THE FIRST HUNDRED BROWN DWARFS DISCOVERED BY THE WIDE-FIELD INFRARED SURVEY EXPLORER (WISE)

Before beginning the hunt for brown dwarfs, it is necessary to establish empirically the locus of known brown dwarfs in WISE color space and to understand what other kinds of astrophysical objects might fall in the same area. This will not only inform the search of WISE color space itself but also dictate the kinds of photometric follow-up that need to take place before time-intensive spectroscopic characterization begins.

We have performed a positional cross-correlation of nearby stars from Dwarf Archives²⁶ against source lists derived from the WISE co-added data. Many of these stars are known to have substantial proper motion, so it was necessary to verify each cross-match by visually inspecting the WISE and Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006) images. The final cross-identifications are given in Table 1, which lists photometry²⁷ from 2MASS (when detected) and WISE for 118 previously cataloged T dwarfs, 142 L dwarfs, and 92 M dwarfs. Figure 1 shows the resulting trend of WISE W1 − W2 color as a function of spectral type for these objects, ranging from early-M through late-T. Note that there is a slow increase in the W1 − W2 color between early-M and early-L, with the color stagnating near 0.3 mag between early- and mid-L. The W1 − W2 color then rapidly increases at types later than mid-L, corresponding to the appearance of the methane fundamental band at 3.3 μm (Noll et al. 2000). The average W1 − W2 color is ∼0.6 mag at T0 and ∼1.5 mag at T5, with the color increasing to above 3.0 mag at late-T.

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The red W1 − W2 colors (>1.7 mag) of dwarfs of type mid-T and later are almost, but not entirely, unique among astrophysical sources. Dust-obscured galaxies (DOGs) and asymptotic giant branch stars (AGBs) are the major sources of contamination at these red W1 − W2 colors, as analysis of the Spitzer Deep Wide-Field Survey (SDWFS) results of Eisenhardt et al. (2010) has shown. The three short-wavelength bands of WISE—which are close in wavelength to the 3.6, 4.5, and 8.0 μm bands (hereafter denoted as ch1, ch2, and ch4, respectively) of the Infrared Array Camera (IRAC) on board the Spitzer Space Telescope—can help to distinguish between these populations. As Figure 1 of Eisenhardt et al. (2010) shows, most AGBs with very red W1 − W2 (or ch1 − ch2) colors can be distinguished by their very red W2 − W3 (or ch2 − ch4) colors. Brown dwarfs with similar W1 − W2 colors are much bluer in W2 − W3 color than these contaminants. Similarly, DOGs should be easily separable from brown dwarfs because, like AGBs, their W2 − W3 (or ch2 − ch4) colors tend to the red for objects with very red W1 − W2 colors. This is further demonstrated in Figure 12 of Wright et al. (2010), where the bulk of the extragalactic menagerie, including red active galactic nuclei (AGNs), can be distinguished from cold brown dwarfs using a color of W2 − W3 ≈ 2.5 as the dividing line.

As with any set of generic color cuts, however, one should be ever vigilant for exceptions. As Figures 1 and 2 show, very late T dwarfs have colors approaching W2 − W3 ∼ 2.0 mag, near the locus of extragalactic sources, but their W1 − W2 colors are extreme (>3.0 mag). Few extragalactic sources have W1 − W2 colors this red, so the W2 − W3 color criterion can be relaxed for the coldest objects (see Figure 3). Indeed, brown dwarfs with T_eff < 300 K are expected to turn to the red in W2 − W3 color (Figure 14 of Wright et al. 2010). It should also be noted that the location of low-gravity or low-metallicity brown dwarfs may not follow the general rule set by normal-gravity, solar-metallicity cases, so it is important to use other data (proper motion, parallax) when possible to identify brown dwarfs independent of photometric selections. Nonetheless, a number of possibly low-metallicity T dwarfs have been uncovered using these same photometric selections, as further discussed in the Appendix.

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We have used two different sets of criteria to search the WISE source lists for nearby brown dwarfs.

• 1.  
  To find the coldest brown dwarfs, we selected high signal-to-noise (S/N > 3 at W2) detections having W1 − W2 colors (or limits) greater than 1.5 mag, corresponding roughly to types ⩾T5. (Because of the relative depths of the W1 and W2 bands, the W1 − W2 requirement imposes a more severe W2 S/N limit of its own, generally W2 S/N > 7.) In order to assure that an object is real, we required it to have been detected at least eight times in the individual W2 exposures; this eliminated spurious sources like cosmic rays and satellite trails that would otherwise not be eliminated during the outlier rejection step in co-add image creation (see Section IV.5.a.v of the Explanatory Supplement to the WISE Preliminary Data Release²⁸). For our initial candidate selection, we also required W2 − W3 < 3.0 mag if the object has a detection in W3.
• 2.  
  To find bright, nearby (i.e., high proper motion) L and T dwarfs that other surveys have missed, we searched for objects with W1 − W2 colors greater than 0.4 mag (roughly types ⩾L5), W2 S/N values greater than 30, and no association with a 2MASS source (implying that the J − W2 color is either very red or the object has moved). It should be noted that the WISE source lists report 2MASS associations falling within 3 arcsec of each WISE source.²⁹ As with the first search, we required the object to have been detected at least eight times in W2 to assure its reliability. To eliminate extragalactic contaminants, we imposed one additional criterion that W1 − W2 > 0.96(W2 − W3) − 0.96 (see dashed line in Figure 3).³⁰

For both searches, no constraint on galactic latitude was imposed, although additional constraints were placed on object detections in order to assure that they were real, particularly for our earliest searches of the WISE source lists. First, the reduced χ² value from the Point Spread Function photometric fitting ("rchi2" in the WISE Preliminary Release Source Catalog) was required to fall between 0.5 and 3.0 to assure that the source was pointlike. Second, the early version of the WISE data processing pipeline automatically flagged artifacts—bright star halos, diffraction spikes, latent images, ghost reflections from bright stars, etc.—only on individual frames and not on the co-added images. For search 2 above, because those objects all have high-S/N W2 detections, we are able to use these individual frame flags to remove objects marked as spurious. For fainter objects found in search 1, we created three-color images from the W1 (blue), W2 (green), and W3 (red) co-added images, which were then inspected by eye to eliminate artifacts. Third, for all objects passing the above tests, we created finder charts showing the Digitized Sky Survey (DSS; B, R, I), the Sloan Digital Sky Survey (SDSS; York et al. 2000—u, g, r, i, and z, if available), 2MASS (J, H, K_s), and WISE (W1, W2, W3, W4, + three-color image made from W1+W2+W3) images. A visual inspection of these finder charts allowed us to remove other spurious sources and objects clearly visible in the short-wavelength optical bands, while also allowing us to check for proper motion between surveys for objects bright enough to have been detected at shorter wavelengths, such as J and H for brighter T dwarf candidates.

Example images are shown in Figure 4 for our spectroscopically confirmed candidates. WISE photometry for these same sources is given in Table 2.

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View extended figure (20 panels)

Follow-up imaging observations of WISE candidates are important not only for verifying that the source has the characteristics of a brown dwarf at shorter wavelengths but also for determining how bright the object is at wavelengths observable from the ground. This latter knowledge is necessary for determining which facility to use for spectroscopic confirmation.

Ground-based near-infrared observations at J and H bands are technically the easiest to acquire. Before discussing specifics, it should be noted that the two main near-infrared filter systems being used today—the 2MASS system and the Mauna Kea Observatories Near-infrared (MKO-NIR, or just MKO) system—will yield somewhat different results for the same objects. The 2MASS bandpasses are illustrated in Figure 2 of Skrutskie et al. (2006), and the MKO filter profiles are shown in Figure 1 of Tokunaga et al. (2002). A comparison of the two filter sets is illustrated in Figure 4 of Bessell (2005). For J and H bands, the main difference between the two systems lies in the width of the J-band filter; the H-band filters are very similar. The 2MASS J-band profile extends to bluer wavelengths than does the MKO J-band profile, and the overall shapes of the two J filters are quite different, the 2MASS J filter lacking the top-hat shape that is characteristic of most filter profiles. As a result, the measured J-band magnitude of a brown dwarf, whose spectral signature is also quite complex at these same wavelengths, can be considerably different between the two systems. This is dramatically illustrated in Figure 3 of Stephens & Leggett (2004), which shows that although the H-band magnitudes are (as expected) very similar between the two systems for a wide range of brown dwarf types, the J-band magnitudes (and hence, J − H colors) can differ by as much as 0.5 mag for late-type T dwarfs. In the discussion that follows, we note the systems on which our photometry was obtained and we mark photometry from the two systems with different colors and symbols on the plots.

As Figures 5 and 6 show, mid- to late-T dwarfs (W1 − W2 > 1.5 mag) have relatively blue colors, J − H ≲ 0.4 mag, on the 2MASS filter system. The upper right-hand panel of Figure 5 of Leggett et al. (2010) shows the trend of J − H color versus spectral type using the MKO filter system, and there we find that J − H ≲ −0.1 mag for dwarfs ⩾T5. These blue colors in both systems are a consequence of stronger methane bands and collision-induced H₂ absorption at H band compared to J band. This color stands in contrast to the majority of other astrophysical sources, whose J − H colors are much redder than this. For example, Figure 19 of Skrutskie et al. (2006) shows the 2MASS J − H color distribution of detected sources at high Galactic latitude and confirms that most 2MASS objects have colors redder than those of mid- to late-T dwarfs. Nevertheless, there are true astrophysical sources—e.g., main-sequence stars earlier than type K0 (Table 2 of Bessell & Brett 1988); certain AGNs, particularly those with 0.7 < z < 1.1 (Figure 2 of Kouzuma & Yamaoka 2010)—that are not brown dwarfs and have J − H colors below 0.4 mag.

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Fortunately, other colors like J − W2 and H − W2 can also be used to distinguish populations. Figures 7 and 8 show these colors as a function of spectral type and demonstrate that the J − W2 color of mid- to late-T dwarfs runs from ∼2.0 mag at T5 to >4.0 mag at late-T; H − W2 color runs from ∼1.5 mag to ∼5.0 mag for the same range of types. Figures 9 and 10 show the trend of J − W2 and H − W2 with W1 − W2 color. The correlation is very tight for M and L dwarfs (W1 − W2 < 0.6 mag), but at redder W1 − W2 colors, corresponding to the L/T transition and beyond, there is a much larger spread of J − W2 and H − W2 colors at a given W1 − W2 color. Nonetheless, both J − W2 and H − W2 color increase dramatically beyond W1 − W2 >1.5 mag (>T5).

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With our list of brown dwarf candidates in hand, we have obtained J and H observations—and in some cases, Y and K_s as well—using a variety of different facilities in both hemispheres. Details of those observations are given below, and a listing of the resultant photometry can be found in Table 3.

3.1.1. Fan Mountain/FanCam

3.1.2. Magellan/PANIC

3.1.3. Mt. Bigelow/2MASS

3.1.4. PAIRITEL

3.1.5. Palomar/WIRC

3.1.6. Shane/Gemini

3.1.7. SOAR/SpartanIRC

3.1.8. Keck/NIRC2

3.1.9. CTIO-4m/NEWFIRM

3.1.10. 2MASS and UKIDSS

Some of the coldest brown dwarf candidates detected by WISE have W1 − W2 color limits because these sources are too faint to be detected in the W1 band. Acquiring deeper images at similar bandpasses would therefore be extremely beneficial in further deciding which of the candidates are the most interesting for spectroscopic follow-up. Fortunately, the two shortest wavelength bandpasses of the IRAC (Fazio et al. 2004) on board the Spitzer Space Telescope (Werner et al. 2004) are operating during the Warm Spitzer mission and can be used to provide this missing info. Although these bandpasses—at 3.6 and 4.5 μm (also known as ch1 and ch2, respectively)—are similar to the two shortest wavelength bands of WISE (see Figure 2 of Mainzer et al. 2011), they were not designed specifically for brown dwarf detection and therefore yield less extreme colors (ch1 − ch2 versus W1 − W2) for objects of the same spectral type. Nonetheless, IRAC photometry in the Warm Spitzer era provides a powerful verification tool for WISE brown dwarf candidates.

Figure 11 shows the trend of ch1 − ch2 color versus spectral type for early-M through late-T dwarfs taken from Patten et al. (2006), Leggett et al. (2009), and Leggett et al. (2010). As noted by these authors, there is a clear trend of increasing ch1 − ch2 color with later spectral type, as expected. Figure 12 maps the ch1 − ch2 color onto W1 − W2 color for these same sources. Two additional plots, Figures 13 and 14, show composite colors made from ground-based near-infrared and Spitzer follow-up and demonstrate that both J − ch2 and H − ch2 colors can serve as proxies for spectral type for objects of type mid-T and later. Plots of H − ch2 color versus type have been presented in earlier papers (the upper left-hand panel of Figure 6 of Leggett et al. 2010; Figure 5 of Eisenhardt et al. 2010). Even earlier, Warren et al. (2007) noted the tight correlation between H − ch2 color and effective temperature for later T dwarfs and suggested that the color is relatively insensitive to gravity and metallicity, which makes it a reliable indicator of T_eff or type (see also Burningham et al. 2008).

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We have therefore obtained IRAC ch1 and ch2 photometry of many of our WISE brown dwarf candidates (Program ID = 70062; PI: J. D. Kirkpatrick). Data were collected in both channels using a five-position, medium-scale "cycling" dither script. Single images were 30 s per position, for a total on-source exposure time of 150 s per channel.

Although the Spitzer Science Center (SSC) suggests performing photometry on custom-built mosaics from the basic calibrated data (BCD) rather than the post-BCD mosaics, we have found that the photometric differences between the two mosaics are negligible for our data sets. Therefore, photometry of our sources was measured on the post-BCD mosaics as produced by the SSC IRAC Pipeline, software version S18.18. The post-BCD mosaics have a pixel scale of 06 pixel⁻¹, which is half of the native pixel scale. We used a 4 pixel aperture, a sky annulus of 24–40 pixels, and applied the aperture corrections listed in Table 4.7 of the IRAC Instrument Handbook³⁵ to account for our non-standard aperture size. Resulting IRAC photometry for those confirmed candidates observed so far is listed in Table 3.

The Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) at the 10 m W. M. Keck Observatory atop Mauna Kea, Hawai'i, uses two channels to simultaneously observe blue and red optical wavelengths. Our observational setup employed only the two 2k × 4k CCDs in the red channel. When used with the 400 lines mm⁻¹ grating blazed at 8500 Å and a 1'' slit, the red channel produces 10 Å resolution spectra covering the range from 6300 to 10100 Å. The OG570 order-blocking filter was used to eliminate second-order light. Flat-field exposures of the interior of the telescope dome were used to normalize the response of the detector, and HgNeAr arc lamps were taken after each program object to obtain the wavelength calibration. Because our targets were late-T dwarfs, for which the 9300 Å band of H₂O is the most important spectral diagnostic, observations of G0 dwarf stars near in airmass and near in time were needed to correct for telluric H₂O at these same wavelengths. Observations were typically acquired with the slit oriented to the parallactic angle to minimize wavelength-dependent slit losses. Once per night, a standard star from the list of Hamuy et al. (1994) was observed to provide flux calibration. The data were reduced and calibrated using standard IRAF routines as described in Kirkpatrick et al. (1999) and Kirkpatrick et al. (2006).

SpeX, a medium-resolution spectrograph and imager at NASA's 3 m Infrared Telescope Facility (IRTF) on Mauna Kea, Hawai'i, uses a 1024 × 1024 InSb array for its spectroscopic observations (Rayner et al. 2003). We used the prism mode with a 05 wide slit to achieve a resolving power of R ≡ λ/Δλ ≈ 150 over the range 0.8–2.5 μm. A series of 120 s or 180 s exposures were typically obtained at two different nod positions along the 15'' long slit. A0 dwarf stars at similar airmass to the target were observed near in time for telluric correction and flux calibration. Observations were typically obtained with the slit oriented to the parallactic angle to minimize slit loses and spectral slope variations due to differential atmospheric refraction. Finally, a set of exposures of internal flat field and argon arc lamps were obtained for flat fielding and wavelength calibration.

The data were reduced using Spextool (Cushing et al. 2004) the IDL-based data reduction package for SpeX. The raw images were first corrected for nonlinearity, pair subtracted, and then flat fielded. For some of the fainter sources, multiple pair-subtracted images were averaged in order to facilitate tracing. The spectra were then optimally extracted (e.g., Horne 1986) and wavelength calibrated using the argon lamp exposures. Multiple spectra were then averaged and the resulting spectrum was corrected for telluric absorption and flux calibrated using observations of an A0 V star using the technique described in Vacca et al. (2003).

The Near-Infrared Spectrometer (NIRSPEC; McLean et al. 1998, 2000) at the 10 m W. M. Keck Observatory on Mauna Kea, Hawai'i, uses a 1024 × 1024 InSb array for spectroscopy. In a 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 either or both of the N3 and N5 configurations (see McLean et al. 2003) that cover the portion of the J-band window from 1.15 to 1.35 μm and the portion of the H-band window from 1.5 to 1.8 μm.

Data were typically obtained in four or more sets of dithered pairs, with a 300 s exposure obtained at each dither position. To measure telluric absorption and to calibrate the flux levels, A0 dwarf stars were observed near in time and airmass to the target. Other calibrations consisted of neon and argon arc lamp spectra, dark frames, and spectra of a flat-field lamp. We employed standard reductions using the REDSPEC package, as described in McLean et al. (2003).

The Folded-port Infrared Echellette (FIRE; Simcoe et al. 2008, 2010) at the 6.5 m Magellan Baade Telescope uses a 2048 × 2048 HAWAII-2RG array. In its high-throughput prism mode, it covers the wavelength range from 0.8 to 2.5 μm at a resolution ranging from R = 500 at the J band to R = 300 at the K band for a slit width of 06. Typically, each observation used the 50'' long slit aligned to the parallactic angle, and consisted of a series of nod pairs taken with exposure times not exceeding 120 s per position. The spectrograph detector was read out using the four-amplifier mode at "high gain" (1.2 counts per e⁻) with the Fowler-8 sampling mode. We also obtained exposures of a variable voltage quartz lamp (set at 1.2 V and 2.2 V) for flat-fielding purposes and neon/argon arc lamps were used for wavelength calibration. A0 dwarf stars were used for telluric and flux calibration.

Data were reduced using a modified version of Spextool. In contrast to SpeX, the spatial axis of the FIRE slit is not aligned with the columns of the detector so that the wavelength solution is not only a function of the column number but also of the row number. We therefore derived a two-dimensional (2D) wavelength solution in two steps. First, a one-dimensional (1D) wavelength solution applicable to the center of the slit was determined using the night-sky OH emission lines (Cushing et al. 2004). Second, the OH emission lines were used to map the optical distortions in the spatial and dispersion axes within each order. The 1D wavelength solution and distortion maps were then combined to assign a wavelength and spatial position to each pixel in each order.

With the wavelength calibration completed, the remainder of the reduction steps could proceed. Pairs of images taken at different positions along the slit were subtracted in order to remove the bias and dark current as well as to perform a first-order sky subtraction. The resulting pair-subtracted image was then flat fielded using a normalized flat constructed from dome flats taken at the start of each night. The spectral extraction followed the technique described in Smith et al. (2007). A set of "pseudorectangles" was defined spanning each order to map out positions of constant wavelength on the detector. These rectangles are themselves composed of pseudopixels with a width and height of ∼1 detector pixel. The pseudorectangles were then extracted using a polygon clipping algorithm (Sutherland & Hodgman 1974), producing 1D profiles of the slit at each wavelength. Spectral extraction including residual background subtraction could then proceed in the standard way. The raw spectra were then combined and corrected for telluric absorption and flux calibrated using the observations of an A0 V star and the technique described in Vacca et al. (2003).

The Triple Spectrograph (TSpec) at the 5 m Hale Telescope at Palomar Observatory uses a 1024 × 2048 HAWAII-2 array to cover simultaneously the range from 1.0 to 2.45 μm (Herter et al. 2008). With a 1 × 30 arcsec slit, it achieves a resolution of ∼2700. Observations were acquired in an ABBA nod sequence with an exposure time per nod position not exceeding 300 s to mitigate problems with changing OH background levels. Observations of A0 dwarf stars were taken near in time and near in airmass to the target objects and were used for telluric correction and flux calibration. Dome flats were taken to calibrate the pixel-to-pixel response. Data reduction is identical to that discussed above for FIRE because Spextool required the same changes for TSpec reductions as it did for FIRE reductions.

The Ohio State Infrared Imager/Spectrometer (OSIRIS) mounted at the 4.1 m Southern Astrophysical Research Telescope (SOAR) located at Cerro Pachón, Chile, uses a 1024 × 1024 HgCdTe array. The 10 wide slit yields a resolving power of R ≈ 1400 across the 1.18–2.35 μm wavelength range in three spectral orders. Short exposures (180 s) were taken at six or seven positions nodded along the 24'' long slit. A0 dwarf stars were observed for telluric correction and flux calibration. Wavelength calibration was based on the OH airglow lines. The data were reduced using a modified version of the Spextool data reduction package. (See Section 4.2 for a description of Spextool.) The three spectral orders were then merged into a single spectrum covering the entire wavelength range.

The Wide Field Camera 3 (WFC3) on board the Hubble Space Telescope (HST) employs a 1024 × 1024 HgCdTe detector with a plate scale of 013 pixel⁻¹ to image a field of view of 123 × 126 arcsec. We used the G141 grism to acquire slitless spectroscopy over the 1.1–1.7 μm range for faint targets not observable from ground-based facilities (Program 12330; PI: J. D. Kirkpatrick). The resulting resolving power, R ≈ 130, is ideal for the broad characterization of faint sources. Three spectra—those of WISEPC J145018.40+553421.4, WISEPA J173835.53+273258.9, and WISEPA J182831.08+265037.8—were obtained with this setup. For each target, we first obtained four direct images through the F140W filter in MULTIACCUM mode using the SPARS25 sampling sequence. The telescope was offset slightly between each exposure. We then obtained four dispersed images with the G141 grism using MULTIACCUM mode and a SPARS50 sequence. These dispersed images were acquired at the same positions/dithers as used in the direct images.

Bias levels and dark current were first subtracted from the data images using version 2.3 of the CALWFC3 pipeline. CALWFC3 also flat fields the direct images, but the grism images are flat fielded during the extraction process described below. Spectra were then extracted using the aXe software (Kümmel et al. 2009). Because aXe requires knowledge of the position and brightness of the targets in the field of view, we combined the four direct images using MULTIDRIZZLE (Koekemoer et al. 2002) and the latest Instrument Distortion Coefficient Table (IDCTAB). SExtractor (Bertin & Arnouts 1996) was then used to produce a catalog of objects in the field. For each cataloged object, 2D subimages centered on the first-order spectra of each object were combined using AXEDRIZZLE to produce a final spectral image. These subimages were used to extract flux-calibrated spectra. Additional details on the data reduction process are discussed in Cushing et al. (2011).

The list of spectroscopically confirmed WISE brown dwarfs is given in Table 4. Abbreviated source names³⁶ are shown in Column 1; optical spectral types are shown in Column 2; near-infrared types are shown in Column 3; and the source of the spectrum, integration time, telluric corrector star (for ground-based observations), and observation date are shown in Columns 4–7. The optical and near-infrared classifications of these sources are discussed further below.

5.1.1. Optical Spectral Types

Keck/LRIS spectra were obtained for seven of our candidates. Reduced spectra from 8000 to 10000 Å are shown in Figure 15, all of which have been corrected for telluric absorption over the regions 6867–7000 Å (the Fraunhofer B band, caused by O₂ absorption), 7594–7685 Å (the Fraunhofer A band, again caused by O₂), and 7186–7273, 8162–8282, and ∼8950–9650 Å (all caused by H₂O absorption). These spectra show the hallmarks of T dwarf optical spectra: strong H₂O absorption with a bandhead at 9250 Å, along with Cs i absorption at 8521 and 8943 Å in the earlier objects and CH₄ absorption between 8800 and 9200 Å in the later objects.

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By-eye comparisons to the T dwarf optical spectral standards of Burgasser et al. (2003a) show that these spectra range in type from T_o5 for WISE 1841+7000 to later than T_o8 for WISE 1741+2553. (The "o" subscript is used to denote spectral types assigned based on optical spectra.) This latter spectrum is unusual in that it has stronger 8800–9200 Å CH₄, stronger 9250–9400 Å H₂O bands of the 3(ν₁,ν₃) transition, and stronger 9450–9800 Å H₂O bands of the 2(ν₁,ν₃) + 2(ν₂) transition than the latest T dwarf optical standard, the T_o8 dwarf 2MASS J04151954−0935066 (Burgasser et al. 2003a). We therefore propose that WISE 1741+2553 be the spectral standard for a newly adopted T_o9 spectral class. Figure 16 illustrates the entire sequence of T dwarf optical standards from Burgasser et al. (2003a) appended with the proposed T_o0 standard SDSSp J083717.22−000018.3 from Kirkpatrick (2008) and this newly proposed T_o9 standard.

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Further evidence in support of a new optical standard is shown in Figure 17. Shown here is a comparison of the spectrum of WISE 1741+2553 with our LRIS spectrum of the bright, late-T dwarf UGPS J072227.51−054031.2, which Cushing et al. (2011) have proposed as the infrared spectral standard for type T9. As our comparison shows, the CH₄ and H₂O depths are very similar between these two objects and both are distinctly different from the T_o8 standard. Thus, identifying WISE 1741+2553 as the new T_o9 anchor point would help link the optical and near-infrared sequences, especially since WISE 1741+2553 is also classified as a T9 on the near-infrared scheme. See further discussion in the Appendix.

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5.1.2. Near-infrared Spectral Types

All of the confirmed brown dwarfs listed in Table 4 have near-infrared follow-up spectra. These spectra were classified using the near-infrared M and L sequences of Kirkpatrick et al. (2010) and the near-infrared T0-to-T8 dwarf sequence of Burgasser et al. (2006b). Cushing et al. (2011) have extended classifications to T9 and Y0 and have reclassified previously discovered >T8 dwarfs from the literature on this system. This extension of the classification system uses UGPS 0722−0540 as the near-infrared T9 standard and WISE 1738+2732 as the Y0 standard.

Assignment of spectral types was done by overplotting spectra of these standards onto the candidate spectra and determining by-eye which standard provided the best match. In some cases two adjacent standards, such as T7 and T8, provided an equally good match, so the candidate spectrum was assigned an intermediate type, in this case, of T7.5. For L dwarfs, the comparison was done at J band and, following the prescription discussed in Kirkpatrick et al. (2010), any anomalies at the H and K bands were noted. Spectra that did not match any of the standards well are marked with a "pec" suffix to indicate that they are peculiar. As a further example, an object that best fit the L9 spectral standard at the J band but failed to provide a good match to the L9 standard at longer wavelengths because it was considerably redder than the standard was assigned a type of "L9 pec (red)." See Kirkpatrick et al. (2010) for examples of similar classifications.

In Figures 18–25, we show the near-infrared spectra for each of our sources. Because of the narrow wavelength ranges covered by the Keck/NIRSPEC and SOAR/OSIRIS spectra, those data are plotted separately in Figures 26 and 27.

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5.1.3. Discussion

Near-infrared spectral types (and optical spectral types, for those with Keck/LRIS spectra) are listed in Table 4 for all WISE brown dwarf discoveries. For objects with near-infrared spectral types of T0 or later, Figure 28 shows the number of newly discovered objects per spectral type bin compared to the number of objects previously published. Whereas there were 16 objects known previously with types of T8 or later (Burgasser et al. 2002; Tinney et al. 2005; Looper et al. 2007; Warren et al. 2007; Delorme et al. 2008, 2010; Burningham et al. 2008, 2009, 2010b, 2011a; Goldman et al. 2010; Lucas et al. 2010), the tally now stands at 58 once our objects are added. WISE has already identified seventeen new objects with types equal to or later than the T9 UGPS J072227.51−054031.2, the previous record holder for latest measured spectral type, and six of these belong to the Y dwarf class (Cushing et al. 2011).

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Figures 1–3 and 5–14, discussed previously, show the locations of these newly discovered WISE brown dwarfs (black symbols) in color space. The T9, T9.5, and early-Y dwarfs continue the trend toward redder W1 − W2, ch1 − ch2, J − W2, H − W2, J − ch2, and H − ch2 colors, with the reddest object being the >Y0 dwarf WISE 1828+2650 (J − W2 = 9.39 ± 0.35 mag; J on the MKO filter system). The blueward trend in J − H color seen for later T dwarfs, however, begins to reverse near a spectral type of Y0. In particular, the J − H color of WISE 1828+1650 is dramatically redder (J − H = 0.72 ± 0.42 mag; MKO filter system) than any of the late-T or Y0 dwarfs, the latter of which show a large scatter in J − H colors themselves. Cushing et al. (2011) explore the trend of J − H colors in more detail and show that the synthetic photometry derived from our observed spectra generally agree with photometry measured from direct imaging. Given the large spread in J − H color observed for the six Y dwarfs already identified, JHK_s colors alone cannot be used to confirm or deny objects as cold as Y dwarfs.

Distances to the new WISE brown dwarf discoveries can be estimated based on their W2 magnitudes and measured spectral types. First, however, the relation between absolute W2 magnitude and spectral type needs to be established using objects with measured trigonometric parallaxes and WISE W2 detections. Figure 29 shows the trend of absolute W2 magnitude as a function of near-infrared spectral type for previously published objects whose measured parallaxes are at least three times the measurement error (Table 5). A third-order least-squares relation, weighted by the errors on the M_W2 values, is shown by the black curve in Figure 29. For this fit, objects known to be binary (red points) have been omitted. The resulting relation is

$$\begin{eqnarray*} M_{W2} &=& 9.692 + 0.3602({\rm Type}) - 0.02660({\rm Type})^2 \nonumber\\ &&+ 0.001020({\rm Type})^3, \end{eqnarray*}$$

where Type is the near-infrared spectral type on the system where L0 = 0, L5 = 5, T0 = 10, T5 = 15, and Y0 = 20.

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Table 5. L and T Dwarfs with Measured Trigonometric Parallaxes

Object Name	πtrig	Ref.	NIR Sp.	W2	H
	(mas)		Type	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)
(a) Objects not known to be binary
UGPS J072227.51−054031.2	246 ± 33	2	T9	12.197 ± 0.027	16.147 ± 0.205
DENIS J081730.0−615520	203 ± 13	3	T6	11.237 ± 0.017	13.526 ± 0.031
DENIS-P J0255−4700	201.37 ± 3.89	4	L8	10.190 ± 0.021	12.204 ± 0.024
2MASSI J0415195−093506	174.34 ± 2.76	5	T8	12.232 ± 0.026	15.537 ± 0.113
Gliese 570D	169.3 ± 1.7	6	T7.5	12.105 ± 0.026	15.268 ± 0.089
2MASSI J0937347+293142	163.39 ± 1.76	7	T6	11.652 ± 0.023	14.703 ± 0.068
2MASSW J1507476−162738	136.4 ± 0.6	8	L5	10.367 ± 0.022	11.895 ± 0.024
2MASSW J0036159+182110	114.2 ± 0.8	8	L3.5	10.239 ± 0.020	11.588 ± 0.029
2MASSI J0727182+171001	110.14 ± 2.34	5	T7	12.969 ± 0.033	15.756 ± 0.171
CFBDS J005910.90−011401.3	108.2 ± 5.0	1	T8.5	13.668 ± 0.044	18.270 ± 0.050
2MASS J05591914−1404488	97.7 ± 1.3	8	T4.5	11.891 ± 0.023	13.679 ± 0.044
ULAS J133553.45+113005.2	96.7 ± 3.2	1	T8.5	13.839 ± 0.046	18.250 ± 0.010
2MASS J12373919+6526148	96.07 ± 4.78	5	T6.5	12.922 ± 0.028	15.739 ± 0.145
2MASSI J0825196+211552	93.8 ± 1.0	8	L7.5	11.574 ± 0.022	13.792 ± 0.032
2MASSI J0243137−245329	93.62 ± 3.63	5	T6	12.929 ± 0.030	15.137 ± 0.109
SDSSp J162414.37+002915.6	90.9 ± 1.2	9	T6	13.077 ± 0.032	15.524 ± 0.100
2MASSI J1217110−031113	90.8 ± 2.2	9	T7.5	13.195 ± 0.035	15.748 ± 0.119
2MASSI J1546291−332511	88.0 ± 1.9	9	T5.5	13.439 ± 0.039	15.446 ± 0.092
SDSSp J125453.90012247.4	84.9 ± 1.9	8	T2	12.391 ± 0.037	14.090 ± 0.025
ULAS J003402.77−005206.7	78.0 ± 3.6	1	T8.5	14.465 ± 0.076	18.490 ± 0.040
SDSSp J053951.99−005902.0	76.12 ± 2.17	5	L5	11.569 ± 0.021	13.104 ± 0.026
2MASSW J1439284+192915	69.6 ± 0.5	8	L1	10.936 ± 0.021	12.041 ± 0.019
2MASSI J2356547−155310	68.97 ± 3.42	5	T5.5	13.641 ± 0.041	15.630 ± 0.100
SDSSp J134646.45−003150.4	68.3 ± 2.3	9	T6.5	13.560 ± 0.042	15.459 ± 0.118
2MASSW J1632291+190441	65.6 ± 2.1	8	L8	12.598 ± 0.028	14.612 ± 0.038
DENIS-P J1058.7−1548	57.7 ± 1.0	8	L3	11.758 ± 0.023	13.226 ± 0.025
2MASSW J1658037+702701	53.9 ± 0.7	8	L1	11.388 ± 0.022	12.470 ± 0.032
Gliese 584C	53.70 ± 1.24	6	L8	12.996 ± 0.033	14.928 ± 0.081
SDSSp J132629.82−003831.5	49.98 ± 6.33	5	L8	12.718 ± 0.030	15.050 ± 0.060
SDSS J015141.69+124429.6	46.73 ± 3.37	5	T1	13.823 ± 0.053	15.603 ± 0.112
SDSSp J144600.60+002452.0	45.46 ± 3.25	5	L6	12.882 ± 0.034	14.514 ± 0.035
SDSSp J175032.96+175903.9	36.24 ± 4.53	5	T3.5	14.414 ± 0.057	15.952 ± 0.132
2MASSW J0030300−145033	37.42 ± 4.50	5	L7	13.241 ± 0.034	15.273 ± 0.100
2MASSI J1711457+223204	33.11 ± 4.81	5	L6.5	13.802 ± 0.040	15.797 ± 0.109
GD 165Ba	31.7 ± 2.5	10	L4	13.042 ± 0.032	14.781 ± 0.070
2MASSW J1328550+211449	31.0 ± 3.8	8	L5	13.383 ± 0.036	15.002 ± 0.081
2MASSW J0326137+295015	31.0 ± 1.5	8	L3.5	12.746 ± 0.029	14.395 ± 0.050
SDSSp J003259.36+141036.6	30.14 ± 5.16	5	L8	13.600 ± 0.041	15.648 ± 0.142
SDSS J020742.48+000056.2	29.3 ± 4.0	1	T4.5	15.035 ± 0.100	>16.396
ULAS J082707.67−020408.2	26.0 ± 3.1	1	T5.5	15.290 ± 0.142	17.440 ± 0.050
HD 89744B	25.65 ± 0.70	6	L0	12.759 ± 0.029	14.022 ± 0.033
SDSSp J225529.09−003433.4	16.19 ± 2.59	5	L0	13.715 ± 0.052	14.756 ± 0.058
(b) Known binaries/multiples:
Ind Bab	275.76 ± 0.69	6	T1	9.443 ± 0.020	11.510 ± 0.020
2MASSI J0746425+200032	81.9 ± 0.3	8	L0.5	9.889 ± 0.022	11.007 ± 0.022
2MASS J12255432−2739466	75.1 ± 2.5	9	T6	12.692 ± 0.030	15.098 ± 0.081
2MASSI J1534498−295227	73.6 ± 1.2	9	T5.5	12.592 ± 0.029	14.866 ± 0.102
SDSSp J042348.57−041403.5	65.93 ± 1.70	5	T0	11.559 ± 0.025	13.463 ± 0.035
HN Peg B	54.37 ± 0.85	6	T2.5	12.574 ± 0.029	15.400 ± 0.030
Kelu-1AB	53.6 ± 2.0	8	L2	10.918 ± 0.025	12.392 ± 0.025
DENIS-P J0205.4−1159	50.6 ± 1.5	8	L7	11.724 ± 0.030	13.568 ± 0.037
DENIS-P J1228.2−1547	49.4 ± 1.9	8	L5	11.675 ± 0.034	13.347 ± 0.032
Gliese 417BC	46.04 ± 0.90	6	L4.5	11.616 ± 0.023	13.499 ± 0.032
2MASSW J1728114+394859	41.49 ± 3.26	5	L7	12.597 ± 0.017	14.756 ± 0.066
G 124-62B	36.39 ± 3.57	4	L0.5	12.077 ± 0.026	13.190 ± 0.031
SDSS J102109.69−030420.1	34.4 ± 4.6	9	T3	13.773 ± 0.041	15.346 ± 0.101
2MASSW J2101154+175658	30.14 ± 3.42	5	L7.5	13.512 ± 0.036	15.861 ± 0.182

Notes. ^aIt is assumed that most of the W2 flux comes from the L dwarf companion and not the white dwarf primary. References. (1) Marocco et al. 2010; (2) Lucas et al. 2010; (3) Artigau et al. 2010; (4) Costa et al. 2006; (5) Vrba et al. 2004; (6) Perryman et al. 1997; (7) Schilbach et al. 2009; (8) Dahn et al. 2002; (9) Tinney et al. 2003; (10) van Altena et al. 1995.

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Using this relation, we have estimated distances to our WISE discoveries. These are given in Column 2 of Table 6. (The distance to the lone M dwarf, WISE 0106+1518, was estimated using 2MASS magnitudes and the near-infrared absolute magnitudes listed in Table 3 of Kirkpatrick & McCarthy 1994.) These distance estimates for the late-T dwarfs and Y dwarfs are shown graphically in Figure 30. Also shown in the figure are previously published late-T dwarfs from other surveys. WISE has sufficient sensitivity to detect the latest T dwarfs out to 15–20 pc and because of its all-sky coverage can complete the census of the solar neighborhood for these objects. As the figure shows, 12 of our objects have estimated distances placing them within 10 pc of the Sun, and 2 of these have estimates placing them within 5 pc. It should also be noted that the fitted relation shown in Figure 29 may lead to overestimated distances for objects at the latest types because the relation falls above all four of the previously published T8.5 and T9 dwarfs on that plot. Furthermore, the extrapolation of this relation to even later Y dwarf types may lead to even more discrepant distance overestimates, as discussed further in the caption to Figure 29. Measuring trigonometric parallaxes for more of these latest T dwarfs and early-Y dwarfs will be an important, early step in characterizing the physical nature of these objects.

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Because these objects should all lie very close to the Sun, their observed parallaxes will be large. Thanks to its survey strategy, WISE performed its two passes of the sky with observations always near 90° solar elongation, thus capitalizing on the maximum parallactic angle at both epochs. (For objects observed during the final ∼2 weeks of WISE operations, three epochs of WISE data are available.) Objects will, of course, also show displacements due to proper motion, so observations at other epochs and/or from other surveys are necessary to disentangle the two effects. Hence, ancillary astrometry from 2MASS and SDSS and our own follow-up observations from the ground and from space (Spitzer and HST) are invaluable. Currently available astrometric data points³⁷ are shown in Columns 3–8 of Table 6.

It should be noted here that positions of objects in the WISE preliminary data release may be offset from their true positions by many times the quoted positional uncertainty. Approximately 20% of the sources fainter than W1 ≈ 14.5 mag in the Preliminary Release Source Catalog suffer from a pipeline coding error that biases the reported position by ∼0.2–1.0 arcsec in the declination direction while an increasingly smaller fraction of the sources suffer this effect to magnitudes as bright as W1 ≈ 13.0 mag. The Cautionary Notes section of the WISE Preliminary Release Explanatory Supplement describes the origin and nature of this effect in detail. For this paper, we have rerun the WISE images for our sources through a version of the WISE pipeline that eliminates this source of systematic error, and we list those remeasured positions in Table 6. This version of the pipeline is essentially the same one used to process data for the WISE Final Data Release.

Astrometric fits were made to the multiple observations of each source. These fits solved for five parameters: initial (time = t_i) positional offsets of Δα and Δδ in right ascension (α) and in declination (δ), the right ascension component of proper motion (μ_α = (cos δ)dα/dt), the declination component of proper motion (μ_δ = dδ/dt), and the parallax (π_trig). For all but four sources, the data were not sufficient to find an accurate distance, so the distance was forced to equal the spectrophotometric estimate, and the fit only solved for the first four parameters; the four sources with a preliminary parallax measurement are listed in Table 7 and are discussed individually in the Appendix. The equations used are

$$\begin{eqnarray*} &&\cos \delta _1 (\alpha _i-\alpha _1) = \Delta \alpha + \mu _\alpha (t_i-t_1) + \pi _{{\rm trig}} \vec{R}_i \cdot \hat{W}, \;\;{\rm and} \end{eqnarray*}$$

$$\begin{eqnarray*} &&\delta _i-\delta _1 = \Delta \delta +\mu _\delta (t_i-t_1) - \pi _{{\rm trig}} \vec{R}_i \cdot \hat{N}. \end{eqnarray*}$$

The subscript i refers to the individual astrometric measurements, where t_i is the observation time in years, and R_i is the vector position of the observer relative to the Sun in celestial coordinates and astronomical units. $\hat{N}$ and $\hat{W}$ are unit vectors pointing north and west from the position of the source. R_i is the position of the Earth for 2MASS, SDSS, WISE, and HST observations; for Spitzer observations, R_i is the position of the spacecraft. The observed positional difference on the left-hand side is in arcseconds, the parameters Δα and Δδ are in arcseconds, the proper motion μ_α and μ_δ are in arcsec yr⁻¹, and the parallax π_trig is in arcsec.

These equations are solved using standard weighted least-squares techniques, which also provide the uncertainties in the parameters. These uncertainties come from propagating the uncertainties in the input. The χ² and number of degrees of freedom are also given and can be used to assess the quality of the fit. The resulting proper motions in R.A. and decl. are listed in Columns 9 and 10 of Table 6. For motions with a significance of >3σ, the total proper motion is listed in Column 11 along with the tangential velocity in Column 12.

The brown dwarf discoveries presented here represent only a fraction of the brown dwarf candidates identified so far from WISE data. WISE co-added data are not available across the entire sky, and many of those co-adds do not reach the full survey depth. Nonetheless, we can use these preliminary results to assess our progress toward completing the tally of cold brown dwarfs in the Solar Neighborhood and gauging the functional form of the mass function for these objects by using lower limits to their space densities.

Our goal is to complete an all-sky census of objects out to a specified maximum distance for each spectral subtype of T6 or later. Table 8 divides our discoveries into six spectral type bins (Column 1) from T6 through >Y0. The approximate range in effective temperature is given for each bin in Column 2. These temperature bins are assigned as follows. We took the values of T_eff for T dwarfs of type T6 and later as computed by Warren et al. (2007), Delorme et al. (2008), Burningham et al. (2008), Burgasser et al. (2010b), Lucas et al. (2010), Burgasser et al. (2011a), Burningham et al. (2011b), Burningham et al. (2011a), Bochanski et al. (2011), and Cushing et al. (2011) or compiled by Kirkpatrick (2005). Then, when necessary, we re-assigned spectral types to these objects so that they matched the near-infrared spectral classification scheme of Burgasser et al. (2006b) or its extension beyond T8 by Cushing et al. (2011). We then examined the distribution of temperature within each integral spectral type bin and found that a 150 K width for each bin was enough to encompass the T_eff values for most of the objects. The final assignments are given in Column 2 of Table 8.

As shown in Figure 30, the depth of our current search translates to different distances for each bin. In the spirit of determining the space density using a well defined census of the solar neighborhood, we limit our sample to those objects falling within 20 pc of the Sun even if WISE can sample that spectral type to larger distances. Only in the last three bins—the T9–T9.5 bin and the Y dwarf bins—is WISE incomplete at this distance, so those bins are limited to volumes with smaller radii. These values, called d_max, are listed in Column 3.

Next, the number of objects per spectral type bin lying closer than the value of d_max is tabulated for previously published objects (Column 4), for our new WISE discoveries (Column 5), and in total (Column 6). Distances are determined using trigonometric parallaxes, if available, or spectrophotometric estimates if no parallax has been measured. The resulting space density in each bin is given in Column 7.

This simple calculation of the space densities can be overestimated for the following reasons.

• 1.  
  Spectrophotometric distance estimates have an inherent bias. The absolute magnitude versus spectral type relation is based on parallaxes, and those parallax measurements lead to a bias in estimated distances because a parallax value of π_trig ± σ is more likely to represent an object farther away (π_trig − σ) than an object closer (π_trig + σ) because the volume of space between parallax values of π_trig and π_trig − σ is larger than that sampled between parallax values of π_trig and π_trig + σ. Thus, the observed values of π_trig are larger than the true values and the measured absolute values will be systematically too large. A correction can be applied that depends only on the value of σ/π_trig (see Table 1 of Lutz & Kelker 1973). Most of the parallaxes in Table 5 have σ/π_trig values of less than 5% where the correction to the absolute magnitude is ⩽0.02 mag, and those with larger errors have already been downweighted in our fit. We therefore conclude that the Lutz–Kelker effect is negligible here.
• 2.  
  Both the Malmquist bias and the Eddington bias can be largely accounted for by limiting the sample over which we derive our space densities. Malmquist bias (Malmquist 1920), in which more luminous objects can preferentially bias statistics in a magnitude limited sample, can be eliminated by calculating space densities in narrow spectral type bins in which all objects have the same (or nearly the same) intrinsic luminosity. The Eddington bias (Eddington 1913; Eddington 1940), in which random errors will bias magnitude measures to brighter values due to the fact that there are more objects in the more distant (fainter) population than in the closer (brighter) one, can be reduced by operating at magnitudes where the random errors are still small. By using the brighter and better measured W2 values to estimate distances, we can reduce the effects of Eddington bias on our derived densities. (For further discussion, see also Teerikorpi 2004.)
• 3.  
  Unresolved binarity will cause distances to be underestimated. This may cause a more distant object to appear closer than it really is and falsely inflate the space density. Empirical data presented earlier can be used to estimate this degree of binary contamination. Figure 29 shows a well-defined binary sequence (red) overlying the sequence of single objects on the M_W2 versus spectral type diagram. If we compute the ratio of known binaries to total objects between L0 and T4, we find that 12/35, or 34%, are binary. (See also Section 7.4 of Burgasser et al. 2006b for an in-depth discussion of intrinsic binarity, which varies from ∼20% at early-L to ∼42% at the L/T transition.) While this is a sizable percentage, it does not mean that all of the unresolved binaries fall outside of the sample considered. Some small fraction will still be contained within the distance limit and will have been undercounted by a factor of two. Nonetheless, binarity is likely the largest contributor to inflating density estimates.

On the other hand, other biases discussed below lead to an underestimate in the space densities. These effects are believed to overwhelm the effects detailed above, and hence our simple space density calculations, although preliminary, can be considered as lower limits to the true densities.

• 1.  
  Although WISE has taken data covering the entire sky at multiple epochs, the available co-added data cover less than 75% of the entire sky. Also, none of the sky has been co-added to its full depth using all available frames and the detection threshold for first-pass processing was set higher, in units of S/N, than it will be for final processing. The latter points are particularly important as they will, in the future, enable more robust colors or color limits for potential Y dwarf candidates. Moreover, we have followed up less than 50% of the brown dwarf candidates already culled from sections of the sky for which we have access. Thus, we believe that our current space density estimates are gross underestimates.
• 2.  
  Except for 2MASS, other surveys providing data in Column 4 of Table 8 do not have all-sky coverage and can only provide limited help in completing this nearby sample. Moreover, none of the current or planned ground-based surveys canvassing the sky for brown dwarfs can reach sizable populations of the coldest objects because Y dwarfs are intrinsically dim at ground-observable wavelengths. This is highlighted in Figure 31, which shows the absolute H-band magnitude as a function of spectral type. Note that the Y0 dwarf WISE 1541−2250 has M_H = 23.7 ± 0.9 mag; its absolute magnitude is M_J = 23.9 ± 0.8 mag and it is presumably even fainter than this shortward of J band. WISE operates at wavelengths where these objects are their brightest—five thousand times brighter at W2 than at the J and H bands, in the case of WISE 1828+2650—so it is the only survey capable of detecting the coldest brown dwarfs in significant numbers.
• 3.  
  As mentioned earlier, the M_W2 versus spectral type relation of Figure 29 likely overpredicts distances to dwarfs of type ⩾T9. This means that our surveyed volume may be overestimated, leading to an underestimate of the space density.
• 4.  
  Despite the all-sky coverage of WISE, the galactic plane will restrict our ability to probe to the same depths as other parts of the sky due to higher backgrounds and confusion. This loss of coverage is not currently accounted for in our density estimates.

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We have checked the distance distribution of objects in each spectral type bin by performing the V/V_max test (Column 8 of Table 8). This test was first proposed by Schmidt (1968) to check the uniformity of a distribution of objects in space. The quantity V is the volume of space interior to object i at distance d_i, and V_max is the full volume of space contained within the distance limit, d_max, of the sample. For a uniform sample, the average value, 〈V/V_max〉, should be 0.5 because half of the sample should lie in the nearer half of the volume and the rest should lie in the farther half. If this number is not near 0.5, then the sample is either non-isotropic or incomplete. For our sample we find that the T dwarf bins have 〈V/V_max〉 values considerably less than 0.5. This points to incompleteness in the sample—our low 〈V/V_max〉 values are almost certainly a consequence of the fact that the brighter (closer) candidates tend to be followed up first. This gives further credence to the assertion that our number densities are lower limits only. For the Y dwarf bins, however, the values of 〈V/V_max〉 are above 0.5, which further suggests that our assumed distances to these objects are overestimates.

Figure 32 shows these preliminary results (Column 9 of Table 8) relative to measurements made by other surveys and relative to predictions based on different forms of the underlying mass function. Previous results by Metchev et al. (2008), Burningham et al. (2010b), and Reylé et al. (2010) are shown by the open symbols and, with the possible exception of the Burningham et al. (2010b) point, support values of α of zero or greater, where the functional form is given as dN/dM∝M^−α. Our incomplete, volume-limited sample so far fails to put tighter constraints on the mass function at warmer temperatures than previously published work, but the preliminary lower limit to the Y0 space density already rules out the α = −1.0 model and may soon, with additional Y0 discoveries, be able to distinguish between the α = 0.0 and α = +1.0 models. Results for the early-Y dwarfs already suggest that the low-mass cutoff of star formation must be below 10 M_Jup if α ⩽ 0. This result is in accordance with findings in young star formation regions (e.g., Luhman et al. 2000; Muench et al. 2002; Lucas et al. 2006; Luhman 2007), but the derived masses for those objects should be considered cautiously, as discussed in Baraffe et al. (2003), because models with ages of ∼1 Myr or younger are highly sensitive to untested assumptions about initial conditions. Using models of older ages is far less sensitive to these assumptions, so field brown dwarfs provide a better check of star formation's low-mass cutoff. Model fits by Cushing et al. (2011) suggest that our Y dwarf discoveries have masses as high as 30 M_Jup or as low as 3 M_Jup or less, which agrees roughly with the mass values inferred from Figure 32.

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The J-band spectrum of this object, which was earlier cataloged as SIPS J0031−3840 and identified to be a nearby star via its high proper motion by Deacon et al. (2005), is a good match to the spectrum of the L2 standard (Figure 33), but the spectrum is much bluer than the standard at H and K bands. Because this source does not exhibit other telltale signs of low metallicity, such as strong hydride bands, we classify it as an "L2 pec (blue)." Martín et al. (2010) give an optical spectral type of L2.5 and do not note any peculiarities that might be attributable to low metallicity, either. Its near-infrared spectral morphology and discrepancy relative to its nearest standard is most similar to the "L1 pec (sl. blue)" object 2MASS J14403186−1303263 shown in Figure 32 of Kirkpatrick et al. (2010). Furthermore, this object has a larger W1 − W2 color than a typical L2 (see Figure 1) and a bluer J − H color (see Figure 5). As discussed in Kirkpatrick et al. (2010), the physical interpretation of these "blue L dwarfs" is not fully known and may differ from object to object. Some blue L dwarfs are blue, for example, because they are composite L + T dwarf binaries (e.g., Burgasser 2007). Model fitting suggests that others have thin cloud decks and/or large grains in their atmosphere, though neither seems to be directly attributable to gravity or metallicity effects (Burgasser et al. 2008). Kinematic analysis by Faherty et al. (2009) has shown that the blue L dwarfs have kinematics older than the field L dwarf population, but not nearly as old as that of low-metallicity M dwarfs. It is possible that some of the blue L dwarfs may be slightly metal poor, and that even a subtle lowering of the metal abundance in these objects may result in the directly measurable effects on the spectral energy distribution seen here.

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Despite the fact that the spectrum of this object matches very well to the J-band spectrum of the M8 standard, the H-band spectrum is more peaked than that seen in a normal M8, with the H₂O bands on either side of the H peak being stronger than in the standard (Figure 34). This object, which we classify as "M8 pec," is similar to the peculiar late-M dwarf 2MASS J18284076+1229207 shown in Figure 38 of Kirkpatrick et al. (2010). The cause of the peculiarity is not known, but appears not to be due to low gravity, as there are no peculiarities in the strength of the FeH bands between 0.9 and 1.3 μm when compared to the M8 standard. (See, for example, near-IR spectra of low-gravity late-M dwarfs in Figure 14 of Kirkpatrick et al. 2010.) This object also has a larger W1 − W2 color than a typical M8 (see Figure 1) and a bluer J − H color (see Figure 5). Curiously, this object has a sizable motion—μ = 0.412 ± 0.006 arcsec yr⁻¹—and a tangential velocity of 85.5 ± 1.3 km s⁻¹, suggesting that it may belong to an old population. The peculiar spectroscopic features may be caused in part by a slightly subsolar metallicity. Deacon et al. (2009) also identified this object as the high motion source ULAS2MASS J0106+1518, and their proper-motion determination (μ = 0.407 arcsec yr⁻¹) agrees with the one we derive here.

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The near-infrared spectrum of this object, discussed in Cushing et al. (2011), is distinctly later in type than the T9 near-infrared standard, UGPS J072227.51−054031.2, and is therefore classified as T9.5. Our spectrophotometric distance places it at 12.1 pc (Table 6). This is the only one of our ⩾T9.5 discoveries not detected in W3 and along with WISE 1738+2732 is one of only two ⩾T9.5 dwarfs detected in W1 (Table 2).

The J-band spectrum of this object closely matches that of the L9 spectral standard, but the H- and K-band portions are much redder than those of the standard L9 (Figure 35). This extremely red color is supported by independent photometry, namely J − K_s = 2.007 ± 0.137 mag, from the 2MASS All-Sky Point Source Catalog. This color is somewhat redder than the mean J − K_s color, ∼1.78 mag, of very late L's (Figure 14 of Kirkpatrick 2008). Because of its spectral peculiarity, we classify this object as "L9 pec (red)," and add it to the growing list of L dwarfs that appear red for reasons not obviously attributable to low gravity (see Table 6 of Kirkpatrick et al. 2010). The underlying physical cause for these "red L dwarfs" is not known, although two have been studied in detail by Looper et al. (2008). Using the small sample of red L dwarfs then known, Kirkpatrick et al. (2010) found that these objects, unlike young, low-gravity L dwarfs that are also redder than spectral standards of the same type, appear to have older kinematics than that of the field L dwarf population.

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This object is a nearby T8 dwarf at a spectrophotometric distance of d = 6.9 pc. Our astrometry (Table 6) over a 10.4yr baseline indicates a high motion of μ = 2.546 ± 0.046 arcsec yr⁻¹ and a large tangential velocity of 83.3 ± 1.5 km s⁻¹. Our preliminary trigonometric parallax measurement (Table 7) places this object at 6.1^+2.3_−1.4 pc, in excellent agreement with the spectrophotometric estimate.

This T8.5 dwarf has a spectrophotometric distance estimate of only 8.1 pc.

The near-infrared spectrum of this object, discussed in Cushing et al. (2011), is classified as Y0. Our distance estimate places it 9.0 pc from the Sun, and our measurement of the proper motion indicates that it may also be a high mover—μ = 2.429 ± 0.334 arcsec yr⁻¹—although the error bar is large (Table 6). As with most of the other Y dwarf discoveries, this object is detected by WISE only in bands W2 and W3 and not in W1 or W4 (Table 2).

The depths of the H₂O and CH₄ absorption bands in the J- and H-band spectra of this object best fit the T5 standard; however, the spectrum shows excess flux in the Y band around 0.95 to 1.10 μm and a flattening of the entire K-band spectrum (Figure 36). We therefore classify this object as a "T5 pec." Excess flux at Y band and a flattening at K have also been noted in Burgasser et al. (2006a) for the T6 pec dwarf 2MASS J09373487+2931409, which may be slightly metal-poor ([M/H] ≈ -0.5 to −0.1) based on fits to model spectra. Burgasser et al. (2011a) and Burgasser et al. (2010a) have noted the same peculiarities in the spectrum of the T7.5 dwarf ULAS J141623.94+134836.3 (Scholz 2010a; Burningham et al. 2010a), which is a common proper-motion companion to the nearby, late-L dwarf SDSS J141624.08+134826.7 (Schmidt et al. 2010; Bowler et al. 2010). The latter is classified by Kirkpatrick et al. (2010) as sdL7 and by Burningham et al. (2010a) as d/sdL7. Given that the two objects are presumably coeval, it can be assumed that they have the same metallicity and that the peculiar features in the spectrum of ULAS J141623.94+134836.3—and by extension, WISE 0448−1935—are caused by a metal content below solar. The high motion of WISE 0448−1935—μ = 1.168 ± 0.029 arcsec yr⁻¹, which translates into a tangential velocity of 118.5 ± 2.9 km s⁻¹ for an estimated distance of 21.4 pc—also indicates that this object belongs to an old kinematic population.

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This object was discussed in detail by Mainzer et al. (2011). Our distance estimate of 7.3 pc assumes a single source, but analysis of laser guide star adaptive optics data from Gelino et al. (2011) indicates that the source is a double in which the components have ΔJ ≈ ΔH ≈ 1 mag. Individual magnitudes are measured as J_A = 17.50 ± 0.09, J_B = 18.48 ± 0.12 and H_A = 17.81 ± 0.13, H_B = 18.81 ± 0.17 on the MKO filter system. Gelino et al. (2011) suggest an actual distance to the system of 12.3 ± 2.3 pc and individual spectral types of T8.5 and T9.

The J-band spectrum of this object best fits the T6 standard, but there are discrepancies at Y and K bands. At Y band the spectrum of WISE 0525+6739 shows excess flux relative to the standard, and at K band the spectrum shows less flux relative to the standard (Figure 37). We therefore classify this object as a "T6 pec." The physical cause, as discussed above for WISE 0448−1935, may be low metal content.

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The J-band spectrum of this object best fits the T7 standard, but there are discrepancies at the Y and K bands. At the Y band the spectrum of WISE 0528−3308 shows excess flux relative to the standard, and at the K band the spectrum shows less flux relative to the standard (Figure 38). We therefore classify this object as a "T7 pec." The physical cause, as discussed above for both WISE 0448−1935 and WISE 0525+6739, may be low metal content.

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The J-band spectrum of this object best fits the T8 standard, but there are major discrepancies at the Y and K bands. At the Y band the spectrum of WISE 0836−1859 shows excess flux relative to the standard, and at the K band the spectrum shows less flux relative to the standard (Figure 39). We therefore classify this object as a "T8 pec." Several other objects discussed in this section—WISE 0448−1935, WISE 0525+6739, WISE 0528−3308, WISE 1436−1814, WISE 2134−7137, and WISE 2325−4105—have similar Y- and K-band discrepancies, which may result from low metal content, but none are as severe as the discrepancies in this object. Unlike in those objects, the H-band flux in WISE 0836−1859 is markedly lower than the closest matching standard at J, making this object the most peculiar one of the group, and perhaps also the most metal poor.

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