THE COLOR DIFFERENCES OF KUIPER BELT OBJECTS IN RESONANCE WITH NEPTUNE

There is still a debate as to where the objects in the Kuiper Belt came from. It is likely that objects that originally formed in the giant planet region currently reside in the Kuiper Belt along with objects that formed beyond the giant planets (Gomes 2003; Levison & Morbidelli 2003; Levison et al. 2008; Walsh et al. 2011). These various origins for the Kuiper Belt objects (KBOs) are one of the explanations as to why the colors of the KBOs have been found to be so diverse (Luu & Jewitt 1996). The environmental conditions experienced by KBOs such as space weathering, cratering, and fragmentation may also cause the surfaces of the KBOs to change over time. Thus, the surface color of a particular KBO is likely a combination of its original formation location within the solar nebula and the environmental conditions the KBO has experienced over the age of the solar system.

Dynamically there appear to be three main types of KBOs. (1) Objects that have their perihelion near Neptune (q ∼ 25–35 AU) and have large eccentricities (e > 0.4) are called scattered disk objects. The scattered disk was likely created through KBOs having strong dynamical interactions with Neptune (Duncan & Levison 1997; Duncan 2008; Gomes et al. 2008). The detached disk objects, like the scattered disk, have moderate to large eccentricities (e > 0.25) but with higher perihelia (q ≳ 40 AU) and are thus unlikely to have been scattered by Neptune in the current solar system configuration. Detached disk objects are likely just fossilized scattered disk objects from the time when Neptune was still migrating outward (Gladman et al. 2002; Lykawka & Mukai 2006; Gomes 2011). (2) Objects with semimajor axes 42 ≲ a ≲ 48 AU with moderate to low eccentricities are considered to be in the main Kuiper Belt and are called classical KBOs. The classical objects are usually split into two sub-categories based on inclination (Brown 2001). Objects with inclination less than 5° to 10° are called low-inclination or "cold" classical KBOs while those with higher inclinations are considered the "hot" classical KBOs. The low-inclination "cold" classicals are redder, smaller, and more prevalent in equal-sized binaries than other populations (Tegler & Romanishin 2000; Levison & Stern 2001; Trujillo & Brown 2002; Stern 2002; Gulbis et al. 2006; Noll et al. 2008; Peixinho et al. 2008). Tegler & Romanishin (2000) suggest that redder objects are based on eccentricity and perihelion distance and not simply inclination, with redder objects having larger eccentricities and perihelia. We find there is no significant canonical hot classical population as almost all objects with inclinations above 10° in the classical region have much larger eccentricities and lower perihelia than the cold classicals. Thus, the standard hot classical population is more like the scattered disk objects than classical objects. The cold classical population likely formed relatively nearby their current locations as indicative of their low inclinations and eccentricities. In contrast, the hot and scattered population were likely scattered and captured into their current orbits based on their highly disturbed inclinations and eccentricities (Batygin et al. 2011; Wolff et al. 2012; Dawson & Murray-Clay 2012). (3) Resonant KBOs, the main focus of this work, are objects that are in mean motion resonance with Neptune (Figures 1 and 2: see Elliot et al. 2005; Lykawka & Mukai 2007; Gladman et al. 2008 for definitions of the various mean motion resonances with Neptune and www.boulder.swri.edu/∼buie/kbo/kbofollowup.html for an updated list of Neptune resonant objects kept by Marc Buie). Resonant objects were likely captured into their respective resonance from the outward migration of Neptune in the early solar system (Malhotra 1995; Chiang & Jordan 2002; Chiang et al. 2003; Hahn & Malhotra 2005; Murray-Clay & Chiang 2005; Levison et al. 2008). The resonances with sizable known populations are the Neptune Trojans (1:1), the resonances with semimajor axes interior to the main classical Kuiper Belt 5:4, 4:3, and 3:2 (called Plutinos because Pluto is in this resonance), the 5:3 and 7:4 which have semimajor axes within the main classical Kuiper Belt, and the outer resonances with semimajor axes exterior to the main classical Kuiper Belt 2:1 (called the Twotinos), 7:3, 5:2, and 3:1.

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Where the resonant objects originated and how the resonant objects came to reside where they are today is still unknown. The dynamical and physical properties of KBOs in resonance with Neptune are extremely valuable since these objects were likely captured into these resonances from the outward migration of Neptune. The various orbital and physical characteristics of the resonant objects will help constrain the migration and evolution of the planets. It is likely that the different resonances swept up or captured objects from different initial locations. One way to try to understand how the resonances became populated is to determine the physical characteristics of individual resonance objects and compare them to other populations of small solar system objects.

Were the ultra-red objects emplaced into the Kuiper Belt or did they form in situ? One of the simplest ways to try to answer this question is to catalog the current locations of ultra-red objects (S ≳ 25: Jewitt 2002; Sheppard 2010). Ultra-red material is mostly associated with the dynamically stable cold classical KBOs and possibly the Oort Cloud (Tegler & Romanishin 2000; Trujillo & Brown 2002; Peixinho et al. 2008; Sheppard 2010). Ultra-red colors are likely created from material rich in very volatile ices and organics and is mostly only seen on objects kept far from the Sun (Jewitt 2002; Grundy 2009; Sheppard 2010; Brown et al. 2011; Merlin et al. 2012).

This work observed the various KBOs in mean motion resonance with Neptune for their surface colors in order to look for similarities and differences between the objects in resonances and other classes of small solar system objects. The 3:2 resonance objects have been well explored physically because they are relatively brighter objects as they are located near the inner edge of the Kuiper Belt. Thus, past color data of the 3:2 resonance objects are used and the focus of the new observations presented in this work is on the colors of the objects in the little explored more distant heavily populated resonances such as the 5:4, 4:3, 5:3, 7:4, 2:1, 5:2, and 3:1 as well as a few lesser populated resonances and Neptune Trojans in the 1:1 resonance with Neptune.

All new KBO color measurements presented in this work are from observations using the Magellan 6.5 m telescopes at Las Campanas, Chile. Table 1 shows the geometry of the observations for the 58 objects observed. One of three imaging cameras was used during the observations with a standard set of Sloan filters. All observations were calibrated to Southern Sloan standard star fields G158-100, PG1633+099, or DLS-1359-11 (Smith et al. 2005). The LDSS3 imager on the Magellan-Clay telescope was used on the nights of 2009 August 26 and 2010 March 20 and 21. LDSS3 is a CCD imager with one STA0500A 4064 × 4064 CCD and 15 μm pixels. The field of view is about 8.3 arcmin in diameter with a scale of 0.189 arcsec pixel⁻¹. The IMACS camera on the Magellan-Baade telescope was used on the nights of 2010 April 20–21, August 18, September 11–12, 2011 September 27–28, and 2012 March 23–25. IMACS is a wide-field CCD imager that has eight 2048 × 4096 pixel CCDs with a pixel scale of 0.20 arcsec pixel⁻¹. The eight CCDs are arranged in a box pattern with four above and four below and about 12 arcsec gaps between chips. Only chip 2 of IMACS, which is just north and west of the camera center, was used in this analysis. The MegaCam imager on the Magellan-Clay telescope was used on the nights of 2010 October 9–10. MegaCam has 36 CCDs of 2048 × 4608 pixels each with a pixel scale of 0.08 arcsec pixel⁻¹ giving a total field of view of 24' × 24'. Only chip 23, near the center, was used in this analysis.

Table 1. Circumstances of the Observations

Name	UT Date	R	Δ	α	EXP$_{g^{\prime }}$	EXP$_{r^{\prime }}$	EXP$_{i^{\prime }}$
		(AU)	(AU)	(deg)	(s)	(s)	(s)
(26375) 1999 DE9	2010 Apr 20.983	36.38	35.58	0.96	600	600	600
(38084) 1999 HB12	2010 Mar 21.177	33.16	32.32	0.97	600	600	600
(79969) 1999 CP133	2010 Mar 21.135	32.83	31.83	0.05	600	600	600
(79978) 1999 CC158	2010 Apr 21.066	44.36	44.00	1.21	1200	900	1200
(118378) 1999 HT11	2010 Apr 20.148	40.58	39.59	0.31	1050	700	1050
(119878) 2002 CY224	2010 Apr 21.028	37.21	36.80	1.42	750	750	750
(119956) 2002 PA149	2010 Oct 09.143	43.36	42.42	0.44	1050	600	1050
(119979) 2002 WC19	2010 Mar 20.997	42.40	42.66	1.30	600	600	600
(126154) 2001 YH140	2010 Mar 20.066	36.59	36.07	1.34	300	300	300
(126154) 2001 YH140	2010 Mar 21.065	36.59	36.09	1.35	300	300	300
(126619) 2002 CX154	2010 Apr 21.117	39.54	38.72	0.83	1050	1050	1050
(127871) 2003 FC128	2010 Mar 20.173	33.23	32.24	0.12	300	300	300
(127871) 2003 FC128	2010 Mar 21.163	33.23	32.24	0.14	300	300	300
(130391) 2000 JG81	2010 Mar 20.316	35.01	34.56	1.47	1200	900	1200
(131696) 2001 XT254	2012 Mar 24.008	35.96	35.44	1.37	1050	1050	1050
(131696) 2001 XT254	2012 Mar 25.007	35.96	35.46	1.38	350	350	350
(131697) 2001 XH255	2012 Mar 23.014	33.39	32.85	1.45	700	700	700
(131697) 2001 XH255	2012 Mar 24.055	33.39	32.87	1.47	350	000	350
(131697) 2001 XH255	2012 Mar 25.024	33.39	32.88	1.48	700	350	700
(135024) 2001 KO76	2010 Mar 20.187	44.97	44.35	1.01	1200	900	1200
(135571) 2002 GG32	2010 Mar 21.280	36.81	36.33	1.36	1200	700	1050
(136120) 2003 LG7	2010 Mar 20.362	34.02	33.72	1.61	1200	350	900
(136120) 2003 LG7	2010 Mar 21.392	34.02	33.70	1.60	1200	350	1200
(137295) 1999 RB216	2010 Oct 10.220	33.71	32.72	0.14	1050	1050	1050
(143685) 2003 SS317	2010 Sep 11.152	27.87	26.97	0.93	900	900	900
(143707) 2003 UY117	2010 Sep 11.333	32.75	32.02	1.25	700	700	700
(149349) 2002 VA131	2010 Oct 10.308	38.14	37.24	0.60	600	600	600
(160147) 2001 KN76	2010 Mar 20.280	40.19	39.51	1.06	900	900	900
(181871) 1999 CO153	2010 Apr 20.024	41.60	41.30	1.32	2000	1200	1750
(308379) 2005 RS43	2010 Aug 18.260	42.33	41.73	1.12	600	600	600
(308460) 2005 SC278	2010 Oct 10.272	33.85	32.85	0.20	600	600	600
1998 UU43	2010 Oct 09.364	36.20	35.45	1.00	1050	900	1050
1999 CX131	2010 Mar 20.126	40.63	39.82	0.83	1200	900	1200
1999 HG12	2010 Mar 21.233	41.49	40.71	0.87	1400	700	1050
2000 CQ104	2010 Mar 21.201	38.03	37.08	0.41	900	900	900
2000 QL251	2010 Oct 09.090	39.38	38.39	0.30	700	700	700
2000 QN251	2010 Aug 18.369	37.05	36.37	1.17	1750	1050	1400
2001 FQ185	2010 Mar 20.233	36.76	35.86	0.69	1400	700	1050
2001 QE298	2010 Aug 18.327	37.14	36.33	0.96	1050	700	1050
2001 UP18	2010 Aug 18.285	50.64	50.17	1.03	1050	700	1050
2001 XP254	2010 Mar 20.037	33.13	32.69	1.55	900	600	900
2001 XP254	2010 Mar 21.049	33.13	32.70	1.57	350	350	350
2001 XQ254	2010 Apr 19.977	31.07	31.08	1.85	1050	1050	1050
2002 GD32	2010 Apr 21.165	50.46	49.56	0.13	1050	700	1050
2002 GS32	2010 Mar 21.321	37.84	37.34	1.32	1200	700	1050
2002 VV130	2010 Oct 09.242	36.23	35.28	0.50	1050	700	1050
2003 QW111	2010 Oct 09.050	44.32	43.46	0.70	1050	700	1050
2003 YW179	2010 Mar 20.080	35.73	35.19	1.34	1200	900	1200
2004 EG96	2010 Apr 20.097	32.08	31.09	0.26	1350	700	1350
2004 HM79	2012 Mar 23.333	38.47	37.66	0.88	600	600	600
2004 HM79	2012 Mar 24.355	38.47	37.65	0.86	1200	700	900
2004 HO79	2012 Mar 23.380	39.94	39.44	1.25	700	700	700
2004 OQ15	2011 Sep 26.994	39.78	39.35	1.31	1200	700	1200
2004 OQ15	2011 Sep 27.997	39.78	39.37	1.32	350	350	350
2004 PW107	2010 Sep 11.099	38.46	37.46	0.22	1200	1200	1200
2004 PW107	2010 Sep 12.118	38.46	37.46	0.20	600	600	600
2004 TT357	2010 Oct 09.325	31.65	30.88	1.17	700	600	700
2004 TV357	2010 Oct 09.290	35.83	35.09	1.10	600	600	600
2004 TX357	2010 Oct 10.338	28.95	28.25	1.44	600	600	600
2005 CA79	2010 Mar 21.079	37.26	36.62	1.18	600	600	600
2005 ER318	2010 Mar 21.108	31.00	30.07	0.68	600	600	600
2005 SE278	2010 Sep 11.292	37.83	37.01	0.91	1200	900	900
2005 SE278	2010 Sep 12.271	37.83	37.00	0.89	350	350	350
2005 SF278	2010 Oct 10.355	36.00	35.10	0.70	600	600	600
2006 CJ69	2012 Mar 23.050	34.30	33.51	1.03	1750	1050	1400
2006 CJ69	2012 Mar 24.076	34.30	33.52	1.05	700	700	700
2006 CJ69	2012 Mar 25.050	34.30	33.53	1.07	700	350	700
2006 QJ181	2010 Sep 12.381	34.21	34.05	1.67	600	600	600
2006 RJ103	2009 Aug 26.306	30.50	29.90	1.55	900	900	900
2006 SG369	2010 Sep 11.366	30.25	29.66	1.57	350	350	350
2006 SG369	2010 Sep 12.335	30.25	29.65	1.55	1050	700	1050
2007 VL305	2009 Aug 26.342	28.14	27.69	1.86	600	600	600

Notes. Quantities are the heliocentric distance (R), geocentric distance (Δ), and phase angle (α). UT Date shows the year, month, and time of day at the start of the observations for each object on each night it was observed. The total exposure time in each filter (g', r', i') for each object on each night is given in the last three columns. Individual exposure times were 300 or 350 s and filters were rotated after each observation to prevent any rotational light curves from influencing the color calculations.

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The data analysis was done in the same way as described in Sheppard (2010). Biases and dithered twilight and dome flats were used to reduce each image. Images were obtained through either the Sloan g', r', or i' filter while the telescope was auto-guiding at sidereal rates using a nearby bright star. Exposure times were between 300 and 350 s. Filters were rotated after each observation to prevent a light curve from influencing the color calculations. To be able to directly compare our results with previous works, the Sloan colors were converted to the Johnson–Morgan–Cousins BVRI color system using transfer equations from Smith et al. (2002): B = g' + 0.47(g' − r') + 0.17, V = g' − 0.55(g' − r') − 0.03, V − R = 0.59(g' − r') + 0.11, and R − I = 1.00(r' − i') + 0.21. These transformation equations from Sloan to the BVRI color system were shown in Sheppard (2010) to be good to within a hundredth of a magnitude by observing bright TNOs with well-known BVRI colors with the Sloan filters. The Sloan photometric observations are shown in Table 2 (Figure 3) and the BVRI-derived photometric results are shown in Table 3 (Figure 4) with the orbital information of the objects given in Table 4.

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Table 2. New Sloan g', r', i' Optical Photometry

Name	$m_{r^{\prime }}$	i	Sa	g' − r'	r' − i'	g' − i'
	(mag)	(deg)		(mag)	(mag)	(mag)
1:1 Nept. Trojans
2006 RJ103	22.51 ± 0.02	08.2	7.3 ± 4	0.62 ± 0.05	0.19 ± 0.04	0.81 ± 0.05
2007 VL305	22.85 ± 0.05	28.1	12.1 ± 5	0.58 ± 0.07	0.35 ± 0.06	0.93 ± 0.07
5:4
(308460) 2005 SC278	22.22 ± 0.03	01.5	34.5 ± 3	1.07 ± 0.04	0.45 ± 0.03	1.51 ± 0.04
(127871) 2003 FC128	22.34 ± 0.02	02.4	35.6 ± 3	0.98 ± 0.02	0.53 ± 0.02	1.51 ± 0.03
(131697) 2001 XH255	23.61 ± 0.04	02.9	14.6 ± 4	0.64 ± 0.04	0.36 ± 0.06	1.01 ± 0.05
(79969) 1999 CP133	22.55 ± 0.02	03.2	7.5 ± 2	0.57 ± 0.03	0.24 ± 0.03	0.81 ± 0.03
4:3
2004 HM79	23.41 ± 0.04	01.2	10.7 ± 4	0.61 ± 0.06	0.29 ± 0.06	0.88 ± 0.05
(143685) 2003 SS317	22.23 ± 0.02	05.9	27.2 ± 5	0.86 ± 0.05	0.46 ± 0.03	1.32 ± 0.06
1998 UU43	22.79 ± 0.03	09.6	16.0 ± 3	0.73 ± 0.04	0.32 ± 0.04	1.03 ± 0.05
2005 ER318	22.76 ± 0.03	10.4	10.6 ± 2	0.63 ± 0.03	0.27 ± 0.03	0.90 ± 0.03
2000 CQ104	23.82 ± 0.03	13.5	8.7 ± 3	0.62 ± 0.04	0.23 ± 0.04	0.85 ± 0.05
2004 TX357	23.35 ± 0.05	16.2	15.3 ± 3	0.77 ± 0.04	0.27 ± 0.03	1.04 ± 0.04
5:3
2000 QN251	23.56 ± 0.05	00.3	22.8 ± 5	0.82 ± 0.06	0.40 ± 0.07	1.21 ± 0.07
2003 YW179	22.91 ± 0.03	02.4	29.7 ± 3	1.01 ± 0.04	0.40 ± 0.04	1.39 ± 0.03
2002 VV130	23.36 ± 0.02	02.4	32.5 ± 2	1.00 ± 0.02	0.46 ± 0.02	1.46 ± 0.02
2001 XP254	22.97 ± 0.02	02.6	24.1 ± 2	0.87 ± 0.03	0.39 ± 0.04	1.25 ± 0.03
2002 GS32	23.49 ± 0.03	04.3	26.2 ± 4	0.90 ± 0.04	0.41 ± 0.04	1.32 ± 0.05
2005 SE278	22.76 ± 0.04	06.9	31.8 ± 2	0.94 ± 0.04	0.49 ± 0.04	1.45 ± 0.03
(149349) 2002 VA131	22.48 ± 0.03	07.1	36.6 ± 3	1.11 ± 0.03	0.46 ± 0.03	1.57 ± 0.04
1999 CX131	23.22 ± 0.03	09.8	15.9 ± 2	0.75 ± 0.03	0.30 ± 0.03	1.05 ± 0.03
(126154) 2001 YH140	21.23 ± 0.05	11.1	16.2 ± 2	0.76 ± 0.02	0.30 ± 0.02	1.06 ± 0.02
2006 CJ69	22.90 ± 0.02	17.9	33.5 ± 4	1.00 ± 0.03	0.48 ± 0.02	1.46 ± 0.04
7:4
(181871) 1999 CO153	23.23 ± 0.02	00.8	29.3 ± 2	1.07 ± 0.03	0.35 ± 0.03	1.42 ± 0.03
1999 HG12	23.71 ± 0.03	01.0	24.9 ± 3	0.81 ± 0.04	0.45 ± 0.03	1.26 ± 0.04
(135024) 2001 KO76	23.38 ± 0.03	02.2	29.8 ± 2	0.93 ± 0.03	0.46 ± 0.03	1.39 ± 0.03
(160147) 2001 KN76	22.88 ± 0.02	02.6	24.1 ± 2	0.83 ± 0.03	0.42 ± 0.03	1.25 ± 0.02
2003 QW111	23.42 ± 0.03	02.7	23.9 ± 3	0.85 ± 0.06	0.40 ± 0.04	1.20 ± 0.05
2004 PW107	23.67 ± 0.11	02.8	22.9 ± 9	0.93 ± 0.12	0.32 ± 0.13	1.24 ± 0.14
2001 QE298	23.32 ± 0.05	03.7	29.1 ± 5	0.98 ± 0.07	0.41 ± 0.06	1.38 ± 0.06
(119956) 2002 PA149	22.80 ± 0.02	04.1	24.0 ± 2	0.92 ± 0.02	0.35 ± 0.02	1.27 ± 0.02
(118378) 1999 HT11	23.09 ± 0.02	05.1	29.7 ± 2	0.94 ± 0.04	0.45 ± 0.03	1.39 ± 0.03
2004 OQ15	23.19 ± 0.04	09.7	8.6 ± 3	0.65 ± 0.05	0.20 ± 0.05	0.85 ± 0.05
2005 SF278	22.07 ± 0.03	13.3	32.7 ± 3	1.05 ± 0.04	0.43 ± 0.04	1.48 ± 0.04
9:5
2002 GD32	23.11 ± 0.03	6.6	30.1 ± 2	0.91 ± 0.04	0.48 ± 0.04	1.39 ± 0.03
2:1 Twotinos
2001 UP18	23.22 ± 0.04	01.2	16.0 ± 4	0.73 ± 0.04	0.32 ± 0.05	1.04 ± 0.05
2001 FQ185	23.30 ± 0.03	03.2	34.2 ± 2	0.96 ± 0.04	0.52 ± 0.04	1.48 ± 0.03
2000 QL251	22.72 ± 0.02	03.7	11.3 ± 2	0.65 ± 0.03	0.27 ± 0.03	0.91 ± 0.04
(119979) 2002 WC19	20.81 ± 0.01	09.2	28.4 ± 1	0.92 ± 0.01	0.44 ± 0.01	1.36 ± 0.01
2004 TV357	22.24 ± 0.02	09.7	00.4 ± 1	0.47 ± 0.02	0.13 ± 0.02	0.60 ± 0.02
(308379) 2005 RS43	21.39 ± 0.02	10.0	11.2 ± 2	0.66 ± 0.03	0.26 ± 0.03	0.92 ± 0.03
2005 CA79	20.83 ± 0.02	11.7	21.9 ± 2	0.90 ± 0.03	0.32 ± 0.03	1.22 ± 0.03
(137295) 1999 RB216	22.22 ± 0.04	12.7	18.0 ± 2	0.75 ± 0.03	0.35 ± 0.03	1.10 ± 0.03
2006 SG369	22.23 ± 0.02	13.6	26.0 ± 2	0.91 ± 0.04	0.40 ± 0.04	1.31 ± 0.03
2000 JG81	23.33 ± 0.03	23.5	10.9 ± 2	0.58 ± 0.04	0.32 ± 0.04	0.89 ± 0.04
7:3
(131696) 2001 XT254	23.05 ± 0.03	00.5	7.9 ± 3	0.64 ± 0.04	0.19 ± 0.05	0.84 ± 0.04
12:5
(119878) 2002 CY224	21.85 ± 0.01	15.7	29.9 ± 3	0.96 ± 0.03	0.44 ± 0.03	1.39 ± 0.04
(79978) 1999 CC158	22.16 ± 0.03	18.8	23.4 ± 3	0.89 ± 0.03	0.36 ± 0.03	1.25 ± 0.04
5:2
2004 HO79	23.33 ± 0.06	05.6	23.6 ± 8	0.75 ± 0.07	0.47 ± 0.08	1.22 ± 0.09
2001 XQ254	22.81 ± 0.03	07.1	11.0 ± 2	0.56 ± 0.03	0.34 ± 0.03	0.90 ± 0.04
(143707) 2003 UY117	20.90 ± 0.01	07.5	19.7 ± 1	0.76 ± 0.01	0.38 ± 0.01	1.14 ± 0.01
(26375) 1999 DE9	20.37 ± 0.02	07.6	18.4 ± 1	0.80 ± 0.02	0.32 ± 0.02	1.12 ± 0.02
2004 TT357	22.80 ± 0.04	09.0	14.3 ± 2	0.74 ± 0.03	0.27 ± 0.04	0.99 ± 0.04
(38084) 1999 HB12	22.16 ± 0.03	13.2	14.7 ± 1	0.69 ± 0.03	0.32 ± 0.03	1.01 ± 0.02
(135571) 2002 GG32	23.04 ± 0.02	14.7	33.9 ± 3	1.01 ± 0.03	0.48 ± 0.04	1.49 ± 0.04
2004 EG96	23.13 ± 0.04	16.2	11.6 ± 3	0.67 ± 0.05	0.26 ± 0.03	0.93 ± 0.05
3:1
2006 QJ181	22.47 ± 0.04	20.0	14.0 ± 4	0.73 ± 0.06	0.27 ± 0.04	1.01 ± 0.06
(136120) 2003 LG7	23.85 ± 0.04	20.1	9.8 ± 5	0.55 ± 0.06	0.32 ± 0.05	0.85 ± 0.07
11:3
(126619) 2002 CX154	23.46 ± 0.03	16.0	22.2 ± 4	0.79 ± 0.05	0.41 ± 0.05	1.18 ± 0.06

Note. ^aThe normalized spectral gradient for the optical colors of the observed objects using the g' and i' measurements.

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Photometry was performed by optimizing the signal-to-noise ratio of the faint small outer solar system objects. Aperture correction photometry was done by using a small aperture on the TNOs (064 to 1'' in radius) and both the same small aperture and a large aperture (224 to 36 in radius) on several nearby unsaturated bright field stars with similar point-spread functions (PSFs). The magnitude within the small aperture used for the TNOs was corrected by determining the correction from the small to the large aperture using the PSF of the field stars (cf. Tegler & Romanishin 2000; Jewitt & Luu 2001; Sheppard 2010).

The BVRI colors are shown by Neptune resonance membership in Table 3 and Figure 4 for the new observations presented in this work. BVRI results for the already well-observed 3:2 resonance as well as the few known measurements of other resonance objects are shown in Figure 5. Ultra-red color (S ≳ 25) was coined by Jewitt (2002) and is defined here as the color 75% of all cold classical Kuiper Belt objects have. Very red (S ≳ 20) is defined as the 90th percentile of all object colors in the cold classical Kuiper Belt (Table 5). The correlated broadband optical colors of TNOs in Figure 4 show that they have a nearly linear red slope in their optical colors. This near-linear optical color slope has been confirmed through spectroscopy and correlation analysis on other TNOs (Doressoundiram et al. 2008). The spectral gradient, S, is the percent of reddening per 100 nm in wavelength. Following our earlier paper (Sheppard 2010), we express the spectral gradient as S(λ₂ > λ₁) = (F_{2, V} − F_{1, V})/(λ₂ − λ₁), where λ₁ and λ₂ are the central wavelengths of the two filters used for the calculation and F_{1, V} and F_{2, V} are the flux of the object in the two filters normalized to the V-band filter. To compute the spectral gradient of the observed objects in this work with the Sloan filters, we used the g' and i' measurements. The g' and i' filters have well-separated central wavelengths of 481.3 and 773.2 nm, respectively.

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Table 5. Spectral Gradients of Various Reservoirs

Type	N	Very-red	Ultra-red	i < 10	i < 5	$\overline{S}$	Reference
		(S > 20)	(S > 25)	(deg)	(deg)
1:1	6	0%	0%	67%	33%	9.3 ± 3	1,2
5:4	4	50%	50%	100%	100%	20 ± 10	1
4:3	6	17%	17%	50%	17%	14 ± 3	1
3:2	28	54%	32%	46%	25%	19 ± 15	3,4,5,6,7
5:3	10	80%	60%	80%	50%	28 ± 4	1
7:4	14	86%	50%	78%	57%	26 ± 3	1,7,11,12
2:1	12	50%	42%	42%	25%	20 ± 15	1,3
7:3	3	67%	67%	67%	33%	25 ± 10	1,7,9,10
5:2	14	21%	14%	57%	7%	17 ± 5	1,6,7,8,12,14
3:1	3	0%	0%	0%	0%	13 ± 2	1,8
Scattered KBOs	22	18%	18%	18%	0%	16 ± 4	8,10,11
Detached disk	12	0%	0%	17%	8%	14 ± 3	8
Cold classical	26	92%	75%	100%	100%	27 ± 3	3,10,15,16
Outer classical	5	80%	40%	40%	40%	23 ± 3	8
Inner Oort Cloud	3	100%	67%	0%	0%	25 ± 2	8

Notes. N is the number of objects used in the statistics. S is the spectral gradient as defined in the text using known B or g' and I or i'-band photometry normalized to the V band. Very red is defined as S > 20, which is the spectral gradient that 90% of the cold classical objects are redder than. Ultra-red is defined as S > 25, which is the spectral gradient that 75% of the cold classical objects are redder than. The ± on the average spectral gradient, $\overline{S}$, is not an error but displays the general range the type of objects span. Percent of inclinations less than 10° or 5° is only for those objects that have known good color measurements. References for TNO colors used in statistics: (1) this Work; (2) Sheppard & Trujillo 2006; (3) Tegler & Romanishin 2000; (4) Jewitt & Luu 2001; (5) Delsanti et al. 2001; (6) Doressoundiram et al. 2002; (7) Peixinho et al. 2004; (8) Sheppard 2010; (9) Luu & Jewitt 1996; (10) Trujillo & Brown 2002; (11) Boehnhardt et al. 2002; (12) Santos-Sanz et al. 2009; (13) Tegler et al. 2003; (14) Doressoundiram et al. 2005; (15) Peixinho et al. 2008; (16) Gulbis et al. 2006.

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It is immediately clear from Table 3 and Figure 4 that the various Neptune mean motion resonances have significantly different color distributions. Just looking at colors versus resonance occupation shows that the Neptune Trojans are all just slightly red, similar to the Jupiter Trojans (Karlsson et al. 2009). The inner 4:3 and outer 5:2 Neptune resonances are mostly moderately red objects like those found in the scattered disk (Hainaut & Delsanti 2002) and detached disk (Sheppard 2010). The middle 5:3 and 7:4 Neptune resonances are dominated by ultra-red objects like those found in the low-inclination cold classical belt (Tegler & Romanishin 2000; Trujillo & Brown 2002; Peixinho et al. 2008). The 3:2 and 2:1 Neptune resonances have a wide range of colors from neutral to ultra-red. Assuming the surface colors of KBOs are related to their formation location, it is likely that the 3:2 and 2:1 Neptune resonances have a greater mix of objects from around the solar system than the other reservoirs above. The 5:4 and 12:5 Neptune resonances have few known objects, but both appear to have significant numbers of ultra-red objects. The 3:1 resonance, with only three measured objects, does not have any known ultra-red members.

3.1. Size of Resonance Objects

3.2. Orbital Parameters and Colors of Objects

Inclination has been found to be important for classical KBOs as objects with inclinations less than about 5° to 10° are dominated by ultra-red colors (Tegler & Romanishin 2000; Trujillo & Brown 2002; Stern 2002; Gulbis et al. 2006; Peixinho et al. 2008). Table 4 shows the orbital elements of the resonant KBOs observed in this work. Tables 2 and 3 also show inclinations arranged in ascending order for each resonance. Inclination appears to be of some importance in terms of the number of known objects in each resonance (Figure 6). There are many more known low-inclination objects in the 5:4, 5:3, and 7:4 resonance populations with few known high-inclination objects compared to the other resonances (see Table 5). These three resonances also have the highest fraction of very red and ultra-red objects (Table 5).

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The spectral gradients versus inclinations for Neptune resonant objects are shown in Figures 7 and 8. Even though the 5:3 and 7:4 have mostly low inclination objects, they also have ultra-red objects at high inclinations. These ultra-red, high-inclination 5:3 and 7:4 resonant objects could have once been on low-inclination orbits that were excited to higher inclinations through resonance pumping (Lykawka & Mukai 2005a, 2005b; Volk & Malhotra 2011). The 5:4 only has very low inclination members with measured colors (Figure 8), but even with so few of them known, it appears to have a mix of colors and not be as dominated by ultra-red material as the 5:3 and 7:4 resonances (Table 5). In contrast, the 12:5 only has known high-inclination members, of which both have ultra-red colors (Figure 8). The 3:1 has no ultra-red objects but all measured 3:1 objects are of high inclination (Figure 8).

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The only non-ultra-red objects in the 5:3 and 7:4 resonances have inclinations greater than about 10°, suggesting 10° is the place to distinguish between the low-inclination cold classical and high-inclination classical belt populations. All objects in the 5:3 and 7:4 resonances below about 10° are ultra-red. More low-inclination 4:3 and high-inclination 5:3 and 7:4 resonant objects need to be found and measured for colors to determine how statistically significant inclination is. As of the time of this writing, the known numbers of objects at some inclinations are very low in these resonances. It seems that the 5:4 and 3:1 resonant objects may only occupy low- and high-inclination orbits, respectively.

Tegler & Romanishin (2000) suggest that high perihelion distance and low eccentricity are also important quantities for the ultra-red material in the classical Kuiper Belt. Figures 9–11 compare the spectral gradient of the resonance objects to their perihelion distances, eccentricities, and semimajor axes. There are no obvious strong correlations, but there is a moderate correlation at about the 97% confidence level (Pearson coefficient of 0.28 with a sample of 58 objects) that resonant objects with high perihelion distances are redder (Figure 9). These object color results versus the dynamics of the objects are similar to the cold classical object results for the location of ultra-red material. There is still a strong debate as to why objects with higher perihelia would have redder colors and thus likely different surface compositions than objects with lower perihelia. This color difference could be related to the retention and/or irradiation of very volatile ices such as ammonia, methane, or methanol at large heliocentric distances (Schaller & Brown 2007; Grundy 2009; Brown et al. 2011; Merlin et al. 2012). For example, methane's condensation temperature is around 40 K, which in our solar system happens around 48 AU (Youdin & Kenyon 2012). This is a similar distance as the cold classical Kuiper Belt and 5:3 and 7:4 resonances.

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4.1. Resonant Colors Compared

To compare the various resonant color populations directly, the Kolmogorov–Smirnov test and Student's t-test were calculated using the known color data (Student 1908; Kolmogorov 1933; Smirnov 1948). Figure 12 displays the data graphically while the results are shown in Table 6. Both the 5:3 and 7:4 resonances have a very similar ultra-red color distribution and thus could be drawn from the same parent population. The 4:3 and 5:2 Neptune resonances also have similar color distributions, being mostly moderately red objects. It is possible that the 4:3 and 5:2 populations are from the same parent population. As shown in Table 6, the 5:3/7:4 resonant objects can be rejected as having the same common parent population as the 4:3/5:2 resonant objects at about the 99% confidence level, assuming that the currently observed KBO colors are from the original formation location within the solar system. The 2:1 and 3:2 resonant colors both cover a much wider color distribution than the other resonances and could be drawn from the same parent population. The 2:1 and 3:2 seem to have a mix of object colors and may represent many different originally separate parent populations. The 3:2 also appears to have the only significant population of neutral colored objects within the resonant populations. The Neptune Trojans seem to be unique and do not appear to be drawn from the same parent population as any of the other Neptune resonances.

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Table 6. T-test and Kolmogorov–Smirnov Color Test Results

Type 1a	Type 2a	Nb	t-statc	t-testd	D-state	K-Sd
Both Types may be Drawn from the Same Parent Population:
Cold classical	7:4	40	1.79	56%	0.31	70%
Cold classical	5:3	36	0.85	12%	0.36	76%
Scattered disk	4:3	28	1.31	23%	0.27	19%
Scattered disk	5:2	36	0.45	42%	0.27	52%
Scattered disk	2:1	34	−0.18	75%	0.35	77%
Scattered disk	3:2	50	−0.20	76%	0.35	93%
Detached disk	Scattered disk	34	2.02	69%	0.23	24%
Detached disk	4:3	18	0.51	36%	0.33	33%
Detached disk	5:2	26	−0.86	92%	0.43	86%
2:1	3:2	40	0.79	17%	0.20	16%
4:3	5:2	20	1.80	56%	0.36	45%
5:3	7:4	24	0.35	48%	0.33	53%
Reject Both Types Being Drawn from the Same Parent Population:
Cold classical	2:1	38	2.88	92%	0.46	96%
Scattered disk	1:1	28	4.10	99.53%	0.68	98.78%
Cold classical	3:2	54	3.96	99.45%	0.49	99.82%
Cold classical	4:3	32	5.10	99.36%	0.79	99.84%
Scattered disk	5:3	32	−2.50	99.82%	0.68	99.85%
Scattered disk	7:4	36	−2.35	99.80%	0.70	99.98%
Cold classical	5:2	40	5.32	99.96%	0.71	99.99%
Cold classical	1:1	32	16.4	99.99%	1.00	99.99%
5:3 or 7:4	5:2 or 4:3	...	...	∼99%	...	∼98%
1:1	Any other	...	...	∼99%	...	∼99%

Notes. ^aThe dynamical groups being tested. ^bThe number of objects used in the test. ^cThe t-statistic from the t-test. ^dThe level of confidence that the two groups are not drawn from the same parent population using the t-test or Kolmogorov–Smirnov (K-S) test. ^eThe D-statistic from the Kolmogorov–Smirnov test.

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4.2. Resonant Colors Compared to Other KBO Classes

Figure 13 further compares the various resonant color populations to the main Kuiper Belt reservoirs defined in the Introduction such as the cold classical Kuiper Belt, scattered disk, and detached disk. As shown in Table 6, the ultra-red dominated 5:3 and 7:4 Neptune resonances appear to be drawn from the same parent population as the cold classical belt objects. This suggests that the 5:3 and 7:4 resonant objects are just a continuation of the cold classical Kuiper Belt. If true, high-inclination objects may not be expected to be a significant fraction of the 5:3 and 7:4 populations, though some orbit inclination modification is expected for objects in and around the 5:3 and 7:4 resonances (Lykawka & Mukai 2005a, 2005b; Volk & Malhotra 2011).

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In contrast, the 4:3 and 5:2 resonances may have similar origins as the scattered disk, detached disk, and/or high-inclination classical belt objects based on colors. Though it has low number statistics, the 3:1 resonance is probably similar to the 4:3 and 5:2 resonances. A similar origin for the 4:3, 5:2, and 3:1 resonances would not only explain their similar colors but also these populations' lack of low-inclination members. The low number of ultra-red type objects in the 4:3, 5:2, and 3:1 suggests that these objects might have once been much closer to the Sun, where, as discussed in Section 3.2, highly volatile ice-rich ultra-red material on their surfaces could be destroyed. These objects could have been later scattered and captured into their current distant, mostly high-inclination, resonant orbits.

4.3. Neptune's Migration History

Fifty-eight Neptune mean motion resonance objects were observed for their optical surface colors. The various Neptune mean motion resonances were found to have significantly different object surface color distributions. This indicates vastly different origins and evolutions for the objects in resonance with Neptune. Ultra-red color (S ≳ 25, g' − i' ≳ 1.2 mag, B − I ≳ 2.2 mag) is defined here as the color 75% of all cold classical Kuiper Belt objects have. Very red color (S ≳ 20) is defined as the 90th percentile of all object colors in the cold classical Kuiper Belt.

• 1.  
  The 5:3 and 7:4 Neptune resonances are composed of mostly ultra-red objects. The few known high-inclination objects in these resonances are also ultra-red in color. The colors of the 5:3 and 7:4 resonant objects are statistically identical to the low-inclination cold classical belt colors. Thus, the 5:3 and 7:4 resonant objects are likely just an extension of the cold classical belt. If true, the 5:3 and 7:4 objects should have a significant number of ultra-red, equal-sized binaries as have been found in the cold classical belt. The only non-very-red colored objects in the 5:3 and 7:4 resonances all have inclinations near 10°, suggesting this is the inclination region that separates the low-inclination cold classical and high-inclination classical belt populations.
• 2.  
  The inner 4:3 and outer 5:2 Neptune resonances have few ultra-red objects and are composed of mostly moderately red objects. These two resonances, along with the sparsely sampled 3:1 Neptune resonance, appear to have a similar color distribution as the scattered disk (including the high-inclination, moderate eccentricity classical objects) and the detached disk. If these populations all have a similar origin, it would also explain the abundance of high-inclination objects and lack of low-inclination objects found in these three Neptune resonances.
• 3.  
  In contrast to the narrow color distributions found for the above resonances, the 2:1 and 3:2 resonances have a very wide color distribution. This indicates these two resonances likely captured objects that formed in many different places within the solar system, assuming the colors are uniquely associated with origin radius.
• 4.  
  The Neptune Trojans appear to be unique in surface color for outer solar system objects as these objects are only slightly red. They are very similar to the Jupiter Trojans in color.
• 5.  
  There is a moderate correlation that the higher perihelion resonant objects have redder surfaces, but it is only significant at about the 97% confidence level. This correlation could be related to the retention and irradiation of very volatile ices such as ammonia, methane, and methanol at large heliocentric distances.
• 6.  
  If there are low-inclination "cold" components of the inner 3:2 and 5:4 resonances, they could be composed of a large fraction of ultra-red objects, like those found for the middle 5:3 and 7:4 resonances. This is because there are many objects with low inclinations in the 3:2 and 5:4 with very red colors. With the limited color data to date, the outer 2:1 and 5:2 resonances do not show a high fraction of ultra-red objects at low inclinations. This suggests if there is a cold component in the outer resonances, the surfaces of the objects are different than the cold components of the middle Neptune resonances as well as the cold classicals. If true, this makes it unlikely Neptune had a significant slow smooth migration phase in its past since these outer resonances would be expected to have a significant cold component similar to the ultra-red objects in the cold classical Kuiper Belt that the resonances would have swept through.

The author thanks C. Trujillo and S. Benecchi for helpful comments and suggestions while writing this manuscript. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. S.S. was partially supported by the National Aeronautics and Space Administration through the NASA Astrobiology Institute (NAI) under Cooperative Agreement No. NNA04CC09A issued to the Carnegie Institution of Washington.