SEGUE 3: AN OLD, EXTREMELY LOW LUMINOSITY STAR CLUSTER IN THE MILKY WAY's HALO

We observed Segue 3 using Magellan/IMACS during engineering time on 2010 August 21 with bright conditions and excellent ∼03 seeing. We used the IMACS in f/4 mode, giving a pixel scale of 0111 pixel⁻¹ and a 155 × 155 field of view. We obtained a total integration time of 1620 s in each of the g and r Sloan filters, using observations which were dithered across the sky.

Individual chip images were reduced and stacked to create a weighted mosaic using SExtractor, SCAMP, and SWarp (Bertin & Arnouts 1996; Bertin et al. 2002; Bertin 2006), with Sloan Digital Sky Survey Data Release 7 (SDSS DR7) providing the astrometric calibration. Normalized flats were used to weight the images, with zero weightings given for known defects. The stacked mosaics were then photometered using the stand-alone DAOPHOT II/Allstar package (Stetson 1987).

The photometry was calibrated to SDSS by astrometrically matching the stars and then fitting for the difference between instrumental and SDSS magnitudes and colors. To robustly determine the calibration parameters, we used a 1000 iteration bootstrap method which calibrated our detections to SDSS sources within our region of interest in the color–magnitude diagram (CMD): sources with g and r magnitudes between 18.0 and 22.5, and 0.1 < g − r < 0.5. For each iteration, we first use an iterative 3σ clip to remove outliers and then do an uncertainty weighted fit for the zero points and color terms. We adopt the median values of the bootstrap analysis for the calibration, along with their standard deviations. The calibration we determine is

$$\begin{eqnarray*} g &=& g_{\rm inst} + 1.588 \pm 0.017 - 0.079\pm 0.016(g_{\rm inst}-r_{\rm inst}), \nonumber \\ r &=& r_{\rm inst} + 1.887 \pm 0.014 - 0.018\pm 0.017(g_{\rm inst}-r_{\rm inst}). \nonumber \end{eqnarray*}$$

After calibration, we conducted Monte Carlo tests to assess the completeness of our photometric data. Specifically, completeness limits were calculated by injecting the mosaic image with a 250 × 250 grid of artificial stars, spaced 30 pixels apart in x and y directions plus a small random offset. We repeated this injection 24 times for a total of 1,500,000 artificial stars in each filter. For each star, we randomly assign a magnitude between 18 and 25 and subsequently detected the stars using the same criteria as the real data. We set valid detections as those with a position within 1 pixel of the input position, and measure the fraction recovered as a function of magnitude. We find that the 90% completion limits for our g- and r-band data are 23.7 and 23.9, respectively.

The spectroscopic data were taken with the Keck II 10 m telescope and the DEIMOS spectrograph (Faber et al. 2003). To select spectroscopic targets, we used the SDSS DR7 photometry, because the IMACS photometry discussed in Section 2.1 was not available at the time. Candidate Segue 3 member stars were identified by comparison to a Padua theoretical isochrone for an age of 13 Gyr and a metallicity of [Fe/H]=−2.3 (Marigo et al. 2008). Stars within 0.1 mag of this isochrone and brighter than r = 22 were given the highest priority for spectroscopy; stars within 0.2 mag of the isochrone were given lower priority, all other stars observed were selected in order to fill in the mask. Slit masks were created using the DEIMOS dsimulator slit mask design software.

Two Keck/DEIMOS multislit masks were observed on 2009 November 16 and a third mask on 2010 May 16. The masks were observed for one hour each with the 1200 line mm⁻¹ grating covering a wavelength region 6400–9100 Å. The spectral dispersion of this setup is 0.33 Å, and the resulting spectral resolution, taking into account the anamorphic distortion, is 1.37 Å (FWHM, equivalent to 47 km s⁻¹ at the Ca ii triplet). The spatial scale is 012 pixel⁻¹ and slitlets were 07 wide. The minimum slit length was 4'' which allows adequate sky subtraction; the minimum spatial separation between slit ends was 04 (3 pixels).

Spectra were reduced using a modified version of the spec2d software pipeline (version 1.1.4) developed by the DEEP2 team at the University of California-Berkeley for that survey. A detailed description of the reductions can be found in Simon & Geha (2007). The final one-dimensional (1D) spectra are rebinned into logarithmic wavelength bins with 15 km s⁻¹ pixel⁻¹. Radial velocities were measured by cross-correlating the observed science spectra with a series of high signal-to-noise stellar templates. We calculate and apply a telluric correction to each science spectrum by cross-correlating a hot stellar template with the night sky absorption lines following the method in Sohn et al. (2007). The telluric correction accounts for the velocity error due to mis-centering the star within the 07 slit caused by small mask rotations or astrometric errors. We apply both a telluric and heliocentric correction to all velocities presented in this paper.

We determine the random component of our velocity errors using a Monte Carlo bootstrap method. Noise is added to each pixel in the 1D science spectrum, we then recalculate the velocity and telluric correction for 1000 noise realizations. Error bars are defined as the square root of the variance in the recovered mean velocity in the Monte Carlo simulations. The systematic contribution to the velocity error was determined by Simon & Geha (2007) to be 2.2 km s⁻¹ based on repeated independent measurements of individual stars. The systematic error contribution is expected to be constant as the spectrograph setup and velocity cross-correlation routines are identical. We add the random and systematic errors in quadrature to arrive at the final velocity error for each science measurement. Radial velocities were successfully measured for 163 of the 205 extracted spectra across. The fitted velocities were visually inspected to ensure reliability. Our final sample consists of 149 measurements of 132 unique stars, presented in Tables 1 and 2. Of the 17 stars with repeat measurements, we identify one binary star candidate (ID 9, Table 1), with velocities which differ by more than 3σ between observation epochs. The remaining stars exhibit velocities consistent within 2σ. For our analysis below, we use a combined velocity for all stars with repeat measurements, but exclude the identified binary when calculating the velocity dispersion of Seg 3.

Table 1. Photometric and Kinematic Data for Keck/DEIMOS Sample—I. Candidate Members

				Radial
ID	Date	α (J2000)	δ (J2000)	Distance	r	(g − r)	vhelio
	(yyyy-mm-dd)	(h m s)	(° ' '')	(')	(mag)	(mag)	(km s−1)
1	2009-11-16	21:21:31.4	+19:07:00.3	0.11	20.1	0.23	−162.0 ± 4.5
2	Combined	21:21:31.5	+19:07:04.0	0.11	20.2	0.22	−158.9 ± 3.2
	2009-11-16						$\hspace{4.3pt}-179.3\pm 10.6$
	2010-05-16						−157.9 ± 3.2
3	2009-11-16	21:21:31.5	+19:07:09.6	0.17	20.7	0.25	−160.9 ± 7.6
4	2009-11-16	21:21:30.3	+19:06:58.5	0.18	20.0	0.22	−170.0 ± 3.8
5	Combined	21:21:30.4	+19:07:13.4	0.23	21.2	0.30	−168.9 ± 5.4
	2009-11-16						−168.7 ± 6.8
	2010-05-16						−169.2 ± 8.0
6	2009-11-16	21:21:29.9	+19:07:07.7	0.28	20.6	0.23	−153.3 ± 5.9
7	2010-05-16	21:21:30.0	+19:06:52.2	0.28	21.9	0.41	−171.3 ± 9.6
8	Combined	21:21:30.3	+19:06:45.6	0.32	20.4	0.22	−167.6 ± 4.7
	2009-11-16						−170.1 ± 9.1
	2010-05-16						−166.1 ± 5.2
9	Combined	21:21:32.7	+19:06:57.4	0.42	20.5	0.27	−161.2 ± 3.1
	2009-11-16						−176.3 ± 3.8
	2010-05-16						−146.3 ± 3.8
10	2009-11-16	21:21:29.4	+19:07:12.5	0.42	19.8	0.20	−163.2 ± 3.0
11	2010-05-16	21:21:29.0	+19:07:19.6	0.56	22.1	0.49	−172.5 ± 7.8
12	2009-11-16	21:21:29.8	+19:07:30.4	0.56	21.1	0.28	−175.7 ± 6.3
13	Combined	21:21:33.1	+19:06:40.3	0.61	20.5	0.23	−166.1 ± 4.2
	2009-11-16						$\hspace{4.3pt}-155.7\pm 11.3$
	2010-05-16						−167.4 ± 4.4
14	2009-11-16	21:21:30.8	+19:06:21.5	0.68	20.4	0.23	−155.2 ± 4.0
15	2009-11-16	21:21:31.1	+19:07:51.9	0.83	19.4	0.28	−163.5 ± 2.8
16	2009-11-16	21:21:32.7	+19:07:47.9	0.86	21.6	0.38	−169.9 ± 5.3
17	Combined	21:21:33.6	+19:06:23.8	0.88	20.0	0.22	−162.7 ± 2.7
	2009-11-16						−158.6 ± 3.3
	2010-05-16						−165.4 ± 3.0
18	2010-05-16	21:21:29.1	+19:06:15.3	0.89	21.2	0.33	−167.7 ± 4.6
19	2009-11-16	21:21:27.1	+19:07:12.5	0.94	21.4	0.32	−165.3 ± 3.6
20	Combined	21:21:26.4	+19:06:35.6	1.18	20.4	0.25	−182.4 ± 3.0
	2009-11-16						−184.6 ± 4.0
	2010-05-16						−181.1 ± 3.8
21	Combined	21:21:31.0	+19:08:16.6	1.24	20.5	0.24	−166.6 ± 3.4
	2009-11-16						−167.7 ± 4.5
	2010-05-16						−165.9 ± 4.0
22	Combined	21:21:38.1	+19:07:33.5	1.75	21.7	0.36	−183.1 ± 4.7
	2009-11-16						$\hspace{4.3pt}-167.9\pm 10.8$
	2010-05-16						−186.0 ± 5.1
23	Combined	21:21:32.0	+19:08:52.5	1.86	21.2	0.31	−167.6 ± 4.5
	2009-11-16						$\hspace{4.3pt}-158.5\pm 11.4$
	2010-05-16						−168.8 ± 4.7
24	Combined	21:21:36.2	+19:08:27.2	1.88	21.6	0.36	−166.8 ± 5.5
	2009-11-16						−162.4 ± 6.2
	2010-05-16						$\hspace{4.3pt}-180.7\pm 10.6$
25	2010-05-16	21:21:33.2	+19:05:05.1	2.02	19.2	0.34	−169.8 ± 2.4
26	2010-05-16	21:21:39.0	+19:07:51.7	2.06	22.0	0.39	−152.9 ± 7.3
27	Combined	21:21:32.8	+19:10:02.8	3.04	19.4	0.32	−183.3 ± 2.3
	2009-11-16						−180.2 ± 2.9
	2010-05-16						−184.0 ± 2.4
28	2009-11-16	21:21:16.9	+19:06:32.8	3.37	21.4	0.35	−159.5 ± 6.7
29	2010-05-16	21:21:24.7	+19:03:52.9	3.49	21.0	0.28	−175.6 ± 7.9
30	2009-11-16	21:21:15.9	+19:05:25.4	3.92	20.7	0.27	−173.6 ± 4.8
31	Combined	21:21:31.2	+19:12:36.2	5.57	19.2	0.30	−153.5 ± 2.4
	2009-11-16						−156.9 ± 2.7
	2010-05-16						−151.8 ± 2.5
32	2009-11-16	21:21:05.8	+19:05:33.3	6.14	19.9	0.18	−169.6 ± 4.0

Note. Velocity error bars were determined from measurement overlaps as discussed in Section 2.2.

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Table 2. Photometric and Kinematic Data for Keck/DEIMOS Sample—II. Non-members

				Radial
ID	Date	α (J2000)	δ (J2000)	Distance	r	(g − r)	vhelio
	(yyyy-mm-dd)	(h m s)	(° ' '')	(')	(mag)	(mag)	(km s−1)
33	2009-11-16	21:21:33.9	+19:07:21.5	0.75	16.7	0.51	−60.6 ± 2.2
34	2009-11-16	21:21:27.9	+19:07:19.3	0.78	21.5	0.47	$-237.3\pm 4.5\hspace{4.5pt}$
35	2009-11-16	21:21:32.7	+19:06:12.8	0.91	17.8	0.44	−54.9 ± 2.2
36	2009-11-16	21:21:34.6	+19:06:33.1	0.98	16.6	0.53	−96.6 ± 2.2
37	Combined	21:21:32.0	+19:08:02.5	1.04	19.8	0.25	$-161.8\pm 2.6\hspace{4.5pt}$
	2009-11-16						$-159.6\pm 3.1\hspace{4.5pt}$
	2010-05-16						$-163.4\pm 2.9\hspace{4.5pt}$
38	Combined	21:21:28.4	+19:06:00.7	1.20	19.3	0.48	$-171.7\pm 2.4\hspace{4.5pt}$
	2009-11-16						$-171.0\pm 2.6\hspace{4.5pt}$
	2010-05-16						$-172.3\pm 2.6\hspace{4.5pt}$
39	2009-11-16	21:21:32.3	+19:05:52.2	1.20	19.2	0.49	$-163.3\pm 2.3\hspace{4.5pt}$
40	2009-11-16	21:21:27.6	+19:06:06.1	1.23	21.5	0.49	$-353.7\pm 4.7\hspace{4.5pt}$
41	2009-11-16	21:21:34.0	+19:05:56.9	1.29	16.1	0.72	−35.1 ± 2.2
42	2009-11-16	21:21:29.6	+19:05:25.3	1.64	18.6	0.51	−79.9 ± 2.2
43	2009-11-16	21:21:25.3	+19:06:05.9	1.65	16.9	0.44	−22.0 ± 2.2
44	2009-11-16	21:21:36.0	+19:05:44.2	1.75	16.6	0.43	$\phantom{-} 28.8\pm 2.2$
45	2009-11-16	21:21:38.8	+19:07:10.0	1.84	21.2	0.41	$-166.1\pm 6.2\hspace{4.5pt}$
46	2009-11-16	21:21:39.6	+19:06:14.2	2.19	18.5	0.54	−49.0 ± 2.2
47	2009-11-16	21:21:21.4	+19:07:26.6	2.31	16.1	0.56	$\hspace{4.0pt} -3.6\pm 2.2$
48	2009-11-16	21:21:22.5	+19:08:12.6	2.33	16.3	0.54	−14.5 ± 2.2
49	2010-05-16	21:21:29.2	+19:09:26.9	2.45	19.4	0.48	−98.2 ± 2.3
50	2009-11-16	21:21:42.6	+19:07:08.1	2.74	19.0	0.34	$-120.5\pm 2.4\hspace{4.5pt}$
51	2009-11-16	21:21:38.3	+19:04:46.0	2.84	17.8	0.39	$\phantom{-}\hspace{4.0pt} 3.2\pm 2.2$
52	2010-05-16	21:21:25.9	+19:09:42.5	2.94	20.9	0.44	$\phantom{-} 27.7\pm 5.2$
53	2010-05-16	21:21:32.7	+19:04:02.1	3.03	17.4	0.36	$-109.6\pm 2.2\hspace{4.5pt}$
54	2010-05-16	21:21:20.7	+19:05:11.9	3.05	18.5	0.49	$\hspace{4.0pt} -8.4\pm 2.2$
55	2009-11-16	21:21:44.2	+19:07:35.6	3.16	19.4	0.37	$-221.1\pm 2.5\hspace{4.5pt}$
56	2009-11-16	21:21:28.7	+19:10:13.1	3.23	18.3	0.42	−40.2 ± 2.3
57	2009-11-16	21:21:40.4	+19:04:28.4	3.39	18.4	0.53	−42.7 ± 2.2
58	2009-11-16	21:21:16.7	+19:06:33.2	3.40	21.3	1.17	$\phantom{-} 25.7\pm 3.2$
59	2009-11-16	21:21:24.4	+19:03:58.8	3.42	18.7	0.51	−31.3 ± 2.3
60	2009-11-16	21:21:43.3	+19:08:56.1	3.47	17.8	0.37	$\phantom{-}\hspace{4.0pt} 2.7\pm 2.2$
61	2010-05-16	21:21:32.9	+19:10:29.3	3.48	19.8	1.15	−19.5 ± 7.1
62	2009-11-16	21:21:39.3	+19:04:06.2	3.53	19.0	0.37	$-323.2\pm 2.4\hspace{4.5pt}$
63	2009-11-16	21:21:33.9	+19:10:30.8	3.55	17.1	0.43	−45.6 ± 2.2
64	2009-11-16	21:21:34.8	+19:03:30.9	3.63	18.3	0.37	$-115.2\pm 2.3\hspace{4.5pt}$
65	2009-11-16	21:21:30.6	+19:10:43.4	3.69	19.5	0.46	−67.3 ± 2.3
66	2009-11-16	21:21:15.0	+19:06:31.5	3.82	16.4	0.48	$\phantom{-}\hspace{4.0pt} 6.6\pm 2.2$
67	2009-11-16	21:21:29.9	+19:10:54.1	3.88	19.8	0.33	$-300.6\pm 3.3\hspace{4.5pt}$
68	2009-11-16	21:21:14.2	+19:07:52.7	4.07	17.1	0.51	−89.6 ± 2.2
69	2009-11-16	21:21:47.5	+19:08:21.6	4.11	17.4	0.58	−69.4 ± 2.3
70	2009-11-16	21:21:22.7	+19:03:25.2	4.11	18.3	0.38	$-113.2\pm 2.5\hspace{4.5pt}$
71	2009-11-16	21:21:38.9	+19:10:49.6	4.22	18.0	0.55	$\phantom{-}\hspace{4.0pt} 2.4\pm 2.2$
72	2009-11-16	21:21:22.7	+19:03:15.4	4.25	20.7	0.81	$-117.3\pm 2.8\hspace{4.5pt}$
73	Combined	21:21:37.6	+19:03:03.9	4.26	17.1	0.37	$-160.6\pm 2.2\hspace{4.5pt}$
	2009-11-16						$-160.7\pm 2.2\hspace{4.5pt}$
	2010-05-16						$-160.6\pm 2.2\hspace{4.5pt}$
74	2010-05-16	21:21:35.1	+19:11:11.6	4.27	22.2	0.58	$-331.8\pm 5.1\hspace{4.5pt}$
75	2010-05-16	21:21:34.4	+19:02:48.1	4.31	18.7	0.34	$-274.2\pm 2.3\hspace{4.5pt}$
76	2009-11-16	21:21:48.0	+19:05:20.7	4.36	19.5	0.39	−97.4 ± 2.4
77	2009-11-16	21:21:26.9	+19:02:44.6	4.40	16.4	0.63	−19.4 ± 2.2
78	2010-05-16	21:21:23.4	+19:11:06.5	4.45	16.2	0.51	−30.9 ± 2.2
79	2009-11-16	21:21:34.1	+19:02:37.2	4.47	18.2	0.48	−83.2 ± 2.3
80	2009-11-16	21:21:13.1	+19:05:26.9	4.52	18.8	0.52	−39.1 ± 2.3
81	2009-11-16	21:21:35.5	+19:11:26.1	4.53	16.9	0.59	−62.8 ± 2.2
82	2009-11-16	21:21:11.8	+19:07:03.2	4.55	18.3	0.54	−90.0 ± 2.2
83	2009-11-16	21:21:49.8	+19:08:15.6	4.61	18.3	0.45	−76.6 ± 2.2
84	2009-11-16	21:21:12.5	+19:05:25.2	4.66	17.9	0.47	−71.9 ± 2.2
85	2009-11-16	21:21:11.1	+19:06:23.1	4.75	21.4	0.41	$-162.4\pm 3.9\hspace{4.5pt}$
86	2010-05-16	21:21:38.7	+19:11:29.3	4.81	20.0	0.30	$-177.3\pm 2.9\hspace{4.5pt}$
87	2009-11-16	21:21:29.9	+19:11:52.0	4.84	19.8	0.28	$-239.4\pm 2.8\hspace{4.5pt}$
88	2009-11-16	21:21:39.2	+19:02:32.3	4.89	17.5	0.32	−75.9 ± 2.2
89	2010-05-16	21:21:22.7	+19:11:37.5	4.99	17.1	0.55	$\phantom{-} 29.8\pm 2.2$
90	2009-11-16	21:21:31.1	+19:12:05.1	5.05	17.0	0.48	−39.3 ± 2.2
91	2010-05-16	21:21:22.5	+19:11:42.4	5.09	18.6	0.63	−23.7 ± 2.2
92	2010-05-16	21:21:22.5	+19:11:45.0	5.13	16.7	0.63	−54.1 ± 2.2
93	2009-11-16	21:21:40.9	+19:11:41.9	5.21	17.3	0.59	−30.0 ± 2.2
94	2009-11-16	21:21:52.9	+19:07:43.9	5.23	15.9	0.67	$\phantom{-} 30.2\pm 2.2$
95	2009-11-16	21:21:08.8	+19:07:14.0	5.24	21.4	0.44	$-172.2\pm 9.6\hspace{4.5pt}$
96	2009-11-16	21:21:52.6	+19:05:42.5	5.27	20.9	0.31	$-298.4\pm 6.9\hspace{4.5pt}$
97	2010-05-16	21:21:22.3	+19:02:02.0	5.40	18.2	0.45	$\hspace{4.0pt} -4.6\pm 2.2$
98	2010-05-16	21:21:22.5	+19:12:03.4	5.41	21.6	1.01	−48.1 ± 5.6
99	2009-11-16	21:21:32.5	+19:12:26.7	5.42	18.0	0.32	−27.5 ± 2.2
100	2009-11-16	21:21:08.0	+19:06:54.5	5.44	18.6	0.45	−37.8 ± 2.3
101	2009-11-16	21:21:10.5	+19:09:40.1	5.51	20.7	0.35	$-133.1\pm 3.7\hspace{4.5pt}$
102	2010-05-16	21:21:37.1	+19:01:34.1	5.65	20.9	0.31	$-438.2\pm 4.4\hspace{4.5pt}$
103	2009-11-16	21:21:07.5	+19:08:45.9	5.81	17.5	0.55	−31.7 ± 2.3
104	2010-05-16	21:21:24.9	+19:01:22.3	5.84	17.6	0.48	−55.9 ± 2.2
105	2009-11-16	21:21:56.9	+19:05:50.4	6.23	16.3	0.53	−17.7 ± 2.2
106	Combined	21:21:28.7	+19:13:19.1	6.31	21.2	0.17	$-284.5\pm 5.0\hspace{4.5pt}$
	2009-11-16						$\hspace{4.3pt}-297.5\pm 11.8\hspace{4.5pt}$
	2010-05-16						$-282.2\pm 5.3\hspace{4.5pt}$
107	2009-11-16	21:21:57.5	+19:08:07.8	6.36	17.9	0.57	−55.7 ± 2.2
108	2010-05-16	21:21:33.0	+19:13:33.1	6.54	16.6	0.51	−21.3 ± 2.2
109	2009-11-16	21:21:56.5	+19:09:40.7	6.58	18.5	0.55	−55.7 ± 2.2
110	2010-05-16	21:21:28.3	+19:13:48.3	6.80	17.3	0.38	$\phantom{-}\hspace{4.0pt} 0.5\pm 2.2$
111	2010-05-16	21:21:39.5	+19:00:31.0	6.82	16.6	0.55	−27.9 ± 2.7
112	2009-11-16	21:21:59.9	+19:07:31.5	6.85	17.1	0.44	$\hspace{4.0pt} -2.2\pm 2.2$
113	2009-11-16	21:21:29.3	+19:13:53.3	6.87	17.1	0.64	−41.3 ± 2.2
114	2009-11-16	21:21:24.8	+19:13:44.8	6.87	16.7	0.41	−97.1 ± 2.2
115	2009-11-16	21:21:32.6	+19:13:59.2	6.96	17.1	0.38	−10.4 ± 2.2
116	2009-11-16	21:21:58.4	+19:09:41.7	7.01	17.0	0.60	$\phantom{-}\hspace{4.0pt} 6.2\pm 2.2$
117	2009-11-16	21:22:01.1	+19:06:38.3	7.11	17.8	0.50	$\phantom{-}\hspace{4.0pt} 3.4\pm 2.2$
118	2010-05-16	21:21:30.6	+19:14:09.9	7.13	16.1	0.48	−47.2 ± 2.2
119	2009-11-16	21:21:37.7	+19:14:06.8	7.25	18.6	0.46	−44.8 ± 2.3
120	2009-11-16	21:21:39.0	+19:14:22.4	7.58	17.8	0.49	−34.9 ± 2.2
121	2009-11-16	21:22:03.7	+19:06:59.6	7.72	18.6	0.32	−62.7 ± 2.3
122	2009-11-16	21:22:03.3	+19: 8:35.9	7.80	16.3	0.52	$\phantom{-} 14.0\pm 2.2$
123	2010-05-16	21:21:21.1	+19:14:48.2	8.11	18.2	0.44	−26.4 ± 2.5
124	2009-11-16	21:21:39.6	+19:14:54.8	8.14	21.3	0.24	$-236.6\pm 5.9\hspace{4.5pt}$
125	2010-05-16	21:21:30.8	+19:15:12.7	8.18	18.5	0.48	$\phantom{-}\hspace{4.0pt} 6.2\pm 2.2$
126	2009-11-16	21:21:39.5	+19:15: 1.9	8.25	18.3	0.46	$-273.7\pm 2.3\hspace{4.5pt}$
127	2009-11-16	21:21:24.0	+19:15:26.8	8.57	18.2	0.63	−17.8 ± 2.2
128	2009-11-16	21:21:37.1	+19:15:40.8	8.77	18.4	0.35	−26.4 ± 2.3
129	2009-11-16	21:22: 8.7	+19: 7:42.4	8.94	17.9	0.41	−51.5 ± 2.2
130	2009-11-16	21:21:38.0	+19:15:56.8	9.07	18.0	0.34	−53.9 ± 2.2
131	2010-05-16	21:21:30.0	+19:16:21.1	9.32	17.6	0.54	−32.6 ± 2.3
132	2009-11-16	21:21:38.1	+19:16:18.5	9.42	18.7	0.41	$-285.0\pm 2.4\hspace{4.5pt}$

Note. Velocity error bars were determined from measurement overlaps as discussed in Section 2.2.

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Examining our sample of Seg 3 member stars, we find a number of stars which lie at large distances (up to 14r_1/2) from the center of Seg 3. We consider the possibility that these stars, and those at smaller radii, might instead be foreground Milky Way contaminants. To estimate the degree of foreground contamination in our member sample, we utilize the Besancon model of the Milky Way (Robin et al. 2003). The estimate does not include possible contamination in our Seg 3 member sample from halo substructures or from unbound stars that are physically associated with Seg 3.

For our estimation we select all Besancon stars that are within one degree of the center of Seg 3, and are within a 10σ average photometric uncertainty region about our fiducial isochrone (a factor two larger than for our Seg 3 members). Of these stars, we find that the number of stars that meet our above kinematic criteria is 3.66% ± 0.18% of those that do not. In our spectroscopic sample we find 11 stars that satisfy CMD criteria but are not within our kinematic window, implying an average of 0.40 ± 0.02 stars are contaminating our sample of Seg 3 members. From this average, we quantify the frequency of larger numbers of contaminants using Poisson statistics. We find that N = {1, 2, 3, 4} contaminants occur with a frequency of {26.2, 5.52, 0.78, 0.06}%. Thus, we conclude that the likely number of Milky Way field halo contaminants is ⩽2 at ∼95% confidence.

We now use our spectroscopically selected members to derive the age, [Fe/H], and distance of Seg 3, using a maximum likelihood method which closely follows that described by Frayn & Gilmore (2002). For the procedure, a suite of isochrones are fit to a sample of stars, assigning to each a bivariate Gaussian probability function whose variance is set by the associated photometric errors. We apply this analysis using all stars in our photometric data within a radius 39'' from the object's center (r_1/2 from Belokurov et al. 2010), to which we add the 17 spectroscopically confirmed member stars that lie outside that area, resulting in a total sample of 125 stars.

For a given isochrone i we compute the likelihood

$$\begin{eqnarray} &&\mathcal {L}_i=\prod _j p(\lbrace g,g-r\rbrace _j|i,\lbrace g,g-r\rbrace _{ij},{\rm dm}_{0,i}), \end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray} &&p(\lbrace g,g-r\rbrace _j|i,\lbrace g,g-r\rbrace _{ij},{\rm dm}_{0,i})=\frac{1}{\sqrt{2\pi} \sigma _{g_j}\sigma _{(g-r)_j}} \nonumber\\ &&\quad\times \exp \left(-\frac{1}{2}\left[\left(\frac{g_j-(g_{ij}+{\rm dm}_{0,i})}{\sigma _{g_j}}\right)^2 \right.\right.\nonumber\\ &&\left.\left. \quad+\, \left(\frac{(g-r)_j-(g-r)_{ij}}{\sigma _{(g-r)_j}}\right)^2 \right]\right). \end{eqnarray} \tag{ 2 }$$

For each star, j, {g, g − r}_ij, and dm_{0, i} are, respectively, the magnitude, color, and de-reddened distance modulus values for isochrone i that maximize the likelihood of the entire data set {g, g − r}_j in Equation (2). We take an approximate solution to finding the values of {g, g − r}_ij and dm_{0, i} by searching over a series of fine steps in g, g − r, and dm₀ values for each isochrone. Input isochrones are supplied by the Dartmouth library (Dotter et al. 2008), and interpolated so g, g − r values step by 0.001 mag in the two-dimensional (2D) color–magnitude space. The distance modulus dm₀ = m−M is sampled over a range of 15.0 < dm₀ < 17.0 in steps of 0.01 mag.

We calculate the maximum likelihood values $\mathcal {L}_i$ over a grid of isochrones, covering an age range from 8 to 14 Gyr and metallicity range −2.5 ⩽ [Fe/H] ⩽−0.9 dex. Grid steps are 0.5 Gyr in age and 0.1 dex in [Fe/H]. With a grid of $\mathcal {L}_i$ values, we can locate the most likely value and compute confidence intervals by interpolating between grid points. In addition to this interpolation, we smooth the likelihood values over ∼2 grid points in order to provide a more conservative estimate of parameter uncertainties. In Figure 4, we present the relative density of likelihood values for the sample described above. We find that the isochrone with the highest probability has an age of 12.0 Gyr and [Fe/H] =−1.7, with 68% and 95% confidence contours presented in the figure. The marginalized uncertainties about this most probable location correspond to an age of 12.0^+1.5_{− 0.4} Gyr, a metallicity of [Fe/H] =−1.7^+0.07_{− 0.27} dex, and a distance modulus of dm₀ = 16.14 ± 0.09 mag (d = 16.9  ±  0.7 kpc). We assume a distance of 17 kpc in the calculation of physical size and absolute magnitude in Section 4.2.

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To assess how much the inclusion of the 17 spectroscopic members outside of 39'' has influenced the above results, we repeat the above computation using only the 32 spectroscopic members found above. We find that parameters derived for this subsample are consistent with the larger sample but have larger uncertainties, with age =13.5^+1.5_{− 1.3} Gyr, [Fe/H] =−1.9^+0.20_{− 0.39} dex, and dm₀ = 16.08 ± 0.13 mag (d = 16.4 ± 1.0 kpc).

We present a new determination of the structural parameters of Seg 3, using the photometry presented in Section 2.1. For our analysis we follow the maximum likelihood method of Martin et al. (2008), as described in Muñoz et al. (2010). This method starts by assuming an analytic surface density profile, and then fits the profile parameters using all stars meeting CMD criteria, thus avoiding the need to bin or smooth data. We fit structural parameters for Seg 3 using two choices of density profiles commonly used to describe the light distribution in ultra-faint systems, an exponential and a Plummer (Plummer 1911) profile. In both cases, the parameters we calculate are the scale length of the system, the coordinates of its center, its ellipticity, position angle, and the foreground/background stellar density. To estimate parameter uncertainties, we carry out a bootstrap analysis using 10⁴ realizations of the photometric data.

Before proceeding with our analysis of the structure of Seg 3, we must carefully consider which photometric data to use. We note in Section 2.1 that the 90% completeness limit of our data is at a magnitude of ∼23.8 for g and r filters. However, due to the increased contamination of unresolved galaxies beyond a magnitude of r ∼ 23, we conservatively limit our structural analysis to stars brighter than r ∼ 22.5. In Table 3, we present the results for both Plummer and exponential density profiles. We find structural parameters very similar to those of Belokurov et al. (2010), with most results within 1σ of values previously reported. A notable exception, however, is our determination of the half-light radius of r_1/2 = 28'' ± 8'' and 26'' ± 5'', or 2.2 ± 0.7 pc and 2.1 ± 0.4 pc for an exponential and Plummer profile, respectively. While within ∼1.5σ from the value of Belokurov et al., these are ∼30% smaller than previously found. We attribute such discrepancies to our higher quality photometric data, and to the different analysis techniques used here. In Figure 5, we present the 1D surface density profile and 2D surface brightness contours for Seg 3. Both the Plummer and exponential profiles are found to provide good fits to the data, while 2D contours reveal a circularly symmetric profile, with little evidence for strong tidal distortion.

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Table 3. Structural Parameters for Segue 3

Quantity	Symbol	Value
Exponential Profile
Right ascension	α0	21:21:31.05 ± 16
Declination	δ0	+19:07:02.6 ± 24
Half-light radius ('')	r1/2	28 ± 8
Half-light radius (pc)a		2.2 ± 0.7
Ellipticity		0.24 ± 0.14
Position angle	θ	25° ± 17°
Number of starsb	N*	65 ± 6
Absolute magnitudea	MV	−0.06 ± 0.78
Central surface brightness	μV, 0	23.9+1.0− 0.8 mag arcmin−1
Plummer Profile
Right ascension	α0	21:21:31.02 ± 18
Declination	δ0	+19:07:03.7 ± 26
Half-light radius ('')	r1/2	26 ± 5
Half-light radius (pc)a		2.1 ± 0.4
Ellipticity		0.23 ± 0.11
Position angle	θ	33° ± 36°
Number of starsb	N*	64 ± 6
Absolute magnitudea	MV	−0.04 ± 0.78
Central surface brightness	μV, 0	24.1+1.0− 0.8 mag arcmin−1

Notes. ^aUsing a distance of 17 kpc for Segue 3. ^bFor stars with r < 22.5 mag.

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In addition to structural properties, we estimate the absolute magnitude of Seg 3 following the method described in Muñoz et al. (2010). Previous estimates of the absolute magnitude by Belokurov et al. (2010) reported a value of M_V = −1.2 for Seg 3. Such a low magnitude makes traditional methods for calculating total luminosities, such as adding individual stellar fluxes, too sensitive to the inclusion (or exclusion) of potential members (outliers; e.g., Walsh et al. 2008; Martin et al. 2008; Muñoz et al. 2010). To alleviate issues related to low number statistics, the method used here relies solely on the total number of stars that belong to the satellite and not on their individual magnitudes.

In short, our method estimates the absolute magnitude by integrating a theoretical luminosity function, using the above structural analysis. Following the results of Section 4.1, we use a luminosity function for a 12 Gyr stellar population with an [Fe/H] =−1.7 from Dotter et al. (2008), assuming a Salpeter initial mass function (IMF). We then integrate this luminosity function down to the magnitude limit of r = 22.5, and scale the results to match the number of stars found by our structural analysis. Our final estimate of the absolute magnitude, therefore, is the integral of this scaled luminosity function, integrated down to the limiting mass of the Salpeter IMF (0.1M_☉). Like our structural parameters, the uncertainty of the absolute magnitude is estimated by bootstrapping the data 10⁴ times. This method yields M_V = −0.06 ± 0.78 or L_V = 90⁺⁹⁵_{− 56} L_☉ for an exponential profile. If we use a Plummer profile instead, we obtain M_V = −0.04 ± 0.78 which translates into L_V = 89⁺⁹³_{− 45} L_☉. While the uncertainties are significant, these values make Segue 3 the lowest luminosity stellar system known to date. This tiny luminosity combined with the small size of Seg 3 yields a brighter central surface brightness (μ_{0, V} = 23.90^+1.0_{− 0.8} for an exponential profile, μ_{0, V} = 24.10^+1.0_{− 0.8} for a Plummer profile) than that of the most diffuse Milky Way companions.

We note, in fact, that our values for the luminosity and surface brightness of Seg 3 may be overestimated if stars fainter than the magnitude limit of our observations have been preferentially lost due to relaxation (see Section 6). While it is unclear whether relaxation is significant in Seg 3, such an effect would result in only a small change in our estimates, since low-mass stars do not contribute much to the total luminosity. For the remainder of the analysis presented here, we adopt the structural parameters and absolute magnitude obtained from using a Plummer profile above.

We present in Figure 6 the distribution of velocities for Seg 3 spectroscopic members. We find that the majority of the members (66%) lie at small projected radii (⩽3r_1/2), with the remainder up to 14 half-light radii from the center of Seg 3. We consider these 11 spatially outlying stars, as well as other lines of evidence, as possible signs of stellar mass loss in Seg 3 (discussed below in Section 6).

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To obtain a reasonable estimate of the velocity dispersion (and hence dynamical mass) of Seg 3, we choose to focus on the velocity measurements within 3r_1/2 only, and exclude the binary star identified by repeat velocity measurements (ID 9, Table 1). This choice excludes distant candidate member stars potentially unbound to Seg 3, and reduces the amount of foreground contamination, since foreground stars are more likely at larger radii. In estimating the velocity dispersion, we use the maximum likelihood technique described by Walker et al. (2006).

If we naively include all 20 stars within 3r_1/2, we infer a velocity dispersion of 5.3 ± 1.3 km s⁻¹ for Seg 3. However, this relatively large dispersion is primarily driven by the presence of a single outlying star (ID 20, Table 1), with a measured velocity of −182 ± 3 km s⁻¹, ∼5σ away from the systemic velocity of Seg 3. Omitting this star, our estimate of the velocity dispersion plummets to 1.2 ± 2.6 km s⁻¹, a value consistent with zero.

Inclusion of the outlying star has a profound consequence on the nature of Seg 3. If included, we must necessarily infer the presence of significant amounts of dark matter in Seg 3, since the velocity dispersion would imply a mass-to-light ratio of 645⁺¹²⁸⁶_{− 442} within r_1/2.⁷ If omitted, the velocity distribution allows very small values of the dispersion, giving dynamical masses consistent with stellar material alone. We must, therefore, carefully consider whether to omit the outlying star.

We use Monte Carlo simulations to test the hypothesis that the outlying star is revealing the true velocity dispersion, rather than being a genuine outlier from the velocity distribution. First, we assume a value for the true, intrinsic velocity dispersion of Seg 3 ranging from 0 to 10 km s⁻¹. We then repeatedly generate a sample of 20 stars with velocities drawn randomly from a Gaussian corresponding to the intrinsic dispersion, convolved with our DEIMOS measurement uncertainties. Of these samples, we take those which have a dispersion between 5.3 ± 1.3 km s⁻¹ and ask how frequently the dispersion is reduced to below 3.8 km s⁻¹, once we omit the largest outlier. Our simulations indicate that the highest frequency occurs at an intrinsic dispersion of 5.8 km s⁻¹, at a rate of 3.8%. Therefore, at >95% confidence, our simulations indicate that the outlying star within 3r_1/2 is not due to low-number statistics, but is instead a genuine outlier from the distribution. With this conclusion, we assume that it is reasonable to omit the outlying star, and infer a velocity dispersion of 1.2 ± 2.6 km s⁻¹ within 3r_1/2. By adopting such a velocity dispersion, we can infer a mass-to-light ratio of 33⁺¹⁵⁶_{− 144} within r_1/2.⁷ While inconclusive, from this mass-to-light ratio alone there is no compelling evidence for significant dark matter content in Segue 3.

Properties of the stellar populations of Milky Way satellites have proven to be a useful indicator for the presence of an underlying dark matter halo. In short, the deeper potential well provided by non-baryonic material enables star formation processes to withstand feedback effects from, e.g., supernovae, facilitating more extended episodes of star formation. This effect manifests itself in the presence of a range of metallicities among stars, since metals from earlier generations of stars may be incorporated into subsequent ones. Ultra-faint satellites have demonstrated this phenomenon, showing internal [Fe/H] spreads up to 0.5 dex or more (Simon & Geha 2007; Kirby et al. 2008, 2011; Simon et al. 2011; Willman et al. 2011).

In Figure 7, we present the effect of varying the age and metallicity of isochrones from our fiducial values of 12 Gyr and [Fe/H] =−1.7. In the right panel, we see that the members of Seg 3 are consistent with a spread in [Fe/H] <0.3 dex, within the photometric errors. Such dispersions in [Fe/H] are smaller than values typically found in ultra-faint systems (Frebel et al. 2010; Kirby et al. 2011), indicating the stellar population of Seg 3 may be quite different from dark matter dominated satellites.

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In addition to internal spreads in metallicity, the average value of [Fe/H] in stars can also be used to test whether Seg 3 may contain significant dark matter. Kirby et al. (2011) show a strong correlation between the total luminosity and [Fe/H] for Milky Way dwarf galaxies, such that the faintest satellites are the most metal poor. Extrapolating the relation from Kirby et al., we find Seg 3, with an absolute magnitude of M_V ∼ 0.0, should exhibit a mean [Fe/H] <−3.0, far lower than the −1.7^+0.07_{− 0.27} dex we observe. For comparison, Segue 1 (M_V ∼ −1.5) has a value of [Fe/H] ∼ − 2.5 (Simon et al. 2011). For this to be a meaningful comparison, we assume that Seg 3 would not have undergone massive stellar loss if it contains significant dark matter.

The low spread and (relatively) high mean of [Fe/H] values inferred from isochrone comparisons indicate that the metallicity characteristics of Seg 3 are distinct from that of dark matter dominated ultra-faint satellites. While enticing, several caveats exist. First, our sample of Seg 3 members is small, totaling 32 stars. More extensive samples might show larger scatter than seen here. In addition, significant uncertainties exist in the values of theoretical isochrones, especially under the correlated effects of varying age and [Fe/H] values. We have only explored one such set of isochrones here (Dotter et al. 2008). To avoid such uncertainties, a definitive measurement of the metallicity would require spectroscopic measurements of [Fe/H] values. For our current data, this would require a calibration of the relationship between [Fe/H] and the Ca ii triplet for main-sequence stars. Since no such relation exists, we do not attempt to relate the values of the Ca ii triplet in our spectra to [Fe/H]. Nevertheless, we note that the scatter in Ca ii equivalent width is consistent with no abundance spread.

A final diagnostic tool for discriminating star clusters from satellites with dark matter halos is the relationship between size and luminosity of Milky Way objects. In Figure 8, we show the sizes and luminosities of Milky Way halo objects (distances >15 kpc). Of these systems we consider two classes, stellar systems with dark matter (dwarf spheroidal, ultra-faint dwarf galaxies) and those without dark matter (e.g., globular clusters). A clear trend is present between the two: at fixed luminosity, objects with dark matter are consistently larger in size, often by up to an order of magnitude, than objects classified as star clusters. Segue 3's size and luminosity are far smaller than those of objects known to be dominated by dark matter. This difference provides additional circumstantial evidence that Seg 3 is a star cluster. Such a conclusion is further supported by theoretical arguments, which expect low-mass dwarf galaxies to be significantly larger in size (e.g., Bullock et al. 2010) than Seg 3.

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Under the three lines of evidence presented in this section, we conclude that Segue 3 is likely a star cluster with little to no dark matter content. This hypothesis is further supported by tentative signs for stellar mass loss (see below), which has also been seen in the majority of small and faint stellar clusters.