BVI Photometric Study of the Old Open Cluster Ruprecht 6

TL;DR

This study provides detailed photometric analysis of Ruprecht 6, determining its distance, age, metallicity, and contributing to understanding the metallicity gradient of old open clusters in the Milky Way.

Contribution

It offers the first comprehensive photometric parameters for Ruprecht 6 and analyzes its metallicity in relation to the Galactic radial gradient.

Findings

Distance to Ruprecht 6 is approximately 5.86 kpc.

Age of Ruprecht 6 is about 3.16 Gyr.

Metallicity [Fe/H] is approximately -0.42 dex.

Abstract

We present a BVI optical photometric study of the old open cluster Ruprecht 6 using the data obtained with the SMARTS 1.0 m telescope at the CTIO, Chile. Its color-magnitude diagrams show the clear existence of the main-sequence stars, of which turn-off point is located around V ~ 18.45 mag and B-V ~ 0.85 mag. Three red clump (RC) stars are identified at V = 16.00 mag, I = 14.41 mag and B-V = 1.35 mag. From the mean Ks-band magnitude of RC stars (Ks=12.39 +- 0.21 mag) in Ruprecht 6 from 2MASS photometry and the known absolute magnitudes of the RC stars (M_Ks = -1.595 +- 0.025 mag), we obtain the distance modulus to Ruprecht 6 (m-M)_0 = 13.84 +- 0.21 mag (d=5.86 +- 0.60 kpc). From the (J-K_s) and (B-V) colors of the RC stars, comparison of the (B-V) and (V-I) colors of the bright stars in Ruprecht 6 with those of the intrinsic colors of dwarf and giant stars, and the PARSEC isochrone fittings, we derive the reddening values of E(B-V) = 0.42 mag and E(V-I) = 0.60 mag. Using the PARSEC isochrone fittings onto the color-magnitude diagrams, we estimate the age and metallicity to be: log (t) =9.50 +- 0.10 (t =3.16 +- 0.82 Gyr) and [Fe/H] = -0.42 +- 0.04 dex. We present the Galactocentric radial metallicity gradient analysis for old (age > 1 Gyr) open clusters of Dias et al. catalog, which likely follow a single relation of [Fe/H] =(-0.034 +- 0.007) R_GC + (0.190 +- 0.080) (rms = 0.201) for the whole radial range or dual relation of [Fe/H] =(-0.077 +- 0.017) R_GC + (0.609 +- 0.161) (rms = 0.152) and constant ([Fe/H] ~ -0.3 dex) value, inside and outside of R_GC ~ 12 kpc, respectively. The metallicity and Galactocentric radius (13.28 +- 0.54 kpc) of Ruprecht 6 obtained in this study seem to be consistent with both of the relations.

Tables

Table 1. Table 1: Basic Information of the Open Cluster Ruprecht 6

Parameter	Ruprecht 6	Reference
Other name	C 0653-132	SIMBAD
${\delta }_{J2000}$, ${\alpha }_{J2000}$	06h 56m 06s, $-13$∘  15′  00′′	Hasegawa et al. (2008)
$l$,$b$	225.∘28, $-4.{}_{}{}^{\circ }98$	Hasegawa et al. (2008)
Reddening, $E\left(B-V\right)$	$0.42$ mag	This study
Reddening, $E\left(V-I\right)$	$0.60$ mag	This study
Distance modulus, ${\left(m-M\right)}_0$	$13.84\pm 0.21$ mag	This study
Distance, $d$	$5.86\pm 0.60$ kpc	This study
Galactocentric distance, $R_{\mathrm{GC}}$	$13.28\pm 0.54$ kpc	This study
Metallicity, [Fe/H]	$-0.42\pm 0.04$ dex	This study
Age, $t$	$3.16\pm 0.82$ Gyr ($\log t=9.50\pm 0.10$)	This study
Trumpler type	III 1 p	Dias et al. (2002)

Table 2. Table 2: Photometry data of the bright stars with V < 19 𝑉 19 V<19 mag in Ruprecht 6

ID	R.A.(J2000)	Decl.(J2000)	$B$	$\sigma \left(B\right)$	$V$	$\sigma \left(V\right)$	$I$	$\sigma \left(I\right)$	$\chi$	sharpness
	hh:mm:ss	dd:mm:ss
1	06:55:58.41	$-$13:15:02.73	20.25	0.012	18.99	0.005	17.46	0.006	1.010	$-$0.108
2	06:55:58.57	$-$13:15:20.15	19.97	0.009	18.95	0.006	17.68	0.011	1.312	0.176
3	06:55:59.86	$-$13:14:29.15	20.07	0.012	18.97	0.005	17.59	0.011	1.062	0.002
4	06:55:59.96	$-$13:15:59.53	20.11	0.010	18.80	0.005	17.37	0.005	1.004	$-$0.061
5	06:55:59.97	$-$13:15:13.03	19.00	0.006	17.91	0.003	16.62	0.008	1.032	$-$0.041
6	06:56:00.08	$-$13:15:17.20	20.15	0.019	18.75	0.005	17.18	0.005	1.180	0.122
7	06:56:00.13	$-$13:14:44.95	19.22	0.008	18.21	0.004	16.97	0.005	0.704	0.036
8	06:56:00.20	$-$13:14:42.57	16.64	0.002	15.71	0.002	14.62	0.004	1.335	$-$0.092
9	06:56:00.32	$-$13:15:08.39	19.65	0.006	18.75	0.006	17.56	0.008	1.198	0.170
10	06:56:00.51	$-$13:15:12.44	19.95	0.009	18.60	0.005	17.11	0.005	1.084	$-$0.091
11	06:56:00.61	$-$13:14:30.98	19.34	0.006	18.50	0.005	17.40	0.015	1.152	$-$0.034
12	06:56:00.98	$-$13:14:15.08	19.36	0.006	18.51	0.004	17.40	0.006	1.071	$-$0.012
13	06:56:01.08	$-$13:14:28.63	18.47	0.004	17.59	0.006	16.40	0.005	1.184	0.000
14	06:56:01.19	$-$13:13:53.88	19.29	0.007	18.45	0.006	17.39	0.006	1.242	0.000
15	06:56:01.21	$-$13:14:02.25	18.27	0.004	17.37	0.003	16.17	0.005	1.275	$-$0.082
16	06:56:01.47	$-$13:15:20.49	18.71	0.004	17.88	0.003	16.84	0.006	1.181	$-$0.049
17	06:56:01.65	$-$13:14:46.83	19.85	0.009	18.96	0.007	17.79	0.013	1.495	0.382
18	06:56:02.10	$-$13:15:55.44	18.96	0.004	18.15	0.003	17.09	0.005	1.008	$-$0.014
19	06:56:02.11	$-$13:16:43.81	17.84	0.003	17.02	0.002	16.04	0.004	1.110	0.049
20	06:56:02.26	$-$13:16:00.20	19.88	0.010	18.60	0.005	17.19	0.006	1.120	$-$0.092
21	06:56:02.41	$-$13:14:17.13	17.09	0.002	16.17	0.002	15.14	0.003	1.198	$-$0.050
22	06:56:03.23	$-$13:15:15.03	20.38	0.013	18.89	0.005	17.17	0.007	1.200	$-$0.092
23	06:56:03.85	$-$13:15:02.43	19.38	0.006	18.51	0.004	17.41	0.007	1.073	0.010
24	06:56:03.99	$-$13:15:28.30	18.79	0.008	17.95	0.009	16.77	0.007	1.288	0.172
25	06:56:04.02	$-$13:16:35.93	19.78	0.008	18.70	0.004	17.44	0.006	1.026	0.045
26	06:56:04.04	$-$13:15:08.75	18.86	0.005	17.99	0.003	16.83	0.005	1.175	$-$0.025
27	06:56:04.34	$-$13:15:24.36	20.15	0.012	18.70	0.005	16.89	0.005	1.165	0.016
28	06:56:04.46	$-$13:15:18.99	19.32	0.006	18.25	0.004	17.00	0.004	1.022	$-$0.018
29	06:56:04.67	$-$13:15:10.95	19.59	0.059	18.70	0.027	17.48	0.020	1.059	0.008
30	06:56:04.77	$-$13:14:22.56	19.60	0.007	18.36	0.004	16.95	0.005	1.069	$-$0.072
31	06:56:04.79	$-$13:14:53.61	18.05	0.003	17.21	0.002	16.10	0.004	1.152	$-$0.025
32	06:56:04.86	$-$13:15:02.45	19.55	0.007	18.68	0.005	17.55	0.007	1.071	0.006
33	06:56:04.94	$-$13:13:34.16	18.45	0.004	17.29	0.003	15.98	0.003	1.111	$-$0.037
34	06:56:04.96	$-$13:15:16.51	19.15	0.006	18.20	0.004	17.01	0.005	1.147	0.014
35	06:56:05.07	$-$13:15:02.69	19.58	0.007	18.71	0.005	17.56	0.007	1.082	0.009
36	06:56:05.21	$-$13:16:29.75	16.74	0.002	16.20	0.002	15.52	0.003	1.084	$-$0.031
37	06:56:05.51	$-$13:13:29.11	19.69	0.009	18.49	0.005	17.11	0.004	1.089	$-$0.050
38	06:56:05.53	$-$13:15:09.85	19.45	0.008	18.60	0.005	17.47	0.007	0.921	$-$0.025
39	06:56:05.57	$-$13:15:18.62	18.47	0.004	17.62	0.003	16.52	0.005	1.142	$-$0.035
40	06:56:05.65	$-$13:15:11.24	19.32	0.007	18.46	0.004	17.33	0.006	1.103	$-$0.004
41	06:56:05.66	$-$13:14:26.70	18.30	0.003	16.89	0.003	15.26	0.004	1.273	$-$0.074
42	06:56:05.80	$-$13:16:23.78	18.84	0.004	18.02	0.003	16.94	0.005	1.095	0.046
43	06:56:05.85	$-$13:16:30.40	19.67	0.023	18.75	0.005	17.54	0.007	1.769	0.413
44	06:56:05.91	$-$13:15:08.33	19.10	0.015	18.21	0.004	17.05	0.005	1.701	0.493
45	06:56:05.91	$-$13:14:55.77	19.52	0.033	18.63	0.020	17.48	0.007	2.310	$-$0.213
46	06:56:06.16	$-$13:14:29.79	19.81	0.008	18.91	0.006	17.75	0.007	1.073	$-$0.042
47	06:56:06.17	$-$13:14:06.92	19.54	0.007	18.40	0.004	17.05	0.005	1.087	$-$0.039
48	06:56:06.32	$-$13:14:58.41	18.88	0.007	18.05	0.006	16.97	0.006	1.180	0.153
49	06:56:06.37	$-$13:15:24.27	17.25	0.002	15.86	0.003	14.24	0.004	1.603	$-$0.126
50	06:56:06.41	$-$13:15:51.58	16.56	0.002	15.14	0.002	13.52	0.045	6.578	0.075
51	06:56:06.51	$-$13:14:43.98	18.95	0.005	18.03	0.005	16.83	0.006	1.353	0.080
52	06:56:06.61	$-$13:13:15.27	20.35	0.015	18.88	0.007	17.20	0.006	1.025	0.008
53	06:56:06.62	$-$13:13:12.91	18.71	0.005	17.82	0.003	16.65	0.005	1.157	$-$0.038
54	06:56:06.63	$-$13:13:31.33	17.93	0.003	16.92	0.003	15.63	0.004	1.279	$-$0.105
55	06:56:06.67	$-$13:14:53.42	19.84	0.010	18.56	0.005	17.13	0.006	1.227	$-$0.083
56	06:56:06.95	$-$13:15:13.87	19.15	0.005	18.28	0.004	17.08	0.007	1.035	0.009
57	06:56:07.03	$-$13:16:04.54	19.68	0.008	18.82	0.005	17.67	0.007	1.083	$-$0.030
58	06:56:07.12	$-$13:15:48.73	18.75	0.006	17.88	0.003	16.74	0.004	1.192	0.111
59	06:56:07.21	$-$13:14:52.38	18.99	0.008	18.08	0.004	17.03	0.005	0.918	0.090
60	06:56:07.28	$-$13:14:53.50	19.53	0.010	18.57	0.005	17.32	0.006	0.909	0.052
61	06:56:07.46	$-$13:14:32.94	19.60	0.014	18.41	0.004	16.97	0.005	1.430	0.009
62	06:56:07.53	$-$13:13:12.23	18.18	0.003	17.29	0.003	16.12	0.004	1.126	$-$0.071
63	06:56:07.57	$-$13:13:40.53	19.14	0.005	18.32	0.004	17.17	0.006	1.155	$-$0.025
64	06:56:07.58	$-$13:14:39.80	18.88	0.005	18.03	0.004	16.90	0.005	1.103	0.021
65	06:56:07.63	$-$13:14:23.84	19.31	0.006	18.46	0.004	17.32	0.005	1.028	$-$0.076

Table 3. Table 3: Photometry data of the bright stars with V < 19 𝑉 19 V<19 mag in Ruprecht 6

ID	R.A.(J2000)	Decl.(J2000)	$B$	$\sigma \left(B\right)$	$V$	$\sigma \left(V\right)$	$I$	$\sigma \left(I\right)$	$\chi$	sharpness
	hh:mm:ss	dd:mm:ss
66	06:56:07.93	$-$13:13:37.70	19.65	0.007	18.76	0.005	17.60	0.006	1.025	$-$0.065
67	06:56:08.14	$-$13:16:27.92	19.95	0.010	18.60	0.005	16.97	0.005	1.029	$-$0.058
68	06:56:08.23	$-$13:14:37.70	19.91	0.010	18.75	0.005	17.39	0.006	1.089	0.004
69	06:56:08.44	$-$13:16:27.10	18.09	0.003	17.21	0.003	16.03	0.004	1.099	$-$0.030
70	06:56:08.65	$-$13:14:44.54	18.85	0.005	17.97	0.003	16.84	0.004	1.001	$-$0.021
71	06:56:09.07	$-$13:14:46.01	17.22	0.002	16.37	0.003	15.30	0.003	1.372	$-$0.033
72	06:56:09.56	$-$13:13:57.52	19.16	0.005	18.51	0.005	17.65	0.008	1.169	$-$0.114
73	06:56:09.62	$-$13:15:22.41	19.26	0.047	18.36	0.021	17.19	0.012	4.276	2.010
74	06:56:09.64	$-$13:16:32.90	17.36	0.002	16.07	0.002	14.55	0.003	1.227	$-$0.073
75	06:56:09.71	$-$13:15:42.04	19.68	0.008	18.81	0.005	17.68	0.006	1.058	0.098
76	06:56:09.72	$-$13:14:09.50	19.82	0.008	18.76	0.005	17.44	0.006	1.042	0.066
77	06:56:10.02	$-$13:13:49.08	18.05	0.003	17.10	0.003	15.93	0.003	1.137	$-$0.077
78	06:56:10.05	$-$13:13:42.90	19.45	0.006	18.58	0.004	17.45	0.005	1.004	$-$0.012
79	06:56:10.24	$-$13:15:41.29	19.31	0.007	18.43	0.004	17.31	0.007	1.135	$-$0.014
80	06:56:10.24	$-$13:14:28.93	19.42	0.008	18.55	0.006	17.38	0.007	1.100	0.082
81	06:56:10.50	$-$13:13:56.56	20.10	0.010	18.63	0.005	16.88	0.004	1.047	$-$0.175
82	06:56:10.76	$-$13:15:55.35	20.06	0.010	18.73	0.005	17.26	0.006	1.127	$-$0.034
83	06:56:11.08	$-$13:15:46.69	19.38	0.006	18.52	0.004	17.45	0.005	0.985	0.024
84	06:56:11.30	$-$13:14:25.49	17.47	0.003	16.08	0.002	14.44	0.003	1.214	$-$0.058
85	06:56:11.40	$-$13:13:52.18	17.95	0.003	17.08	0.002	15.96	0.004	1.198	0.011
86	06:56:11.41	$-$13:15:40.76	19.71	0.007	18.82	0.005	17.68	0.008	1.092	$-$0.053
87	06:56:11.44	$-$13:14:24.73	19.82	0.012	18.90	0.009	17.66	0.012	0.598	$-$0.023
88	06:56:11.96	$-$13:14:12.16	17.24	0.002	16.35	0.002	15.20	0.003	1.199	$-$0.021
89	06:56:12.02	$-$13:13:41.90	19.22	0.006	18.36	0.004	17.21	0.005	1.047	$-$0.025
90	06:56:12.16	$-$13:14:52.31	16.12	0.002	15.40	0.002	14.54	0.003	1.330	$-$0.083
91	06:56:12.16	$-$13:14:14.52	19.92	0.010	18.80	0.005	17.44	0.006	0.954	$-$0.010
92	06:56:12.26	$-$13:15:10.06	18.89	0.005	17.72	0.003	16.38	0.004	1.174	$-$0.086

Table 4. Table 4: Mean I 𝐼 I -band absolute magnitudes of RC stars †

$M_I$	Reference	Comments
$-0.279\pm 0.088$	Paczyński & Stanek (1998)	Includes reddening correction
$-0.23\pm 0.03$	Stanek & Garnavich (1998)	Volume limited to 70 pc
$-0.209$	Girardi et al. (1998)	Lutz-Kelker bias corrected
$-0.22\pm 0.03$	Groenewegen (2008)	First uses revised Hipparcos parallaxes
$-0.24\pm 0.01$	Francis & Anderson (2014)	Peak of luminosity distribution

Table 5. Table 5: 2MASS Photometry of the RC stars in Ruprecht 6

IDs†	R.A.(J2000)	Decl.(J2000)	$J$	$\sigma \left(J\right)$	$H$	$\sigma \left(H\right)$	$K_s$	$\sigma \left(K_s\right)$	$J-K_s$
	hh:mm:ss	dd:mm:ss
49	06:56:06.37	$-$13:15:24.27	13.004	0.023	12.350	0.026	12.120	0.024	0.884
74	06:56:09.64	$-$13:16:32.90	13.383	0.024	12.764	0.029	12.634	0.028	0.784
84	06:56:11.30	$-$13:14:25.49	13.184	0.026	12.564	0.027	12.400	0.029	0.749

Table 6. Table 6: Slope and intercept values in the equation of < [ F ​ e / H ] > = a × R GC + b expectation delimited-[] 𝐹 𝑒 𝐻 𝑎 subscript 𝑅 GC 𝑏 <[Fe/H]>=a\times R_{\mathrm{GC}}+b

Reference	Radial Coverage	$a$	$b$	RMS	N
This study	All	$-0.034\pm 0.007$	$0.190\pm 0.080$	0.201	81
This study	kpc	$-0.077\pm 0.017$	$0.609\pm 0.161$	0.152	49
This study	$R>12$ kpc	$0$	$-0.3$	–	27
Ryu & Lee (2011)	kpc	$-0.076\pm 0.013$	$0.600\pm 0.116$	0.029	186
Ryu & Lee (2011)	$R>12$ kpc	$0$	$-0.3$		186
Andreuzzi et al. (2011)	All	$-0.04$	–	–	177
Andreuzzi et al. (2011)	kpc	$-0.07$	–	–	177
Andreuzzi et al. (2011)	$R>12$ kpc	$0$	$-0.35$	–	177
Kim (2006)	All	$-0.067\pm 0.009$	–	–	53
Kim et al. (2005)	All	$-0.064\pm 0.009$	–	–	51
Kim et al. (2005)	–	$-0.066\pm 0.019$	–	–	$†$
Friel et al. (2002)	All	$-0.059\pm 0.010$	–	–	39
Piatti et al. (1995)	All	$-0.07\pm 0.01$	–	0.13	63

Equations

$$B=b-0.285(\pm 0.009)X_b-0.127(\pm 0.005)(B-V)-1.903(\pm 0.013)$$

$$V=v-0.157(\pm 0.007)X_v+0.027(\pm 0.004)(B-V)-1.693(\pm 0.011)$$

$$I=i-0.056(\pm 0.007)X_i+0.019(\pm 0.003)(V-I)-2.712(\pm 0.010)$$

Full text

$BVI$ Photometric Study of the Old Open Cluster Ruprecht 6

Sang Chul KIM

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Korea University of Science and Technology (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea

Visiting astronomer, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

Jaemann Kyeong

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Hong Soo Park

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Korea University of Science and Technology (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea

Visiting astronomer, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

Ilseung Han

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Kyungpook National University, Republic of Korea;

Joon Hyeop Lee

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Korea University of Science and Technology (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea

Dae-Sik Moon

Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada;

Youngdae Lee

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Seongjae Kim

Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea;

Kyungpook National University, Republic of Korea;

sckim, jman, hspark, jhl, ylee@kasi.re.kr

ihan@knu.ac.kr, ksj6283@naver.com

moon@astro.utoronto.ca

(Received May 4, 2017; accepted June 8, 2017)

\jkashead

1 Introduction

The Galactocentric radial metallicity gradient in the disk of the Milky Way (MW) has been studied for a long time (e.g., Twarog et al. 1997; Park & Lee 1999; Chen, Hou, & Wang 2003; Tadross 2003; Kim 2006; Carraro et al. 2007; Paunzen et al. 2010; Netopil et al. 2016; Cantat-Gaudin et al. 2016; Jacobson et al. 2016; Tissera et al. 2016), for which open clusters (OCs) have been under intense studies, alongside with Cepheids (Andrievsky et al. , 2004; Cescutti et al. , 2007), globular clusters (Yong et al. , 2008), red clump (RC) stars (Önal Taş et al. , 2016), planetary nebulae (Stanghellini, & Haywood , 2010), H ii regions (Rudolph et al. , 2006; Fernández-Martín et al. , 2017), field stars (Xiang et al. , 2015), etc. The disk metallicity gradient can give information on the disk formation processes, star formation processes, and chemical evolution of the spiral galaxies (Tissera et al. , 2016). One notable recent result is that of Anders et al. (2017), who have claimed the slopes of the Galactic radial metallicity gradient to be $\simeq-0.066$ dex kpc*-1* for the age range of $1-4$ Gyr and $\simeq-0.03$ dex kpc*-1* for $6-10$ Gyr, using 418 red giant stars observed by CoRoT-APOGEE with $6<R_{\mathrm{GC}}$ $\;\buildrel<\over{\sim}\;$13 kpc and $\mid Z_{gal}\mid<0.3$ kpc (where $R_{\mathrm{GC}}$ is the Galactocentric distance and $Z_{gal}$ is the vertical distance from the Galactic plane).

OCs, especially the old ones, are a good laboratory for verifying stellar evolution theories, and they are also good tracers of the star formation and evolutionary history of the Galactic disk. While Lyngå (1987) published data for over 1200 OCs, the observed number of OCs including candidates has increased to 2167 in the latest version (3.5; 2016 January 28) of Dias et al. (2002) (hereafter DAML02) catalog111http://www.wilton.unifei.edu.br/ocdb/. Among the 2167 objects in the DAML02 OC catalog, only 298 (13.8%) have metallicity estimates (Oliveira et al. , 2013; Krisciunas et al. , 2015), while 703 (32.4%) have radial velocity estimates, 2013 (92.9%) have age estimates, 2025 (93.4%) have reddening estimates, 2040 (94.1%) have distance estimates, and 2104 (97.1%) have proper motion estimates. Kharchenko et al. (2013) presented MW object catalog for 3006 objects including 2808 OCs, 147 globular clusters and 51 associations, almost complete up to 1.8 kpc from the Sun, where only 386 out of 3006 have metallicity values. Considering the estimated total number of MW OCs ($\sim 100,000$; Piskunov et al. (2006); Tadross (2011)), more surveys and detailed photometric and spectroscopic studies on individual clusters are awaited.

Ruprecht 6 (Ruprecht , 1966) is an old OC, located in the constellation of Canis Major and at very large distance ($\sim 13.28\pm 0.54$ kpc; see Table 1 below) from the Galactic center. It is one of the small-size and poor OCs, which means it contains not so many number of member stars. This could be the reason why there have been few studies on the cluster. Hasegawa et al. (2008), which seems the only previous observational study on this cluster, have used 65-cm telescope, AP8 1024 px CCD, and $BVI$ filters at Gunma Astronomical Observatory (FoV = 10.3\hbox{{}^{\prime}}\times 10.3\hbox{{}^{\prime}}) to study 36 old OCs, and included Ruprecht 6 in their study. They obtained some physical parameters for Ruprecht 6 from Padova isochrone fitting : age = 3.2 Gyr (${\rm log}~{}t=9.50$), $Z=0.008$ ([Fe/H] $=-0.41$), $E(V-I)=0.60$ mag, and $(m-M)_{0}=14.43$ ($d=7.7$ kpc), and these values are enlisted in the DAML02 catalog. Some basic physical parameters are summarized in Table 1. The last parameter in Table 1 presents the Trumpler class of Ruprecht 6 to be III 1 p, which means, respectively, (i) Ruprecht 6 is detached and shows no noticeable concentration, (ii) most stars in the cluster are of nearly the same apparent brightness, and (iii) it is poor containing less than 50 stars (Trumpler , 1930; Dias et al. , 2002). In this study, using the $BVI$ optical imaging data obtained by using the CTIO 1.0 m telescope, we present the photometric analysis and physical parameters of the OC Ruprecht 6.

Section 2 describes the observations and data reduction processes. Section 3 presents the results in this study: cluster center position, color-magnitude diagrams, reddening and distance estimations, and PARSEC isochrone fitting results. In Sections 4 and 5, we discuss the Galactocentric metallicity distribution and summarize our results, respectively.

2 Observations and Data Reduction

Observations have been done using the Small and Moderate Aperture Research Telescope System (SMARTS) 1.0 m telescope and Y4KCam CCD at the Cerro-Tololo Inter-American Observatory (CTIO, Chile) on 2010 December 13 (UT). The Y4KCam CCD made at the Ohio State University is composed of $4104\times 4104$ pixels (each 15 $\mu$m, \sim 0.289\hbox{{}^{\prime\prime}} pixel*-1*) at the Cassegrain focus of the telescope, while it becomes $4064\times 4064$ pixels (19.57\hbox{{}^{\prime}}\times 19.57\hbox{{}^{\prime}}) after excluding the 40 pixel wide gaps on either horizontal and vertical center separating the CCD into four quadrants and reading out the pixel values 222http://www.astronomy.ohio-state.edu/Y4KCam/detector.

For the OC Ruprecht 6, we have obtained three 1200 sec, three 900 sec, and two 800 sec images for $B,V,$ and $I$ filters, respectively, under 1.5\hbox{{}^{\prime\prime}} median seeing conditions. The final images are average combined for each filter. Figure 1 displays the combined grey-scale image of three $V$-band frames for the OC Ruprecht 6, where red circles show the region of Ruprecht 6 with radius of 2′.

The raw observation data have been processed with the IRAF333IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation./CCDRED package with standard procedure. That is, the overscan correction, bias correction, and the twilight sky flattening have been made. Since interference patterns are seen in the $I$-band images, we made $I$-band supersky image using all the $I$-band images obtained on the same night and performed second flattening. In addition, because of the large format of the detector and the slow speed of the shutter, the shutter shading correction is applied. The IRAF script (y4kshut.cl) given at the CTIO homepage is used for the correction.

Photometry was performed using the DAOPHOT II/ALLSTAR stand-alone package after separating the CCD quadrants to treat them as four separate CCD chips (Stetson , 1990). This is also because each chip has different gain and readout noise. Due to the large field of view, we adopt the quadratic variable point spread function. Aperture corrections were obtained with $20-30$ isolated, bright, and unsaturated stars in each CCD quadrant. Figure 2 shows the error distribution of the $BVI$ photometry results. The photometric errors typically attain 0.1 mag at $B\approx 22.7$ mag, $V\approx 22.4$ mag and $I\approx 21.2$ mag (Kim et al., 2009), indicating ten times of object signal above the background.

Four Landolt (1992, 2007, 2009) standard star fields (PG0231+051, LB1735, LSS982, Rubin 149) were observed during the four nights of the observing run (2010 December $11-14$, UT) to obtain the standardization equations for this run and to convert the instrumental magnitudes to the standard magnitudes. The transformation equations are

[TABLE]

where small and capital letters represent instrumental and standard magnitudes, respectively, and $X$ is the airmass for each filter. We also have obtained the secondary extinction coefficient ($k_{2B}=-0.052\pm 0.016$) as a free parameter. Including the secondary extinction coefficient, however, caused the errors of other parameters increase and the overall residual remained at the same value (0.037). So we decided not to adopt $k_{2B}$ but follow the simple solution. Figure 3 (a), (b), and (c) show the standardization residuals for the magnitude differences, where the rms of the fits are $\Delta B=0.037$, $\Delta V=0.030$, $\Delta I=0.029$. Figure 3 (d) and (e) show the standardization residuals for the color differences, where the rms of the fits are $\Delta(B-V)=0.017$, and $\Delta(V-I)=0.019$. Astrometry was done using the routines provided in astrometry.net (Lang et al. , 2010).

The total number of stars with photometry is 5570, while that for the region of Ruprecht 6 with radius <2\hbox{{}^{\prime}} is 296. Table 2 lists the photometry of 92 stars of Ruprecht 6 with $V<19$ mag.

3 Results

3.1 Cluster Center and Size

For the center coordinates of the OC Ruprecht 6, Hasegawa et al. (2008) presents $\alpha_{J2000}$ = 06h 56m 06s, $\delta_{J2000}$ = $-13$∘  15′  00*′′, which we adopt in this study. While Dias et al. (2002) (Version 3.5, 2016 January 28) lists $\alpha_{J2000}$ = $06^{h}$ 56m* 00s, $\delta_{J2000}$ = -13\hbox{{}^{\circ}}~{}17\hbox{{}^{\prime}}~{}00\hbox{{}^{\prime\prime}} and SIMBAD gives $\alpha_{J2000}$ = 06h 55m 55.2s, $\delta_{J2000}$ = $-13$∘  16′  48*′′*, both of these values result in poor identifications of the cluster center. The coordinates given by Hasegawa et al. (2008) point to the cluster center more accurately as seen in Figure 1.

Using the bright stars ($V\leq 20$ mag) with the cluster center fixed as above, we plotted the radial number density profile with the bin size of 0.5\hbox{{}^{\prime}} in Figure 4. We determined the radius of Ruprecht 6 to be 2.0\hbox{{}^{\prime}}, in which radius most of the member stars are located.

3.2 Color-Magnitude Diagrams

Figure 5 shows the $V-(B-V)$ (panel a), $V-(V-I)$ (panel b), $B-(B-V)$ (panel c), and $I-(V-I)$ (panel d) color-magnitude diagrams (CMDs) of the OC Ruprecht 6 for the radial range of <2\hbox{{}^{\prime}} obtained in this study, while Figure 6 shows the comparison region (3\hbox{{}^{\prime}}<R<3.6\hbox{{}^{\prime}}) with the same area. Some characteristic features that can be found for Ruprecht 6 in these CMDs are : (i) main-sequence stars are clearly seen and red dotted lines show the blue turn-off point at $B\approx 19.30$ mag, $V\approx 18.45$ mag, $I\approx 17.30$ mag, $B-V\approx 0.85$ mag, and $V-I\approx 1.15$ mag (see Figure 2 of Kaluzny (1994) for the definition of the blue turn-off), (ii) some red giant stars evolved after the turn-off are found, and (iii) three RC stars are seen and denoted as boxes in Figure 5 with mean magnitudes and colors of $B=17.36\pm 0.09$ mag, $V=16.00\pm 0.10$ mag, $I=14.41\pm 0.13$ mag, $B-V=1.35\pm 0.05$, mag $V-I=1.59\pm 0.05$ mag.

To further check the membership probability of the three RC stars statistically, we extracted all stars with similar magnitudes and colors to the RC stars in the whole observed area of 19.57\hbox{{}^{\prime}}\times 19.57\hbox{{}^{\prime}}. Figure 7 shows the spatial distribution of the resultant 10 stars located in the RC box area of Figure 5 and Figure 6, including the three RC stars in Ruprecht 6. The stellar spatial density of the three stars in the cluster area is $3/(\pi 2^{2})=0.239~{}{\rm arcmin}^{-2}$, while that of the seven stars outside of the cluster area is $7/(19.57^{2}-\pi 2^{2})=0.019~{}{\rm arcmin}^{-2}$. The stellar density of the cluster area is $0.239/0.019=12.58$ times more higher than that of the background area, and thus we conclude that the three RC stars in Ruprecht 6 are members of the cluster with high probability.

3.3 Distance Estimation

RC giant stars are low-mass stars at the evolutionary stage of core-helium-burning, that define a sharpest feature (almost constant absolute magnitude) in the CMDs of stellar systems like nearby galaxies and star clusters (Paczyński & Stanek (1998); Kim & Sung (2003); Kim et al. (2005); Kyeong et al. (2011); Karaali et al. (2013); Girardi (2016); Davies et al. (2017), but, see also Wan et al. (2015)). In the near-infrared (NIR), especially in the $K_{S}$-band, the RC is known to have small dependence on metallicity and age, showing $M_{K_{S}}=-1.595\pm 0.025$ mag and an intrinsic color of $(J-K_{S})_{0}=0.612\pm 0.003$ mag (Yaz Gökçe et al. , 2013; Özdönmez et al. , 2016). Recently, Girardi (2016) published a detailed review paper on the RC stars, and summarized the mean absolute magnitudes of these stars, which could possibly be used to estimate the distances and extinctions to stellar systems with the age of 1 to 10 Gyr though with some caveats such as population effects. Table 4 shows the mean $I$-band absolute magnitudes of RC stars from Girardi (2016) and the mean values of the five data is $\langle M_{I}\rangle=-0.236\pm 0.024$ mag.

Since it is known that the near-infrared $K$-band magnitude of the RC stars is not sensitive to the age and metallicity of the star cluster than the optical $I$-band magnitude (Sarajedini , 1999; Grocholski & Sarajedini , 2002; Kyeong et al. , 2011), we mainly used the mean $K$(RC) magnitude of the RC stars in Ruprecht 6. Table 5 shows the $JHK_{s}$ magnitudes of the three RC stars in Ruprecht 6 extracted from the 2MASS (Two Micron All Sky Survey444available at http://www.ipac.caltech.edu/2mass/releases/allsky/, Skrutskie et al. (1997, 2006)) data archive. Using the mean $K$(RC) magnitude of $\langle K_{s}\rangle=12.39\pm 0.21$, the extinction value of $A_{V}=1.30$ (see Section 3.4), and the extinction ratio of $A_{K}=0.118A_{V}=0.15$ (Dutra et al. , 2002), we obtain $(m-M)_{0}=K_{s}-M_{K_{s}}-A_{K}=12.39-(-1.595)-0.15=13.84\pm 0.21$ ($d=5.86\pm 0.60$).

3.4 Reddening Estimation

For the estimation of the interstellar reddening value toward the OC Ruprecht 6, we adopted the following four methods. First, we have used the mean NIR color of the RC stars ($\langle J-K_{s}\rangle=0.81\pm 0.06$) from Table 5 and the intrinsic color of RC stars ($(J-K_{s})_{0}=0.612\pm 0.003$ mag) mentioned in Section 3.3, we obtain $E(J-K_{s})=(J-K_{s})-(J-K_{s})_{0}=0.20\pm 0.06$. Using the relation $E(J-K_{s})=0.488E(B-V)$ (Kim , 2006), we obtain $E(B-V)=0.41\pm 0.06$.

Secondly, we have used the mean optical color of the RC stars in Ruprecht 6: $B-V=1.35\pm 0.05$ (Section 3.2). Janes & Phelps (1994) gave the mean color and magnitude of the RC stars in old OCs as $(B-V)_{0,RC}=0.95\pm 0.10$ and $M_{V,RC}=0.90\pm 0.40$, when the $V$ magnitude difference between the RC stars and the main sequence turn-off of the clusters, $\delta V$, is greater than one (Kim & Sung , 2003). Since $\delta V\approx 18.45-16.00>1$ for Ruprecht 6, we obtain $E(B-V)=(B-V)-(B-V)_{0}=1.35-0.95=0.40\pm 0.11$.

Thirdly, we have used the $(B-V)$ versus $(V-I)$ diagram of bright stars with $V<19$ mag and stars of $19<V<20$ mag in Ruprecht 6 at radius <2\hbox{{}^{\prime}} as shown in Figure 8. Solid and dotted lines show the intrinsic relations for the dwarf and giant stars, respectively, from Sung et al. (2013), which are shifted according to the reddenings of $E(B-V)=0.40$ and $E(V-I)=0.59$. Although the reddening vector in the diagram is very similar to the distribution of main-sequence and giant stars, we can get a hint of the amount of the reddening values from this diagram. From the comparison of the observed colors of the bright stars of Ruprecht 6 and the intrinsic colors, we derive the reddening values of $E(B-V)=0.40\pm 0.10$ and $E(V-I)=0.59\pm 0.10$.

Finally, PARSEC isochrone fittings are made as shown in Section 3.5, which gives the best match with $E(B-V)=0.42$ and $E(V-I)=0.60$, which are in agreement with the values above within uncertainties.

Considering the results of these four methods, we assume that the true reddening values toward Ruprecht 6 are in the range of $E(B-V)=0.40-0.42$ and $E(V-I)=0.59-0.60$, and in this study we adopt the values of $E(B-V)=0.42$ and $E(V-I)=0.60$ which afford the best isochrone matches (see Section 3.5). This is in very good agreement with the value ($E(B-V)=0.43$) listed in the DAML02 catalog. The interstellar extinction laws given by Cardelli et al. (1989) are used to calculate the extinctions for other colors for the total-to-selective extinction ratio of $R_{V}=3.1$ : $A_{B}=4.14E(B-V)=1.74$, $A_{V}=3.10E(B-V)=1.30$, $A_{I}=1.48E(B-V)=0.62$ (Lee & Kim , 2000; Kim et al., 2012).

3.5 PARSEC Isochrone Fittings

In Figure 9, we have plotted the $V$ versus $(B-V)$ (a), $V$ versus $(V-I)$ (b), $B$ versus $(B-V)$ (c), and $I$ versus $(V-I)$ (d) CMDs for Ruprecht 6 together with the theoretical PAdova and TRieste Stellar Evolution Code (PARSEC) isochrones (Bertelli et al. , 1994; Girardi et al. , 2000, 2002; Bressan et al. , 2012). The best matched isochrones are for the parameters of log (age) $=9.50\pm 0.10$ (t $=3.16\pm 0.82$ Gyr) and [Fe/H] $=-0.42\pm 0.04$ dex shifted according to $E(B-V)=0.42$, $E(V-I)=0.60$, $B-M_{B}=15.58$, $V-M_{V}=15.14$, and $I-M_{I}=14.46$. The metallicity and age values obtained in this study are in excellent agreement with those of Hasegawa et al. (2008) ([Fe/H] $=-0.41$ and log (t) $=9.50$, t $=3.2$ Gyr) and DAML02 ([Fe/H] $=-0.38$ and log (t) $=9.50$).

With the limited data of $BVI$ photometry only, it is not an easy task to determine the reddening, distance, age, and metallicity simultaneously from the isochrone fitting due to the degeneracy of parameters. We, therefore, have used pre-determined values of distance (Section 3.3) and reddening (Section 3.4) for the isochrone fittings just to find optimum values of age and metallicity, after which slight fine-tunings are made. Good matches of the theoretical isochrones and the observed photometry data lend support for the distance and reddening values, and the newly obtained values of age and metallicity.

4 Discussion

4.1 Red Clump Stars

Among the 10 RC stars shown in Figure 7, one star is located just outside of the 2\hbox{{}^{\prime}} radius circle of Ruprecht 6, with its coordinates R.A. $(J2000)=06^{h}$ 56m 6.366s and Decl. (J2000)=-13\hbox{{}^{\circ}}~{}15\hbox{{}^{\prime}}~{}24.27\hbox{{}^{\prime\prime}}. Since it is very likely that this star could also be a member of the cluster considering its close location to the cluster area, we can include it in our estimation of the cluster parameters. The optical and 2MASS NIR photometry results of the star are : $B=17.358\pm 0.003$ mag, $V=15.912\pm 0.002$ mag, $I=14.273\pm 0.004$ mag, $J=12.981\pm 0.026$ mag, $H=12.229\pm 0.022$ mag, $K_{S}=12.065\pm 0.024$ mag, and $(J-K_{s})=0.916$ mag.

Inclusion of this star results in the mean $K(RC)$ magnitude to be $\langle K_{s}\rangle=12.31\pm 0.23$ mag and this gives the distance modulus to be $(m-M)_{0}=K_{s}-M_{K_{s}}-A_{K}=12.31-(-1.595)-0.15=13.76\pm 0.23$ ($d=5.65\pm 0.63$ kpc, still using the reddening values obtained in Section 3.4), which agrees within the error range but somewhat shorter than that in Section 3.3. The mean NIR color of the four RC stars including the above one is $\langle(J-K_{s})\rangle=0.83\pm 0.07$ mag and this results in a little bit larger reddening values of $E(J-K_{s})=(J-K_{s})-(J-K_{s})_{0}=0.22\pm 0.07$ and $E(B-V)=0.45\pm 0.07$.

4.2 Galactocentric Metallicity Distribution

OCs have been used as one of the tools to probe the Galactocentric radial metallicity distribution in our own Galaxy (Kim & Sung , 2003; Wu et al. , 2009; Ryu & Lee , 2011). This radial variation of the metallicity in the disk of the Galaxy is a powerful tool for the understanding of the star formation and chemical evolution of the system (Fernández-Martín et al. , 2017). Kim et al. (2005) have compiled the slope ($=\Delta$[Fe/H]$/\Delta R_{\mathrm{GC}}$) values of the Galactocentric radial metallicity gradient published up to then. Using the nine published slope values, they obtained the mean value of the slope $\Delta$[Fe/H]$/\Delta R_{\mathrm{GC}}=-0.066\pm 0.019$. In Table 6, we have compiled again the slopes and intercept values incorporating recently published results for OCs.

For the OCs in the DAML02 catalog, we have calculated the Galactocentric distances using the distance estimates, Galactic coordinates in the catalog and the equation : $R_{\mathrm{GC}}=\sqrt{[d~{}{\rm cos}(b)~{}{\rm cos}(l)-R_{0}]^{2}+d^{2}~{}{\rm cos}^{2}(b)~{}{\rm sin}^{2}(l)+d^{2}~{}{\rm sin}^{2}(b)}$, where $d$ is the heliocentric distance to the cluster, $l$ and $b$ are the Galactic longitude and Galactic latitude, respectively, of the cluster, $R_{0}$ is the distance of the Sun from the Galactic center ($8.5$ kpc is used in this study). Out of 2167 OCs listed in the DAML02 catalog, only 298 clusters have both of metallicity and distance estimates, which are shown in Figure 10 as a function of the Galactocentric distance, $R_{\mathrm{GC}}$.

We have performed the least square fitting for all the 298 OCs with both metallicity and distance estimates, and obtained [Fe/H] $=(-0.034\pm 0.005)R_{\mathrm{GC}}+(0.204\pm 0.053)$ with rms = 0.229 for all the radial range of the Galaxy (shown as blue dashed line in Figure 10 (a)). Assuming the outer ($R>12$ kpc) clusters might follow constant ([Fe/H] $\sim-0.3$ dex) metallicity trend, we also made the least square fitting only for the inner ($R_{\mathrm{GC}}<12$ kpc) OCs with 2$\sigma$ clipping, which returns [Fe/H] $=(-0.061\pm 0.008)R_{\mathrm{GC}}+(0.479\pm 0.071)$ with rms = 0.155 (N = 231) (shown as red solid line in Figure 10 (a)).

Taking into account only the old OCs with age $>1$ Gyr, we plotted the same plot in Figure 10 (b). The 81 objects in the whole radial range give the relation of [Fe/H] $=(-0.034\pm 0.007)R_{\mathrm{GC}}+(0.190\pm 0.080)$ with rms = 0.201 (blue dashed line in Figure 10 (b)), and the 49 clusters at $R_{\mathrm{GC}}<12$ kpc left after the 2$\sigma$ clipping process returns [Fe/H] $=(-0.077\pm 0.017)R_{\mathrm{GC}}+(0.609\pm 0.161)$ with rms = 0.152 (red solid line in Figure 10 (b)). This result is in very good agreement with those obtained recently by Ryu & Lee (2011) and Andreuzzi et al. (2011), while the number of OCs used in this study is smaller than those of the previous studies which resulted from introduction of the process of extracting only the old and good (by 2$\sigma$ clipping) clusters for the analysis.

Whether we adopt the single relation for the whole radial range or the dual relation broken at $R_{\mathrm{GC}}\sim 12$ kpc, Ruprecht 6 seems to conform either of the radial metallicity trends at its location of $R_{\mathrm{GC}}=13.28\pm 0.54$ kpc.

The metallicity estimates from photometric indices are less reliable than those from spectroscopic observations. $(U-B)$ colors for late-F to early-K-type stars, Washington and DDO photometric systems for G and K-type giants can give some reliable values. However, while the DAML02 catalog gives detailed references for proper motions and radial velocities, the sources for the metallicity estimates are not listed. Among the 81 objects in Figure 10 (b), there are 18 objects for which $N\geq 10$ stars are used to determine the metallicity, 40 objects for which $1\leq N\leq 9$ stars are used, and no information is given for the other 23 objects. Investigating the sources of the metallicity estimates again is beyond the scope of this paper, but compilation and classification of these estimates using the criteria of the methods to find abundances and number of stars used will be a good approach to obtain more reliable Galactocentric radial metallicity distribution of the OCs in the Milky Way.

5 Summary

We derived the physical parameters of the small-size and poorly studied old OC Ruprecht 6 using the $BVI$ optical photometry data. The main results obtained in this study are :

$\bullet$ The color-magnitude diagrams of Ruprecht 6 show clear MS stars. The MS turn-off point is at $V\approx 18.45$ mag and $B-V\approx 0.85$ mag.

$\bullet$ Three RC stars are at $V=16.00$ mag, $I=14.41$ mag and $B-V=1.35$ mag. The mean $K_{s}$-band magnitude of RC stars ($K_{s}=12.39\pm 0.21$ mag) and the known absolute magnitude of the RC stars ($M_{K_{S}}=-1.595\pm 0.025$ mag), the distance modulus to Ruprecht 6 is obtained to be $(m-M)_{0}=13.84\pm 0.21$ mag ($d=5.86\pm 0.60$ kpc).

$\bullet$ From the $(J-K_{s})$ and $(B-V)$ colors of the RC stars, comparison of the $(B-V)$ and $(V-I)$ colors of the bright stars in Ruprecht 6 with those of the intrinsic colors of dwarf and giant stars, and the PARSEC isochrone fittings, we derive the reddening values of $E(B-V)=0.42$ mag and $E(V-I)=0.60$ mag.

$\bullet$ Using the PARSEC isochrone fittings onto the color-magnitude diagrams, we obtain the age and metallicity values to be : log (t) $=9.50\pm 0.10$ (t $=3.16\pm 0.82$ Gyr) and [Fe/H] $=-0.42\pm 0.04$ dex.

$\bullet$ For the old (age $>1$ Gyr) OCs of DAML02 catalog, we obtain the Galactocentric radial metallicity relations of either (i) a single relation of [Fe/H] $=(-0.034\pm 0.007)R_{\mathrm{GC}}+(0.190\pm 0.080)$ (rms = 0.201) or (ii) dual relation of [Fe/H] $=(-0.077\pm 0.017)R_{\mathrm{GC}}+(0.609\pm 0.161)$ (rms = 0.152) at $R_{\mathrm{GC}}<12$ kpc and constant ([Fe/H] $\sim-0.3$ dex) value at $R_{\mathrm{GC}}>12$ kpc.

Acknowledgements.

We thank the anonymous referee and the Scientific Editor for the thorough review and helpful comments that helped to improve the manuscript. The participation of I. H. and S. K. in this project was made possible by UST Research Internship for Undergraduates grant in 2016 July. Based on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory (NOAO Prop. ID 2010B-0178, PI Sang Chul KIM), which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.