A Volume-limited Sample of Ultracool Dwarfs. I. Construction, Space Density, and a Gap in the L/T Transition

Best et al. (2020, hereinafter Best20) used UKIRT/WFCAM to obtain parallaxes for 348 L0–T8 dwarfs with declinations −30° ≤ δ ≤ 60° and photometric distances ${d}_{\mathrm{phot}}\leqslant 25\,+1{\sigma }_{\mathrm{dist}}$ pc (i.e., no further beyond 25 pc than the distance uncertainty) based on AllWISE W2-band photometry (Cutri et al. 2014), with the goal of completing a volume-limited 25 pc sample for this portion of the sky (68.3% of the full sky). Additionally, we searched the literature for all spectroscopically confirmed objects in Best20's spectral type and decl. ranges that had parallax measurements with errors <20%, including parallaxes from Gaia DR2 (Gaia Collaboration et al. 2018). As in Best20, in all instances where an object has both an optical and an NIR spectral type, we adopted the optical types for L dwarfs and the NIR types for T dwarfs. After merging the Best20 and literature parallax lists and choosing the most precise parallax available for each object, we removed objects with parallaxes <40 mas (i.e., distances >25 pc) to define our volume-limited sample.

We present our volume-limited sample in Table 1. The sample includes 369 L0–T8 dwarfs and is constructed from 128 Best20 parallaxes, 121 from Gaia DR2, and 120 from other literature sources. Figure 1 shows the spectral-type distribution of our sample, featuring a clear deficit at early-T spectral types. This deficit was predicted by evolutionary models (e.g., Saumon & Marley 2008, hereinafter SM08) and seen in previous photometrically selected samples (Burgasser 2007a; Metchev et al. 2008; Reid et al. 2008b; Marocco et al. 2015; Best et al. 2018), and is now confirmed in our volume-limited sample, indicating that brown dwarfs cool through these spectral types (${T}_{\mathrm{eff}}$ ≈ 1400–1100; Luhman et al. 2007; Cushing et al. 2008; Stephens et al. 2009; King et al. 2010; Deacon et al. 2012a, 2012b, 2017b; Reylé et al. 2014; Filippazzo et al. 2015; Dupuy & Liu 2017) in a relatively short time. We also note an uneven distribution of L0–L5 dwarfs whose origin is unclear given that our sample is ≳90% complete at these types (Section 2.3). One possible contributing factor is that the spectral types are a mixture of optical and NIR assignments by many different astronomers using several methods. At the L0 boundary of our sample in particular, this lack of consistency in typing could potentially have impacted the choice of objects we included in our sample (we included L0 and later types, but not M9.5 and earlier types). However, the relative lack of L0 dwarfs compared with L1 dwarfs was seen previously in the more homogenously typed 20 pc samples of Cruz et al. (2007), Reid et al. (2008b), and BG19, which also included late-M dwarfs, suggesting that the L0 deficit is not a selection effect at the spectral-type boundary of our sample.

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Table 1.  Our Volume-limited 25 pc Sample of L0–T8 Dwarfs

Object	Distance	Parallax	Spectral Typea	Flagb	${Y}_{\mathrm{MKO}}$	${J}_{\mathrm{MKO}}$	${H}_{\mathrm{MKO}}$	${K}_{\mathrm{MKO}}$	References
	(pc)	(mas)	(Optical/NIR)		(mag)	(mag)	(mag)	(mag)	(Discovery; $\varpi$; SpT; Flag; Phot)
SDSS J000013.54+255418.6	14.1 ± 0.4	70.8 ± 1.9	T5/T4.5	⋯	15.80 ± 0.06	14.73 ± 0.03	14.74 ± 0.03	14.82 ± 0.03	108; 64; 153,29; –; 64,108
2MASS J00132229−1143006	24.8 ± 1.9	40.3 ± 3.1	.../T3pec	⋯	⋯	16.05 ± 0.02	[[15.74 ± 0.22]]	[[15.76 ± 0.22]]	97; 9; 97; –; 1,9,51
2MASSW J0015447+351603	17.06 ± 0.11	58.6 ± 0.4	L2/L1.0	⋯	[14.95 ± 0.05]	13.74 ± 0.02	[12.96 ± 0.02]	[12.25 ± 0.02]	101; 77; 101,5; –; 1,9
PSO J004.6359+56.8370	21.5 ± 1.8	46.5 ± 3.9	.../T4.5	⋯	⋯	16.22 ± 0.02	⋯	⋯	125; 9; 125; –; 9
2MASS J00282091+2249050	24.2 ± 1.2	41.3 ± 2.0	.../L7:	⋯	[16.82 ± 0.05]	15.49 ± 0.02	[14.55 ± 0.06]	[13.77 ± 0.06]	37; 77; 37; –; 1,9
WISE J003110.04+574936.3	14.1 ± 1.0	71.0 ± 5.0	.../L9	B	[15.92 ± 0.05]	14.796 ± 0.012	13.862 ± 0.014	[13.21 ± 0.03]	185; 9; 10; 12; 1,10
PSO J007.9194+33.5961	22.0 ± 1.8	45.4 ± 3.8	.../L9	⋯	[17.48 ± 0.06]	16.38 ± 0.02	[15.46 ± 0.05]	[14.67 ± 0.05]	11; 9; 11; –; 1,9
2MASS J00320509+0219017	24.4 ± 0.3	41.0 ± 0.4	L1.5/M9	⋯	15.443 ± 0.004	14.220 ± 0.002	13.446 ± 0.002	12.797 ± 0.002	164; 77; 164,193; –; 111
2MASS J00332386−1521309	22.9 ± 0.5	43.6 ± 0.9	L4 β/L1: fld-g	Y	[16.38 ± 0.08]	[15.22 ± 0.06]	[14.26 ± 0.04]	[13.39 ± 0.04]	84; 77; 48,3; 48,3; 1
2MASS J00345157+0523050	8.3 ± 0.2	120.1 ± 3.0	.../T6.5	⋯	16.213 ± 0.007	15.140 ± 0.004	15.576 ± 0.010	16.07 ± 0.03	26; 107; 29; –; 111
2MASSW J0036159+182110	8.74 ± 0.02	114.4 ± 0.2	L3.5/L4:	B	13.58 ± 0.06	12.30 ± 0.03	11.64 ± 0.03	11.04 ± 0.03	160; 77; 101,108; 8,156; 64,108
HD 3651B	11.137 ± 0.007	89.79 ± 0.06	.../T7.5	C	[17.12 ± 0.06]	16.16 ± 0.03	16.68 ± 0.04	16.87 ± 0.05	147; 77; 132; 147,132; 1,132
WISE J004024.88+090054.8	14.3 ± 0.3	69.8 ± 1.5	.../T7	⋯	17.15 ± 0.02	16.131 ± 0.011	16.56 ± 0.02	16.55 ± 0.05	135; 107; 135; –; 111
2MASSW J0045214+163445	15.38 ± 0.05	65.0 ± 0.2	L2 β/L2: vl-g	BY	[14.22 ± 0.05]	[12.98 ± 0.02]	[12.12 ± 0.02]	[11.33 ± 0.02]	193; 77; 48,3; 156,48,3; 1
WISE J004542.56+361139.1	18.7 ± 1.8	53.4 ± 5.2	.../T5	⋯	[16.81 ± 0.05]	15.91 ± 0.02	[16.13 ± 0.05]	[16.07 ± 0.05]	135; 9; 135; –; 1,9
WISEPC J004928.48+044100.1	16.0 ± 0.7	62.6 ± 2.9	.../L9	⋯	16.903 ± 0.012	15.767 ± 0.008	14.802 ± 0.006	14.131 ± 0.006	105; 9; 105; –; 111
SIPS J0050−1538	24.80 ± 0.15	40.3 ± 0.2	L1:/L0.5	⋯	[14.68 ± 0.05]	13.69 ± 0.02	[13.15 ± 0.03]	[12.62 ± 0.03]	54; 77; 47,5; –; 1,9
WISEA J010202.11+035541.4	24.9 ± 1.7	40.2 ± 2.8	.../L9	⋯	17.82 ± 0.03	16.67 ± 0.02	15.753 ± 0.012	15.066 ± 0.012	172; 9; 172; –; 111

Notes. This table lists all spectroscopically confirmed L0–T8 dwarfs having declinations between −30° and +60° and parallax-determined distances less than 25 pc. The table is available in its entirety in machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content. The full table contains 369 rows. ${Y}_{\mathrm{MKO}}$, ${J}_{\mathrm{MKO}}$, ${H}_{\mathrm{MKO}}$, and ${K}_{\mathrm{MKO}}$ photometry enclosed in single brackets indicates synthetic photometry (Section 2.5); double brackets indicates photometry converted from 2MASS into the MKO system using ${M}_{{Ks},2\mathrm{MASS}}$ and the polynomials of Dupuy & Liu (2017).

^aβ, γ, and δ indicate classes of increasingly low gravity based on optical (Kirkpatrick 2005; Cruz et al. 2009) or near-infrared (Gagné et al. 2015b; Cruz et al. 2018) spectra. fld-g indicates near-infrared spectral signatures of field-age gravity, int-g indicates intermediate gravity, and vl-g indicates very low gravity (Allers & Liu 2013). ^bB = binary (presented here as a single unresolved source); C = companion (resolved) to another star or brown dwarf; Y = young (≲200 Myr); S = subdwarf.

References. (1) This work, (2) Albert et al. (2011), (3) Allers & Liu (2013), (4) Artigau et al. (2006), (5) Bardalez Gagliuffi et al. (2014), (6) Beamín et al. (2013), (7) Beichman et al. (2014), (8) Bernat et al. (2010), (9) Best20, (10) Best et al. (2013), (11) Best et al. (2015), (12) W. Best et al. (2021, in preparation), (13) Bihain et al. (2013), (14) Boccaletti et al. (2003), (15) Bouy et al. (2003), (16) Bouy et al. (2005), (17) Bowler et al. (2010a), (18) Burgasser et al. (1999), (19) Burgasser et al. (2000a), (20) Burgasser et al. (2000b), (21) Burgasser et al. (2002), (22) Burgasser et al. (2003a), (23) Burgasser et al. (2003c), (24) Burgasser et al. (2003b), (25) Burgasser et al. (2003d), (26) Burgasser et al. (2004), (27) Burgasser et al. (2005b), (28) Burgasser et al. (2005a), (29) Burgasser et al. (2006a), (30) Burgasser et al. (2006b), (31) Burgasser & McElwain (2006), (32) Burgasser (2007b), (33) Burgasser et al. (2008a), (34) Burgasser et al. (2008b), (35) Burgasser et al. (2008c), (36) Burgasser et al. (2010b), (37) Burgasser et al. (2010a), (38) Burgasser et al. (2011), (39) Burningham et al. (2010b), (40) Burningham et al. (2010a), (41) Burningham et al. (2013), (42) Castro & Gizis (2012), (43) Castro et al. (2013), (44) Chiu et al. (2006), (45) Cruz et al. (2003), (46) Cruz et al. (2004), (47) Cruz et al. (2007), (48) Cruz et al. (2009), (49) Cushing et al. (2011), (50) Cushing et al. (2014), (51) Cutri et al. (2003), (52) Dahn et al. (2002), (53) Dahn et al. (2017), (54) Deacon et al. (2005), (55) Deacon et al. (2011), (56) Deacon et al. (2012a), (57) Deacon et al. (2012b), (58) Deacon et al. (2014), (59) Deacon et al. (2017a), (60) Deacon et al. (2017b), (61) Delfosse et al. (1997), (62) Delfosse et al. (1999), (63) Dupuy et al. (2009b), (64) Dupuy & Liu (2012), (65) Dupuy & Liu (2017), (66) Dupuy et al. (2020), (67) T. Dupuy (private communication), (68) Faherty et al. (2010), (69) Faherty et al. (2012), (70) Faherty et al. (2016), (71) Fan et al. (2000), (72) Folkes et al. (2012), (73) Gagné et al. (2015b), (74) Gagné et al. (2015a), (75) Gagné et al. (2017), (76) Gagné & Faherty (2018), (77) Gaia Collaboration et al. (2018), (78) Gauza et al. (2015), (79) Geballe et al. (2002), (80) Gelino et al. (2014), (81) Gizis et al. (2000a), (82) Gizis et al. (2001), (83) Gizis (2002), (84) Gizis et al. (2003), (85) Gizis et al. (2011b), (86) Gizis et al. (2011a), (87) Gizis et al. (2013), (88) Gizis et al. (2015b), (89) Goldman et al. (2010), (90) Gomes et al. (2013), (91) Goto et al. (2002), (92) Hall (2002a), (93) Hall (2002b), (94) Harris et al. (2015), (95) Hawley et al. (2002), (96) Kellogg et al. (2015), (97) Kellogg et al. (2017), (98) Kendall et al. (2004), (99) Kendall et al. (2007), (100) Kirkpatrick et al. (1999), (101) Kirkpatrick et al. (2000), (102) Kirkpatrick et al. (2001), (103) Kirkpatrick et al. (2008), (104) Kirkpatrick et al. (2010), (105) Kirkpatrick et al. (2011), (106) Kirkpatrick et al. (2014), (107) Kirkpatrick et al. (2019), (108) Knapp et al. (2004), (109) Koerner et al. (1999), (110) Lawrence et al. (2007), (111) Lawrence et al. (2012), (112) Leggett et al. (2000), (113) Leggett et al. (2002a), (114) Leggett et al. (2002b), (115) Leggett et al. (2009), (116) Leggett et al. (2010), (117) Liebert et al. (2003), (118) Liu et al. (2002), (119) Liu & Leggett (2005), (120) Liu et al. (2010), (121) Liu et al. (2011), (122) Liu et al. (2012), (123) Liu et al. (2013), (124) Liu et al. (2016), (125) M. Liu et al. (in prep), (126) Lodieu et al. (2005), (127) Lodieu et al. (2007), (128) Lodieu et al. (2012), (129) Looper et al. (2007b), (130) Looper et al. (2008b), (131) Lucas et al. (2012), (132) Luhman et al. (2007), (133) Luhman et al. (2012), (134) Luhman & Sheppard (2014), (135) Mace et al. (2013a), (136) Mace et al. (2013b), (137) Mamajek et al. (2018), (138) Manjavacas et al. (2013), (139) Marocco et al. (2010), (140) Marocco et al. (2013), (141) Marocco et al. (2015), (142) Martín et al. (1999a), (143) Martín et al. (2010), (144) Martin et al. (2018), (145) McMahon et al. (2013), (146) Metchev et al. (2008), (147) Mugrauer et al. (2006), (148) Murray et al. (2011), (149) Muzic et al. (2012), (150) Nakajima et al. (1995), (151) Peña Ramírez et al. (2015), (152) Phan-Bao et al. (2008), (153) Pineda et al. (2016), (154) Pinfield et al. (2008), (155) Pinfield et al. (2012), (156) Pope et al. (2013), (157) Potter et al. (2002), (158) Radigan et al. (2008), (159) Rebolo et al. (1998), (160) Reid et al. (2000), (161) Reid et al. (2001), (162) Reid et al. (2006b), (163) Reid et al. (2006a), (164) Reid et al. (2008b), (165) Ruiz et al. (1997), (166) Sahlmann et al. (2014), (167) Sahlmann et al. (2016), (168) Salim et al. (2003), (169) Schilbach et al. (2009), (170) Schmidt et al. (2010a), (171) Schmidt et al. (2010b), (172) Schneider et al. (2016a), (173) Scholz & Meusinger (2002), (174) Scholz (2010a), (175) Scholz (2010b), (176) Scholz et al. (2011), (177) Scholz et al. (2012), (178) Scholz et al. (2014), (179) Seifahrt et al. (2010), (180) Smart et al. (2013), (181) Smart et al. (2018), (182) Smith et al. (2018), (183) Strauss et al. (1999), (184) Stumpf et al. (2009), (185) Thompson et al. (2013), (186) Thorstensen & Kirkpatrick (2003), (187) Tinney et al. (2003), (188) Tinney et al. (2005), (189) Tinney et al. (2018), (190) Tsvetanov et al. (2000), (191) Vrba et al. (2004), (192) Wilson et al. (2001), (193) Wilson et al. (2003), (194) Zhang et al. (2017), (195) van Leeuwen (2007).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Figure 2 shows our volume-limited sample in an NIR color–magnitude diagram (CMD), highlighting the young (≲200 Myr) objects and binary systems (Sections 2.6 and 2.7 respectively). We have removed objects with parallax uncertainties ≥20% of the parallax and objects with ${(J-K)}_{\mathrm{MKO}}$ uncertainties ≥0.2 mag from the figure. The CMD clearly shows the established evolutionary sequence for brown dwarfs (e.g., Dahn et al. 2002; Knapp et al. 2004; Dupuy & Liu 2012, hereinafter DL12): L dwarfs (J − K > 1 mag) moving down the right-hand sequence as they cool and their luminosities decline; the L/T transition (types ≈L8–T4) where brown dwarfs become ≈2 mag bluer in J − K, moving right to left on the CMD, while brightening by ≈0.5 mag in J band; followed by a drop in NIR absolute magnitudes and widening spread of J − K colors for cooling late-T dwarfs. We note that types ≲L4 are mostly hydrogen-burning stars (Dupuy & Liu 2017) that will remain at M_J ≲ 12.5 mag throughout their main-sequence liftetimes. Our volume-limited CMD exhibits a clear, previously unidentified gap in the L/T transition at ${(J-K)}_{\mathrm{MKO}}\approx 0.9$–1.4 mag which we discuss in detail in Sections 3 and 4.

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We assessed the completeness of our volume-limited sample using the $V/{V}_{\max }$ statistic (Schmidt 1968). Here V is the volume of space enclosed at the distance to a given object in the sample, and V_max is the volume of space enclosed by the outer boundary of the sample. $V/{V}_{\max }$ thus quantifies the position of a given object within the sample with a value between 0 and 1; objects in the inner half of the sample's volume have $V/{V}_{\max }\lt 0.5$, while objects in the outer half have $V/{V}_{\max }\gt 0.5$. For a sample with uniform spatial distribution, the expectation value is therefore $\langle V/{V}_{\max }\rangle =0.5$. Significant differences from $\langle V/{V}_{\max }\rangle =0.5$ indicate that a sample is not uniformly distributed in its volume. Our 25 pc volume resides near the midplane of the Galaxy and contains no clusters, so uniform spatial distribution is a reasonable assumption for our sample, and thus deviations from $\langle V/{V}_{\max }\rangle =0.5$ would imply incompleteness. Because more distant objects in samples are fainter and more difficult to observe, samples centered on the Sun tend to be less complete in their outer portions. Determining $\langle V/{V}_{\max }\rangle$ for a sample over a series of distances can reveal the extent to which a sample becomes incomplete approaching its outer boundary.

Figure 3 shows $\langle V/{V}_{\max }\rangle$ as a function of boundary distance for our volume-limited sample. We estimated uncertainties for our $\langle V/{V}_{\max }\rangle$ calculations using the method described in Appendix A. Our full volume-limited sample has $\langle V/{V}_{\max }\rangle =0.50\pm 0.05$ at 16 pc (132 objects), indicating completeness at this distance. $\langle V/{V}_{\max }\rangle$ is within 1σ of 0.5 (implying consistency with completeness) out to 20 pc, and the steady decrease of $\langle V/{V}_{\max }\rangle$ beyond 16 pc implies that the sample is becoming less complete. At 25 pc, $\langle V/{V}_{\max }\rangle =0.41\pm 0.03$, indicating $83 \% \pm 5 \%$ completeness for our full sample.

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Figure 3 also breaks our sample into four spectral type bins. The $\langle V/{V}_{\max }\rangle$ trends imply completeness out to ≈22 pc for L dwarfs and the full 25 pc for T0–T4.5 dwarfs, suggesting that our sample is complete at 22 pc through the L/T transition. The sample is complete at ≈16 pc for T5-T8 dwarfs. At the 25 pc limit of our sample, it is $90 \% \pm 8 \%$ complete for L dwarfs and $69 \% \pm 8 \%$ for T5–T8 dwarfs. We expected our sample to be less complete for spectral types later than T6 due to the limiting magnitude of the WISE survey (Wright et al. 2010), the primary source of late-T dwarf discoveries in our sample. We present our $\langle V/{V}_{\max }\rangle$ values for our sample and several subsets thereof, including the four spectral type bins shown in Figure 3 as well as individual spectral subtypes, in Table 2.

Table 2.  Space Density and $\langle V/{V}_{\max }\rangle$ for Our 25 pc Sample of L0–T8 Dwarfs

				Space Density
				(10−3 objects pc−3)
Objects	Number	$\langle V/{V}_{\max }\rangle$ a	Corrected Numbera	Value	σbinomial	σPoisson
L0  ≤ SpT < L1	13	0.47 ± 0.14	14.2 ± 2.1	0.32	0.05	0.09
L1  ≤ SpT < L2	27	0.50 ± 0.10	28.0 ± 3.0	0.63	0.07	0.12
L2  ≤ SpT < L3	18	0.49 ± 0.12	19.6 ± 2.5	0.44	0.06	0.10
L3  ≤ SpT < L4	13	0.34 ± 0.13	20.4 ± 3.1	0.46	0.07	0.13
L4  ≤ SpT < L5	20	0.46 ± 0.12	21.8 ± 2.7	0.49	0.06	0.11
L5  ≤ SpT < L6	26	0.42 ± 0.10	30.7 ± 3.5	0.69	0.08	0.14
L6  ≤ SpT < L7	13	0.42 ± 0.15	15.4 ± 2.6	0.34	0.06	0.10
L7  ≤ SpT < L8	15	0.47 ± 0.14	15.8 ± 2.3	0.35	0.05	0.09
L8  ≤ SpT < L9	17	0.40 ± 0.12	22.2 ± 3.0	0.50	0.07	0.12
L9  ≤ SpT < T0	17	0.45 ± 0.13	17.9 ± 2.6	0.40	0.06	0.10
T0  ≤ SpT < T1	6	0.60 ± 0.22	5.8 ± 1.4	0.13	0.03	0.05
T1  ≤ SpT < T2	7	0.45 ± 0.21	8.2 ± 1.8	0.18	0.04	0.07
T2  ≤ SpT < T3	12	0.41 ± 0.15	15.7 ± 2.6	0.35	0.06	0.10
T3  ≤ SpT < T4	11	0.62 ± 0.17	8.4 ± 1.6	0.19	0.04	0.06
T4  ≤ SpT < T5	13	0.45 ± 0.14	16.2 ± 2.5	0.36	0.06	0.10
T5  ≤ SpT < T6	34	0.41 ± 0.09	40.7 ± 4.2	0.91	0.09	0.16
T6  ≤ SpT < T7	31	0.35 ± 0.09	43.4 ± 4.6	0.97	0.10	0.18
T7  ≤ SpT < T8	41	0.33 ± 0.07	62.4 ± 5.8	1.40	0.13	0.22
T8  ≤ SpT < T8.5	35	0.29 ± 0.08	60.0 ± 6.3	1.34	0.14	0.23
L0  ≤ SpT < L5	91	0.46 ± 0.05	99 ± 6	2.22	0.13	0.23
L5  ≤ SpT < T0	88	0.43 ± 0.05	98 ± 6	2.20	0.14	0.24
T0  ≤ SpT < T5	49	0.50 ± 0.07	50 ± 4	1.12	0.10	0.16
T5  ≤ SpT ≤ T8	141	0.35 ± 0.04	200 ± 10	4.48	0.23	0.39
L0  ≤ SpT < T0	179	0.45 ± 0.04	197 ± 9	4.41	0.19	0.33
T0  ≤ SpT ≤ T8	190	0.39 ± 0.04	243 ± 11	5.45	0.24	0.40
Single	301	0.41 ± 0.03	363 ± 13	8.13	0.28	0.48
Binary/tripleb	44	0.50 ± 0.08	43 ± 4	0.97	0.09	0.15
Companionc	27	0.37 ± 0.03	36 ± 4	0.81	0.09	0.16
Young	22	0.45 ± 0.11	24 ± 3	0.54	0.07	0.12
All	369	0.42 ± 0.03	438 ± 13	9.80	0.30	0.52

Notes. Number: number of objects in our volume-limited sample. $\langle V/{V}_{\max }\rangle$: calculated for our volume-limited sample. A sample with uniform spatial distribution will have $\langle V/{V}_{\max }\rangle =0.5$. Twice the $\langle V/{V}_{\max }\rangle$ gives an estimate of the volume-completeness of each sample bin (1 = complete). Corrected Number: number of objects in each bin, corrected for incompleteness (i.e., divided by $2\times \langle V/{V}_{\max }\rangle$). The numbers in smaller bins may not add up to the numbers in larger bins because the Monte Carlo trials were run separately for each bin. Space Density: corrected number for each bin divided by the volume of our sample (44703.031 pc³). σ_binomial describes how precisely our space density measurements represent the full 25 pc volume around the Sun. σ_Poisson describes how precisely our space density measurements represent brown dwarfs in our general neighborhood of the Galaxy. The calculation of σ_binomial and σ_Poisson is described in Appendix B.

^aMean and standard deviation from Monte Carlo trials that resample the parallaxes from their errors and incorporate binomial uncertainties to account for statistical fluctuations in our sample (Appendix B). ^bClose binaries and triples are counted as single objects with unresolved spectral types. ^cThree companions are themselves binaries (see the text for details) and are also included in the binary/triple bin.

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The fact that the L dwarfs in our sample appear to be complete out to a smaller distance than the T0–T4.5 dwarfs is somewhat surprising, since later-type objects are overall less luminous and should in principle be more difficult to detect. Given that the $\langle V/{V}_{\max }\rangle$ values for the L0–L4 dwarfs (0.46 ± 0.05), L5–L9 dwarfs (0.43 ± 0.05), and T0–T4 dwarfs (0.50 ± 0.07) are all within 1σ of each other out to 25 pc, the greater completeness of the early-Ts could simply be a random statistical feature arising from our smaller spectral type subsamples. However, it could also arise from selection effects that may have impacted our volume-limited sample, which we consider briefly here. The objects in our sample were discovered by multiple searches using different telescopes and methods, but nearly all relied on photometry from large sky surveys, in particular 2MASS (Skrutskie et al. 2006), the Pan-STARRS1 3π Survey (PS1; Chambers et al. 2020), WISE, SDSS (York et al. 2000), and UKIDSS (Lawrence et al. 2007). Searches using PS1 (optical; e.g., Best et al. 2015), 2MASS (NIR; e.g., Kirkpatrick et al. 2000; Reid et al. 2008b), and WISE (mid-infrared (MIR); e.g., Mace et al. 2013a; Thompson et al. 2013) cover the entire area of our volume-limited sample in 12 bands spanning the full spectral energy distribution of L0–T8 dwarfs, and each alone is sensitive enough to detect all of the spectral types in our sample out to 25 pc, except for the more distant T6–T8 dwarfs (detected only by WISE). SDSS (optical; e.g., Chiu et al. 2006; Schmidt et al. 2010b) and UKIDSS (NIR; e.g., Burningham et al. 2013; Marocco et al. 2015) discovered many objects in smaller regions of the sky, with the depth of UKIDSS also contributing to the discovery of numerous late-T dwarfs. While each search used different surveys and criteria, in aggregate they have enabled detection of all late-L and early-T spectral types to well beyond 25 pc. In particular, the targeted search for L6–T4.5 dwarfs by Best et al. (2015), which discovered 24% of the objects with those spectral types in our volume-limited sample, also discovered objects beyond 30 pc. Many of the searches avoided the Galactic plane ($| b| \lesssim 20^\circ$), and many looked only for objects with clear proper motion, so it is possible that the majority of the undiscovered objects are concentrated in the Galactic plane and/or are slow-moving, although there is no reason why these factors would lead to the discovery of T dwarfs at greater distances than L dwarfs. We therefore conclude that if the early-T dwarfs in our volume-limited sample are truly complete to a greater depth than the L dwarfs, it is most likely a statistical fluctuation arising from the smaller sizes (<100 objects) of these spectral-type bins.

2.3.1. Anisotropy

Our primary tool for analyzing the completeness of our sample, the $V/{V}_{\max }$ statistic, is unable to account for anisotropies over the sky. We consider two possible cases of anisotropy by other means. One is the claim by Bihain & Scholz (2016) of a highly non-uniform distribution of brown dwarfs within 6.5 pc, whereby 21 out of 26 objects lie ahead of the Sun in its Galactic orbit. K19 found no such anisotropy in their complete samples of early-L dwarfs (out to 20 pc) and late-T dwarfs (out to 12.5 pc), describing the distribution of the smaller Bihain & Scholz (2016) sample as a random statistical effect. Our larger 25 pc volume-limited sample spanning L0–T8 spectral types can provide a robust assessment of this claim, but we must account for the declination limits in our sample that exclude more of the space trailing the Sun than leading. In a model population of isotropically distributed objects filling our sample's volume, we find 59% of the objects are ahead of the Sun and 41% are behind. For our volume-limited sample, 60% of the objects are ahead of the Sun and 40% behind. We thus find no evidence for anisotropy in our sample relative to the Sun's Galactic orbit other than the cuts imposed by our declination limits, supporting K19's explanation.

The other anisotropy to consider is motivated by the fact that many searches for ultracool dwarfs eschewed the Galactic plane ($| b| \lesssim 20^\circ$), and by K19's finding that their own 20 pc sample was deficient at low Galactic latitudes. To assess whether our volume-limited sample is similarly deficient, we take the same approach as K19, dividing the sky into eight equal-area slices at Galactic latitudes b = 0°, ±1447, ±3000, and ±4849, except that we combine slices that have the same absolute Galactic latitudes to obtain four bins, each covering 25% of the sky. We then count the number of objects in each bin, calculating uncertainties from the binomial distribution as described in Appendix B (Equation (B2)). Since our sample does not cover the full sky, we must also account for the fact that the declination limits of our sample include different fractions of the Galactic latitude bins. Specifically, our sample covers 62.4% of the $0^\circ \leqslant | b| \lt 14\buildrel{\circ}\over{.} 47$ slices, 62.8% of the $14\buildrel{\circ}\over{.} 47\leqslant | b| \lt 30\buildrel{\circ}\over{.} 00$ slices, 70.0% of the $30\buildrel{\circ}\over{.} 00\leqslant | b| \lt 48\buildrel{\circ}\over{.} 49$ slices, and 77.2% of the $48\buildrel{\circ}\over{.} 49\leqslant | b| \leqslant 90^\circ$ slices. We use the coverage fractions to convert the number of objects in each bin into a number of objects per square degree. We show the resulting distribution of objects as a function of absolute Galactic latitude in Figure 4. There is a clear deficit at low Galactic latitudes, echoing what K19 saw in their 20 pc sample, and confirming the combined impact of many brown dwarf searches that avoided the Galactic plane. If we assume the sample is complete for $| b| \geqslant 14\buildrel{\circ}\over{.} 47$, then the deficit seen at lower Galactic latitudes would comprise ≈13% of a complete sample, consistent with our $83 \% \pm 5 \%$ completeness estimate. This indicates that most objects missing from our volume-limited sample reside at $| b| \lt 14\buildrel{\circ}\over{.} 47$.

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We calculated the space density of our 25 pc volume-limited sample and several subsets thereof, including young objects (Section 2.6), binaries, triples, and companions (Section 2.7), and single objects. We divided the number of objects in each sample or subset by twice the corresponding $\langle V/{V}_{\max }\rangle$ value to obtain an estimate of the true number of objects in our 25 pc volume, including objects missing from our sample. We then divided these corrected numbers of objects by our sample volume (44703.031 pc³) to obtain space densities. We present our results in Table 2, including two different sets of uncertainties (σ_binomial and σ_Poisson) for the space densities whose calculation and purpose we describe in Appendix B. Briefly, the binomial uncertainties ${\sigma }_{\mathrm{binomial}}$ are appropriate for estimating how well our volume-limited sample's space density represents the full 25 pc volume, of which our sample covers 68.3%. The Poisson uncertainties σ_Poisson are appropriate for estimating how well our volume-limited sample represents L0–T8 dwarfs in the much larger local neighborhood of our Galaxy. Both of these uncertainties also incorporate the parallax uncertainties of individual objects in our sample, whose impact is small compared to the statistical fluctuations described by σ_binomial and σ_Poisson. For our discussion here, we adopt the Poisson uncertainties in order to comment on the space density of L0–T8 dwarfs in general and compare with previous estimates (which adopt Poisson uncertainties). Like previous studies, we do not account in this work for uncertainties in the spectral types themselves.

The uncertainties on our space densities for L and T0–T8 dwarfs are <10%, making ours the most precise estimates to date spanning these spectral-type ranges. (BG19 quote a similar precision for their M7–L5 sample.) Our $(4.41\pm 0.33)\times {10}^{-3}$ pc⁻³ space density for L dwarfs and subsets thereof are consistent with most previous estimates (Cruz et al. 2007; Reylé et al. 2010; Marocco et al. 2015; K19), but are a factor of 1.8 smaller for L0–L5 dwarfs than the estimate of BG19. The latter work attempts to correct for sample selection effects as well as incompleteness in their sample. BG19 identify their completeness correction as larger than their correction for selection effects, so the most straightforward explantion for their much larger space density is that their adopted sample completeness is underestimated.

For T dwarfs, our space densities are consistent with most previous estimates (Kirkpatrick et al. 2012; Burningham et al. 2013; Marocco et al. 2015). Our overall T0–T8 dwarf space density of $(5.45\pm 0.40)\times {10}^{-3}$  pc⁻³ is lower than the ≈(7 ± 3) × 10⁻³ pc⁻³ estimates of Metchev et al. (2008) and Reylé et al. (2010), with much of the discrepancy coming at later T6–T8 dwarfs, although our estimate differs by less than 1σ due to the large uncertainties presented in those studies. K19 present their space densities using bins of ${T}_{\mathrm{eff}}$, which do not necessarily map to specific spectral types, but assuming that their bins spanning 600–1050 K correspond approximately to spectral types T6–T8, their estimate for those types appears also to be ≈40% higher than ours. If this discrepancy is real, its source is unclear, as our sample includes all of the ${\rm{T}}6\leqslant \mathrm{SpT}\leqslant {\rm{T}}8$ dwarfs in K19's 20 pc sample, and the incompleteness of our sample beyond 20 pc for these spectral types is addressed by our $\langle V/{V}_{\max }\rangle$ analysis (Figure 3) and consequent correction for completeness.

Table 1 reports YJHK photometry on the Maunakea Observatories system (MKO; Simons & Tokunaga 2002; Tokunaga et al. 2002) for our volume-limited sample. Best20 used the J band for parallax observations, providing us with ${J}_{\mathrm{MKO}}$ photometry for those objects. For other objects, we use ${J}_{\mathrm{MKO}}$ photometry from the literature where available, and for all objects we use ${Y}_{\mathrm{MKO}}$, ${H}_{\mathrm{MKO}}$, and ${K}_{\mathrm{MKO}}$ photometry from the literature where available.

When MKO photometry was not available, we calculated synthetic MKO photometry using SpeX prism spectra (Rayner et al. 2003) from the SpeX Prism Library (Burgasser et al. 2014) or from the literature. We calibrated our synthetic photometry with 2MASS photometry in the same band when available, or MKO photometry from another NIR bandpass. We calculated uncertainties in a Monte Carlo fashion using the measurement uncertainties of the spectrum, adding in quadrature the uncertainties from the calibrating photometry. Following the analysis of DL12, we added an additional 0.05 mag uncertainty in quadrature for all synthesized colors between bands within a photometry system (e.g., ${(J-H)}_{\mathrm{MKO}}$), but added no additional uncertainty for conversions between systems in a single band (e.g., ${J}_{\mathrm{MKO}}-{J}_{2\mathrm{MASS}}$).

When no prism spectra were available, we converted 2MASS magnitudes into the MKO system using ${M}_{{Ks},2\mathrm{MASS}}$ and the polynomials of Dupuy & Liu (2017, Appendix A.2).

Our volume-limited sample contains 22 young objects (≲200 Myr), identified as such via spectroscopic indications of low surface gravity, lithium absorption, or Hα emission, and/or kinematic association with a young moving group. With completeness corrections, our sample implies a population that is $5.5 \% \pm 1.2 \%$ young (assuming Poisson statistics), more than the expected ≈2% (7 ± 3 objects in our sample) for a commonly assumed uniform age distribution in a 10 Gyr old galaxy. This suggests that the local population of brown dwarfs is not uniform and skews toward younger ages. BG19 similarly identify 33 out of 410 (8%) of the M7–L5 dwarfs in their sample as young, and Kirkpatrick et al. (2008) found that 7.6% ± 1.6% of a sample of 303 L dwarfs are younger than 100 Myr. These young-leaning samples echo the 0.4–4 Gyr distribution (median age 1.3 Gyr) derived by Dupuy & Liu (2017) from evolutionary models using individual luminosities and dynamical masses of 20 resolved L and T dwarfs in binaries, as well as the 0.5–2 Gyr age distribution found by Zapatero Osorio et al. (2007) in the kinematics of nearby 21 L and T dwarfs, but are less consistent with the statistical 3–8 Gyr kinematic age found by Faherty et al. (2009) from the proper motions of 184 L0–T8 dwarfs. Dupuy & Liu (2017) point out that a young-leaning age distribution such as ours is consistent with a constant star formation rate coupled with dynamical heating, which tends to scatter older objects out of the Galactic plane where our Sun resides. Congruently, our volume-limited sample contains only three likely old objects (completeness-corrected $2.6 \% \pm 1.6 \%$): the T8 subdwarf WISE J200520.38+542433.9 (Mace et al. 2013b), and the two components of the comoving brown dwarf pair SDSS J141624.08+134826.7 (sdL6; Bowler et al. 2010a; Kirkpatrick et al. 2010; Schmidt et al. 2010a) and ULAS J141623.94+134836.3 ((sd)T7.5; Burgasser et al. 2010b; Burningham et al. 2010a; Scholz 2010b). More analysis of our volume-limited sample, including its kinematics and comparison to synthetic populations of differing ages, will yield better constraints on its age distribution.

Figure 2 shows the positions of the young objects in the M_J versus J − K CMD of our volume-limited sample. All but three of these young objects are L dwarfs, which display the previously observed trends (e.g., Liu et al. 2013, 2016; Faherty et al. 2016) of redder colors and (for late-L types) lower J-band luminosities than field-age L dwarfs. In general we would expect T dwarfs to be older than L dwarfs because brown dwarfs cool as they age, but since there are currently no clear spectroscopic identifiers of youth for ≥L8 dwarfs, it is possible that our sample contains T dwarfs with unrecognized young ages, which would make the fraction of young objects in our sample even higher. The three identified young T dwarfs in our sample are the T2.5 dwarf companion HN Peg B, age 300 ± 200 Myr (Luhman et al. 2007), the T2.5 dwarf SIMP J013656.5+093347.3 (Artigau et al. 2006) in the 200 ± 50 Myr old Carina-Near Moving Group (Zuckerman et al. 2006; Gagné et al. 2017), and the T5.5 dwarf SDSS J111010.01+011613.1 (hereinafter SDSS J1110+0116; Geballe et al. 2002) in the ${149}_{-19}^{+51}$ Myr old AB Doradus Moving Group (Bell et al. 2015; Gagné et al. 2015a). Atmospheric models predict a wide range of J-band luminosities for the L/T transition as a function of gravity (e.g., SM08; Charnay et al. 2018), though Liu et al. (2016) do not find such a wide range in their parallax sample. Consistently with Liu et al. (2016), we see an ≈1 mag spread of ${M}_{{J}_{\mathrm{MKO}}}$ in the L/T transition of our volume-limited sample, which could be an indication of a variety of gravities. All three of the young T dwarfs in our sample are part of the group of young benchmark T dwarfs that Zhang et al. (2020) describe as marginally (≲0.5 mag) fainter in ${J}_{\mathrm{MKO}}$ than older objects of the same spectral type. We note that none of these T dwarfs has ages less than 100 Myr, so they are not as young as many of the young L dwarfs in our sample.

Figure 2 also shows the positions of two of the subdwarfs (SDSS J141624.08+134826.7 and ULAS J141623.94+134836.3) on our volume-limited CMD, both of which are among the bluest objects in their respective regions of the brown dwarf evolutionary sequence. The third subdwarf in our sample, WISE J200520.38+542433.9, does not appear on our CMD plot because it lacks ${K}_{\mathrm{MKO}}$ photometry.

Binaries and multiples require special consideration in population studies. These systems can be considered separately from single objects, or the components can be treated as individual objects; both of these approaches require identification of the binaries and multiples in the sample. Alternatively, the impact of unresolved binaries on the photometry, luminosity, and mass of the sample can be accounted for statistically (e.g., Metchev et al. 2008; Day-Jones et al. 2013). We searched the literature to identify binaries in our volume-limited sample detected via high-angular resolution imaging, radial velocity measurements, or astrometric signatures. Contemporaneously with observations for the Best20 parallaxes, we also conducted our own high-angular resolution imaging survey of candidate members of the volume-limited sample lacking previous such observations across all spectral types, using laser guide star adaptive optics (LGSAO) on Keck II/NIRC2 at ≈005–010 resolution (W. Best et al. 2021, in preparation). The overwhelming majority of our sample (88%) has now been observed with high-angular resolution, without preference for particular spectral types, meaning that our full L0–T8 evolutionary sequence has been explored for binaries. (The remaining objects were largely not observed due to the lack of tip-tilt guide stars needed for LGSAO, which is also independent of spectral type.)

We identified 44 binaries in our volume-limited sample, from which we calculate a $9.9 \% \pm 1.6 \%$ binary fraction for L0–T8 dwarfs, correcting for spatial incompleteness (Section 2.3) and assuming Poisson statistics.⁵ (Two-thirds of these binaries have resolved J- and K-band photometry.) This includes two systems that are thought to include a third component: DENIS J020529.0−115925 (Bouy et al. 2005) and 2MASS J07003664+3157266 (Dupuy & Liu 2017); for simplicity, we include these systems in the category of "binaries" for this work. Figure 2 highlights the binaries (with unresolved photometry) in the M_J versus J − K CMD of our volume-limited sample. Unresolved binaries combine the light of two objects and are therefore more luminous than single objects, so their tendency to sit higher (brighter M_J) than single objects on the CMD is expected.

A total of 27 of the binaries have L-dwarf primaries in our volume-limited sample. After correcting for spatial incompleteness (Section 2.3), we find a $15.1 \% \pm 3.2 \%$ L-dwarf binary fraction, consistent with previous estimates (Gizis et al. 2003; Reid et al. 2008a) for binaries resolvable with high-angular resolution imaging (≳1.5 au), but somewhat lower than the ≈24% fraction estimate of Reid et al. (2006a) that includes L-dwarf binaries with smaller separations (see also Bardalez Gagliuffi et al. 2015). It is therefore reasonable to expect that our volume-limited sample contains ≈10 unresolved binaries with L-dwarf primaries. For T dwarfs, 17 (corrected $5.9 \% \pm 1.6 \%$) in our sample are binaries, a fraction consistent with the recent comprehensive assessment of Fontanive et al. (2018).

Our volume-limited sample also contains 27 L and T dwarfs that are companions to hotter objects (corrected $8.3 \% \pm 1.7 \%$). These L and T dwarfs were identified as resolved (typically >10'') common proper motion companions mostly to main-sequence stars, but also include VHS J125601.92−125723.9 b (hereinafter VHS J1256−1257b; Gauza et al. 2015), whose primary is a young M7 binary with component masses near the stellar/substellar boundary (Stone et al. 2016; Dupuy et al. 2020), and the wide sdL7+(sd)T7.5 pair SDSS J141624.08+134826.7 and ULAS J141623.94+134836.3. Three of the companions—Gl 337CD (Wilson et al. 2001; Burgasser et al. 2005a), Gl 417BC (Kirkpatrick et al. 2000; Bouy et al. 2003), and Gl 564BC (Potter et al. 2002)—are themselves close binaries and are included in the preceding discussion of binaries. Figure 2 shows the positions of our non-binary companions in the M_J versus J − K CMD. The companions include a smaller fraction of early-L dwarfs and a larger fraction of late-T dwarfs than the full volume-limited sample, but otherwise appear to follow the same sequence on the CMD as the single L and T dwarfs.

Unresolved binaries blend the light of two objects and therefore do not accurately represent the evolution of individual objects on a CMD. The components of binaries and the resolved companions, on the other hand, are as much individual ultracool dwarfs as the isolated ones. However, these components and companions may have different distributions of masses from the single objects, in which case they could be distributed differently along the L and T dwarf sequence in Figure 2. The overabundance of late-T type companions, for example, is suggestive of a different underlying distribution. Previous efforts to constrain the mass distribution of companions have found results consistent with most substellar initial mass function (IMF) constraints (within large error bars; e.g., Brandt et al. 2014; Baron et al. 2019; Bowler 2016; Nielsen et al. 2019). However, those studies have primarily focused on planetary-mass companions found by adaptive optics surveys, and have not encompassed the full range of brown dwarf masses and separations that characterize the mostly wide companions in our volume-limited sample. There is also evidence that the mass distribution of the components of binaries is different from single objects. The mass ratio distribution of brown dwarf binaries skews strongly toward equal masses (Burgasser et al. 2006b), whereas the IMF for brown dwarfs is thought to be roughly flat: for a power-law IMF of the form ($\tfrac{{dN}}{{dM}}\propto {M}^{-\alpha }$), most studies have found −0.5 ≲ α ≲ 0.5 (e.g., Allen et al. 2005; Metchev et al. 2008; Day-Jones et al. 2013; K19). In addition, to the extent that selection effects are present in our sample, they may be different for companions and binaries as a result of different goals and methods used for past searches (compared with field objects). In short, since the singles, companions, and components of close binaries in our sample may all have different mass distributions, it is appropriate to consider those groups separately, especially when studying their population properties. Therefore, we have removed the known binaries and companions from our volume-limited sample for the remainder of this paper. This allows us to present a clean picture of the NIR photometric evolution of single brown dwarfs, uncluttered by the blended photometry of unresolved binaries and free of any bias from possible differences in the mass distributions of binary components or companions.

L/T transition dwarfs simultaneously brighten in the J band while dimming in the K band as they cool through the transition (e.g., Tinney et al. 2003; DL12). This behavior is thought to be caused by a depletion of condensate clouds (e.g., Ackerman & Marley 2001; Burrows et al. 2006) or the evolution of thermochemical instabilities (Tremblin et al. 2016; Leconte 2018). The gap we identify suggests that the distinctive blueward evolution of the L/T transition is occurring much more quickly at ${(J-K)}_{\mathrm{MKO}}\approx 1$ mag than in subsequent parts of the transition.

In Figure 8 we present CMDs of single objects in our volume-limited sample using eight different colors spanning Pan-STARRS1 ${y}_{{\rm{P}}1}$ (0.96 μm) to WISE W2 (4.6 μm). We highlight the objects inside, above, and at the edges of the ${(J-K)}_{\mathrm{MKO}}$ L/T transition gap to illustrate the location (or lack) of the gap in other colors. The gap appears widest in ${(J-K)}_{\mathrm{MKO}}$, but is also clearly visible in ${(J-H)}_{\mathrm{MKO}}$ and ${J}_{\mathrm{MKO}}-{\rm{W}}1$, underscoring the importance of J-band flux in the L/T transition evolution. The gap is also apparent in similar colors that replace ${J}_{\mathrm{MKO}}$ with ${y}_{{\rm{P}}1}$ including ${y}_{{\rm{P}}1}-{K}_{\mathrm{MKO}}$ and ${y}_{{\rm{P}}1}-{\rm{W}}1$, and is also visible (although narrower) in ${y}_{{\rm{P}}1}-{J}_{\mathrm{MKO}}$. The gap is not visible at all in ${J}_{\mathrm{MKO}}-{\rm{W}}2$ and ${\rm{W}}1-{\rm{W}}2$, indicating a more gradual evolution in these colors.

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Assuming the L/T transition gap represents a rapid phase of brown dwarf evolution, single objects with gap photometry (J − K ≈ 1 mag, M_J ≈ 14.5 mag) should be relatively rare. The gap in Figure 5 is not completely empty, featuring three objects within the gap and four directly above it (highlighted in the first panel of Figure 8 and labeled in Figure 9), suggesting that L/T transition objects may have gap colors for a brief but observable period of time.

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However, another type of object could appear in or directly above the gap: an unresolved binary with components that individually sit on either side of the gap but whose blended color overlaps the gap. To assess the possibility that the seven objects in and above the gap are unrecognized binaries, we performed spectral decomposition (e.g., Burgasser et al. 2005b, 2010a, hereinafter B10; Liu et al. 2006) of these objects following the method described in DL12. Briefly, we used the library of 178 IRTF/SpeX prism spectra from B10—for which they determined uniform NIR spectral types and removed binaries, young objects, and other unusual spectra—as templates to create blended spectra. For each template pairing we determined the scale factor needed to minimize the χ² of the difference with the spectrum of a gap object. We then examined the resulting best pairing to determine the component spectral types, taking into account spectral-type uncertainties in the best-match templates. We estimated the flux ratios for the template pairings in standard NIR bandpasses and J − K colors using our χ² values and the weighting scheme described in B10. For the J − K colors, we added 0.05 mag in quadrature to the uncertainties to account for systematic uncertainties we have previously found in colors derived from low-resolution NIR spectra (DL12). The best template pairings for the gap objects are listed in Table 3, placed on the M_J versus J − K color–magnitude diagram in Figure 10, presented in Figures 11 and 12, and discussed below. Unlike the approach used by B10, our analysis does not make any prior assumptions about the flux ratios of the components (e.g., based on spectral types), nor does it assess whether pairs of templates are better matches to our observed spectra than single-object templates.

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Table 3.  Spectral Decomposition of Objects in or above the L/T Transition Gap

			MKO Photometry
Object	Primary	Secondary	MJ (combined)	J − K (primary)	J − K (secondary)	ΔJ	ΔH	${\rm{\Delta }}{\mathrm{CH}}_{4}\mathrm{short}$	ΔK
	(SpT)	(SpT)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
SDSS J015141.69+124429.6	L7.5 ± 2	T2 ± 1	14.74 ± 0.16	1.45 ± 0.06	0.48 ± 0.07	−0.07 ± 0.25	0.34 ± 0.23	0.21 ± 0.24	0.89 ± 0.22
WISE J092055.40+453856.3	L7.5 ± 1	T2 ± 2	14.54 ± 0.11	1.45 ± 0.05	0.73 ± 0.12	1.22 ± 0.91	1.45 ± 0.69	1.39 ± 0.75	1.66 ± 0.50
PSO J180.1475−28.6160	L7.5 ± 1	T2 ± 1	14.01 ± 0.29	1.44 ± 0.11	0.58 ± 0.32	0.43 ± 0.52	0.79 ± 0.70	0.67 ± 0.66	1.29 ± 0.78
SDSS J120747.17+024424.8	L6 ± 1	T2 ± 1	13.72 ± 0.17	1.40 ± 0.05	0.86 ± 0.06	0.28 ± 0.05	0.50 ± 0.06	0.39 ± 0.06	0.82 ± 0.06
SDSS J133148.92−011651.4	L6.5 ± 1	T5 ± 1	13.82 ± 0.20	1.34 ± 0.05	−0.30 ± 0.31	1.97 ± 0.18	2.86 ± 0.37	2.55 ± 0.31	3.61 ± 0.48
PSO J272.0887−04.9943	L9 ± 1	T3 ± 1	15.14 ± 0.11	1.10 ± 0.33	1.43 ± 0.51	1.09 ± 1.22	0.93 ± 0.83	0.98 ± 0.94	0.76 ± 0.46
PSO J319.3102−29.6682	L7.5 ± 1	T3 ± 1	14.05 ± 0.28	1.45 ± 0.06	0.35 ± 0.40	1.13 ± 0.49	1.66 ± 0.75	1.51 ± 0.68	2.23 ± 0.85

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We note that four of our seven decompositions identified the L7.5 dwarf SDSS J152039.82+354619.8 (Chiu et al. 2006) as the primary component template. This brown dwarf has inconsistent NIR spectral types in the literature—T0 ± 1 from Chiu et al. (2006) and L7.5 from B10, and visually matches well the NIR L9 standard DENIS-P J025503.3−470049 (Martín et al. 1999b; Kirkpatrick et al. 2010)—but otherwise has no unusual features. In the end, only one of the decompositions using SDSS J152039.82+354619.8 as the primary template (for PSO J319.3102−29.6682) is plausible, as discussed below.

4.2.1. Objects inside the Gap

4.2.2. Objects above the Gap

4.2.3. No Suggestion of Binarity in the Astrometric Solutions

4.2.4. Objects outside the Volume-limited Sample

Figure 13 shows the density map of the 25 pc volume-limited sample from Figure 5 overlaid with the L0–T8 objects having published parallaxes that are not part of our volume-limited sample, including apparently single objects beyond 25 pc and known binaries at any distance. The known binaries are clearly ≈0.5–0.7 brighter as a population than the single objects, indicating that the brightest putatively single objects in the L/T transition may indeed be unrecognized binaries. Most of the objects directly above the gap are known binaries, suggesting that their apparent colors may be a blend of two components on either side of the gap similar to our decompositions for PSO J180.1−28.6 and SDSS J1207+0244. We note there are also several known binaries in our full volume-limited sample (included in Figure 2 and excluded from Figure 5) that lie in the same region directly above the gap.

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The "hybrid" models of SM08 are the only models that agree with the mass–luminosity relationship of L/T transition dwarfs (Dupuy et al. 2015; Dupuy & Liu 2017). Briefly, the hybrid models are a set of evolutionary models coupled to cloudy atmospheres for objects with ${T}_{\mathrm{eff}}$ > 1400 K (essentially L dwarfs), clear atmospheres for objects with ${T}_{\mathrm{eff}}\leqslant 1200$ K (mid-T and later dwarfs), and a linear interpolation between the two for $1200\lt {T}_{\mathrm{eff}}\leqslant 1400$ K (the L/T transition), interpolating the surface boundary condition in ${T}_{\mathrm{eff}}$ for each value of gravity. We note that this modeling of the L/T transition was developed to explore the ramifications of cloud clearing in a notional sense and does not invoke a specific physical explanation for the cloud clearing. The starting and ending ${T}_{\mathrm{eff}}$ for the transition were chosen to approximate the NIR colors of the ultracool dwarf sequence.

We compare the volume-limited synthetic population of L and T dwarfs generated by SM08 from their hybrid models to our volume-limited sample of single objects in Figure 14. The hybrid models generally reproduce the overall shape of the L and T dwarf evolutionary sequence, but predict ${(J-K)}_{\mathrm{MKO}}$ colors that are too blue for early-L and late-T dwarfs and too red for late-L dwarfs. As described in SM08, this synthetic population did not attempt to fully capture the observed scatter within the sequence, which is likely due to variations in gravity, cloud properties, and/or metallicity, but SM08 also generated alternative populations based on different assumptions to explore the effects of these variations. The original synthetic population shown in Figure 14 assumes a 0–10 Gyr uniform age distribution, and the visible scatter in luminosities originates from this spread of ages, as younger brown dwarfs have larger radii (lower gravity) and are therefore more luminous. We note that this uniform age distribution is not consistent with the expected younger age distribution of our sample (Section 2.6).

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For comparison, SM08 generated a younger population (0–5 Gyr) that spreads the population somewhat toward brighter absolute magnitudes (lower gravity), better matching the scatter in our volume-limited sample. SM08 also generated an old-skewing population (exponential decline in star formation rate with characteristic time 5 Gyr) which makes their sequence thinner and clearly a worse match to our volume-limited sample, especially along the L dwarf sequence where the color offset is exaggerated for this population.

The SM08 synthetic population in Figure 14 also assumes a power-law IMF of the form ($\tfrac{{dN}}{{dM}}\propto {M}^{-\alpha }$) with α = 1; we note that while α is poorly constrained by observations, most estimates have found −0.5 ≲ α ≲ 0.5 (e.g., Allen et al. 2005; Metchev et al. 2008; Burningham et al. 2013; K19). Using a log-normal IMF, SM08 also generated a population with fewer low-mass (and thus low-gravity and low-${T}_{\mathrm{eff}}$) objects, so this synthetic sequence is narrower toward the cooler end, which is again a poorer match to our volume-limited sample, supporting their initial assumption of a bottom-heavy IMF. Finally, SM08 use cloudless models (appropriate for later-T dwarfs) with a moderate range of metallicities ($-0.9\leqslant [{\rm{M}}/{\rm{H}}]\leqslant 0.3$) to generate a synthetic population that displays considerably more scatter in its CMD sequence, suggesting that metallicity contributes significantly to the scatter for the T dwarfs in our volume-limited sample.

In the L/T transition, the SM08 hybrid models approximately replicate the slopes of each of the NIR CMDs (Figure 14), and show an uneven distribution of objects across the J − K colors (Figure 15) that is reminiscent of the gap and clumps in our volume-limited sample. However, the peaks of the model color distribution are inconsistent with our sample; in particular, the models predict a "pileup" of objects at the $J-K\approx 1$ mag location of our gap, as well as a clear paucity of objects at $J-K\approx 0.3$–0.5 mag where our volume-limited sample shows only a marginal underdensity. Our volume-limited sample instead has clumps of objects at the beginning ($J-K\approx 1.5$ mag) and end ($J-K\approx -0.5$ mag) of the L/T transition. To quantitatively assess the degree of consistency of these J − K distributions, we performed a two-sided Kolmogorov–Smirnov test and found a probability of 0.06 that the two sets of L/T transition colors are drawn from the same population.

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SM08 attributed their pileup to a slowdown in the cooling of L/T transition dwarfs, as heat trapped by L-dwarf clouds takes time to radiate away when the clouds begin to clear. Figure 16 demonstrates that this pileup in J − K corresponds directly to a maximum in the ${T}_{\mathrm{eff}}$ distribution at ≈1300 K. This suggests that the disagreement in color distribution with our volume-limited sample could be mitigated by adjusting the SM08 temperature prescription for the L/T transition to move their pileup to ≈0.5 mag bluer colors (Figure 15).

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