THE ALLWISE MOTION SURVEY AND THE QUEST FOR COLD SUBDWARFS

The AllWISE time baseline is typically between six months and a year for any point on the sky. Except for ecliptic polar regions, the time sampling will be confined to discrete epochs separated by roughly six months. Multiple measurements, spanning the range of a few days, are taken at each epoch. Most of the sky has two epochs covering six months, and ∼20% of the sky has three epochs spanning a time range of one year.

It is important to understand what this time sampling means for motion measurements. In general, it is the closest objects to the Sun that exhibit the largest proper motions. Being close, these objects will also exhibit substantial parallax. Because data are taken near 90° solar elongation, WISE observed these objects at their maximum parallax factors. As an example, an object seen at two WISE epochs will have motion that is a combination of half its yearly proper motion (because the two epochs are only separated by six months) and twice its parallax (because the vantage point between epochs has shifted by 2 AU). Having only two epochs, AllWISE cannot disentangle the effects of parallax and proper motion and thus measures only apparent motion on the sky as opposed to proper motion.

Figure 1 (top panel) shows the individual Level 1b frame measurements of the position of the nearby L+T dwarf binary WISE J104915.57−531906.1. This source has three epochs of coverage in AllWISE. The motion is not linear because this binary's parallax (π = 050) and proper motion (μ = 278 yr⁻¹) are comparable in size (Luhman 2013). It would be possible to measure the proper motion by using only the epoch 1 and epoch 3 points, since these clusters of points were taken at the same parallax factor; however, AllWISE uses data from all three epochs and thus will measure a motion that is not the actual "proper" motion. The extreme M subdwarf LHS 161 in Figure 1 (bottom panel) demonstrates a case at the opposite extreme, where the parallax is swamped by a much larger proper motion (π = 0025 and μ = 1455 yr⁻¹; van Altena et al. 1995). As expected for this case, the three separate epochs of data more closely follow a linear progression in time.

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This can be further demonstrated with a couple of examples drawn from areas with two-epoch coverage, which represents the majority of WISE data. Figure 2 shows the predicted path of the white dwarf LHS 239 on the sky, and Figure 3 shows the path for the T dwarf Gliese 570 D. In each of these plots, the gray track shows the predicted path of the object from the date of the first WISE epoch to a date one year later. The date of the second (i.e., final) WISE epoch, approximately six months after the first, is also noted. The motion that AllWISE measures is the positional difference between the start of the track and the point six months later, whereas the true proper motion would be that measured between the start of the track and the point twelve months later. The true proper motion and parallax, the predicted motion from AllWISE, and the actual AllWISE values are given in the legend of both figures. Note that the actual AllWISE measurements are, within their errors, identical to the predicted values, although not necessarily close to the true proper motion measures. As stated earlier, these AllWISE measurements should be regarded as apparent motion values (parallax + proper motion) and not as pure proper motion values.

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Figure 4 illustrates the predicted sky path for the K dwarf Gliese 554, located in an area with three epochs of coverage. In this case, the WISE data fall almost perfectly along the proper motion vector. It would be expected that the AllWISE motion measure would be very close to the true proper motion value, which is indeed the case. It should be noted that a measurement using only epoch 1+2 data would have a larger motion than a measurement using only epoch 2+3 data, although both would have the correct position angle.

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Because the AllWISE-measured motions do not decouple proper motion and parallax, these motions cannot be used to predict source positions at other epochs. Rather, their utility is in identifying potentially interesting, nearby objects for further follow-up.

3.2.1. What is the Largest Motion Measurable?

AllWISE is able to identify objects with very high motion. Table 1 lists the 11 highest proper motion systems known (μ > 46 yr⁻¹) and compares their published proper motions to the motions derived by AllWISE. Most of these sources are extremely bright and heavily saturated on the WISE detectors. Agreement between published values and those in AllWISE is not expected due both to saturation effects and to parallax. Nonetheless, the comparison shows that the highest motion stars can be identified as such in AllWISE data.

Table 1. Motion Comparisons for the Eleven Highest Proper Motion Systems Known

Object Name	Sp. Type	AllWISE	AllWISE	AllWISE	AllWISE	Published μα	Published μδ	Published π	Ref.
		Designation	W1	R.A. Motion	Decl. Motion	(mas yr−1)	(mas yr−1)	(mas)
			(mag)	(mas yr−1)	(mas yr−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
Barnard's Star	M5 V	WISEA J175747.94+044323.8	5.02	−1630 ± 71	13703 ± 65	−798.58 ± 1.72	10328.12 ± 1.22	548.31 ± 1.51	1, 9
Kapteyn's Star	sdM1p	WISEA J051146.81−450204.5	4.92	8166 ± 29	−8065 ± 32	6505.08 ± 0.98	−5730.84 ± 0.96	255.66 ± 0.91	3, 9
Groombridge 1830	G7 V+	WISEA J115302.28+374206.6	4.33	2224 ± 59	−14307 ± 66	4003.98 ± 0.37	−5813.62 ± 0.23	109.99 ± 0.41	4, 9
Lacaille 9352	M2 V	WISEA J230557.86−355057.2	2.59	1866 ± 56	−841 ± 60	6768.20 ± 0.59	1327.52 ± 0.68	305.26 ± 0.70	5, 9
CD−37 15492	M3 V	WISEA J000529.35−372151.0	4.40	−471 ± 77	−2662 ± 86	5634.68 ± 0.86	−2337.71 ± 0.71	230.42 ± 0.90	5, 9
61 Cygni A	K5 V	WISEAR J210657.70+384530.8a	0.18	−4028 ± 52	5420 ± 54	4168.31 ± 6.57	3269.20 ± 12.08	286.82 ± 6.78	1, 9
61 Cygni B	K7 V	WISEA J210658.89+384504.5	0.97	−1171 ± 58	215 ± 66	4106.90 ± 0.32	3144.68 ± 0.44	285.88 ± 0.54	1, 9
Ross 619	M4 V	WISEA J081158.31+084529.4	7.18	1661 ± 34	−5277 ± 32	1081.4 ± 1.6	−5087.3 ± 1.6	145.5 ± 3.9	2, 11
Teegarden's Star	M6.5 V	WISEA J025303.34+165213.2	7.15	3471 ± 56	−3666 ± 25	3403.8 ± 2.2	−3807.0 ± 2.2	260.63 ± 2.69	6, 10
Lalande 21185	M2 V	WISEA J110319.67+355722.4	2.47	338 ± 50	786 ± 48	−580.27 ± 0.62	−4765.85 ± 0.64	392.64 ± 0.67	1, 9
Ind A	K2 V	WISEA J220326.69−564735.5	0.87	1218 ± 32	−26 ± 36	3960.93 ± 0.24	−2539.23 ± 0.17	276.06 ± 0.28	8, 9
Ind BaBb	T1+T6	WISEA J220415.75−564724.4	10.72	3132 ± 41	−3124 ± 38	3960.93 ± 0.24b	−2539.23 ± 0.17b	276.06 ± 0.28b	7, 9
Wolf 359	M6 V	WISEA J105626.19+070025.0	5.84	−2618 ± 44	−4881 ± 42	−3838.6 ± 0.2	−2697.8 ± 0.2	418.9 ± 2.4	1, 12

Notes. References for spectral type and high-precision astrometry: (1) Kirkpatrick et al. 1991; (2) Henry et al. 1994; (3) Keenan & Pitts 1980; (4) Keenan & Keller 1953; (5) Walker 1983; (6) Teegarden et al. 2003; (7) McCaughrean et al. 2004; (8) van de Kamp 1953; (9) van Leeuwen 2007; (10) Henry et al. 2006; (11) Harrington & Dahn 1980; (12) Harrington et al. 1993. ^a61 Cygni A is the only one of these sources failing to satisfy the criteria for inclusion in the AllWISE Source Catalog. This object is part of a small-separation same-tile (SSST) source group (see Section 3.4.3). Unfortunately, despite best efforts to recover such sources, neither member of the 61 Cyg A SSST group satisfies all the criteria necessary for Catalog consideration. The entry for 61 Cyg A can, however, be found in the AllWISE Reject Table, as the source designation indicates. ^bThe published astrometry for Ind A is used here for Ind BaBb.

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Objects with motions as high as Barnard's Star (104 yr⁻¹) can be successfully recovered with AllWISE, but what is the theoretical limit to the largest motion that AllWISE can measure for a real, astrophysical source? There are sources in the combination of the AllWISE Source Catalog and Reject Table that have single-axis motions as large as 670'' yr⁻¹ (670,000 mas yr⁻¹); spot checks of these sources show them to be artifacts associated with extended structures like diffraction spikes and optical ghosts. Ultimately, the algorithm of χ² minimization is only limited by the detection step on the coadd images; that is, as long as a source is identified on the coadds, extremely large motions can be recovered in the Level 1b images. The only real sources that will not have a coadd detection are those moving so fast that outlier rejection will have eliminated them from the coadd entirely. Real examples of this include main belt asteroids and near-earth objects. Outlier rejection is more likely to eliminate objects seen less than 50% of the time in the frame stack.¹⁶ So it is just possible, in the two-epoch case, for an object near the ecliptic plane moving at ∼2.5 × FWHM between the first and last exposures over one epoch, or 15'' per ∼2 days (∼2700'' yr⁻¹), to have survived coaddition and be detected. For areas of sky with three epochs of coverage, assuming equal numbers of frames per epoch, a source moving at ∼2700'' yr⁻¹ would be seen within a 2.5 × FWHM window only 33% of the time, and would thus be removed from the coadd because it fails to meet the 50% outlier threshold. For such a three-epoch case, the motion limit is more likely to be ∼2.5 × FWHM between two consecutive epochs, or ∼15'' per 6 months (∼30'' yr⁻¹).

3.2.2. What is the Smallest Motion Measurable?

Figure 5 shows the motion measurement uncertainties for sources in a typical AllWISE Atlas Image plotted against W1 magnitude. Bright sources free of saturation effects (8 < W1 < 10 mag) approach an asymptote of ∼0035 yr⁻¹ in their per-axis errors. Requiring a 3σ detection per axis means that the smallest significant motion¹⁷ that is measurable is ∼015 yr⁻¹. At fainter magnitudes, the smallest measurable significant motion increases dramatically as the minimum motion errors themselves increase. At W1 = 15 mag, for example, the motion errors are roughly 10 × larger, meaning that the smallest measurable significant motion is ∼15 yr⁻¹.

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The Atlas Image used in this example, 2243m213_ac51, has an average depth of coverage of ∼24 framesets, as is typical of Atlas Tiles located near the ecliptic plane and observed at two WISE epochs. Atlas Tiles farther from the ecliptic will have greater coverage depths. For these cases, and for any Tiles with three WISE epochs, motion limits will be even smaller than those quoted above.

Despite the fact that AllWISE measures an apparent motion over only a short time baseline, these measurements can still be compared to proper motion values determined for stars specifically targeted in astrometric monitoring campaigns as long as the sample size is statistically significant and scattered over the entire sky so that the influence of parallax is suppressed. In the first subsection below, the AllWISE motion measurements are compared to published proper motion values for an all-sky collection of late-type dwarfs. In the second subsection, the internal repeatability of the AllWISE measurements is checked using the individual components of widely separated common-proper-motion binary systems.

3.3.1. External Comparisons Using Previously Known Motion Objects

A typical user of the AllWISE data products may wish to check how the AllWISE measurements compare to published values from a favorite motion catalog. As demonstrated in Section 3.1, parallax contributes to the AllWISE motion measurements, making a direct comparison difficult. Are other statistical effects seen when a large sample is used? To this end, the AllWISE measurements have been compared to published astrometry for a set of known low-mass stars and brown dwarfs. These objects were selected because they have high signal-to-noise ratios in one or more WISE bands but are generally not saturated. Specifically, objects in the Database of Ultracool Parallaxes,¹⁸ compiled as of 2013 October, were used (Dupuy & Liu 2012). This list contains proper motions for all late-M, L, T, and Y dwarfs that have published parallaxes. After excluding close binaries and blends, 233 objects were available for comparison. Figure 6 shows a comparison of the published values of μ_α, μ_δ, and μ_Total to the R.A., Decl., and total motions measured by AllWISE. The overall agreement is excellent, with the trend very closely following the line of one-to-one correspondence.

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The influence of parallax on the AllWISE motion measurements can be seen in Figure 7. In this figure, the difference between the published proper motions and the AllWISE motions shows a larger dispersion in R.A. than in Decl., and both dispersions are larger than would be expected based on the average AllWISE motion errors, which are 122.3 mas and 129.4 mas for R.A. and Decl., respectively. As shown in Figure 8, which illustrates the motion differences in R.A. and Decl. plotted as a function of parallax, the R.A. differences have a striking dependence on parallax (i.e., objects with the largest differences tend to have the largest parallax values) while the Decl. differences show only a modest increase at the largest parallaxes. Because the ecliptic and equatorial systems are tilted with respect to each other by only ∼23 degrees, parallactic motion, which is primarily manifested in ecliptic longitude, affects equatorial longitude (R.A.) more severely than equatorial latitude (Decl.). Other than this effect, no other issues are seen, as the R.A. and Decl. differences show a mean near zero and have no appreciable skew.

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Figure 9 shows the motion difference plotted as a function of W2 mag, which for most L, T, and Y dwarfs is the WISE band with the highest signal-to-noise ratio and thus the band driving the astrometry. Agreement is best in the range 7 < W2 < 12 mag. Astrometric precision is degraded at brighter magnitudes (W2 < 7 mag) because such objects have saturated image cores, and it quickly degrades at fainter magnitudes (W2 > 12 mag) due to poorer photon counting statistics.

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3.3.2. Internal Consistency Checks Using Common-proper-motion Binaries

As part of AllWISE Quality Assurance checks, the software reported sources in each Atlas Tile that had a high likelihood of being real motion stars. (See Section 3.4 below.) During the course of quality assessment, reviewers noted 55 pairs of objects identified as having significant motions and located within ∼15''–400'' of each other. These pairs were checked in SIMBAD and were confirmed to be known common-proper-motion systems, found to be new ones verified through independent means, or identified as possible new pairs based on independent checks. The AllWISE measured motions should be identical for each member of the pair because the common parallax between components will affect the motion measures identically. Therefore, we can use these systems to perform an internal consistency check to see whether AllWISE motion measurements are the same within the errors.

Table 2 lists these fifty-five common-proper-motion binaries and Figure 10 shows the difference in motion between the two members of each pair. The difference is shown per axis, is expressed in units of the larger motion error within the pair, and is plotted as a function of the W1 profile-fit magnitude of the source with the larger motion error. Overall, agreement is very good. The majority of unsaturated pairs has a difference <2 times the error.

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Table 2. Common-proper-motion Binaries Noted During AllWISE Quality Checks

WISEA Designation	W1	W2	AllWISE	AllWISE	Note
	(mag)	(mag)	R.A. Motion	Decl. Motion
			(mas yr−1)	(mas yr−1)
(1)	(2)	(3)	(4)	(5)	(6)
J012655.16+120022.0	9.872 ± 0.022	9.886 ± 0.021	−83 ± 36	−364 ± 33	NLTT 4817, LSPM J0126+1200N
J012654.11+120002.9	12.830 ± 0.023	12.669 ± 0.027	−151 ± 58	−444 ± 56	NLTT 4814, LSPM J0126+1200S (sep 245)
J013054.96+524442.3	7.915 ± 0.027	7.977 ± 0.020	−222 ± 26	22 ± 24	BD+51 318A
J013056.36+524500.8	9.760 ± 0.024	9.658 ± 0.020	−189 ± 25	−40 ± 25	BD+51 318B (sep 225)
J015329.15+732940.2	8.109 ± 0.023	8.058 ± 0.020	420 ± 31	−208 ± 30	LP 29-233, "LHS 6036"
J015326.94+733015.4	9.124 ± 0.023	8.939 ± 0.020	459 ± 32	−130 ± 31	LP 29-232, "LHS 6035" (sep 364)
J021157.87+042140.9	6.955 ± 0.054	7.020 ± 0.020	−155 ± 26	−11 ± 25	BD+03 301, LSPM J0211+0421
J021159.43+042150.7	9.184 ± 0.023	9.080 ± 0.020	−145 ± 26	−80 ± 26	new cpm companiona (sep 253)
J022104.69+365258.7	8.358 ± 0.024	8.180 ± 0.021	768 ± 26	−562 ± 26	GJ 1047AB, LHS 1393
J022102.54+365241.5	9.256 ± 0.023	9.060 ± 0.020	777 ± 27	−549 ± 26	GJ 1047C, LHS 1392 (sep 310)
J025051.72+033035.6	8.852 ± 0.022	8.904 ± 0.019	175 ± 26	−83 ± 25	BD+02 436A, LSPM J0250+0330N
J025051.32+033006.7	9.023 ± 0.022	9.077 ± 0.019	185 ± 26	−56 ± 25	BD+02 436B, LSPM J0250+0330S (sep 295)
J025403.21−355418.7	5.853 ± 0.119	5.731 ± 0.047	523 ± 26	−150 ± 26	LHS 1466
J025402.74−355454.7	8.179 ± 0.022	8.066 ± 0.019	479 ± 24	−143 ± 24	LHS 1467 (sep 364)
J030531.36+114952.8	7.997 ± 0.023	7.863 ± 0.019	165 ± 26	−254 ± 26	G 5-13, LSPM J0305+1149N
J030530.76+114932.1	8.346 ± 0.023	8.249 ± 0.020	157 ± 26	−254 ± 26	G 5-12, LSPM J0305+1149S (sep 226)
J031407.66+083319.0	8.391 ± 0.023	8.433 ± 0.021	303 ± 38	−14 ± 36	G 79-15, LSPM J0314+0833S
J031408.29+083345.6	8.707 ± 0.022	8.702 ± 0.021	275 ± 37	14 ± 36	G 79-16, LSPM J0314+0833N (sep 282)
J031608.21−374158.4	9.565 ± 0.023	9.624 ± 0.020	65 ± 24	51 ± 24	TYC 7561-77-1
J031606.54−374215.4	13.552 ± 0.024	13.341 ± 0.027	55 ± 42	6 ± 42	new cpm companionb (sep 261)
J033528.69−321806.2	9.007 ± 0.023	8.941 ± 0.020	−292 ± 25	−331 ± 24	LP 888-32, LEHPM 3410
J033530.11−321829.1	10.333 ± 0.023	10.146 ± 0.021	−303 ± 26	−306 ± 25	LP 888-33, LEHPM 3411 (sep 291)
J033936.37+252814.8	7.777 ± 0.024	7.698 ± 0.020	377 ± 36	−497 ± 34	Wolf 204, LHS 1573
J033940.66+252842.2	8.007 ± 0.023	7.919 ± 0.021	319 ± 36	−517 ± 35	Wolf 205, LHS 1574 (sep 644)
J035228.33−315026.6	12.741 ± 0.023	12.499 ± 0.023	231 ± 32	−531 ± 32	LHS 1609
J035227.56−315105.2	13.508 ± 0.023	13.254 ± 0.026	189 ± 41	−506 ± 42	new cpm companionc (sep 398)
J043942.59+095215.6	6.464 ± 0.086	6.406 ± 0.023	−24 ± 37	−456 ± 35	G 83-28
J043943.24+095142.9	9.238 ± 0.023	9.077 ± 0.020	14 ± 39	−456 ± 37	G 83-29 (sep 341)
J044349.59−481934.0	5.706 ± 0.130	5.558 ± 0.046	63 ± 37	347 ± 36	LTT 2077
J044350.89−482003.8	9.517 ± 0.023	9.363 ± 0.020	63 ± 31	297 ± 30	new cpm companiond (sep 325)
J051729.18−345346.0	>1.155	>1.308	712 ± 42y	627 ± 39y	o Columbae, CD−35 2214
J051723.88−345121.8	9.724 ± 0.023	9.538 ± 0.019	253 ± 34	−292 ± 33	new cpm companione (sep 1582)
J065438.74+131038.5	3.694 ± 0.394	3.369 ± 0.283	2033 ± 57y	−1035 ± 64y	38 Geminorum AB, HR 2564
J065448.82+131002.5	9.840 ± 0.023	9.664 ± 0.020	250 ± 38	−21 ± 36	new cpm companionf (sep 1516)
J074020.22−172451.5	9.064 ± 0.022	8.831 ± 0.020	1563 ± 34	−628 ± 33	LHS 235
J074021.62−172454.8	12.440 ± 0.023	12.432 ± 0.025	1928 ± 53	−726 ± 54	LHS 234g (sep 203)
J075812.35+875734.7	8.850 ± 0.022	8.681 ± 0.020	−222 ± 28	−536 ± 28	LHS 1962
J075909.31+875742.9	10.207 ± 0.023	10.001 ± 0.020	−238 ± 30	−556 ± 30	LHS 1965 (sep 315)
J082854.03−243541.8	9.308 ± 0.022	9.185 ± 0.021	200 ± 36	−335 ± 36	WT 1549
J082852.10−243536.5	11.881 ± 0.023	11.665 ± 0.022	297 ± 44	−186 ± 46	new cpm companionh (sep 269)
J103734.02+295955.5	10.092 ± 0.023	9.939 ± 0.021	284 ± 38	−84 ± 38	LP 316-395, LSPM J1037+2959N
J103734.43+295937.9	11.153 ± 0.022	10.967 ± 0.022	327 ± 42	−98 ± 42	LP 316-396, LSPM J1037+2959S (sep 184)
J105607.88−575041.1	10.309 ± 0.022	10.164 ± 0.020	−182 ± 25	125 ± 25	UPM J1056−5750
J105536.09−575042.1	10.366 ± 0.023	10.227 ± 0.020	−160 ± 24	152 ± 25	new cpm companioni (sep 2548)
J110604.58+425246.3	10.323 ± 0.023	10.151 ± 0.020	−156 ± 35	−384 ± 36	G 176-13
J110605.07+425303.3	11.361 ± 0.023	11.111 ± 0.021	−84 ± 39	−325 ± 39	G 176-14 (sep 179)
J113333.55−413954.4	8.675 ± 0.023	8.712 ± 0.020	−140 ± 25	−134 ± 25	CD−40 6796
J113333.67−414016.7	10.589 ± 0.024	10.484 ± 0.020	−186 ± 26	−118 ± 26	new cpm companionj (sep 223)
J120907.21+473602.2	9.166 ± 0.023	8.975 ± 0.021	713 ± 35	−349 ± 35	LHS 2516
J120907.24+473531.8	10.036 ± 0.024	9.856 ± 0.020	804 ± 35	−353 ± 35	LHS 2517 (sep 304)
J121058.01−461917.3	6.042 ± 0.097	5.997 ± 0.040	−4 ± 26	169 ± 25	CD−45 7595, LTT 4560
J121058.26−461204.5	8.822 ± 0.022	8.711 ± 0.020	103 ± 25	129 ± 25	new cpm companionk (sep 4328)
J124007.18+204828.9	6.801 ± 0.066	6.837 ± 0.020	250 ± 35	−449 ± 35	G 59-32, BD+21 2442
J124014.80+204752.7	13.020 ± 0.024	12.803 ± 0.026	426 ± 63	−381 ± 67	new cpm companionl (sep 1127)
J124725.86−434353.2	7.850 ± 0.023	7.893 ± 0.019	−165 ± 24	−162 ± 24	LTT 4892, CD−43 7881
J124726.75−434441.8	12.192 ± 0.023	11.997 ± 0.021	−220 ± 30	−138 ± 30	new cpm companionm (sep 495)
J124737.85−274637.3	9.715 ± 0.022	9.568 ± 0.020	−220 ± 27	−15 ± 26	LP 853-37
J124739.94−274642.7	9.849 ± 0.022	9.700 ± 0.020	−154 ± 28	−60 ± 27	LP 853-38 (sep 284)
J125433.93−381122.7	7.951 ± 0.024	8.016 ± 0.020	208 ± 26	−68 ± 26	TYC 7772-1225-1
J125435.54−381111.7	8.175 ± 0.022	8.209 ± 0.019	161 ± 26	−78 ± 26	possible new cpm companionn (sep 220)
J131407.63+061814.3	11.804 ± 0.022	11.790 ± 0.022	−206 ± 33	−294 ± 33	G 62-19, LSPM J1314+0618S
J131408.36+061828.3	12.291 ± 0.022	12.231 ± 0.022	−152 ± 36	−240 ± 36	G 62-20, LSPM J1314+0618N (sep 178)
J134454.85−453518.5	7.547 ± 0.025	7.570 ± 0.019	−304 ± 33	67 ± 32	LTT 5330
J134457.17−453537.2	9.343 ± 0.022	9.160 ± 0.019	−403 ± 35	68 ± 34	new cpm companiono (sep 307)
J140400.30−592400.5	9.363 ± 0.021	9.179 ± 0.020	−44 ± 34	−418 ± 34	L 197-165, NLTT 36089
J140350.20−592348.0	9.371 ± 0.022	9.194 ± 0.020	−76 ± 35	−396 ± 34	new cpm companionp (sep 781)
J140926.79−305551.4	7.772 ± 0.026	7.819 ± 0.021	−496 ± 29	−271 ± 29	LHS 2807
J140924.56−305534.1	8.728 ± 0.023	8.643 ± 0.020	−492 ± 26	−285 ± 25	new cpm companionq (sep 334)
J141509.28+221537.3	8.877 ± 0.022	8.891 ± 0.020	−212 ± 26	129 ± 26	NLTT 36714, LSPM J1415+2215S
J141509.80+221559.8	8.966 ± 0.022	9.042 ± 0.019	−191 ± 26	110 ± 26	NLTT 36716, LSPM J1415+2215N (sep 237)
J142051.70−045805.5	8.348 ± 0.032	8.393 ± 0.029	−76 ± 25	−75 ± 26	BD−04 3668
J142053.60−050137.8	11.003 ± 0.023	10.877 ± 0.020	−185 ± 29	−56 ± 29	new cpm companionr (sep 2142)
J153519.64+174245.2	7.762 ± 0.022	7.597 ± 0.019	−1455 ± 38	34 ± 34	Ross 513A, LHS 399
J153519.45+174302.6	9.316 ± 0.023	9.081 ± 0.020	−1478 ± 36	−82 ± 33	Ross 513B, LHS 400 (sep 176)
J154850.51+175056.1	8.855 ± 0.023	8.781 ± 0.020	−268 ± 36	165 ± 36	G 137-55, LSPM J1548+1750E
J154848.52+175050.0	9.673 ± 0.022	9.525 ± 0.020	−288 ± 37	157 ± 38	G 137-54, LSPM J1548+1750W (sep 291)
J155306.56+344508.8	6.966 ± 0.034	6.877 ± 0.020	158 ± 32	−470 ± 29	LHS 3129
J155306.84+344442.4	8.009 ± 0.023	7.884 ± 0.020	112 ± 32	−479 ± 31	LHS 3130 (sep 266)
J155831.76+572242.3	7.597 ± 0.030	7.674 ± 0.020	133 ± 24	−241 ± 25	G 225-39
J155831.67+572309.1	10.000 ± 0.023	9.823 ± 0.020	143 ± 24	−209 ± 24	G 225-38 (sep 268)
J164836.25+550743.4	7.273 ± 0.030	7.325 ± 0.020	162 ± 25	−269 ± 25	G 226-28
J164835.74+550809.7	8.379 ± 0.023	8.461 ± 0.020	124 ± 26	−258 ± 25	G 226-27 (sep 266)
J165524.66−081930.5	6.588 ± 0.061	6.374 ± 0.022	−1207 ± 42	−764 ± 40	LHS 427
J165534.68−082349.7	8.619 ± 0.023	8.393 ± 0.020	−1388 ± 37	−781 ± 35	LHS 429, vB 8 (sep 2989)
J170428.76+034342.7	8.570 ± 0.022	8.586 ± 0.020	−408 ± 37	−196 ± 36	G 19-10
J170428.57+034422.7	8.587 ± 0.023	8.648 ± 0.020	−346 ± 37	−170 ± 37	G 19-11 (sep 401)
J171828.99−224630.2	9.217 ± 0.024	9.056 ± 0.020	−270 ± 43	−138 ± 39	new cpm systems
J171826.98−224543.5	9.424 ± 0.023	9.313 ± 0.019	−327 ± 42	−52 ± 40	new cpm systems (sep 543)
J172230.07−695119.2	8.336 ± 0.023	8.243 ± 0.020	−236 ± 40	−221 ± 36	possible new cpm systemt
J172237.14−695112.2	11.426 ± 0.023	11.259 ± 0.021	−81 ± 51	−308 ± 50	possible new cpm systemt (sep 543)
J182000.63−522138.6	9.244 ± 0.023	9.170 ± 0.020	125 ± 39	−308 ± 38	L 272-87, NLTT 46256
J182001.39−522200.7	9.512 ± 0.023	9.399 ± 0.020	151 ± 38	−385 ± 38	L 272-88, NLTT 46257 (sep 231)
J182038.54+404836.0	11.156 ± 0.023	11.047 ± 0.020	−202 ± 39	−264 ± 42	NLTT 46342, LSPM J1820+4048N
J182038.57+404759.2	11.774 ± 0.023	11.609 ± 0.020	−188 ± 41	−274 ± 46	NLTT 46343, LSPM J1820+4048S (sep 369)
J185252.01−570745.3	7.473 ± 0.032	7.462 ± 0.020	−368 ± 35	−836 ± 34	LHS 3421
J185257.45−570821.9	10.804 ± 0.024	10.620 ± 0.020	−466 ± 41	−847 ± 41	2MASS J18525777−5708141 (sep 574)
J190250.67−755058.1	10.928 ± 0.023	10.768 ± 0.021	−13 ± 38	−225 ± 38	SCR J1902−7550A
J190254.95−755110.8	12.353 ± 0.023	12.135 ± 0.023	87 ± 51	−375 ± 56	SCR J1902−7550B (sep 225)
J201605.71−115838.5	8.778 ± 0.022	8.629 ± 0.019	−258 ± 39	−230 ± 37	new cpm systemu
J201605.96−115916.7	8.897 ± 0.022	8.746 ± 0.019	−197 ± 40	−202 ± 38	new cpm systemu (sep 383)
J205103.71−013357.8	9.639 ± 0.023	9.611 ± 0.019	−285 ± 41	−168 ± 40	Wolf 885, NLTT 50000
J205103.50−013342.6	10.248 ± 0.023	10.136 ± 0.019	−310 ± 43	−179 ± 41	Wolf 884, NLTT 49999 (sep 156)
J210630.56−382606.1	12.874 ± 0.023	12.599 ± 0.026	156 ± 67	−530 ± 69	new cpm systemv
J210632.73−382640.4	12.992 ± 0.023	12.717 ± 0.025	40 ± 70	−577 ± 71	new cpm systemv (sep 427)
J214737.18−135422.0	9.809 ± 0.023	9.798 ± 0.020	156 ± 41	−260 ± 42	Ross 208
J214736.41−135335.4	11.575 ± 0.023	11.464 ± 0.021	164 ± 51	−468 ± 50	new cpm companionw (sep 480)
J230213.97+801412.0	6.683 ± 0.071	6.704 ± 0.022	−73 ± 27	168 ± 28	BD+79 762
J230226.16+801241.8	9.417 ± 0.023	9.278 ± 0.020	−108 ± 29	290 ± 30	new cpm companionx (sep 953)
J231049.97+453041.3	5.245 ± 0.174	5.107 ± 0.072	−864 ± 54y	331 ± 55y	HD 218868, LTT 16813, WDS 23108+4531A
J231054.77+453043.5	9.690 ± 0.023	9.515 ± 0.021	−200 ± 36	−396 ± 35	WDS 23108+4531C (sep 505)

Notes. ^aWISEA J021159.43+042150.7: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−140.5  ±  10.2, −65.8  ±  9.3) mas yr⁻¹ for this object. The other component, BD+03 301, has a published motion of (−144.70  ±  1.64, −78.66  ±  1.18) mas yr⁻¹ (van Leeuwen 2007). These motions are identical within their 2σ errors, so this is likely a common-proper-motion system. ^bWISEA J031606.54−374215.4: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (48.0  ±  11.3, 36.3  ±  10.4) mas yr⁻¹ for this object. The other component, TYC 7561-77-1, has a published motion of (57.4  ±  2.2, 30.6  ±  2.1) mas yr⁻¹ (Høg et al. 2000). Although small, these motions are identical within their 1σ errors, so this is likely a common-proper-motion system. ^cWISEA J035227.56−315105.2: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (196.6  ±  11.0, −531.9  ±  10.4) mas yr⁻¹ for this object. The other component, LHS 1609, has a published motion of (219, −533) mas yr⁻¹ (Luyten 1979a). These motions are identical to within 2σ, so this is likely a common-proper-motion binary. ^dWISEA J044350.89−482003.8: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−5.5  ±  9.0, 263.4  ±  8.8) mas yr⁻¹ for this object. The other component, LTT 2077, has a published motion of (4.75  ±  0.37, 276.85  ±  0.43) mas yr⁻¹ (van Leeuwen 2007). These motions are identical to within 2σ, so this is likely a common-proper-motion binary. ^eWISEA J051723.88−345121.8: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (86.7  ±  8.2, −340.4  ±  8.0) mas yr⁻¹ for this object. The other component, o Columbae, has a published motion of (92.67  ±  0.14, −336.23  ±  0.22) mas yr⁻¹ (van Leeuwen 2007). These motions are identical within their 1σ errors, so this is very likely a common-proper-motion system. ^fWISEA J065448.82+131002.5: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (63.7  ±  9.2, −86.2  ±  8.8) mas yr⁻¹ for this object. The other component, 38 Geminorum AB, has a published motion of (68.48  ±  1.78, −72.98  ±  1.46) mas yr⁻¹ (van Leeuwen 2007). These motions are identical within their 2σ errors, so this is likely a common-proper-motion system. ^gWISEA J074021.62−172454.8: This object falls in a tile overlap region, so it was processed twice by AllWISE. The apparition chosen for inclusion in the AllWISE Source Catalog, whose values are listed in the table above, was selected over the other apparition because the former is further from the tile edge. The other apparition, which appears in the AllWISE Reject Table as WISEAR J074021.62−172454.8, has motion values of 1563 ± 50 mas yr⁻¹ and −608 ± 52 mas yr⁻¹ in R.A. and Decl., respectively. The values for the AllWISE Reject source are <1σ discrepant from either apparition of the primary, LHS 235. Because the same underlying frames are used for both tiles, it is unclear why the motion for one of the apparitions of LHS 234 is so wildly discrepant in R.A. ^hWISEA J082852.10−243536.5: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (157.6  ±  10.8, −137.5  ±  10.7) mas yr⁻¹ for this object. The other component, WT 1549, has a published motion of (151  ±  13, −140  ±  13) mas yr⁻¹ (Wroblewski & Torres 1996). These motions are identical within their 1σ errors, so this is very likely a common-proper-motion system. ⁱWISEA J105536.09−575042.1: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−196.5  ±  9.3, 128.2  ±  9.3) mas yr⁻¹ for this object. The other component, UPM J1056−5750, has a published motion of (−194.4  ±  7.4, 121.9  ±  6.9) mas yr⁻¹ (Finch et al. 2010). These motions are identical within their 1σ errors, so this is very likely a common-proper-motion system. ^jWISEA J113333.67−414016.7: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−152.9  ±  9.2, −120.1  ±  8.5) mas yr⁻¹ for this object. The other component, CD−40 6796, has a published motion of (−169.7  ±  1.9, −117.3  ±  1.7) mas yr⁻¹ (Høg et al. 2000). These motions are identical within their 2σ errors, so this is likely a common-proper-motion system. ^kWISEA J121058.26−461204.5: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (101.3  ±  8.3, 167.7  ±  8.1) mas yr⁻¹ for this object. The other component, CD−45 7595, has a published motion of (89.11  ±  0.40, 168.15  ±  0.47) mas yr⁻¹ (van Leeuwen 2007). These motions are identical within their 2σ errors, so this is likely a common-proper-motion system. ^lWISEA J124014.80+204752.7: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (205.6  ±  10.6, −369.1  ±  10.8) mas yr⁻¹ for this object. The other component, BD+21 2442, has a published motion of (202.04  ±  1.44, −368.45  ±  0.99) mas yr⁻¹ (van Leeuwen 2007). These motions are identical within their 1σ errors, so this is very likely a common-proper-motion system. ^mWISEA J124726.75−434441.8: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−182.0  ±  7.1, −95.4  ±  7.1) mas yr⁻¹ for this object. The other component, CD−43 7881, has a published motion of (−196.60  ±  0.80, −94.31  ±  0.89) mas yr⁻¹ (van Leeuwen 2007). These motions are identical within their 2σ errors, so this is likely a common-proper-motion system. ⁿWISEA J125435.54−381111.7: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (161.1  ±  7.9, −25.4  ±  7.8) mas yr⁻¹ for this object. The other component, TYC 7772-1225-1, has a published motion of (149.6  ±  2.8, −40.1  ±  2.7) mas yr⁻¹ (Høg et al. 2000). These motions are identical to within 2σ, so this could be a common-proper-motion binary. In the UCAC4 Catalog this pair has listed motions of (147.6  ±  0.7, −38.2  ±  1.0) mas yr⁻¹ for the brighter component and (144.5  ±  0.8, −29.0  ±  0.8) mas yr⁻¹ for the fainter component. Although the 10σ discrepancy in Decl. would seem to rule these out as a cpm pair, UCAC4 measurements can be unreliable and thus we still list this pair as a possible physical system. ^oWISEA J134457.17−453537.2: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−237.8  ±  8.0, 35.7  ±  8.0) mas yr⁻¹ for this object. The other component, LTT 5330, has a published motion of (−240.51  ±  13.1, 25.99  ±  13.1) mas yr⁻¹ (Röser et al. 2008). These motions are identical within their 1σ errors, so this is very likely a common-proper-motion system. ^pWISEA J140350.20−592348.0: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (30.5  ±  8.7, −494.3  ±  8.5) mas yr⁻¹ for this object. The other component, L 197-165, has a published motion of (33, −469) mas yr⁻¹ (Luyten 1979b). The motion of the unpublished WISE object is identical within its 1σ errors to the R.A. motion of the Luyten object but discrepant by ∼3σ from the Luyten Decl. measurement. Given the large motion in Decl. and the proximity of the sources, this is still likely a common-proper-motion system. ^qWISEA J140924.56−305534.1: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−456.4  ±  8.1, −213.8  ±  8.0) mas yr⁻¹ for this object. The other component, LHS 2807, has a published motion of (−460.60  ±  3.68, −219.82  ±  3.02) mas yr⁻¹ (van Leeuwen 2007). These motions are identical to <1σ, so this is likely a common-proper-motion system. ^rWISEA J142053.60−050137.8: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−131.2  ±  10.2, −55.4  ±  10.0) mas yr⁻¹ for this object. The other component, BD−04 3668, has a published motion of (−137.5  ±  3.5, −58.0  ±  3.2) mas yr⁻¹ (Roeser & Bastian 1988). These motions are identical to <1σ, so this is likely a common-proper-motion system. ^sWISEA J171828.99−224630.2 and WISEA J171826.98−224543.5: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−149.3  ±  8.9, −149.9  ±  8.4) mas yr⁻¹ for the brighter object and (−148.7  ±  8.8, −148.8  ±  8.3) mas yr⁻¹ for the fainter one. These motions are identical to <1σ, so this is very likely a common-proper-motion pair. ^tWISEA J172230.07−695119.2 and WISEA J172237.14−695112.2: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−145.6  ±  10.4, −217.6  ±  8.7) mas yr⁻¹ for the brighter object and (−37.6  ±  11.5, −221.9  ±  9.8) mas yr⁻¹ for the fainter one. Although the (larger) Decl. motions are identical to <1σ, the R.A. motions are discrepant by >9σ. A visual check of the system more strongly supports common proper motion than do the actual measurements. We suspect that the WISE astrometry for the fainter source in the pair may be corrupted by a background object—seen at nearly equal magnitude in the earlier DSS2 images—that lies near its position in the WISE data. ^uWISEA J201605.71−115838.5 and WISEA J201605.96−115916.7: Both of these objects are listed in the UCAC4 Catalog, but no other literature is available. Using the 2MASS-to-WISE time baseline we obtain motions, (μ_α, μ_δ), of (−72.4  ±  8.9, −141.1  ±  7.5) mas yr⁻¹ for the brighter component and (−69.4  ±  9.0, −134.4  ±  7.7) mas yr⁻¹ for the dimmer component, which are identical within their 1σ errors. In the UCAC4 Catalog this pair has listed motions of (−70.9  ±  2.1, −135.6  ±  2.2) mas yr⁻¹ for the brighter component and (−57.3  ±  2.1, −130.5  ±  2.1) mas yr⁻¹ for the fainter component. Although the 6.5σ discrepancy in R.A. would seem to rule these out as a cpm pair, the secondary appears to be blended with another source of nearly equal magnitude in the DSS2 images. Because visual checks strongly suggest this is a co-moving system, we still list this as a possible physical pair. ^vWISEA J210630.56−382606.1 and WISEA J210632.73−382640.4: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (174.9  ±  10.1, −323.4  ±  10.1) mas yr⁻¹ for the brighter object and (187.1  ±  10.3, −323.3  ±  10.2) mas yr⁻¹ for the fainter one. The motions are identical to <2σ, so these are likely a common-proper-motion pair. ^wWISEA J214736.41−135335.4: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (151.6  ±  10.0, −300.2  ±  9.3) mas yr⁻¹ for this object. The other component, Ross 208, has a published motion of (152  ±  5, −296  ±  5) mas yr⁻¹ (Salim & Gould 2003). These motions are identical within <1σ, so this is very likely a common-proper-motion system. ^xWISEA J230226.16+801241.8: Using the 2MASS-to-WISE time baseline we obtain a motion, (μ_α, μ_δ), of (−68.1  ±  9.9, 114.1  ±  9.9) mas yr⁻¹ for this object. The other component, BD+79 762, has a published motion of (−53.2  ±  1.2, 127.2  ±  1.2) mas yr⁻¹ (Høg et al. 2000). These motions are identical within their 2σ errors, so this is likely a common-proper-motion system. ^yThis measurement should be treated with caution because the core of this source is heavily saturated in the WISE images.

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In this section, we examine the distribution of motions for objects in a typical 156 × 156 AllWISE Atlas Image. We then extract sources having statistically significant motions and discuss the average success rate for finding bona fide motion stars. In the final subsection, we take a broader view and categorize the sources of false motion seen during our quality assurance checks (described in more detail in Section 4.1) over the entire sky.

3.4.1. A Typical Distribution of Motion Measurements

Motion measurements for all sources in a typical Atlas Image are illustrated in Figure 11. The total proper motion is plotted as a function of χ²_motion = (pmra/sigpmra)² + (pmdec/sigpmdec)², where pmra and pmdec are the AllWISE-measured R.A. and Decl. motions, respectively, and sigpmra and sigpmdec are their associated uncertainties. AllWISE tiles typically have ∼10⁵ extracted sources, so any source with $Q = e^{-{\chi ^2}_{{\rm motion}}/2} < 10^{-6}$ violates,¹⁹ with a very high degree of confidence, the hypothesis of a real object with zero motion (and errors correctly characterized by the Gaussian uncertainties). This limit on Q corresponds to χ²_motion > 27.63. Sources in this tile that satisfy this criterion are found to the right of the dashed line in Figure 11. Although a few of these objects are motion stars (see Section 3.4.2), other sources have complications that create high values of χ²_motion but do not have real motions. Examples are contaminated and spurious objects flagged as such by ${\it cc}\_{\it flags}$, objects with low signal-to-noise in all bands, and blended or extended sources that can often be identified by the nb, w?chi2, and rchi2 criteria.²⁰ Other examples of false motion sources are given in Section 3.4.3.

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3.4.2. Real Moving Sources

3.4.3. False Moving Sources

False-motion sources generally fall into one of the following categories. Representative examples and their probable causes are discussed below.

• 1.  
  Blended/extended sources: As in any motion survey, blended or extended objects in AllWISE create the potential for false motions. One such source is WISEA J130716.06+061032.7, an object whose AllWISE measurements indicate a significant motion of 4795 ± 471 and 2381 ± 493 mas yr⁻¹ in R.A. and Decl., respectively. A very faint, extended source is seen at this position in the Sloan Digital Sky Survey (SDSS) r and i band imagery taken in 2003 (Figure 12(a)), so the source is clearly not moving at the rates indicated by AllWISE. This source is extended in the W2 band and the photocenters at W1 and W2 do not align, likely giving rise to the false motion.
• 2.  
  Spurious small-separation, same-tile (SSST) sources:²¹ WISEAR J103558.13−370522.0 is a source in the AllWISE Reject Table with a seemingly high and statistically significant motion; AllWISE measures 3527  ±  350 and −1209  ±  119 mas yr⁻¹ in R.A. and Decl., respectively. This, however, is a spurious small-separation, same-tile (SSST) source and is flagged as such by the rel flag in the AllWISE Reject Table. As seen in Figure 12(b), this source falls in the wings of a real object, named WISEA J103558.04−370520.9, that is found in the AllWISE Source Catalog and that has motion measures of −4  ±  44 and 27  ±  44 mas yr⁻¹ in R.A. and Decl., respectively, indicating no apparent motion. Users are cautioned to pay particular attention to the rel flag when using motion measures from the AllWISE Reject Table.
• 3.  
  Flux transients: Flux variables can sometimes trigger false motions. When an object appears at only one epoch, a nearby noise blip at the other epoch(s) may trigger a false, generally large motion. Because the derived motion is so large, it may appear to be statistically significant despite having rather large errors. An example of this is WISEA J122559.53+070005.2, which has AllWISE-reported motions of 24902 ± 4071 and 11567 ± 7922 mas yr⁻¹ in R.A. and Decl., respectively. This object appears only in the first epoch and not the second (Figure 12(c)), as confirmed by the AllWISE Multi-Epoch Source Table, which gives a mean w1mpro value of ∼15.3 mag for the first epoch and limits of >17.0 mag for the second.
• 4.  
  W3- and W4-dominated sources: Sources that are detected only at W3 and/or W4 may show spurious motions. Such sources will be seen only at the earlier epochs before cryogen was exhausted and not at the later epochs when those bands were not operational. Nearby noise blips at the later epochs in W1 and/or W2 can trigger false motions. One such example is the planetary nebula PN SB 24, also known as WISEA J185716.62−175050.4 (Figure 12(d)), which has AllWISE-measured motions of 6243  ±  1101 and −11981  ±  1162 mas yr⁻¹ in R.A. and Decl., respectively, despite the fact that the nebula is known to have near-zero proper motion (Kerber et al. 2008).
• 5.  
  Cosmic rays in low-coverage areas: Areas having less than five frames of coverage do not reap the benefit of outlier rejection²² in the coaddition step, so spurious sources can bleed through into the coadds. In some cases, these spurious sources have falsely measured, yet apparently significant, motions in AllWISE. One example is WISEA J210220.65−083948.6 (Figure 12(e)), a cosmic ray that appears in only one W3 frame (04364a113) in an area of sky where that W3 frame is the only one of acceptable quality for AllWISE processing. A nearby noise blip in another band at a different epoch nonetheless causes AllWISE to measure a large, although false, motion for it of 4573 ± 1094 and 6531 ± 1213 mas yr⁻¹ in R.A. and Decl., respectively.
• 6.  
  Sources falling in a streaked frame in a low-coverage area: Another consequence of low-coverage areas is the increased influence of the occasional poorer quality frame going into the coadd. The most extreme example is one in which only a single frameset is available for one of the WISE epochs, and that frameset has non-optimal image quality. False motions may result, as is the case for source WISEA J061658.37+701209.5 (Figure 12(f)). This object lies in an area of sky with single-frameset coverage (02821a200) at the first epoch, but this frameset is slightly smeared due to momentum dumping²³ by the spacecraft. The astrometric solution for the entire frameset is slightly biased in R.A. because of this smearing. Data at the later epoch are not affected. As a result of the mismatch in positions across epochs, a false motion of 1547  ±  129 and −5  ±  127 mas yr⁻¹ in R.A. and Decl., respectively, is created. It should be noted that this is an extremely rare occurrence in AllWISE, as Quality Assurance flagged almost all of the smeared frames and eliminated them from consideration for coaddition. Nonetheless, users are advised to treat with caution any motion measures in areas of low-coverage at a single epoch.

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3.5.1. Motion Measurements are Quantized

A plot of AllWISE motion measurements in a single Atlas Tile (upper panel of Figure 13) shows that certain, discrete values have a higher frequency of occurrence. The solution for motion values and source positions is an iterative process whereby a minimization of χ² is sought in the phase space of source position and motion. Convergence is rapidly achieved for position estimates, using initial values. On the other hand, convergence on motion values is achieved only after one or more iterative steps. The step size used for motion estimates is 27.5 mas yr⁻¹, and converged motion values are thus quantized at multiples of this value.²⁴

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3.5.2. Spurious Motion Measurements Show "Pile-up" at Large Values

As part of AllWISE pipeline processing at IPAC, the Quality Assurance code filtered the list of detections from each Atlas Tile to identify objects believed to be moving significantly. These criteria were used to select only the choicest motion objects from the source lists and to keep the number of candidates manageable on the tight schedule allotted for AllWISE Quality Assurance checks. The criteria used are as follows.

• 1.  
  To ensure that the object is not flagged as an artifact, the ${\it cc}\_{\it flags}$ parameter was required not to have a capital-letter value at any position in its four-character code, in which the four characters refer to the four WISE bands. Capital letters are used when the software has determined in that band that the object was a spurious detection of either a diffraction ("D") spike, a scattered light halo ("H") surrounding a bright star, an optical ("O") ghost image, or persistence ("P")—i.e., a short-term latent image—left behind by a bright source on the detector. Values of ${\it cc}\_{\it flags}$ having only lower-case versions of these same letters (indicating that the object is likely real and only contaminated by an artifact) or zero (indicating that the source is unaffected by known artifacts) were allowed.
• 2.  
  To ensure that the object is point-like, a value of nb = 1 (no blends) was required. Also, the motion-fit, reduced χ² values in all bands, $w?r{\it chi}2\_pm$, were required to be less than two to eliminate sources that are obviously extended.
• 3.  
  To eliminate more poorly measured sources from consideration, the signal-to-noise ratio, w?snr, was required to be greater than seven in at least one band.
• 4.  
  To ensure that the code selected only those objects with robust and statistically significant motions, the following criteria were applied: (a) The ratio of the reduced χ² value between the stationary and motion fit, $r{\it chi}2/r{\it chi}2\_pm$, was required to be greater than 1.03. This ensures that the motion-fit solution significantly improves the overall reduced χ² value compared to the stationary fit. (b) As explained in Section 3.4 above, the χ²_motion criterion was required to be greater than 27.63 to select only those objects with statistically significant motions. (c) The second and third characters of pmcode were required to be "N" and "0," respectively. A value of "N" means that no blend-swapping has occurred and a value of "0" means that the offset between the stationary-fit and the motion-fit position at the mean epoch is less than 1''. These values were chosen because blended sources often have blend swapping, and spurious sources often have unphysically large positional differences at the mean epoch between the non-motion and motion solutions.²⁶
• 5.  
  To ensure that the motion measurement has a solid foundation of W1- and W2-band data underlying it, we experimented with various values of w1m, w2m, and w1mJDmax − w1mJDmin. The first two parameters specify the number of frames in W1 and W2, and the third parameter specifies the time difference between the earliest and latest frames in W1. In the end, these parameters were all set to be greater than zero because regions of very sparse coverage were found not to contribute a large number of spurious motion sources, mainly because the vast majority of the sky is well covered across two or more epochs.

These criteria were written to eliminate blended/extended sources, spurious objects, and pure noise. Other contaminants listed in Section 3.4.3—the SSST sources, flux transients, W3- and W4-dominated sources, and cosmic rays and streaked frames in low coverage areas—were discovered as a result of these Quality Assurance checks. These contaminants were generally easy to recognize via a visual inspection step, which displayed images of the field in the AllWISE W1, W2, W3, and W4 coadds along with Two Micron All Sky Survey (2MASS) images at J, H, and K_s. For WISE objects that were also visible in 2MASS, which represents the vast majority of sources identified, any motion should be obvious in the 10+ yr between the 2MASS and WISE image sets.²⁷ The Quality Assurance scientists checked these images for all candidate motion objects and retained only those objects having no 2MASS source at the AllWISE position.

The Quality Assurance scientists (J.D.K. and S.F.A.) produced a list of 26,850 candidates as a result of the criteria filtering and image checking discussed above. This list was then run (by J.D.K.) through SIMBAD using a 2' search radius around the AllWISE position to search for previously known objects. If SIMBAD noted a proper motion source within 10'' of the AllWISE position, the object was eliminated from the list.²⁸ When known proper motion sources were found outside of 10'', the AllWISE- and SIMBAD-reported motions were checked to see if the object was a very high-motion source, generally >1'' yr⁻¹. This further check eliminated many known, small-numbered LHS (Luyten Half Second) objects.

The remaining list of objects was then checked (by J.D.K.) against the Fourth US Naval Observatory CCD Astrograph Catalog²⁹ (UCAC4; Zacharias et al. 2013) using a 1' search radius. Objects with significant UCAC4-reported motions were considered to be possible matches to the AllWISE source. The match was considered confirmed if the UCAC4 source appeared to have a motion of the right magnitude and in the correct direction, as inferred from visual inspection of the motion source across the DSS2, 2MASS, and WISE images, to be the AllWISE-selected object. Those objects matching a source with reliable motions in UCAC4 were flagged as such but kept in the object list because they have no SIMBAD entries.

After these checks, the list was run again through SIMBAD and further checked against DwarfArchives.org, against a list of published papers (on low-mass objects) likely not to have been ingested into SIMBAD by 2013 December, and against catalogs housed by VizieR. These checks (by G.N.M. and A.S.) enabled us to eliminate other objects. Objects were kept in the list only when SIMBAD had no reported proper motion information and no links to published papers citing a proper motion value. Thus, a few objects with published spectral types are included in the list because this will be the first refereed publication in SIMBAD giving their motion information. Objects listed only in UCAC4 and other catalogs found in VizieR are noted as such in the final list.

Of the 26,850 motion candidates selected by our Quality Assurance criteria, we found that 18,862 objects (70%) were already published and had motion information available in SIMBAD. Of the remainder, 3583 objects (13%) are new discoveries and 4405 objects (16%) were found to be non-motion sources after visual inspection of the DSS2 images.

The discovery list of 3583 itself is comprised of two sublists. The first (Table 3) contains 3525 objects whose motions could be confirmed using non-WISE data, and the second (Table 4) contains 58 unconfirmed objects lacking counterparts in earlier surveys. For the list of confirmed objects, one of us (A.S.) consulted the 2MASS images to find the WISE source at the 2MASS epoch and then tabulated the 2MASS position and magnitudes from the 2MASS All-Sky Point Source Catalog. These 2MASS associations were then double checked (by J.D.K.) by creating finder charts of DSS, 2MASS and WISE images centered at the position of the 2MASS source. Using these associations, a proper motion was measured for each source using the 2MASS position as the first epoch and the mean WISE All-Sky Source Catalog position as the second epoch.

Because the identification of motion candidates during Quality Assurance took place before selection of objects for the AllWISE Source Catalog (and before the SSST phenomenon was fully recognized), we had to retroactively replace a small number of our motion candidates that appeared only in the AllWISE Reject Table with their more appropriate entry from the AllWISE Source Catalog. In some cases, the entry in the AllWISE Source Catalog does not have a motion significant enough to have been selected by the Quality Assurance criteria. We retain such cases if our independent checks using the 2MASS-to-WISE time baseline confirm that the objects are truly moving. An example of this is WISEA J000205.60−322545.9, which has AllWISE motions of 0 ± 74 and 0 ± 73 mas yr⁻¹ in R.A. and Decl., respectively, but whose comparison with the earlier 2MASS position confirms a motion of 23.8 ± 10.1 and 42.0 ± 9.8 mas yr⁻¹ in R.A. and Decl. This motion is too small to have been legitimately uncovered by AllWISE, but we list it nonetheless as a serendipitous discovery.

The sky distribution of the confirmed motion objects is shown in Figure 14. The top panel shows the ecliptic projection that is the natural system for the WISE scanning pattern. The three-epoch coverage areas³⁰ at ecliptic longitudes of ∼25°–48° and ∼200°–223° are, as expected, seen as overdensities. An underdensity in the number of motion objects is seen toward the Galactic Center and along the Galactic mid-plane (bottom panel of Figure 14), as expected in these regions of source confusion and high backgrounds.

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The sky distribution of the confirmed objects is compared in Figure 15 to the New Luyten Two Tenths Catalog (NLTT; Luyten 1979b), a large compilation of motion objects covering the entire sky. As expected, the majority of new discoveries (middle panel of Figure 15) falls primarily in the southern hemisphere because the NLTT is much less complete in those regions (top panel of Figure 15). The clumpiness of these discoveries in the southern hemisphere (e.g., at 11^h < R.A. <22^h and Decl. <−0°) is largely a consequence of the WISE three-epoch coverage (middle panel of Figure 14) overlapping areas poorly covered by the NLTT.

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The list of all 3525 confirmed AllWISE motion objects is given in Table 3. Column 1 gives the source designation from the AllWISE Source Catalog. Columns 2–4 give the 2MASS J, H, and K_s magnitudes and associated errors of the source, and Columns 5 and 6 give the AllWISE W1 and W2 profile-fit magnitudes and errors. Columns 7 and 8 give the AllWISE-measured motions in R.A. and Decl. whereas Columns 9 and 10 give the proper motions computed using the 2MASS-to-WISE time baseline. Column 11 is a flag column indicating whether the source has an entry in another motion catalog, even though the source itself has no publication history, and Column 12 indicates whether additional information is available in the footnotes.

The 58 AllWISE motion candidates lacking counterparts in 2MASS and other earlier surveys are listed in Table 4. Sixty percent of the objects in this table (35 out of 58) are believed to be flux transients based on their blue W1 −W2 colors and appearance on the WISE All-Sky Release and AllWISE Release Atlas Images. These objects are slightly fainter versions of objects clearly seen in the W1 individual frames at one, and only one, WISE epoch, but because of their faintness, the variability cannot be confirmed by eye using the individual frames. Most of the remaining 40% of the objects may or may not be real motion objects. One of these, WISEA J085510.74−071442.5, was also found by Luhman (2014), and the AllWISE motion values of −4188  ±  267 and 226  ±  283 mas yr⁻¹ in R.A. and Decl., respectively, match well with his measures of −4800 ± 300 and 500 ± 300 mas yr⁻¹ as expected, since these motions are derived from the same data set. Visual inspection of the individual frames also strongly suggests a large motion between the two WISE epochs, but we nonetheless list this source as unconfirmed pending a third-epoch verification.

The next set of plots aim to characterize objects in Table 3. Figure 16 shows the AllWISE-measured motions plotted against the 2MASS-to-WISE motions. Careful analysis of the left and middle panels of this plot shows that, unlike the truth-test cases in Figure 6, the points do not fall along the line of one-to-one correspondence but rather would have a fitted slope much steeper than the one-to-one line. The reason for this is an inherent bias in our selection criteria. By demanding that the motion value be statistically significant compared to its measured errors means that at a given value of R.A. or Decl. motion we preferentially select those that are measured on the high side of the average rather than on the low side. This effect is also seen in the right panel of Figure 16. As expected given this bias, the AllWISE-measured motions tend to be higher than those measured independently.

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Figure 17 shows the AllWISE W1 profile-fit magnitude of each source plotted against the total motion computed from the 2MASS-to-WISE time baseline. As can be seen on the figure, 10 of these objects have motions ⩾1000 mas yr⁻¹, including the three highest movers WISEA J204027.30+695924.1 (μ = 2300 ± 10 mas yr⁻¹; see Section 7), WISEA J154045.67−510139.3 (μ = 2006 ± 12 mas yr⁻¹; see Section 8), and WISEA J070720.50+170532.7 (μ = 1802 ± 15 mas yr⁻¹; Wright et al. 2013).

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Figure 18 shows the 2MASS J-band magnitude plotted as a function of the J − W2 color. As shown in Figure 7 of Kirkpatrick et al. (2011), L and T dwarfs generally have colors of J − W2 > 2.0 mag, so the list of AllWISE motion objects contains approximately 30 new L and T dwarfs. Figure 19 (which can be compared to Figure 9 in Kirkpatrick et al. 2011) breaks the degeneracy between the L and T dwarf populations. Figure 1 of Kirkpatrick et al. (2011) shows that the break between the L and T dwarf populations is near W1 −W2 = 0.6 mag, which means that of the ∼30 new L and T dwarfs, only three are red enough to be T dwarfs themselves. These objects are WISEA J011154.36−505343.4, WISEA J210529.11−623559.3, and WISEA J212100.87−623921.6, all of which lack previous publication, likely because their very southern declinations have made follow-up somewhat more difficult.

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None of these objects is nearly red enough to fall in the Y dwarf regime, which falls very roughly at W1 −W2 > 3.5 mag. It is natural, then, to ask why the AllWISE motion survey wasn't more efficient at picking up T and Y dwarfs. There are two reasons. First, the apparent magnitudes of the nearest T and Y dwarfs are sufficiently faint that AllWISE would only have been able to measure significant motions for the very fastest movers (see Figure 5). Second, several bright, very high motion T and Y dwarfs were picked up by our criteria, but these are not included in Table 3 because they were previously known. In fact, it is hard to imagine a bright, nearby T or Y dwarf that would not have been picked up via color selection because, after all, WISE was designed to be highly sensitive to the methane absorption that defines these spectral types. With longer time baselines, WISE-like data would be able to probe deeper magnitude limits and smaller motions, enabling the discovery of fainter and/or colder objects than color selection itself can provide. Although it is possible that AllWISE has identified a moving W2-only source with a W1 − W2 color limit sufficiently marginal that color-based criteria would not have selected it, our current motion-based criteria did not extract it. Modifying the selection criteria will be further discussed in Section 5.

Finally, we present two plots that help to isolate potentially low-metallicity objects. Figure 20 shows the reduced proper motion at J band plotted against the J − W2 color. The reduced proper motion can be thought of as a poor man's substitute for an absolute magnitude measurement when a parallax is lacking. In the distance modulus equation, the total proper motion is used in place of the parallax (this is done because, to first order, the higher an object's proper motion, the larger its parallax is likely to be) and the "absolute magnitude" that results is called the reduced proper motion. At J band, this would be written as H_J = J + 5log (μ) + 5, where μ is expressed in arcsec yr⁻¹ and the reduced proper motion is in magnitudes. Objects with abnormally high space velocities confound this logic, however—they have high motions not because they are close but because they are old. As a result, these objects have reduced motion values that are significantly fainter than objects of average kinematics (see Reid 1997 for a more extensive discussion). Fortunately, this enables such objects (which tend to be low-metallicity because they are very old) to be easily selected from the bulk of objects (of near solar metallicity) in the Galactic disk. Several objects with reduced proper motion at J band > 19 mag and 0.8 < J − W2 <1.5 mag can be seen in Figure 20 and are prime low-metallicity candidates.

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Figure 21 shows the J − K_s color plotted against the J − W2 color. The locus at lower left near (0.3, 0.3) corresponds roughly to late-F or early-G spectral types (Ali 2014) and marks the earliest spectral types for which we have new motions. The bulk of objects clustered near (1.1, 0.8) are mid-M dwarfs, which by far dominate the solar neighborhood (Figure 11 of Kirkpatrick et al. 2012). The trail of objects into the upper right corner of the figure is the ∼30 L and T dwarfs. This diagram also shows a collection of objects that fall below the standard main sequence. Qualitatively, if we take the long-baseline color, J − W2, to be indicative of temperature or spectral type, and the short-baseline color, J − K_s to sample more specific atmospheric physics, we would expect objects at the same J − W2 value as a standard main sequence star but with a bluer J − Ks value to be low-metallicity because of the increased contribution of collision-induced absorption by H₂ at K band. Hence, this diagram provides another handy way—using colors instead of motions, as in Figure 20—to select low-metallicity candidates.

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One source was observed (by S.F.A.) on the night of 2013 July 07 UT with the Double Spectrograph on the Hale 5m telescope on Palomar Mountain, California. In the red-side spectrograph, a 316 lines mm⁻¹ grating blazed at 7500 Å was used to produce a spectrum covering the range 3800–10500 Å. Standard reduction procedures for CCD data were employed. This night had cirrus clouds.

Six sources were observed (by D.S., M.B., and G.B.L.) on the nights of 2013 October 4–5 UT with the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) at the 10 m W. M. Keck Observatory on Mauna Kea, Hawai'i. The blue side was used with a 600 lines mm⁻¹ grating blazed at 4000 Å, and the red side was used with a 400 lines mm⁻¹ grating blazed at 8500 Å. Objects had very little flux in the blue side so the blue-side spectra are not considered further. The red side produced a spectrum covering the range from 5500 to 10000 Å. Standard reduction procedures for CCD data were employed. The first night had clouds and the second night was clear.

Three sources were observed (by D.S.) on the clear night of 2013 December 11 UT with the Deep Imaging Multi-object Spectrograph (DEIMOS; Faber et al. 2003) at the 10 m W. M. Keck Observatory on Mauna Kea, Hawai'i. The instrument was used in single-object mode utilizing the 1200 line mm⁻¹ grating blazed at 7500 Å to provide continuous wavelength coverage from 6650 to 9300 Å. Standard reduction procedures for CCD data were employed.

Two objects were observed (by J.A.R.) on the clear nights of 2014 January 27 and 28 UT with the Inamori-Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2011) on the 6.5m Walter Baade Telescope at Las Campanas Observatory, Chile. The f/4 camera was used with a Bessel V-band or a CTIO I-band filter for imaging observations and with a 600 lines mm⁻¹ grating for the spectroscopic observations. The grating angle was set for a wavelength coverage of 7100–10400 Å. Standard reduction procedures for CCD data were again employed.

Several sources were observed with SpeX (Rayner et al. 2003) on the NASA 3m Infrared Telescope Facility (IRTF) on Mauna Kea, Hawai'i. The UT dates of observation were 2013 August 14 (by A.J.B.; cirrus and patchy clouds), 2013 October 24 (by A.S.; clear skies), 2013 November 21–22 and 24 (by J.K.F. and N.S.; thick cirrus on the first night but then clear), and 2013 December 14–15 (by A.S.; clear). For all but the October night, SpeX was used in prism mode with a 05 or 08 wide slit to achieve a resolving power of R ≡ λ/Δλ ≈ 100–150 over the range 0.8–2.5 μm. For the October run, SpeX was used in cross-dispersed mode to produce spectra over the range 0.9–2.4 μm with a resolving power of R ≡ λ/Δλ ≈ 1200. All data were reduced using Spextool (Cushing et al. 2004); A0 stars were used for the telluric correction and flux calibration steps following the technique described in Vacca et al. (2003).

Several sources were also observed on the UT nights of 2013 November 20 and 2013 December 14 (by G.N.M. and S.E.L.) with the Near-Infrared Spectrometer (NIRSPEC; McLean et al. 1998, 2000) at the 10 m W. M. Keck Observatory on Mauna Kea, Hawai'i. There was cirrus on the November night and heavier clouds on the December one. In low-resolution mode, use of the 42'' × 038 slit results in a resolving power of R ≡ λ/Δλ ≈ 2500. Our brown dwarf candidates were observed in the N3 configuration (see McLean et al. 2003) that covers part of the J-band window from 1.15 to 1.35 μm. Data were reduced using the REDSPEC package, as described in McLean et al. (2003).

We have typed the optical spectra as follows. Each spectrum was normalized at 7500 Å or 8250 Å and overplotted on a suite of like-normalized LRIS spectra of primary M and L optical spectral standards from Kirkpatrick et al. (1991) and Kirkpatrick et al. (1999). These plots were examined by eye to determine the best match and to look for any peculiarities with respect to the standard sequence. Objects falling midway between integral classes (such as M9 and L0) were assigned the half class in between (in this case, M9.5). Objects showing notable peculiarities were given a suffix of "pec" unless the peculiarities were determined to be caused by low-metallicity, in which case these were reclassified against published optical spectra typed as late-M and early-L subdwarfs and given a prefix of "sd."

We have typed the near-infrared spectra as follows. Each target spectrum was normalized to one at 1.28 μm and compared to the near-infrared spectral standards from Kirkpatrick et al. (2010) normalized the same way. Using the methodology outlined in that paper, the core near-infrared type was determined only from the 0.9–1.4 μm portion, and then the corresponding goodness of fit to the same spectral standard from 1.4–2.5 μm was judged. In most cases the same spectral standard also provided the best fit in this longer-wavelength region. In other cases, the target spectrum was notably much bluer or redder so the fit across the H and K windows was very poor despite the excellent fit in the J window. These peculiar objects were given suffixes of "pec (blue)" or "pec (red)" to denote the slope of the spectrum relative to the standard (see Figure 23). Some of the peculiar spectra were deemed to be low-metallicity (prefix of "sd") and were typed against near-infrared spectra of similar subdwarfs from the published literature.

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Optical and/or near-infrared spectral types are listed in Table 5. Subdwarfs are discussed in Section 7, and two bright M dwarf systems are discussed in Section 8.