	J234446.24+103415.8	T9	4, 8	Table 4	1
WISEPC J234841.10−102844.4	4	J234841.11−102844.1	T7	4	Table 5	1
WISEA J235402.79+024014.1	9	J235402.79+024014.1	Y1	9	Table 4	1
WISE J235716.49+122741.8	8	J235716.49+122741.5	T6	8	Table 4	1

Notes.

^a0039+2115: Also known as HD 3651B. ^b0309−5016: Type estimated from methane imaging. ^c0323−5907: The ch1−ch2 color of 1.244 ± 0.033 mag (Table 2) suggests a type of T6 based on Figure 11 of Kirkpatrick et al. (2011). ^d0628−8057: Type estimated from methane imaging. ^e0807−6618: Given the fact that the absolute ch2 magnitude of this object (15.43 ± 0.09 mag) and ch1−ch2 color (2.81 ± 0.16 mag) are most like the Y1 dwarfs, this object has been assigned a temporary spectral type of Y1. ^f0855−0714: Given the fact that the absolute H and ch2 magnitudes of this object (27.04 ± 0.24 and 17.13 ± 0.02 mag, respectively) are much fainter, and the H–W2 and ch1−ch2 colors (10.13 ± 0.24 and 3.55 ± 0.07 mag, respectively) much redder, than that of the other Y dwarfs typed as late as ≥Y2, this object has been assigned a temporary spectral type of ≥Y4. ^g0950+0117: This is a common-proper-motion companion to LHS 6176. ^h1118+3125: Also known as the distant companion to ξ UMa (Gl 423). ⁱ1231+0837: Object earlier in type than T6, but nonetheless included here because we obtained a parallax with Spitzer. ^j1300+1221: Also known as Ross 458C. ^k1333−1607: The Table 2 colors of ch1−ch2 = 1.811 ± 0.050 mag and H–ch2 = 3.369 ± 0.132 mag suggest, based on Figures 11 and 14 of Kirkpatrick et al. (2011), a type of T7.5. ^l1416+1348: The parallax of the sdL primary is quoted here for the (sd)T companion. ^m1423+0114: Also known as BD+01 2920B. ⁿ1504+0538: Also known as HIP 73786B. ^o1541−2250: Source not extracted in the AllWISE Source Catalog, so this designation is the one from the WISE All-Sky Source Catalog. ^p1758+4633: Also known as GJ 4040B. ^q2017−3421: Type estimated from methane imaging. ^r2146−0010: Also known as Wolf 940B and GJ 1263B. ^s2204−5646: Also known as Indi Bb. ^t2211−4758: Type estimated from methane imaging. ^u2302−7134: Type estimated from methane imaging. Object earlier in type than T6, but nonetheless included here because we obtained a parallax with Spitzer.

References. (1) This paper, (2) Kirkpatrick et al. (2012), (3) Burgasser et al. (2004), (4) Kirkpatrick et al. (2011), (5) Albert et al. (2011), (6) Tinney et al. (2018), (7) Pinfield et al. (2014b), (8) Mace et al. (2013a), (9) Schneider et al. (2015), (10) Cushing et al. (2011), (11) Mainzer et al. (2011), (12) Kirkpatrick et al. (2013), (13) Pinfield et al. (2014a), (14) Luhman (2014b), (15) Kirkpatrick et al. (2014), (16) Luhman (2014a), (17) Tinney et al. (2012), (18) Cushing et al. (2014), (19) Burningham et al. (2013), (20) Thompson et al. (2013), (21) Tinney et al. (2014), (22) Martin et al. (2018), (23) Lodieu et al. (2012), (24) Looper et al. (2007), (25) Mace et al. (2013b), (26) Scholz (2010b), (27) Warren et al. (2007b), (28) Mugrauer et al. (2006), (29) Tinney et al. (2005), (30) Delorme et al. (2008), (31) Burningham et al. (2010b), (32) Burgasser et al. (2002), (33) Scholz et al. (2011), (34) Burgasser et al. (2003c), (35) Bihain et al. (2013), (36) Nakajima et al. (1995), (37) Lucas et al. (2010), (38) Artigau et al. (2010), (39) Lodieu et al. (2007), (40) Leggett et al. (2012), (41) Luhman et al. (2012), (42) Burningham et al. (2008), (43) Burgasser et al. (1999), (44) Wright et al. (2013), (45) Goldman et al. (2010), (46) Burningham et al. (2011), (47) Tsvetanov et al. (2000), (48) Cardoso et al. (2015), (49) Scholz (2010a), (50) Pinfield et al. (2012), (51) Burgasser et al. (2000), (52) Burgasser et al. (2003a), (53) Chiu et al. (2006), (54) Murray et al. (2011), (55) Strauss et al. (1999), (56) Gelino et al. (2011), (57) Knapp et al. (2004), (58) Biller et al. (2006), (59) Burningham et al. (2009), (60) Scholz et al. (2003), (61) Burgasser et al. (2006b), (62) Burgasser et al. (2010b), (63) Kasper et al. (2007), (64) Pinfield et al. (2008), (65) Luhman et al. (2011), (66) Faherty et al. (2012), (67) Dupuy & Liu (2012), (68) Vrba et al. (2004), (69) Subasavage et al. (2009), (70) Marocco et al. (2010), (71) Burgasser et al. (2008b), (72) Gaia Collaboration et al. (2018), (73) Cushing et al. (2016), (74) Smart et al. (2013), (75) van Altena et al. (1995), (76) Tinney et al. (2003), (77) Manjavacas et al. (2013), (78) Henry et al. (2006), (79) Harrington & Dahn (1980).

Download table as:  ASCIITypeset images: 1 2 3 4

Of these 235 dwarfs in Table 1, 142 are being astrometrically monitored by our Spitzer program discussed in Section 4, 41 have high-accuracy parallax measurements from our ground-based programs discussed in Sections 6 and 7, and 49 have high-accuracy¹⁶ parallax measurements from the literature, although four of these are in common with objects in our own parallax programs. Only seven objects lack astrometric monitoring, and these were not added to our Spitzer programs because they either do not have any prior Spitzer measurements—and thus may not have had a large time baseline to decouple proper motion from parallax had we observed them only in Cycle 13—or were published after the Cycle 13 deadline; all of these, however, are being astrometrically monitored by us in our Spitzer Cycle 14 program. For these, the parallax values in column 6 are given in italics and are spectromartphotometric estimates only. With one exception, these estimates take the apparent H and/or W2 magnitudes in Table 2 together with the spectral types in column 4 to compute distance estimates via the equations (those that include the WISE 1828+2650 data point) from Section 4.3 of Kirkpatrick et al. (2012). The sole exception is the parallax estimate of ULAS 0745+2332 (whose photometry was not extracted by the WISE pipeline), which is calculated from the minimum and maximum distance estimates provided by Burningham et al. (2008).

Photometry for these objects is given in Table 2. This table shows an abbreviated name from Table 1 in column 1, the H-band apparent magnitude and its reference in columns 2 and 3, and the WISE W1 through W3 magnitudes in columns 4 through 6. It should be noted that ground-based near-infrared photometry in both the J and H bands has been taken for many of these objects in one of two systems: either the Maunakea Observatories filter set (MKO; Tokunaga et al. 2002) or the filter set established by the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006). Because the J-band filter profiles between the two systems are very different, and the H-band profiles are nearly the same, we list in Table 2 only the H-band magnitudes since those can be intercompared regardless of the system used. Additional discussion on this point can be found in Section 3.1 of Kirkpatrick et al. (2011). Discussion of the measurements of Spitzer magnitudes in columns 7–8 and the Astronomical Observation Requests (AORs) from which they were measured can be found in Section 5.

A list of 142 objects from Table 1 was astrometrically monitored with Spitzer/IRAC. Most of the Spitzer data came from programs 70062, 80109, 90007, 11059, and 13012 (Kirkpatrick, PI). The earliest of these programs, 70062 and 80109, were primarily aimed at photometric characterization of WISE-selected brown dwarf candidates using the 3.6 μm (hereafter, ch1) and 4.5 μm (hereafter, ch2) bandpasses of IRAC. In these two programs, a cycling dither pattern of medium scale and a five-position dither were used with frame times of 30 s in both channels. However, candidates with the reddest WISE W1−W2 colors were also observed at subsequent epochs only in ch2 to provide early astrometric monitoring to supplement Spitzer astrometric programs planned for later. Additional photometric characterization of brown dwarf candidates selected later in the WISE mission was obtained in program 11059. In this program, ch1 and ch2 observations were obtained using a random dither pattern of medium scale and nine dither positions, again with frame times of 30 s. Our main astrometric monitoring campaigns were programs 90007 and 13012, which are described further below.

We chose ch2 for our astrometric follow-up for a variety of reasons, which are listed in Martin et al. (2018) but reiterated here. During Spitzer cryogenic operations, ch1 was more sensitive than ch2, but after cryogen depletion the deep image noise was found to be 12% worse in ch1 and 10% better in ch2, making the channels comparable in sensitivity for average field stars (ch1−ch2 ≈ 0 mag; Carey et al. 2010). Another change during warm operations was the behavior of latent images from bright objects. Whereas latents in ch2 decay rapidly (typically within ten minutes), ch1 latents decay on timescales of hours. Moreover, the ch2 intra-pixel sensitivity variation (aka, the pixel phase effect) is about half that of ch1. Given these points, the fact that the point response function (PRF) is less undersampled in ch2 than in ch1, and the fact that our cold brown dwarfs are also much brighter in ch2 than in ch1 (1.0 < ch1−ch2 < 3.0 mag), we choose to do our imaging in ch2.

Programs 90007 and 13012 were designed exclusively for astrometric monitoring, with program 90007 providing data to satisfy the minimum astrometric requirement and program 13012 extending the time baseline to improve the astrometric uncertainties. The Lutz–Kelker bias sets the fundamental requirement for the precision we targeted. The Lutz–Kelker effect, a systematic error inherent in the measurements of trigonometric parallax for a volume-limited set of stars, is induced as follows. Near the maximum distance, d_max, the volume of stars just inside, (${d}_{\max }-{\rm{\Delta }}d$), is smaller than that just outside, (${d}_{\max }+{\rm{\Delta }}d$), meaning that there are more stars able to scatter into the volume than can scatter outside. This means that the true average parallax is smaller than the average parallax that is measured. Figure 1 of Lutz & Kelker (1973) demonstrates that the astrometric error needed to correct this effect must be ≤15% or else the effect is uncorrectable. For our distance limit of 20 pc (a parallax of 50 mas), this sets the error floor at 7.5 mas. Ideally, we would like to have errors even smaller; for example, an error of 10% (5 mas) reduces the bias on the absolute magnitude determination from 0.28 mag to 0.11 mag (see Table 1 of Lutz & Kelker 1973).

Our AORs for program 90007 were designed so targets were acquired with a signal-to-noise ratio (S/N) of ≥100 per epoch. Theoretically, the best astrometric precision we can expect from a single measurement (see Equation (1) of Monet et al. 2010) is FWHM/(2 × S/N) = 17/(2 × 100) = 8.5 mas, where the FWHM is the ch2 value from Table 2.1 of the IRAC Instrument Handbook.¹⁷ However, our ability to fully correct for astrometric distortion keeps us from reaching this theoretical floor. We conservatively estimated that we could achieve ∼15 mas precision after distortion is taken into account. Because we had already acquired earlier Spitzer epochs that would allow us to measure the proper motion and disentangle it from the parallax, we assumed that the error in the parallax would be roughly equal to the per-epoch-precision divided by the square root of the number of epochs measured in program 90007. For a per-epoch precision of 15 mas and a final parallactic error of <10%, at least nine measurement epochs for each source were required. Hence, in program 90007, the per-epoch goal of S/N > 100 per target was accomplished with a total ch2 integration time of 270 s acquired using a random dither pattern of medium scale, nine dither positions, and individual frame times of 30 s. This same procedure was used for program 13012.

Timing constraints were placed on the observations to optimize the measurement of parallax. The Spitzer viewing zone falls between 825 and 120° solar elongation, which encompasses the maximum parallax factor in ecliptic longitude (at 90°) critical to our program. For targets having two Spitzer visibility windows per year, one AOR was placed within 3.5 days of each maximum parallax factor. The other two or three AORs were evenly spaced through the rest of the visibility period. For targets near, but not in, the Continuous Viewing Zone, five or six observations were obtained at roughly evenly spaced intervals within each window, with an AOR landing within ±3.5 days of each available maximum parallax factor. For targets located within the Continuous Viewing Zone, 10–12 observations were used each year, again with an AOR falling within 3.5 days of each available maximum parallax factor. Slight adjustments to these constraints had to be made to fit within the calendar dates of each cycle, and other post facto adjustments were included when the observed data were corrupted by (rarely occurring) coronal mass ejection events from the Sun. These timing constraints were determined using a program written by one of us (ELW) that calculates the time of maximum parallax factor for each target using the predicted Spitzer ephemerides available from JPL Horizons.¹⁸

Although program 13012 was granted a full two years of observation and is ongoing, this paper uses only those data taken by 2017 October 20 (UT). This date was chosen so that each target will have been observed through at least two maximum parallax factors in Spitzer Cycle 13. Future Cycle 13 observations along with data from our new Cycle 14 program (discussed further in Section 11) to be completed in 2019 November, will be included in a subsequent paper presenting our final parallactic measurements. A listing of the first and last observation date, total time baseline, and number of AORs per program for each target is given in Table 3.

For a few targets, the disentangling of proper motion from parallax benefited from using ch2 observations taken prior to our own:

• 1.  
  WISE 0304−2705 and WISE 2203+4619: We supplemented our data with an earlier observation from program 10135 (D.J. Pinfield, PI) that used a 16 point spiral dither pattern with medium spacing, two frames at each dither position, and exposure times of 30 s per frame.
• 2.  
  WISE 0833+0052 and ULAS 2326+0201: We used an earlier observation from program 80077 (S.K. Leggett, PI) that used a 12 point Reuleaux dither pattern with medium spacing, four frames at each dither position, and exposure times of 30 s per frame.
• 3.  
  WISE 0855−0714: We used earlier observations from programs 90095 and 10168 (K.L. Luhman, PI). Program 90095 acquired three separate epochs on the target object, using a five-point Gaussian dither with small spacing and exposure times of 30 s per frame. Program 10168 acquired four separate epochs using a nine-point random dither pattern of small spacing and exposure times of 30 s per frame.
• 4.  
  CFBDS 1028+5654: An earlier observation from program 70021 (K.L. Luhman, PI) was used to extend our time baseline. This program acquired data using a five-point Gaussian dither with small spacing, one frame per dither position, and exposure times of 30 s per frame.
• 5.  
  ULAS 1043+1048: An observation from program 70058 (S.K. Leggett, PI) was used to extend the time baseline for this object. This program took data using a 16 point spiral dither pattern with medium spacing, six frames at each dither position, and exposure times of 30 s per frame.
• 6.  
  WISE 1828+2650: Data from program 551 (A.K. Mainzer, PI) were the first taken as part of the WISE brown dwarf team's follow-up of WISE color-selected objects. This program, which targeted only WISE 1828+2650 at a single epoch, used a 12 point Reuleaux dither pattern with medium spacing, one frame per dither position, and exposure times of 12 s per frame.
• 7.  
  ULAS 2321+1354: Program 60093 (S.K. Leggett, PI) provided a supplemental data point for this object. Data were taken using a five-point Gaussian dither pattern with medium spacing, one frame per dither, and exposure times of 30 s per frame.

5.1. Photometry in ch1 and ch2

5.2. Astrometry in ch2

Our basic astrometric reduction methodology is discussed in detail in Martin et al. (2018). Whereas ECM wrote Python code for the reductions presented in that paper, JDK wrote independent Interactive Data Language (IDL) code and other wrappers for the reductions presented here, and those included one fundamental change to improve astrometric repeatability. We outline the basic steps below.

5.2.1. Identifying Gaia Astrometric Anchor Points

For each AOR, we created a mosaic from the individual CBCD frames and extracted astrometry and photometry of detected sources using the MOPEX/APEX software. We examined the resulting mosaics at all epochs to ensure that the target object was near the center of the field, as expected. (This step eliminated three AORs for WISE 2301+0216—46523392, 46523136, and 46522880—from further use, due to a typographical error in the requested pointings for those epochs.) In addition to these per-epoch mosaics, we also created a supermosaic and associated source list by combining all available CBCD files for each object over the full time baseline. We then used the tmatch2 routine in the Starlink Tables 1nfrastructure Library Tool Set (STILTS; Taylor 2006) and a three-arcsecond radius to match sources from each per-epoch mosaic source list to the supermosaic source list. Parameters were set so that we retained for each supermosaic source only the closest match in the per-epoch source list (${find}={best}1$) and listed only those supermosaic sources having a match (${join}=1{and}2$).

We then used the IDL to perform a preliminary re-registration on each per-epoch mosaic to place it on the same astrometric grid as the supermosaic. Only those objects with S/N ⪆ 30 on the per-epoch mosaics were used. We found that a simple translation in R.A. and decl. provided excellent results. The per-frame offsets were computed by performing a robust mean of the offsets and including a 3σ clipping of outliers. We uploaded this list of high-S/N re-registration stars into IRSA and matched to the Gaia Data Release 1 (DR1) catalog using a one-arcsecond search radius. Most of these stars have Gaia matches, since they are bright at both Gaia G band and IRAC ch2 band, but we dropped any Gaia matches for which the Gaia DR1 astrometric uncertainties were ⪆100 mas.

Once the Gaia astrometric anchor stars had been identified in each field, more precise refinements to the astrometry could be performed, since the Gaia DR1 positions for these well detected objects typically have uncertainties of under a milliarcsecond. Originally, we wrote code like that described in Martin et al. (2018), to do these refinements on the source lists derived from the per-epoch mosaics, but we found that this was degrading our final astrometric precision. After some experimentation, we concluded that the mosaicking step in MOPEX was responsible. As described below, the actual astrometric measurements for this paper use source positions as measured on the individual frames, not the per-epoch mosaics.

5.2.2. Astrometric Refinements to Frame Source Positions

For each AOR, we ran scripts in MOPEX/APEX to measure the positions and photometry of our target and its associated re-registration stars on each individual frame. These scripts used the CBCD, uncertainty (CBUNC), and mask (BIMSK) files available in the Spitzer Heritage Archive. Data were pulled from the Spitzer Heritage Archive after all image headers had been updated by the Spitzer Science Center to incorporate the new fifth-order correction to the array distortion²⁰ (Lowrance et al. 2014, 2016). PRF fitting was done using a set of warm PRFs built by one of us (JGI), adapted from the cold mission PRFs to mimic the intrapixel gain variations measured with warm IRAC. Because the optical path did not change from the cold to warm Spitzer missions, the optical point-spread function (PSF) did not change, only the overall detector sensitivity. In other words, while the dynamic range of the PRF has changed, its spatial structure has not. As usual, the PRFs we used are tabulated images of point sources at various sub-pixel offsets and therefore strongly mitigate the astrometric bias caused by intrapixel distortion (Ingalls et al. 2012, 2014), which is a consequence of the fact that IRAC data are undersampled and the intrinsic sensitivity of an IRAC detector is not uniform across a pixel. While this analysis was underway, warm mission PRFs developed by Hora et al. (2012) were released on the IRSA website,²¹ but, as expected, the astrometric differences between the official PRFs and the ones used here were found to be negligible.

The resulting, native astrometry of the re-registration stars on each frame was then compared to the Gaia DR1 positions of these same sources. Specifically, we used the (x, y) positions computed by APEX and translated these into (R.A., decl.) using the World Coordinate System (WCS) information in the frame FITS header.²² Naively, one would assume that the (x, y) positions reported by APEX would be true array coordinates, but through experimentation we determined that these positions are actually rubber-sheeted versions; i.e., ones with the fifth-order distortion correction already included. Hence, we were able to convert to (R.A., decl.) using the WCS specifications only.

With the (x, y)-derived sky positions in hand for both the re-registration stars and the target, we converted all to tangent plane coordinates (ξ, η), where we used the mean position of our target across all epochs as the tangent point itself; i.e., (ξ, η) = (0, 0). We then computed the (Δξ, Δη) values between the (x, y)-derived sky positions for the re-registration stars and their Gaia reported positions, and computed a robust mean of the differences using 3σ outlier clipping and a simple (ξ, η) translation. These mean differences were then used to place the (ξ, η) coordinates of the target object and re-registration stars onto the Gaia reference frame.

For most of our targets, we were able to find a sufficient number of Gaia DR1 stars above a single-frame S/N value of 100 to perform an adequate re-registration. For some targets in sparser fields, however, as few as three re-registration stars were found above S/N = 100. (For the two targets closest to the Galactic Center, WISE 1928+2356 and WISE 2000+3629, we had the opposite problem of too many potential re-registration stars, so we reset the selection threshold for re-registration stars to S/N > 500.) For any target having 10 or more re-registration stars with S/N ≥ 100, we found that the inclusion of re-registration stars with 30 < S/N < 100 did not generally decrease the reduced χ² values in the final proper motion and parallax fits. For targets having fewer than 10 re-registration stars with S/N ≥ 100, however, these reduced χ² values were generally much better. For these targets, a single-frame S/N floor of ∼30 was used for selection of the re-registration stars. With this adjustment, no fewer than five re-registration stars were used for each field.

For the target object, the robust mean of these per-frame adjusted positions (again using 3σ clipping) was used as the measured position of the object for this AOR. For the astrometric uncertainty on each AOR position, we use a measurement of the positional repeatability for stars lying at a S/N value similar to the target. Figure 1 illustrates this repeatability. The plot demonstrates that our target T and Y dwarfs, which lie in the single-frame S/N range between 70 and 200, have per-axis astrometric precisions of ∼15 mas. There are some AORs for which, due to small number statistics, this measured repeatability falls below 10 mas. For these, we set a floor of 10 mas on the per-axis positional uncertainty of the target, since the broader analysis in Figure 1 shows this is the best we actually achieve. For each AOR, the mean (ξ, η) position of the target was then converted back to (R.A., decl.). The FITS header of the middle frame in each AOR was then consulted for the UT date and barycentric (X, Y, Z) position of the Spitzer Space Telescope at the time of observation.

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5.2.3. Fitting for Proper Motion and Parallax

For each target, our list of measured astrometry and its uncertainties along with the observation times and locations of the observing platform were fed into a least-squares fitting code to determine the proper motion, parallax, and position at a fiducial time. We supply two nonlinear equations (see Smart 1977; Green 1985; Beichman et al. 2014) to the code:

$$\begin{eqnarray}\begin{array}{rcl}{\alpha }_{\mathrm{residual}} & = & \left(\alpha (t)-{\alpha }^{{\prime} }\right)\cos \,{\delta }^{{\prime} }\\ & & -\left.{\pi }_{\mathrm{trig}}\left(X(t)\sin \,{\alpha }^{{\prime} }-Y(t)\cos \,{\alpha }^{{\prime} }\right)\right)/3600\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}\begin{array}{c}\begin{array}{rcl}{\delta }_{{\rm{residual}}} & = & \delta (t)-{\delta }^{{\rm{{\prime} }}}-\left({\pi }_{{\rm{trig}}}\left(X(t)\cos \,{\alpha }^{{\prime} }\sin \,{\delta }^{{\rm{{\prime} }}}\right.\right.\\ & & +\left.Y(t)\sin \,{\alpha }^{{\prime} }\sin \,{\delta }^{{\rm{{\prime} }}}-Z(t)\cos \,{\delta }^{{\rm{{\prime} }}}\right))/3600\end{array}\end{array}\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray}&&{\alpha }^{{\prime} }={\alpha }_{0}+({\mu }_{\alpha }(t-{t}_{0})/\cos \,{\delta }^{{\prime} })/3600\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\delta }^{{\prime} }={\delta }_{0}+({\mu }_{\delta }(t-{t}_{0}))/3600.\end{eqnarray} \tag{ 4 }$$

Here, α(t) and δ(t) are the R.A. and decl. positions (and their uncertainties) of the target in degrees; X(t), Y(t), and Z(t) are the locations of the spacecraft in astronomical units; t₀ is a fiducial time in years; α₀ and δ₀ are the R.A. and decl. in degrees at time t₀; μ_α and μ_δ are the R.A. and decl. components of the proper motion in arcsec yr⁻¹; and π_trig is the trigonometric parallax in arcseconds. We employed the IDL module mpfitfun (Markwardt 2009), which uses the Levenberg–Marquardt least-squares algorithm to attempt to drive both α_residual and δ_residual simultaneously to zero, given the observational data and their uncertainties.

The fiducial time was chosen to be at a point in the middle of our observational data set, epoch 2014.0, since setting this to be within the timeframe of the observations minimizes the associated uncertainties. Choosing a much later or earlier time, say 2000.0, would result in larger positional uncertainties since the uncertainty from the proper motion compounds with the difference in the time interval between the observations and the chosen fiducial time.

Table 4 gives the best-fitting solutions for each of our 142 targets. The abbreviated object name is in column 1 followed by the position of the object at epoch 2014.0 along with the positional uncertainties in column 2–5. The value of parallax obtained by the best-fit solution above is a measurement relative to the background stars and requires an adjustment to the absolute reference frame as described further below. The resulting value of the absolute parallax and the correction needed to convert from relative to absolute units are given in columns 6 and 7. The best-fit proper motion per axis and its uncertainties are listed in columns 8 and 9. The χ² value of the best fit, the number of degrees of freedom, and the reduced χ² value are listed in columns 10–12. The number of Spitzer epochs used in the solution is shown in column 13. Finally, the number of re-registration stars used along with a flag value for the S/N floor used for registration star selection ("H" for the high S/N cut and "L" for the low S/N cut) is given in column 14.

Table 4.  Parallax and Motion Fits for Objects on the Spitzer Parallax Program

Object	J2000 R.A.	R.A.	J2000 Decl.	Decl.	${\pi }_{\mathrm{abs}}$	${\mathrm{corr}}_{\pi }$	${\mu }_{{\rm{R}}.{\rm{A}}.}$	${\mu }_{\mathrm{Decl}.}$	χ2	Dof	Red.	# of	# of
Name	Ep. 2014.0	Unc.	Ep. 2014.0	Unc.	(mas)	(mas)	(mas yr−1)	(mas yr−1)			χ2	Ep.	Reg.
	(deg)	(mas)	(deg)	(mas)									Starsa
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
WISE 0005+3737	1.324120	2.6	37.622066	2.5	127.0 ± 2.4	1.3 ± 0.4	998.9 ± 1.4	−267.0 ± 1.4	19.925	33	0.604	19	22H
WISE 0015−4615	3.775288	2.7	−46.255526	2.6	71.8 ± 2.7	1.5 ± 0.5	409.7 ± 1.5	−682.9 ± 1.3	30.137	33	0.913	19	15L
WISE 0032−4946	8.128906	3.3	−49.781951	3.0	63.6 ± 2.9	1.4 ± 0.3	−379.3 ± 1.7	−858.1 ± 1.7	28.256	33	0.856	19	13L
2MASS 0034+0523	8.717410	3.3	5.385402	3.7	120.1 ± 3.0	1.6 ± 0.4	672.6 ± 1.7	184.7 ± 1.9	17.909	35	0.512	20	16L
WISE 0038+2758	9.621136	2.5	27.981175	2.5	89.7 ± 2.5	1.5 ± 0.6	−15.4 ± 1.6	96.3 ± 1.5	37.107	39	0.951	22	12H
WISE 0049+2151	12.439742	2.5	21.855396	2.5	139.9 ± 2.5	1.5 ± 0.5	−483.2 ± 1.4	−46.5 ± 1.4	18.928	35	0.541	20	15L
WISE 0123+4142	20.889465	8.1	41.701367	5.6	44.0 ± 4.1	1.3 ± 0.3	601.7 ± 2.6	91.5 ± 1.9	5.439	9	0.604	7	10H
CFBDS 0133+0231	23.260890	3.7	2.524552	2.7	56.3 ± 3.4	2.2 ± 1.2	598.0 ± 2.0	−113.9 ± 1.5	44.910	33	1.361	19	8L
WISE 0146+4234AB	26.735580	2.4	42.569411	2.3	52.5 ± 2.3	1.3 ± 0.3	−452.0 ± 1.2	−27.9 ± 1.2	58.434	37	1.579	21	21H
WISE 0221+3842	35.275000	5.9	38.701001	5.6	36.0 ± 4.1	1.5 ± 0.5	139.6 ± 1.9	−21.7 ± 1.8	10.011	9	1.112	7	13H
WISE 0226−0211AB	36.599702	6.0	−2.195477	5.1	57.3 ± 4.7	0.6 ± 0.1	−294.9 ± 2.1	−436.9 ± 1.7	307.384	13	23.645	9	11L
WISE 0233+3030	38.325104	6.7	30.508434	6.2	31.3 ± 4.2	1.6 ± 0.4	−134.6 ± 2.3	−29.5 ± 2.2	11.591	11	1.054	8	16H
WISE 0241−3653	40.353413	2.4	−36.891001	2.6	52.4 ± 2.7	1.6 ± 0.2	242.0 ± 1.5	148.4 ± 1.4	26.606	37	0.719	21	8H
WISE 0247+3725	41.810711	2.4	37.422967	2.4	64.8 ± 2.6	1.5 ± 0.6	25.3 ± 1.3	−83.2 ± 1.3	23.715	33	0.719	19	21H
WISE 0302−5817	45.656121	14.5	−58.294668	15.9	56.1 ± 4.4	1.3 ± 0.3	41.2 ± 4.9	−76.4 ± 5.2	21.135	13	1.626	9	15L
WISE 0304−2705	46.204500	19.4	−27.085116	17.1	81.5 ± 7.7	1.6 ± 0.3	128.0 ± 7.0	497.2 ± 6.5	25.307	9	2.812	7	5L
WISE 0309−5016	47.332887	4.9	−50.270419	4.3	66.8 ± 3.9	1.8 ± 0.8	521.5 ± 1.7	203.6 ± 1.5	6.397	13	0.492	9	16L
WISE 0313+7807	48.358936	3.5	78.129054	3.6	134.3 ± 3.6	1.0 ± 0.3	71.1 ± 1.2	54.8 ± 1.2	19.065	15	1.271	10	46L
WISE 0316+4307	49.102234	3.0	43.118785	2.8	73.3 ± 2.8	1.0 ± 0.3	372.4 ± 1.5	−225.9 ± 1.5	28.850	27	1.069	16	33H
WISE 0323−5907	50.788921	4.9	−59.130369	5.9	71.5 ± 4.3	1.5 ± 0.6	519.1 ± 1.6	499.6 ± 2.0	16.304	11	1.482	8	18L
WISE 0323−6025	50.907543	2.7	−60.431966	2.8	71.4 ± 2.9	1.5 ± 1.0	506.7 ± 1.3	−173.5 ± 1.5	25.616	31	0.826	18	19L
WISE 0325−3854	51.324053	5.3	−38.915158	6.2	57.2 ± 5.4	1.6 ± 0.5	283.7 ± 1.9	−107.0 ± 1.8	3.098	11	0.282	8	13L
WISE 0325−5044	51.268421	2.9	−50.733514	3.1	36.7 ± 2.7	1.5 ± 0.4	84.6 ± 1.5	−154.3 ± 1.6	121.079	27	4.484	16	21L
WISE 0325+0831	51.449038	3.1	8.521650	3.4	78.5 ± 3.0	1.4 ± 0.3	116.2 ± 1.8	−38.1 ± 1.7	21.917	33	0.664	19	12L
WISE 0335+4310	53.813849	2.4	43.178366	2.3	72.1 ± 2.4	1.0 ± 0.2	825.7 ± 1.2	−787.0 ± 1.2	112.945	35	3.227	20	52H
WISE 0336−0143	54.020859	2.4	−1.732166	2.4	99.0 ± 2.4	1.7 ± 0.4	−257.8 ± 1.2	−1212.3 ± 1.2	55.719	35	1.592	20	20H
WISE 0350−5658	57.501000	2.7	−56.975637	2.7	174.6 ± 2.6	1.4 ± 0.4	−216.5 ± 1.3	−579.0 ± 1.4	28.501	35	0.814	20	20L
WISE 0359−5401	59.891824	2.5	−54.032512	2.6	75.8 ± 2.5	1.5 ± 0.4	−143.0 ± 1.3	−774.8 ± 1.5	92.938	37	2.512	21	16L
WISE 0404−6420	61.181138	3.0	−64.341730	2.9	45.7 ± 2.7	1.8 ± 0.6	−46.8 ± 1.6	−50.2 ± 1.6	38.537	27	1.427	16	11H
WISE 0410+1502	62.595853	2.3	15.044417	2.2	150.2 ± 2.4	1.5 ± 0.5	954.2 ± 1.1	−2213.3 ± 1.1	39.350	39	1.009	22	20H
WISE 0413−4750	63.492451	7.1	−47.843983	7.8	48.2 ± 4.8	1.5 ± 0.6	110.6 ± 2.3	302.2 ± 2.6	9.477	9	1.053	7	18L
WISE 0430+4633	67.721883	6.9	46.559111	6.7	93.9 ± 4.1	0.4 ± 0.1	879.7 ± 2.3	383.8 ± 2.2	2.835	9	0.315	7	63H
WISE 0458+6434AB	74.725158	3.7	64.581566	3.8	109.2 ± 3.6	1.2 ± 0.2	207.7 ± 1.2	291.2 ± 1.2	2.470	13	0.190	9	16H
WISE 0500−1223	75.012144	3.9	−12.394828	3.7	95.1 ± 3.6	1.3 ± 0.6	−536.5 ± 1.3	493.1 ± 1.2	6.578	13	0.506	9	26L
WISE 0512−3004	78.036948	2.4	−30.067509	2.5	48.9 ± 2.6	1.2 ± 0.4	614.2 ± 1.2	187.6 ± 1.3	72.645	37	1.963	21	23L
WISE 0535−7500	83.819481	2.4	−75.006736	2.4	66.4 ± 2.4	1.4 ± 0.5	−123.7 ± 1.1	19.6 ± 1.1	45.380	33	1.375	19	32H
WISE 0540+4832	85.196268	2.5	48.541582	2.5	70.0 ± 2.6	0.8 ± 0.1	246.0 ± 1.5	−626.9 ± 1.5	41.240	29	1.422	17	58H
WISE 0614+0951	93.657701	2.2	9.859608	2.2	65.6 ± 2.2	0.6 ± 0.1	387.0 ± 1.1	−149.8 ± 1.1	39.525	39	1.013	22	74H
WISE 0645−0302	101.368293	4.5	−3.047051	6.5	50.7 ± 4.2	0.4 ± 0.1	−0.8 ± 1.2	−318.9 ± 2.0	10.993	9	1.221	7	55H
WISE 0647−6232	101.846795	2.3	−62.542827	2.4	100.3 ± 2.4	1.3 ± 0.6	2.2 ± 1.0	387.9 ± 1.1	76.198	33	2.309	19	20H
WISE 0713−2917	108.344415	2.5	−29.298188	2.5	107.5 ± 2.4	1.0 ± 0.2	356.5 ± 1.3	−413.8 ± 1.3	28.123	33	0.852	19	87H
WISE 0713−5854	108.257861	6.7	−58.912164	7.5	78.2 ± 4.6	1.6 ± 0.6	82.2 ± 2.1	358.2 ± 2.3	12.659	7	1.808	6	20H
WISE 0723+3403	110.802009	3.8	34.053368	3.7	56.3 ± 3.5	0.5 ± 0.1	−5.0 ± 1.2	−343.8 ± 1.2	28.654	13	2.204	9	40L
WISE 0734−7157	113.681527	2.5	−71.962324	2.5	75.0 ± 2.4	1.2 ± 0.4	−565.5 ± 1.3	−78.9 ± 1.3	88.425	29	3.049	17	21H
WISE 0744+5628	116.238838	2.3	56.471738	2.4	67.1 ± 2.5	1.8 ± 0.6	153.6 ± 1.2	−764.4 ± 1.2	44.682	37	1.208	21	10H
WISE 0759−4904	119.945205	2.4	−49.081446	2.4	89.1 ± 2.4	0.7 ± 0.1	−367.0 ± 1.1	244.3 ± 1.1	21.246	33	0.644	19	55H
WISE 0812+4021	123.084041	2.6	40.351692	2.3	34.2 ± 2.7	1.5 ± 0.7	258.0 ± 1.3	28.8 ± 1.1	74.070	37	2.002	21	20L
WISE 0825+2805	126.280555	2.5	28.096544	2.4	155.8 ± 2.4	1.4 ± 0.2	−63.1 ± 1.3	−232.8 ± 1.2	34.192	35	0.977	20	14H
WISE 0833+0052	128.408480	8.8	0.869044	7.8	82.6 ± 4.5	1.4 ± 0.5	790.1 ± 2.8	−1590.7 ± 2.5	4.356	9	0.484	7	21H
WISE 0836−1859	129.171466	4.0	−18.996471	3.8	40.8 ± 3.6	1.0 ± 0.2	−47.6 ± 1.3	−150.5 ± 1.2	67.391	13	5.184	9	19H
WISE 0855−0714	133.787057	4.5	−7.244431	4.5	438.9 ± 3.0	1.3 ± 0.3	−8118.9 ± 1.9	679.3 ± 1.9	11.154	21	0.531	13	24H
WISE 0857+5604	134.316277	2.3	56.068512	2.5	87.2 ± 2.4	1.3 ± 0.2	−714.8 ± 1.1	−233.5 ± 1.2	43.297	37	1.170	21	12L
WISE 0906+4735	136.704848	3.5	47.593343	3.6	48.4 ± 3.4	1.5 ± 0.2	−545.9 ± 1.2	−709.6 ± 1.2	19.197	15	1.280	10	15L
WISE 0914−3459	138.537222	7.4	−34.994793	7.0	45.2 ± 4.2	1.1 ± 0.2	−19.7 ± 2.2	175.9 ± 2.2	12.900	9	1.433	7	30H
WISE 0940−2208	145.083635	7.3	−22.138988	7.7	38.1 ± 4.7	1.3 ± 0.3	−144.9 ± 2.3	171.2 ± 2.3	5.652	9	0.628	7	14H
WISE 0943+3607	145.775825	2.6	36.122729	2.7	93.8 ± 2.8	1.8 ± 0.9	675.1 ± 1.3	−498.9 ± 1.4	68.309	37	1.846	21	9L
WISE 0952+1955	148.247005	5.1	19.918980	3.7	41.1 ± 3.9	1.4 ± 0.2	−34.4 ± 1.6	−32.1 ± 1.2	18.487	15	1.232	10	13L
WISE 1018−2445	154.533566	4.0	−24.766900	4.0	83.6 ± 3.6	1.0 ± 0.3	54.3 ± 1.3	−821.4 ± 1.3	9.697	13	0.746	9	23L
WISE 1025+0307	156.489211	2.7	3.132060	2.7	85.4 ± 2.5	1.7 ± 0.5	−1199.3 ± 1.4	−144.4 ± 1.3	27.257	31	0.879	18	10H
CFBDS 1028+5654	157.171475	3.2	56.900364	2.8	45.0 ± 2.9	1.4 ± 0.2	200.8 ± 1.5	−12.1 ± 1.4	33.048	33	1.001	19	19L
WISE 1039−1600	159.782034	2.9	−16.000912	2.5	53.4 ± 2.6	1.4 ± 0.4	−189.1 ± 1.5	−119.7 ± 1.2	27.613	35	0.789	20	13H
ULAS 1043+1048	160.980791	9.7	10.800797	6.9	20.8 ± 7.0	1.6 ± 0.3	95.4 ± 3.0	−105.1 ± 2.1	11.428	9	1.270	7	11L
WISE 1050+5056	162.698915	8.0	50.934880	7.4	49.7 ± 5.0	1.8 ± 0.7	−427.5 ± 2.5	−64.0 ± 2.2	26.459	9	2.940	7	15L
WISE 1051−2138	162.875232	3.3	−21.650044	2.8	67.0 ± 3.0	1.1 ± 0.3	137.1 ± 1.5	−156.4 ± 1.3	27.284	31	0.880	18	19L
WISE 1052−1942	163.241771	7.0	−19.714310	5.9	62.3 ± 4.4	1.3 ± 0.4	326.2 ± 2.1	−315.1 ± 1.7	7.594	9	0.844	7	28L
WISE 1055−1652	163.972545	3.0	−16.870933	3.0	72.2 ± 2.7	1.5 ± 0.8	−991.3 ± 1.4	414.9 ± 1.4	28.055	27	1.039	16	13H
WISE 1124−0421	171.158218	3.4	−4.363736	3.2	61.6 ± 3.1	1.5 ± 0.2	−552.4 ± 1.8	67.6 ± 1.4	16.601	31	0.536	18	7H
WISE 1139−3324	174.955011	7.5	−33.407093	7.2	27.0 ± 3.9	1.1 ± 0.3	−97.5 ± 2.3	−51.3 ± 2.2	20.466	11	1.861	8	37L
WISE 1141−3326	175.485224	7.6	−33.443233	8.1	99.7 ± 4.2	1.8 ± 0.8	−904.4 ± 2.3	−76.5 ± 2.5	11.648	11	1.059	8	15H
WISE 1143+4431	175.917700	17.6	44.523342	16.6	38.1 ± 6.5	1.9 ± 0.8	76.9 ± 5.1	−71.0 ± 5.0	7.188	9	0.799	7	10L
WISE 1150+6302	177.558621	3.1	63.044318	2.6	124.5 ± 3.0	1.7 ± 0.5	410.4 ± 1.8	−539.7 ± 1.2	34.761	37	0.939	21	8L
ULAS 1152+1134	178.165841	12.5	11.568698	6.8	49.7 ± 5.1	2.1 ± 0.2	−492.4 ± 3.6	−24.0 ± 2.1	17.856	7	2.551	6	5H
WISE 1206+8401	181.512532	2.8	84.019282	2.4	81.9 ± 2.5	1.3 ± 0.3	−575.0 ± 1.3	−255.7 ± 1.1	44.711	35	1.277	20	19L
WISE 1217+1626AB	184.487872	5.0	16.443394	4.7	104.4 ± 4.7	1.7 ± 0.3	758.1 ± 1.7	−1252.2 ± 1.5	75.092	13	5.776	9	8L
WISE 1220+5407	185.151875	16.9	54.121108	24.9	42.7 ± 7.1	1.6 ± 0.3	192.2 ± 5.6	−310.7 ± 7.8	17.816	9	1.980	7	13L
WISE 1221−3136	185.468474	3.6	−31.599861	2.9	73.8 ± 3.3	1.9 ± 0.6	611.0 ± 1.9	396.7 ± 2.3	17.685	31	0.570	18	6H
WISE 1225−1013	186.495136	2.9	−10.229558	2.9	43.3 ± 3.0	2.1 ± 1.0	−156.6 ± 1.8	−325.5 ± 1.5	47.409	31	1.529	18	10H
2MASS 1231+0847	187.943521	10.3	8.788496	11.7	75.8 ± 4.8	1.7 ± 0.5	−1173.4 ± 3.1	−1034.1 ± 3.5	3.567	11	0.324	8	9L
WISE 1243+8445	190.783116	9.1	84.762718	8.8	48.6 ± 4.5	1.8 ± 0.4	−530.2 ± 2.8	−524.1 ± 2.7	11.855	9	1.317	7	11H
WISE 1254−0728	193.702040	12.0	−7.474752	7.8	47.2 ± 4.4	1.7 ± 1.0	9.0 ± 3.6	−131.3 ± 2.4	13.651	13	1.050	9	15L
WISE 1257+4008	194.316587	19.7	40.148440	15.3	45.7 ± 8.2	1.8 ± 0.8	320.0 ± 5.7	176.5 ± 4.5	7.465	9	0.829	7	10L
VHS 1258−4412	194.520589	6.7	−44.209184	6.7	63.8 ± 4.0	1.3 ± 0.3	143.6 ± 2.3	−150.7 ± 2.2	12.625	9	1.403	7	22H
WISE 1301−0302	195.423510	9.0	−3.037151	7.3	53.8 ± 5.6	1.5 ± 0.4	241.5 ± 2.9	−295.5 ± 2.2	16.300	13	1.254	9	18L
WISE 1318−1758	199.641069	2.6	−17.974000	2.5	57.8 ± 2.7	1.5 ± 0.4	−515.2 ± 1.6	6.8 ± 1.4	61.843	35	1.767	20	11H
WISE 1333−1607	203.249743	8.0	−16.131943	6.0	48.0 ± 4.7	1.4 ± 1.0	−315.3 ± 2.5	−125.7 ± 1.9	11.932	7	1.705	6	14L
WISE 1405+5534	211.322470	3.2	55.572792	2.7	157.9 ± 3.1	2.0 ± 1.1	−2326.5 ± 1.7	236.1 ± 1.3	19.758	33	0.599	19	10H
VHS 1433−0837	218.297357	7.0	−8.626956	4.8	50.9 ± 4.5	1.7 ± 0.6	−284.4 ± 2.4	−204.6 ± 1.8	13.113	13	1.009	9	10H
WISE 1436−1814	219.009079	2.4	−18.239528	2.4	48.3 ± 2.4	1.2 ± 0.3	−67.3 ± 1.3	−86.3 ± 1.3	40.342	37	1.090	21	14H
WISE 1448−2534	222.027086	2.6	−25.573128	2.6	52.5 ± 2.5	1.1 ± 0.3	142.5 ± 1.4	−741.6 ± 1.4	45.332	33	1.374	19	27H
WISE 1501−4004	225.317046	6.8	−40.072132	6.6	69.5 ± 4.0	1.0 ± 0.1	370.2 ± 2.3	−337.3 ± 2.2	22.436	9	2.493	7	39H
WISE 1517+0529	229.337884	6.8	5.491625	6.5	42.1 ± 4.2	1.1 ± 0.2	−55.5 ± 2.3	194.9 ± 2.2	11.812	9	1.312	7	23L
WISE 1519+7009	229.778548	3.0	70.158202	2.7	77.6 ± 2.8	1.5 ± 0.5	325.0 ± 1.5	−501.4 ± 1.2	28.582	33	0.866	19	10H
WISE 1523+3125	230.771352	4.9	31.426572	4.8	61.4 ± 3.8	1.6 ± 0.7	103.9 ± 1.7	−509.2 ± 1.7	10.595	13	0.815	9	15L
WISE 1541−2250	235.464060	2.4	−22.840555	2.3	167.1 ± 2.3	1.1 ± 0.4	−901.2 ± 1.2	−82.4 ± 1.2	42.714	37	1.154	21	31H
WISE 1542+2230	235.557193	6.5	22.501044	5.3	85.6 ± 4.2	1.2 ± 0.3	−974.3 ± 2.2	−391.9 ± 1.8	28.358	13	2.181	9	11L
WISE 1612−3420	243.066007	3.7	−34.341849	3.6	78.3 ± 3.5	0.7 ± 0.1	−289.4 ± 1.2	−586.6 ± 1.2	12.487	13	0.961	9	62H
WISE 1614+1739	243.673390	3.6	17.659388	3.5	97.6 ± 3.4	1.7 ± 0.5	554.5 ± 1.2	−476.7 ± 1.2	5.324	15	0.355	10	10H
2MASS 1615+1340	243.768480	2.5	13.667415	2.4	58.4 ± 2.5	1.3 ± 0.5	291.1 ± 1.4	−325.5 ± 1.3	30.952	35	0.884	20	18H
WISE 1622−0959	245.537284	3.9	−9.992961	3.4	40.2 ± 3.5	1.0 ± 0.2	44.2 ± 1.4	−7.3 ± 1.2	26.773	15	1.785	10	15H
WISE 1639−6847	249.921745	3.0	−68.797280	3.0	211.9 ± 2.7	1.0 ± 0.2	582.0 ± 1.5	−3099.8 ± 1.5	17.158	31	0.553	18	71H
WISE 1653+4444	253.295797	4.1	44.739248	3.9	78.0 ± 4.2	1.4 ± 0.5	−70.7 ± 2.9	−387.3 ± 2.2	12.774	31	0.412	18	13L
WISE 1711+3500AB	257.768950	2.2	35.010157	2.5	40.3 ± 2.4	1.4 ± 0.5	−156.3 ± 1.1	−71.2 ± 1.2	116.848	37	3.158	21	15H
WISE 1717+6128	259.320846	4.5	61.483138	4.0	48.0 ± 3.8	1.6 ± 0.6	81.7 ± 1.4	−30.5 ± 1.3	15.543	13	1.196	9	9H
WISE 1721+1117	260.393469	6.9	11.294412	9.0	42.0 ± 4.0	1.0 ± 0.2	−89.2 ± 2.2	144.5 ± 2.9	5.929	9	0.659	7	22H
WISE 1735−8209	263.963188	6.0	−82.150405	6.2	75.1 ± 4.6	1.3 ± 0.3	−250.2 ± 1.9	−257.8 ± 1.8	16.760	9	1.862	7	11H
WISE 1738+2732	264.648439	2.4	27.549315	2.3	131.0 ± 2.4	1.2 ± 0.4	337.3 ± 1.1	−338.1 ± 1.1	34.296	39	0.879	22	19H
WISE 1804+3117	271.147014	3.4	31.285122	3.5	62.7 ± 3.4	1.5 ± 0.5	−251.7 ± 1.1	7.0 ± 1.1	20.461	15	1.364	10	22H
WISE 1812+2007	273.179657	3.8	20.128953	4.5	47.8 ± 4.0	0.9 ± 0.1	0.7 ± 0.6	−534.4 ± 1.5	17.409	11	1.583	8	34H
WISE 1813+2835	273.372052	2.6	28.591745	2.6	74.9 ± 2.5	1.0 ± 0.2	−204.7 ± 1.3	−462.4 ± 1.3	22.237	33	0.674	19	31H
WISE 1828+2650	277.130718	2.2	26.844010	2.2	100.7 ± 2.3	1.0 ± 0.2	1017.5 ± 1.0	174.5 ± 1.0	32.475	39	0.833	22	38H
WISE 1928+2356	292.171905	2.5	23.934871	2.6	149.9 ± 2.4	0.4 ± 0.1	−241.5 ± 1.3	243.1 ± 1.3	77.458	33	2.347	19	374H
WISE 1955−2540	298.752056	2.5	−25.670762	2.5	36.6 ± 2.4	1.1 ± 0.3	349.8 ± 1.2	−248.3 ± 1.2	49.674	31	1.602	18	43H
WISE 1959−3338	299.773590	2.2	−33.642914	2.2	85.3 ± 2.2	1.1 ± 0.3	−8.6 ± 1.0	−193.2 ± 1.1	29.136	39	0.747	22	28H
WISE 2000+3629	300.209091	2.6	36.497627	2.7	133.1 ± 2.5	1.2 ± 0.3	9.4 ± 1.3	377.9 ± 1.2	16.485	35	0.471	20	343H
WISE 2005+5424	301.333016	3.7	54.408501	3.7	62.9 ± 3.3	1.1 ± 0.2	−1154.4 ± 1.2	−900.4 ± 1.2	16.282	15	1.085	10	41H
WISE 2015+6646	303.942603	2.7	66.779477	2.8	43.1 ± 2.7	1.3 ± 0.5	290.0 ± 1.3	428.3 ± 1.6	35.701	29	1.231	17	17H
WISE 2017−3421	304.453417	6.2	−34.350581	8.3	46.9 ± 4.1	1.2 ± 0.3	192.1 ± 1.9	291.8 ± 2.6	7.140	9	0.793	7	13H
WISE 2019−1148	304.836805	3.9	−11.802130	3.9	77.5 ± 3.5	1.1 ± 0.3	354.2 ± 1.3	−48.3 ± 1.3	11.785	13	0.907	9	16H
WISE 2056+1459	314.121286	2.2	14.998666	2.2	138.3 ± 2.2	1.1 ± 0.4	823.2 ± 1.0	534.1 ± 1.0	40.728	39	1.044	22	52H
WISE 2147−1029	326.778366	4.8	−10.490200	6.8	42.8 ± 4.0	1.3 ± 0.5	89.0 ± 1.5	−135.0 ± 2.0	25.841	11	2.349	8	22L
WISE 2157+2659	329.464040	2.2	26.991920	2.2	59.7 ± 2.2	1.2 ± 0.4	69.6 ± 1.1	−92.2 ± 1.1	32.509	39	0.834	22	31H
WISE 2159−4808	329.956825	2.7	−48.149927	2.5	75.7 ± 2.7	1.2 ± 0.4	316.6 ± 1.4	−1229.8 ± 1.3	36.665	37	0.991	21	22L
WISE 2203+4619	330.769173	12.8	46.322939	13.1	66.0 ± 4.2	0.4 ± 0.1	1284.9 ± 4.4	−270.3 ± 4.3	16.600	11	1.509	8	79H
WISE 2209−2734	332.341272	3.6	−27.578140	5.2	78.2 ± 3.9	2.1 ± 1.2	−781.0 ± 2.4	−430.9 ± 1.9	18.028	37	0.487	21	5L
WISE 2209+2711	332.275276	2.3	27.194171	2.3	161.6 ± 2.4	1.4 ± 0.5	1204.4 ± 1.1	−1357.5 ± 1.1	38.925	37	1.052	21	17H
WISE 2211−4758	332.918711	9.1	−47.974160	8.7	55.8 ± 4.6	1.6 ± 0.3	−117.6 ± 2.8	−50.4 ± 2.6	5.445	9	0.605	7	10H
WISE 2212−6931	333.070499	2.4	−69.522650	2.5	81.9 ± 2.5	1.1 ± 0.4	784.4 ± 1.2	−54.6 ± 1.2	84.780	35	2.422	20	39L
WISE 2220−3628	335.230876	2.4	−36.471641	2.5	97.0 ± 2.4	2.0 ± 0.6	286.8 ± 1.2	−81.4 ± 1.2	47.403	35	1.354	20	14H
WISE 2232−5730	338.019424	6.6	−57.503027	6.5	49.9 ± 4.4	1.3 ± 0.5	405.5 ± 2.0	−102.6 ± 1.9	12.625	11	1.148	8	15L
WISE 2237+7228	339.334691	2.6	72.476000	2.5	62.3 ± 2.5	1.0 ± 0.2	−80.2 ± 1.3	−97.7 ± 1.3	22.397	31	0.722	18	24H
WISE 2255−3118	343.920079	4.7	−31.311886	6.9	70.7 ± 4.2	1.5 ± 0.4	300.2 ± 1.5	−162.1 ± 2.2	16.157	15	1.077	10	11L
WISE 2301+0216	345.388795	3.4	2.276363	3.1	53.0 ± 2.8	1.4 ± 0.3	−82.6 ± 1.6	−88.9 ± 1.6	41.625	29	1.435	17	14L
WISE 2302−7134	345.619196	7.9	−71.578222	6.2	65.1 ± 4.7	1.3 ± 0.6	−106.3 ± 2.4	30.7 ± 2.0	7.049	9	0.783	7	35L
WISE 2313−8037	348.403564	2.8	−80.617175	2.6	93.5 ± 2.7	1.0 ± 0.2	275.1 ± 1.3	−402.2 ± 1.2	23.801	31	0.768	18	35L
WISE 2319−1844	349.913188	3.1	−18.734474	3.1	79.2 ± 3.1	1.5 ± 0.5	65.5 ± 1.6	138.8 ± 1.6	47.327	37	1.279	21	6L
ULAS 2321+1354	350.349333	2.4	13.914238	2.7	83.6 ± 2.4	1.6 ± 0.5	78.7 ± 1.2	−561.6 ± 1.4	25.489	39	0.654	22	12H
ULAS 2326+0201	351.502016	7.1	2.027545	7.8	49.5 ± 4.6	1.5 ± 0.6	299.8 ± 2.2	80.4 ± 2.4	13.197	9	1.466	7	22L
WISE 2332−4325	353.110751	2.4	−43.419959	2.7	65.3 ± 2.6	2.0 ± 0.6	249.7 ± 1.2	−249.9 ± 1.5	46.217	37	1.249	21	10H
WISE 2343−7418	355.965092	2.8	−74.312845	2.4	58.8 ± 2.7	1.7 ± 0.6	380.9 ± 1.4	192.5 ± 1.2	20.757	33	0.629	19	13H
WISE 2344+1034	356.193582	4.1	10.570956	3.9	64.7 ± 3.7	1.6 ± 0.6	942.1 ± 1.4	−23.9 ± 1.3	41.041	13	3.157	9	18L
WISE 2354+0240	358.512041	8.4	2.670263	8.8	124.1 ± 4.9	1.9 ± 0.9	491.1 ± 2.8	−393.1 ± 3.0	14.458	9	1.606	7	16L
WISE 2357+1227	359.318798	7.6	12.460976	9.9	59.5 ± 4.1	1.5 ± 0.4	24.0 ± 2.6	−500.5 ± 3.2	11.415	9	1.268	7	19L

Note.

^aThe letter following the number of re-registration stars indicates whether we used the high-S/N ("H") or low-S/N ("L") limit for their selection. See Section 5.2.2 for details.

Download table as:  ASCIITypeset images: 1 2 3 4

We are measuring parallaxes relative to re-registration stars in each field, so we need to account for the fact that those re-registration stars themselves each have a small parallax that is partially damping the parallactic signal of our target. In order to correct for this, we need estimates of the mean distance to the re-registration stars. To do this, we tabulated the stars' J-band magnitudes measured from the 2MASS All-Sky Point Source Catalog, supplemented in some cases by the 2MASS Survey Point Source Reject Table. The distance to each object is then estimated by comparing that magnitude to a model prediction of Galactic structure for that region of sky, as provided by Mendez & van Altena (1996). For fields where 2MASS J magnitudes were available for all re-registration stars, we found that the correction was very small and varied from 0.4 to 2.2 mas. For some fields, not all of our re-registration stars were detected by 2MASS, so these stars were assigned a floor value for J = 17.0. To test whether this is a reasonable assumption, we chose WISE 0032−4946 because 5 of its 13 re-registration stars have no 2MASS mags. Setting all five of these to have J = 17.0 mag gives a correction of 1.4 ± 0.3 mas. If we instead set all five to an absurdly faint value of J = 19.0 mag, we find a correction of 1.1 ± 0.6 mas. Because these two assumptions give corrections that are essentially identical within the error bars and the former is likely more realistic, we assumed a floor of J = 17.0 mag (or J = 16.5 mag in fields of higher source density) for all 2MASS undetected sources. Plots of our astrometric measurements and their best fits are shown in Figure 2.

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View figure set (142 panels)

Tarball of figure set images

We note from Table 4 that most of our objects have values of reduced χ² near 1.0, confirming that our methodology for measuring the astrometric uncertainties per epoch is sound. This enables us to identify targets for which either our centroiding is poor because a marginally resolved companion creates a profile not well fit by our PRF, or our single-object solution is a poor assumption due to the presence of an unseen companion. Objects with fits having reduced χ² values >2 have been placed on continued monitoring with Spitzer through the end of Cycle 14 to see if any cyclical variations in the residuals, indicative of an unseen astrometric companion, can be found. These and other targets of interest are discussed in Section 8.2.

By design, most of the T dwarfs in our parallax program were selected for observation because they were not being targeted by other ground- or space-based programs. On the other hand, all known Y dwarfs were targeted regardless of whether they had parallaxes measured elsewhere. As a result, only 31 of the 142 objects for which we have Spitzer-measured parallaxes have previously measured values. Figure 3 compares our values to those in the literature for these 31 objects. Three comparison data points fall outside of the boundaries of this plot, but those are attributed to poor measurements in the literature: WISE 0146+4234 and WISE 2220−3628 from Beichman et al. (2014), which are discrepant from our values by ∼9σ, and WISE 1541−2250 from Dupuy & Kraus (2013), which is discrepant from our value by ∼20σ. These literature values are also discrepant with other published values; see the analyses of WISE 2220−3628 in Martin et al. (2018), WISE 1541−2250 in Martin et al. (2018) and Bedin & Fontanive (2018), and WISE 0146+4234 in Leggett et al. (2017).

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We find excellent agreement between our values and ground-based Magellan/FourStar measurements by Tinney et al. (2014), between our values and ground-based United Kingdom Infrared Telescope (UKIRT)/WFCAM measurements by Smart et al. (2017), and between our values and Spitzer/IRAC ch2 measurements by Leggett et al. (2017), some data for which had been published earlier in Luhman & Esplin (2016) and which uses a subset of the Spitzer/IRAC ch2 imaging taken by us. With the exception of the two objects noted above, we also find excellent agreement with a hybrid approach from Beichman et al. (2014) that uses astrometry compiled from Keck/NIRC2, Hubble Space Telescope (HST)/WFC3, WISE, and Spitzer/IRAC.

We can also compare the parallax measurements for objects in common between this paper and Martin et al. (2018). The latter paper uses a subset of the same Spitzer/IRAC ch2 data used in the current paper, but there are a few differences to note: (1) the current paper uses measurements taken from individual frames as opposed to the Martin et al. (2018) method of using measurements from the epochal coadds, (2) the current paper uses a different set of analysis code following the MOPEX frame extraction step, even though the guiding logic is very similar, and (3) the current paper benefits from the longer time baseline afforded by the additional observations in Cycle 13. Of the 22 objects in common between the two papers, 4 have differences exceeding three times the sum of the individual uncertainties. Two of these objects, WISE 0535−7500 and WISE 0647−6323, are located near the Continuous Viewing Zone of Spitzer and thus have frames taken at many different roll angles, where the aforementioned issue with the MOPEX mosaicking step (Section 5.2.1) is known to have problems. A comparison of the parallax-only plots for these two objects (Figure 2, upper right panels) show individual measurements with much smaller uncertainties and a more convincing overall fit than do similar plots in Martin et al. (2018, their Figure 5). For the other two objects—WISE 0825+2805 and WISE 1639−6847—the improved astrometry provided by individual frame measurements along with the added time baseline (an additional three years) appears to have vastly improved the fits and as a consequence moved them significantly from the parallax values determined by Martin et al. (2018).

Just as both Smart et al. (2017) and Martin et al. (2018) found, we see a systematic offset between our values and the parallaxes measured by Dupuy & Kraus (2013), who used Spitzer/IRAC ch1 imaging. Martin et al. (2018) advanced three hypotheses to attempt to explain the discrepancy: (1) chromatic distortion in the ch1 data, (2) a fundamental error in the Dupuy & Kraus (2013) fitting analysis, or (3) an insufficient time baseline with which to beat down random errors and to disentangle proper motion and parallax. Despite testing each of these hypotheses, Martin et al. (2018) were unable to come to a firm conclusion.