SPECTROSCOPIC CONFIRMATION OF THE DWARF GALAXIES HYDRA II AND PISCES II AND THE GLOBULAR CLUSTER LAEVENS 1^*

Martin et al. (2015) discovered Hydra II in SMASH/DECam images. The Hydra II images, taken on 2013 March 20, are publicly available through the NOAO Science Archive.⁵ We downloaded the calibrated images in the DECam g and r filters. These images are flat fielded, and they have astrometry headers. We used SExtractor (Bertin & Arnouts 1996) to identify stars and measure their magnitudes in each of the g and r images. We discarded objects with class_star ≤ 0.8 in order to weed out galaxies and image artifacts. We corrected magnitudes for extinction according to the dust maps of (Schlegel et al. 1998, SFD98).

We selected stars for spectroscopy based on their colors and magnitudes. We drew a region in the color–magnitude diagram (CMD) in the approximate shape of the red giant branch (RGB) and horizontal branch (HB). Figure 1 shows this region in gray. We assigned priorities for spectroscopic selection within the region based on magnitude but not on color. These priorities were used to resolve conflicts where slitmask design constraints forced a choice among two or more stars. Brighter stars were given higher priorities. The stars that were able to be placed on the DEIMOS slitmask are shown as blue points (members) and red crosses (non-members). Figure 2 shows the sky coordinates of the spectroscopic targets.

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Our spectroscopic selection includes two potential HB stars, 189086 and 191385, and one asymptotic giant branch (AGB) star, 194563. Our kinematic membership selection (Section 5.1) includes all three stars. However, star 191385 is 0.4 mag above the HB. Therefore, we ruled it a non-member. Star 189086 has a color and magnitude consistent with the HB. Although it is the most distant member in our Hydra II sample, we kept it in our list of members. These decisions do not affect our results in a measurable way (Section 5.2).

Sand et al. (2012) observed Pisces II with Magellan/Megacam in the g and r filters. We used their published astrometric and photometric catalog. They corrected for extinction using the SFD98 dust map. We drew a spectroscopic selection region around the RGB (Figure 1). Because Pisces II has a smaller half-light radius ($1\buildrel{\,\prime}\over{.} 1$, Sand et al. 2012) than Hydra II ($1\buildrel{\,\prime}\over{.} 7$, Martin et al. 2015), the possible targets are denser on the sky, which causes more conflicts for spectroscopic selection. As a result, the selection region did not include the HB so that RGB stars could be selected instead. (RGB spectra lend themselves more easily to the measurements of radial velocity and metallicity than HB spectra.) As for Hydra II, spectroscopic priority was given to brighter stars.

D. Perley kindly observed Laevens 1 for us with Keck/LRIS (Oke et al. 1995) on 2015 March 23. Simultaneous exposures were obtained for 130 s in the g filter in the blue arm and 120 s in the I filter in the red arm. The images were reduced with LPipe,⁶ which provides flat fielding, astrometric solutions, and photometric calibration.

We identified stars and measured their magnitudes with DAOPHOT (Stetson 1987, 2011). The LRIS point-spread function (PSF) was asymmetric, and it varied over the field. We allowed DAOPHOT to choose the best analytic PSF, which was a Penny function (a two-dimensional Gaussian core with Lorentzian wings). Additionally, there was a look-up table that allowed the PSF to vary linearly over the field. Again, we corrected for extinction using the SFD98 dust map.

Because the half-light radius of Laevens 1 ($0\buildrel{\,\prime}\over{.} 5$–$0\buildrel{\,\prime}\over{.} 6$, Belokurov et al. 2014; Laevens et al. 2014) is even smaller than Pisces II, we again selected stars on the RGB, not the HB. However, we also included three bright, blue stars near the center of the system. The nature of these stars is controversial. Belokurov et al. (2014) speculated that these are core helium-burning blue loop stars, which would imply that Laevens 1 has formed stars within the last few hundred Myr, making it a dwarf galaxy. Laevens et al. (2014) also identified these stars, but they did not favor their interpretation as blue loop stars because young, blue stars at fainter magnitudes were absent. We obtained spectra of all three stars in order to determine if they are members of Laevens 1. We also note that Bonifacio et al. (2015) found a population of stars brighter and bluer than the main sequence turn-off but too faint for spectroscopy. If they are not blue stragglers, these stars could signify the presence of a ∼2 Gyr old population in Laevens 1.

For the purposes of measuring metallicities, it is convenient to have photometry in a uniform system. Therefore, we converted Cousins I magnitudes into SDSS i magnitudes following the conversion formula of Jordi et al. (2006): $i=I+0.21(R-I)+0.34$. The formula depends weakly on $R-I$ color, which we approximated as 0.5 mag for all RGB stars. Due to the imprecision of this assumption, we added 0.05 in quadrature to the i photometric errors. This error floor corresponds to an error in $R-I$ color of 0.2 mag. For comparison, the full range of $R-I$ color for an old, metal-poor RGB is about 0.4 mag.

We observed one slitmask for each satellite with DEIMOS (Faber et al. 2003) on 2015 May 18. Table 1 lists the exposure times of each slitmask. We used the 1200G grating with a ruling of 1200 lines mm⁻¹ and a blaze wavelength of 7760 Å. The grating was tilted such that the center of the CCD mosaic corresponded to 7800 Å. Slits were $0\buildrel{\prime\prime}\over{.} 7$ wide. This configuration gives an approximate wavelength range of 6300–9100 Å at a resolution of 1.3 Å FWHM ($R\sim 6000$ at 7800 Å). The exact wavelength range of each spectrum depends on the location of the slit on the slitmask. The starting and ending wavelengths of the spectra vary by ∼300 Å across the slitmask. We also obtained internal flat field and arc lamp exposures in the afternoon and morning for calibration.

Table 1.  DEIMOS Observations

System	UT Date	# Targets	Airmass	Seeing	Individual Exposures	Total Exposure Time
				('')	(s)	(s)
Milky Way Satellites
M22	2009 Oct 13	64	1.5	0.6	2 × 900	1800
	2009 Oct 14	64	1.5	0.6	$2\times 900+420$	2220
Hydra II	2015 May 18	49	1.6	0.8	$4\times 1200+1\times 900$	5700
Pisces II	2015 May 18	20	1.8	0.8	3 × 1380	4140
Laevens 1	2015 May 18	14	1.4	0.9	3 × 1380	4140
Laevens 1 (star 1717)	2015 Mar 22	1	1.2	0.6	1 × 1800	1800
Radial Velocity Standard Stars
HD 38230	2012 Apr 19	...	1.4	1.0	1 × 120	120
HD 151288	2013 Apr 13	...	1.1	1.0	1 × 80	80
HD 103095	2013 May 5	...	1.1	0.7	1 × 60	60
BD–18° 5550	2013 May 18	...	1.3	0.8	1 × 350	350
HD 88609	2015 May 18	...	1.2	0.8	1 × 240	240
HD 122563	2015 May 18	...	1.4	0.8	1 × 75	75
HD 187111	2015 May 18	...	1.2	0.9	1 × 80	80
BD+23° 3912	2015 May 18	...	1.0	0.9	1 × 300	300
HD 109995	2015 May 19	...	1.1	0.9	1 × 300	300
Telluric Standard Stars
HR 4829	2015 May 19	...	1.1	0.9	1 × 60	60
HR 7346	2015 May 19	...	1.1	0.7	1 × 120	120

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As mentioned above, Belokurov et al. (2014) identified several bright, blue stars in the vicinity of Laevens 1. These stars would be unusual in an old GC or dwarf galaxy. Our slitmask included two of these stars. We observed another blue star, 1717, with a single 07 slit.

We also observed nine radial velocity standard stars and two telluric (hot) stars with a long slit. The slit width was 07. We used a long slit that spanned the entire length of the DEIMOS field of view. This allowed us to refine the wavelength solution based on night sky lines over the entire CCD mosaic. Section 3.2 describes our approach to the wavelength solution.

As in our previous papers (e.g., Simon & Geha 2007; Simon et al. 2011; Kirby et al. 2013a, 2015), we reduced the DEIMOS spectra using a slightly modified version of the spec2d IDL data reduction pipeline developed by the DEEP2 team (Cooper et al. 2012; Newman et al. 2013). We introduced a few updates to those procedures for this data set. The updates include improvements to the wavelength solution as determined from sky emission lines and corrections for the effects of differential atmospheric refraction. In the first stage of the sky line wavelength tweaking, a zero point offset is determined during the main reduction pipeline. We improved the tracing of the sky lines across each slit at low signal-to-noise ratio (S/N), which is particularly important for our long-slit observations of bright template stars with short integration times. We also added a second stage to the sky line fitting: after the reductions are completed, a quadratic fit is performed to the sky line wavelengths in each extracted spectrum, and then the variation of each of the quadratic fit parameters as a function of position on the slit mask is fit with a polynomial. This process corrects for errors in the flexure compensation system as well as temperature changes between the times at which the arc frames and the science frames were obtained (M. Geha et al. 2015, in preparation).

Atmospheric refraction shifts the position of the star light within the slit during the observations. Shifts in the spatial direction (along the slit) result in curvature of the object profile on the detector, and we changed the DEEP2 extraction algorithm to account for this effect (Kirby et al. 2015). Shifts in the wavelength direction (across the slit) result in velocity offsets that vary as a function of wavelength. Using the airmass at the time of observation, the angle between the slit and the parallactic angle, and the measured seeing, we computed a correction for this velocity shift and applied it to the extracted spectra.

In order to take maximum advantage of these improvements, we constructed a new empirical library of template stars for radial velocity measurements to replace the template set most DEIMOS dwarf galaxy studies have employed since Simon & Geha (2007). We selected a sample of metal-poor stars spanning a range of effective temperature, surface gravity, and metallicity, and we observed them by orienting the slit north–south and slowly driving the telescope such that the star moved steadily across the slit. This process ensured that the star light uniformly illuminated the slit during the exposure. To make sure that the template star observations contained strong enough sky lines for accurate adjustments to the wavelength solution (as described above), we integrated for at least 60 s during each template observation even if the star crossed the slit in a much shorter amount of time. We also replaced the telluric template from Simon & Geha (2007) with higher S/N observations using the same techniques.

Figure 3 shows example 1D spectra of one member star in each satellite. The spectra shown for Hydra II and Pisces II have high S/N, while the spectrum for Laevens 1 has low S/N. Also shown are the best-fit model spectra (described in Section 4.2) for the stars with S/N high enough to measure metallicity. Because the S/N is low for the star in Laevens 1, we did not measure a metallicity for it, and no model spectrum is shown.

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We measured radial velocities of stars in the three Milky Way satellites by comparing their spectra to the radial velocity template stars' spectra. In a manner similar to Simon & Geha (2007), we optimized the DEEP2 survey's redshift measurement technique (Newman et al. 2013) for measuring stellar velocities rather than galaxy redshifts. This technique involves computing ${\chi }^{2}={(\mathrm{target}\;\mathrm{flux}-\mathrm{template}\;\mathrm{flux})}^{2}/{(\mathrm{flux}\;\mathrm{error})}^{2}$ for each template star. The relative velocity between the target and the template is shifted to find the minimum χ². The velocity of the star (${v}_{\mathrm{obs}}$) is the one that minimizes χ² among all of the templates. As Newman et al. pointed out, this technique is a generalization of a cross-correlation (Tonry & Davis 1979) that allows for different values of flux error for each pixel.

Small astrometric errors or imprecision in the alignment of the slitmask cause each star to fall at some displacement from the exact center of the slit. Mis-centering translates to a shift in the wavelength scale. Following Simon & Geha (2007), we corrected all of the stellar velocities to a standard geocentric frame by finding the velocity offset (${v}_{\mathrm{geo}}$) required to align the observed telluric absorption features with the features in the hot star spectra. The observed wavelength regions included in the velocity correction were 6866–6912 Å (B-band), 7167–7320 Å, 7593–7690 Å (A-band), and 8110–8320 Å. The velocity corrections were determined with the χ² technique described in the previous paragraph. The velocities quoted in this paper are in the heliocentric frame: ${v}_{\mathrm{helio}}={v}_{\mathrm{obs}}+{v}_{\mathrm{geo}}+{v}_{\mathrm{corr}}$, where ${v}_{\mathrm{corr}}$ is the conversion from the geocentric frame to the heliocentric frame.

We estimated random and systematic uncertainties separately. To estimate the random uncertainty, we resampled the spectra for 10³ Monte Carlo trials. In one trial, the flux of each pixel was drawn from a Gaussian probability distribution. The mean of the distribution was the original flux value, and its variance was the flux variance estimated by spec2d. We re-measured ${v}_{\mathrm{helio}}$ (including both ${v}_{\mathrm{obs}}$ and ${v}_{\mathrm{geo}}$) for all of the trials, and we took the random uncertainty, ${\delta }_{\mathrm{rand}}v$, to be the standard deviation of the ${v}_{\mathrm{helio}}$ measurements.

There is some minimum velocity uncertainty, even for noiseless spectra. This uncertainty can arise due to uncorrected flexure in DEIMOS, spectral template mismatches, errors in the wavelength solution, and unknown causes. We estimated ${\delta }_{\mathrm{sys}}v$ by calculating the difference in ${v}_{\mathrm{helio}}$ for two independent measurements of the same set of stars. The ideal sample for estimating ${\delta }_{\mathrm{sys}}v$ will have many high-S/N spectra. Instead of using the dwarf galaxy sample, we used spectra of 52 red giants in the GC M22. The spectra were taken with the same slitmask on consecutive nights (see Table 1). The data from each night were reduced separately according to Section 3.2. We measured ${v}_{\mathrm{helio}}$ and estimated ${\delta }_{\mathrm{rand}}v$ as described above. We then calculated the quantity $({v}_{\mathrm{helio},1}-{v}_{\mathrm{helio},2})/\sqrt{{\delta }_{\mathrm{rand},1}{v}^{2}+{\delta }_{\mathrm{rand},2}{v}^{2}+2{\delta }_{\mathrm{sys}}{v}^{2}}$ for each pair of observations of the same star. The standard deviation of this quantity should be 1 for well-determined errors. The value of ${\delta }_{\mathrm{sys}}v$ required to satisfy that condition is 1.49 km s⁻¹. The final error bar for each star is $\sqrt{{\delta }_{\mathrm{rand}}{v}^{2}+{\delta }_{\mathrm{sys}}{v}^{2}}$.

Our estimate of ${\delta }_{\mathrm{sys}}v$ ignores some potentially important sources of error. First, the repeat measurements were obtained with the same slitmask. As a result, some of the slit mis-centering—for example, due to astrometric errors in the slitmask design—would be repeated in the same way across the two consecutive nights. Second, the slitmasks were observed at about the same hour angle on each night. Although we applied wavelength corrections for flexure and differential atmospheric refraction, these errors would have been of the same sign and similar magnitude for both nights. Any residual, uncorrected error would be similar across both nights. Third, the M22 spectra have fairly high S/N. Consequently, the same template spectrum was assigned to 47 out of 52 M22 stars. This fraction would be lower in spectra with lower S/N.

All of these effects would potentially lower the measurement of ${\delta }_{\mathrm{sys}}v$ artificially. In order to quantify the effect of a spuriously low value of ${\delta }_{\mathrm{sys}}v$, we also calculated velocity dispersions as described in Section 5.2, assuming ${\delta }_{\mathrm{sys}}v=2.2$ km s⁻¹, the original value calculated by Simon & Geha (2007), instead of 1.49 km s⁻¹. The increased systematic error would make the upper limits on the velocity dispersions about 5% less stringent, and it would reduce the measured velocity dispersion of Pisces II by 13%, well within the uncertainty. In summary, our lower value of ${\delta }_{\mathrm{sys}}v$ than previous works does not change our conclusions.

Table 2 presents the velocities for stars in the satellite galaxies. The table excludes stars where velocity errors exceeded 30 km s⁻¹ and stars where velocity measurement was not possible. Figure 4 shows velocity histograms for each satellite in bins of 2.5 km s⁻¹. The domain of the plots is 100 km s⁻¹ centered on the mean velocity for each satellite. In Section 5, we use these velocities to measure the kinematic properties of each satellite.

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Table 2.  Target List

ID	R. A. (J2000)	decl. (J2000)	g0	${(g-r)}_{0}$	${(g-I)}_{0}$	S/Na	${v}_{\mathrm{helio}}$	Member?	${T}_{\mathrm{eff}}$	$\mathrm{log}g$	[Fe/H]
			(mag)	(mag)	(mag)	(Å−1)	(km s−1)		(K)	(cm s−2)
Hydra II
196246	12 21 27.50	−31 57 22.6	19.68	0.63	...	54	161.8 ± 1.6	N	...	...	...
184647	12 21 28.13	−32 06 36.7	19.75	0.63	...	46	116.3 ± 1.9	N	...	...	...
199452	12 21 30.18	−31 55 58.0	19.94	0.85	...	59	5.1 ± 1.6	N	...	...	...
189524	12 21 32.70	−32 03 51.5	21.90	0.60	...	8	272.9 ± 7.9	N	...	...	...
188838	12 21 33.19	−32 04 29.4	20.66	0.67	...	33	319.0 ± 2.3	N	...	...	...
194103	12 21 34.74	−31 59 21.8	20.93	0.57	...	25	300.0 ± 4.2	Y	5095	2.05	−2.40 ± 0.32
193538	12 21 35.93	−31 59 54.0	19.79	0.67	...	66	304.2 ± 1.7	Y	4918	1.46	−1.95 ± 0.12
198021	12 21 36.31	−31 56 38.1	21.40	0.68	...	19	63.9 ± 3.4	N	...	...	...
195726	12 21 36.74	−31 57 54.1	21.13	0.60	...	22	306.5 ± 3.5	Y	5036	2.11	−2.48 ± 0.33
190646	12 21 38.18	−32 02 38.2	20.23	0.61	...	44	86.6 ± 1.8	N	...	...	...
194563	12 21 38.51	−31 58 56.4	20.57	0.48	...	34	302.9 ± 3.3	Y	...	...	...
191521	12 21 39.68	−32 01 48.8	19.91	0.96	...	45	202.5 ± 1.8	N	...	...	...
191385b	12 21 40.08	−32 01 57.7	20.70	0.16	...	9	316.9 ± 19.9	N	...	...	...
192206	12 21 40.37	−32 01 12.1	19.97	1.02	...	68	28.0 ± 1.5	N	...	...	...
193286	12 21 40.96	−32 00 07.0	21.27	0.54	...	14	299.9 ± 5.4	Y	...	...	...
194920	12 21 41.02	−31 58 34.4	21.58	0.54	...	16	294.5 ± 5.9	Y	...	...	...
194405	12 21 41.05	−31 59 04.1	20.36	0.65	...	48	304.2 ± 1.9	Y	4921	1.73	−1.89 ± 0.13
189086	12 21 41.79	−32 04 15.9	21.46	−0.21	...	4	315.5 ± 23.5	Y	...	...	...
194325	12 21 42.51	−31 59 10.0	21.04	0.51	...	24	301.9 ± 3.0	Y	5171	2.15	−2.76 ± 0.43
197616	12 21 42.62	−31 56 44.2	21.11	0.36	...	15	94.9 ± 6.6	N	...	...	...
201098	12 21 42.78	−31 54 26.7	20.21	0.82	...	22	−85.0 ± 2.3	N	...	...	...
196797	12 21 42.79	−31 57 04.2	22.37	0.43	...	6	300.1 ± 21.8	Y	...	...	...
195247	12 21 44.45	−31 58 21.0	21.92	0.48	...	11	317.5 ± 16.8	Y	...	...	...
196052	12 21 44.57	−31 57 37.6	21.85	0.56	...	12	303.7 ± 4.1	Y	...	...	...
200162	12 21 44.65	−31 55 17.7	19.34	0.98	...	79	68.1 ± 1.5	N	...	...	...
194736	12 21 44.65	−31 58 47.6	21.95	0.49	...	10	288.3 ± 14.5	Y	...	...	...
193869	12 21 45.96	−31 59 34.4	20.11	0.50	...	46	237.3 ± 2.1	N	...	...	...
183842	12 21 46.10	−32 07 02.8	19.79	0.67	...	55	−19.6 ± 1.7	N	...	...	...
202029	12 21 47.09	−31 53 36.0	21.69	0.50	...	6	10.1 ± 9.0	N	...	...	...
197129	12 21 48.34	−31 56 52.2	21.50	0.62	...	17	315.7 ± 3.7	N	...	...	...
192059	12 21 48.39	−32 01 21.8	22.36	0.59	...	7	172.4 ± 10.0	N	...	...	...
Pisces II
9004	22 58 17.52	+05 55 17.5	20.29	0.73	...	58	−224.9 ± 1.6	Y	4787	1.34	−2.38 ± 0.13
9618	22 58 20.35	+05 58 08.8	22.54	0.59	...	8	−301.6 ± 6.5	N	...	...	...
9833	22 58 21.22	+05 57 20.3	21.76	0.61	...	19	−226.9 ± 3.2	Y	...	...	...
10215	22 58 22.88	+05 57 35.5	21.53	0.65	...	21	−25.9 ± 3.1	N	...	...	...
10694	22 58 25.06	+05 57 20.4	19.94	1.05	...	59	−232.0 ± 1.6	Y	4132	0.81	−2.70 ± 0.11
11592	22 58 28.74	+05 56 56.9	19.91	1.08	...	82	4.3 ± 1.5	N	...	...	...
12924	22 58 34.10	+05 57 43.6	21.19	0.63	...	31	−221.6 ± 2.9	Y	4955	1.82	−2.10 ± 0.18
13387	22 58 35.91	+05 57 22.4	22.30	0.49	...	11	−215.8 ± 7.6	Y	...	...	...
13560	22 58 36.71	+05 58 06.2	21.48	0.58	...	23	−232.6 ± 5.3	Y	5049	1.99	−2.15 ± 0.28
13757	22 58 37.49	+05 56 24.8	21.25	0.64	...	27	−102.1 ± 2.3	N	...	...	...
14179	22 58 39.36	+05 56 00.7	22.42	0.54	...	8	−224.8 ± 9.6	Y	...	...	...
16716	22 58 51.19	+05 59 57.1	20.33	0.74	...	25	−5.1 ± 10.9	N	...	...	...
17500	22 58 54.78	+05 57 47.5	20.56	0.83	...	25	83.7 ± 2.2	N	...	...	...
Laevens 1
302	11 36 13.55	−10 53 02.9	20.94	...	1.29	20	149.8 ± 2.9	Y	4977	1.53	−1.59 ± 0.15
374	11 36 13.76	−10 52 48.5	19.90	...	1.32	68	151.9 ± 1.7	Y	4966	1.09	−1.66 ± 0.11
420	11 36 13.90	−10 52 27.3	19.44	...	1.59	105	149.8 ± 1.5	Y	4626	0.69	−1.55 ± 0.11
378	11 36 14.53	−10 52 43.7	21.55	...	1.22	19	153.5 ± 3.1	Y	...	...	...
93	11 36 15.91	−10 52 43.6	19.68	...	1.52	88	147.2 ± 1.6	Y	4726	0.84	−1.65 ± 0.11
1710	11 36 16.52	−10 52 46.7	19.44	...	1.31	16	143.6 ± 4.5	Y	...	...	...
1715	11 36 16.59	−10 52 46.2	18.91	...	0.85	66	72.0 ± 1.8	N	...	...	...
367	11 36 16.89	−10 52 43.7	22.54	...	1.14	8	153.8 ± 10.0	Y	...	...	...
1717	11 36 17.26	−10 52 46.2	18.99	...	0.70	47	266.0 ± 2.2	N	...	...	...
1972	11 36 17.70	−10 52 08.0	22.17	...	1.04	10	141.4 ± 4.7	Y	...	...	...
1997	11 36 18.37	−10 52 00.7	22.60	...	1.07	6	166.6 ± 11.5	N	...	...	...
1684	11 36 18.59	−10 52 49.7	21.23	...	1.23	21	150.9 ± 3.1	Y	5064	1.70	−2.10 ± 0.21
399	11 36 19.58	−10 52 37.1	19.15	...	0.70	80	155.3 ± 1.8	N	...	...	...
963	11 36 20.11	−10 52 38.2	18.90	...	1.87	150	149.2 ± 1.5	Y	4331	0.23	−1.78 ± 0.11

Notes.

^aTo convert to S/N per pixel, multiply by 0.57. ^bNon-member based on CMD position.

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We measured metallicities by fitting synthetic spectra to the observed spectra following the same procedure as Kirby et al. (2008a, 2010). First, we normalized each spectrum to its continuum. To do so, we divided the spectrum by a spline fit to spectral regions generally free of absorption lines. Then, we matched the spectrum to a grid of synthetic spectra generated with ATLAS9 model atmospheres (Kurucz 1993) and the synthesis code MOOG (Sneden 1973). We measured iron abundances, [Fe/H],⁷ by fitting only to iron absorption lines and ignoring other spectral regions. Please refer to Kirby et al. (2010) for more details.

We estimated the random uncertainty on [Fe/H] from the covariance matrix of the χ² fit to the synthetic spectral grid. There is also a systematic uncertainty of 0.11 dex (Kirby et al. 2010). The final error bar is the quadrature sum of the random and systematic uncertainties.

Table 2 gives effective temperatures (${T}_{\mathrm{eff}}$), surface gravities ($\mathrm{log}g$), and [Fe/H] measurements for member stars with $\delta [\mathrm{Fe}/{\rm{H}}]\lt 0.5$ and S/N > 20 Å⁻¹. Figure 5 shows the distribution of these measurements in bins of 0.25 dex. By nature, ultra-faint satellites have only handfuls of red giants bright enough for metallicity measurements. As a result, the metallicity distributions in Figure 5 have only 4–6 stars. Accurate quantification of metallicity distributions and chemical evolution requires larger samples. Nonetheless, we present rudimentary metallicity averages and dispersions in Section 6.

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Bonifacio et al. (2015) obtained VLT/X-Shooter spectra of two stars in Laevens 1. Both stars are also in our spectroscopic sample. We call them 420 and 93, and Bonifacio et al. call them J113613–105227 and J113615–105244. They measured a velocity difference between the two stars of 10.2 ± 5.7 km s⁻¹, whereas we measured a difference of only $2.6\pm 2.2$ km s⁻¹.

Figure 6 shows our DEIMOS spectra in the observer frame. The bold black and red spectra show the spectra as we observed them, and the faded (gray and pink) lines show the spectra as they would have appeared at the velocities measured by Bonifacio et al. (2015). The bold spectra are nearly superposed on top of each other, whereas the faded spectra are visibly separated. Thus, the figure shows that our spectra have the precision to discern between a 10.2 and a 2.6 km s⁻¹ difference.

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There are several possible reasons for the discrepancy between our two studies. First, one or both of the stars could have a variable radial velocity. In that case, we happened to observe the two stars when they had nearly the same radial velocity, and our inability to resolve the velocity dispersion (Section 5.2) is unaffected. Second, one of our studies could be subject to a systematic error. For example, we corrected for slit mis-centering by applying a velocity shift based on telluric absorption. (The wavelength scale in Figure 6 includes the telluric correction.) Bonifacio et al. were unable to apply a similar correction. Therefore, one possible systematic error in their study was slightly different positions of the two stars perpendicular to the X-Shooter slit. Regardless, Bonifacio et al. state that the velocity dispersion of Laevens 1 is consistent with zero when the measurement errors are taken into account. This basic result agrees with our own conclusions (Section 5.2).

We measured $[\mathrm{Fe}/{\rm{H}}]=-1.55\pm 0.11$ and $-1.65\pm 0.11$ for stars 420 and 93, respectively. Bonifacio et al. measured $[\mathrm{Fe}/{\rm{H}}]=-1.73\pm 0.26$ and $-1.67\pm 0.28$ from an equivalent width (EW) analysis using MyGIsFOS (Sbordone et al. 2014). Our measurements are entirely consistent within the measurement uncertainty.

Ultra-faint satellites have very low surface brightnesses. In some cases, most of the point sources in the vicinity of an ultra-faint satellite—even at the center—are foreground dwarf stars. We avoided most of the contamination by selecting stars with colors and magnitudes appropriate for red giants at the distance of each satellite (Section 2 and Figure 1). We removed the remainder of the contaminants by imposing a radial velocity cut.

We determined membership in each satellite by using its mean velocity, $\langle {v}_{\mathrm{helio}}\rangle$, and velocity dispersion, ${\sigma }_{v}$. First, we started with guesses for $\langle {v}_{\mathrm{helio}}\rangle$ and ${\sigma }_{v}$. We required member stars to have $| {v}_{\mathrm{helio}}-\langle {v}_{\mathrm{helio}}\rangle | \lt 2.58{\sigma }_{v}$. For a Gaussian velocity distribution, this cut includes 99% of member stars. Because ${\sigma }_{v}$ for most of the satellites is very small, a hard cut would exclude low-S/N stars whose measured velocities are discrepant by more than $2.58{\sigma }_{v}$ simply because their uncertainties are larger than that. Therefore, we extended the membership criterion to any star whose $1\sigma$ error bar overlaps the velocity range for member stars. We determined $\langle {v}_{\mathrm{helio}}\rangle$ and ${\sigma }_{v}$ from the list of member stars following the procedure in Section 5.2. Then, we used these new values to reform the member list. We repeated this procedure until the member list did not change from one iteration to the next.

Foreground dwarfs can also be identified by spectral features sensitive to surface gravity, such as the Na i doublet at 8190 Å (Spinrad & Taylor 1971; Cohen 1978) and Mg i 8807 (Battaglia & Starkenburg 2012). We found several stars with very strong Na doublets and Mg i lines among the Hydra II and Pisces II samples, but they were already excluded by the radial velocity cut. Hence, we did not need to impose any additional membership criteria. We discuss Mg i again in Section 5.2 in reference to a star that barely missed the membership cut in Hydra II.

Two of the three blue stars that we targeted in Laevens 1 are non-members on the basis of their radial velocities. Belokurov et al. (2014) speculated that these stars might be blue loop stars. If they were, then Laevens 1 must have a young stellar population, which would argue strongly that it is a star-forming galaxy, not a GC. However, the non-membership of these two stars negates most of the evidence that Laevens 1 has a very young stellar population, although Bonifacio et al. (2015) argued that the blue extension of the main sequence might indicate the presence of a ∼2 Gyr old population. The third blue star, 399, has ${v}_{\mathrm{helio}}=155.3\pm 1.8$ km s⁻¹, which is $6.0$ km s⁻¹ from the mean radial velocity. This star formally passes the velocity membership cut. However, in addition to its unusual color, it has a more discrepant radial velocity than any of the other member stars, and it is farther from the center of the cluster than all but one confirmed member. We considered the possibility that this star is a Cepheid member of Laevens 1. However, the Pan-STARRS1 survey (Kaiser et al. 2010) obtained six observations of this star in each of the ${r}_{{\rm{P}}1}$, ${z}_{{\rm{P}}1}$, and ${y}_{{\rm{P}}1}$ bands, and the rms scatter of these observations is consistent with measurement noise (∼0.03 mag, B. Sesar 2015, private communication). Since Population II Cepheids have light curve amplitudes between 0.5 and 1.2 mag in the Johnson R-band (Wallerstein & Cox 1984), we conclude that the blue star is not a Cepheid variable. We discuss the impact that including star 399 as a member would have on ${\sigma }_{v}$ in Section 5.2.

We estimated $\langle {v}_{\mathrm{helio}}\rangle$ and ${\sigma }_{v}$ for the three satellites in the same manner that Kirby et al. (2013a) measured these values for the UFD Segue 2. That method, in turn, was based on Walker et al.'s (2006) procedure for measuring the velocity dispersion of the Fornax dwarf spheroidal galaxy (dSph). The method uses maximum likelihood statistics and a Monte Carlo Markov chain (MCMC). We maximized the logarithm of the likelihood (L) that the given values of $\langle {v}_{\mathrm{helio}}\rangle$ and ${\sigma }_{v}$ described the observed velocity distribution, including the uncertainty estimates for individual stars.

$$\begin{eqnarray}\mathrm{log}L & = & \displaystyle \frac{N\mathrm{log}(2\pi )}{2}+\displaystyle \frac{1}{2}\displaystyle \sum _{i}^{N}(\mathrm{log}({(\delta {v}_{\mathrm{helio}})}_{i}^{2}+{\sigma }_{v}^{2})\\ & & +\displaystyle \frac{1}{2}\displaystyle \sum _{i}^{N}(\displaystyle \frac{{({({v}_{\mathrm{helio}})}_{i}-\langle {v}_{\mathrm{helio}}\rangle )}^{2}}{{(\delta {v}_{\mathrm{helio}})}_{i}^{2}+{\sigma }_{v}^{2}}).\end{eqnarray} \tag{ 1 }$$

As initial guesses for $\langle {v}_{\mathrm{helio}}\rangle$ and ${\sigma }_{v}$, we started with the mean and standard deviation of ${v}_{\mathrm{helio}}$ over the velocity range shown in Figure 4. The final results are not sensitive to these guesses. We explored the parameter space with a Metropolis–Hastings implementation of an MCMC. The length of the chain was 10⁷ trials.

As a test of our procedure, we measured $\langle {v}_{\mathrm{helio}}\rangle =-144.4\pm 1.3$ km s⁻¹ and ${\sigma }_{v}={7.4}_{-0.9}^{+1.0}$ km s⁻¹ for M22 from the 2009 October 14 observation. In comparison, Peterson & Cudworth (1994) measured $\langle {v}_{\mathrm{helio}}\rangle =-148.8\pm 0.8$ km s⁻¹ and ${\sigma }_{v}=6.6\pm 0.8$ km s⁻¹ within $7^{\prime}$ of the cluster center, and Lane et al. (2009) measured $\langle {v}_{\mathrm{helio}}\rangle =-144.9\pm 0.3$ km s⁻¹ and a central dispersion of ${\sigma }_{v}=6.8\pm 0.9$ km s⁻¹. Our measurement of $\langle {v}_{\mathrm{helio}}\rangle$ is consistent with that of Lane et al. and our measurement of ${\sigma }_{v}$ is consistent with both Peterson & Cudworth and Lane et al. The velocity dispersion in M22 decreases to about 5 km s⁻¹ at $8^{\prime}$ from the cluster center (Lane et al. 2009). However, our data is largely insensitive to the decline of ${\sigma }_{v}$ because the maximum radial extent of our spectroscopy is 8', and most of our M22 targets are within 5'.

Table 3 gives $\langle {v}_{\mathrm{helio}}\rangle$ and ${\sigma }_{v}$ with errors. It also gives velocities relative to the Galactic standard of rest (GSR) assuming that the Sun's orbital velocity is 220 km s⁻¹. Hydra II is receding from the Galactic center. Therefore, it is past its pericenter on the way to its apocenter. Its heliocentric radial velocity is also similar to that of the gas in the leading arm of the Magellanic stream (Putman et al. 1998; Brüns et al. 2005; Nidever et al. 2008). This finding strengthens the potential for Hydra II to be associated with the LMC (Bechtol et al. 2015; Deason et al. 2015; Koposov et al. 2015a). Pisces II is approaching the Galactic center, which means that it is on the way to its pericenter. Finally, Laevens 1 has a very small ${v}_{\mathrm{GSR}}$, meaning that it is at pericenter or apocenter. Because it is so distant (at least 140 kpc from the Galactic center), it is either close to apocenter or on a quasi-circular orbit.

Table 3.  Satellite Properties

Property	Hydra II	Pisces II	Laevens 1
${N}_{\mathrm{member}}$	13	7	10
$\mathrm{log}({L}_{V}/{L}_{\odot })$	3.90 ± 0.10	3.93 ± 0.20	3.65 ± 0.08
rh (arcmin)	${1.7}_{-0.2}^{+0.3}$	1.1 ± 0.1	${0.47}_{-0.03}^{+0.04}$
rh (pc)	${66}_{-9}^{+12}$	58 ± 7	19 ± 2
$\langle {v}_{\mathrm{helio}}\rangle$ (km s−1)	303.1 ± 1.4	−226.5 ± 2.7	149.3 ± 1.2
${v}_{\mathrm{GSR}}$ (km s−1)	135.4	−79.9	4.6
${\sigma }_{v}$ (km s−1)	$\lt 3.6$ (90% C.L.)	${5.4}_{-2.4}^{+3.6}$	$\lt 3.9$ (90% C.L.)
	$\lt 4.5$ (95% C.L.)		$\lt 4.8$ (95% C.L.)
$\mathrm{log}({M}_{1/2}/{M}_{\odot })$	$\lt 5.9$ (90% C.L.)	${6.2}_{-0.2}^{+0.3}$	$\lt 5.5$ (90% C.L.)
	$\lt 6.1$ (95% C.L.)		$\lt 5.6$ (95% C.L.)
${(M/{L}_{V})}_{1/2}$ a (${M}_{\odot }/{L}_{\odot }$)	$\lt 200$ (90% C.L.)	${370}_{-240}^{+310}$	$\lt 130$ (90% C.L.)
	$\lt 315$ (95% C.L.)		$\lt 192$ (95% C.L.)
$\langle [\mathrm{Fe}/{\rm{H}}]\rangle$	−2.02 ± 0.08	−2.45 ± 0.07	−1.68 ± 0.05
$\sigma ([\mathrm{Fe}/{\rm{H}}])$	${0.40}_{-0.26}^{+0.48}$	${0.48}_{-0.29}^{+0.70}$	$\lt 0.40$ (90% C.L.)
			$\lt 0.53$ (95% C.L.)

Notes. The measurements of $\mathrm{log}{L}_{V}$ and r_h come from Martin et al. (2015), Belokurov et al. (2010), and Laevens et al. (2014).

^aMass-to-light ratio within the half-light radius.

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Figure 7 shows the distribution of ${\sigma }_{v}$ for accepted MCMC trials. These distributions are equivalent to the probability distribution for ${\sigma }_{v}$. The distribution for Pisces II has a well-defined peak separated from zero. The dashed line shows the median value of ${\sigma }_{v}=5.4$ km s⁻¹. We estimated asymmetric error bars by calculating the values of ${\sigma }_{v}$ that bracket 68.3% of the probability distribution.

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The distributions for Hydra II and Laevens 1 are concentrated near zero. Hence, our measurements cannot resolve ${\sigma }_{v}$ for these two satellites. We estimated two sets of upper limits by finding the value of ${\sigma }_{v}$ that exceeds 90% and 95% of the MCMC trials. Table 3 gives both upper limits for both satellites.

Hydra II and Laevens 1 have three stars with somewhat ambiguous membership. Stars 197129 and 188838 in Hydra II have velocities larger than $\langle {v}_{\mathrm{helio}}\rangle$ by $12.6$ and $15.9$ km s⁻¹. If our membership cut were more inclusive than $2.58{\sigma }_{v}$, then these stars could be considered members. Unfortunately, neither star has a visible Na i doublet to help define its status. The Mg i EW of star 188838 is 0.34 ± 0.07 Å, and the combined EW of of the two redder lines of the Ca ii infrared triplet (CaT) is 4.1 ± 0.3 Å. These measurements fall right on the dividing line between dwarfs and giants defined by Battaglia & Starkenburg (2012). Because most metal-poor dSph stars fall well below the dividing line, this test disfavors membership for star 188838. The Mg i line in star 197129 is too noisy to be useful.

Including star 192179 as a member does not change our qualitative conclusions. Instead, the 90% confidence level (C.L.) upper limit on ${\sigma }_{v}$ rises from $3.6$ to $6.0$ km s⁻¹. On the other hand, including star 188838 resolves the velocity dispersion as ${\sigma }_{v}={6.4}_{-1.8}^{+2.4}$ km s⁻¹. Including both stars results in ${\sigma }_{v}={6.7}_{-1.9}^{+2.4}$ km s⁻¹. However, both stars would be $\gt 2{\sigma }_{v}$ outliers even with the larger ${\sigma }_{v}$. Furthermore, Figure 1 shows that both stars are redder relative to the M92 isochrone than any other member. Figure 2 also shows that star 188838 would be the most distant member of Hydra II. Because the majority of the evidence disfavors membership, we ruled both stars as non-members. Including or excluding the two possible HB stars, 189086 and 191385, changes the limits on ${\sigma }_{v}$ by less than 2%. Based on their CMD positions, we ruled 189086 a member and 191385 a non-member.

Including star 399 in Laevens 1 resolves the velocity dispersion as ${\sigma }_{v}={2.7}_{-1.4}^{+1.8}$ km s⁻¹. As discussed in Section 5.1, the star is bright and blue. As a result, star 399 is probably not a member.

The total mass of a spherical stellar system in dynamical equilibrium is related to the square of the velocity dispersion. Wolf et al. (2010) showed that the total mass is poorly constrained because any possible underlying dark matter has an unknown mass profile, and the velocity anisotropy cannot be determined from a small sample of radial velocities. However, the mass within the half-light radius, ${M}_{1/2}$, is well-constrained: ${M}_{1/2}=4{G}^{-1}{\sigma }_{v}^{2}{r}_{{\rm{h}}}$. Although r_h is the two-dimensional (2D) half-light radius, the formula infers the mass enclosed within the three-dimensional (3D) half-light radius.

Table 3 gives $\mathrm{log}{M}_{1/2}$ for Pisces II and upper limits for Hydra II and Laevens 1, which have only upper limits for ${\sigma }_{v}$. Pisces II has a dynamical mass on par with dwarf galaxies of similar luminosity (Strigari et al. 2008; Wolf et al. 2010). For example, its luminosity and mass are very similar to Canes Venatici II (Simon & Geha 2007). The mass limits for Hydra II and Laevens 1 are not stringent enough to make these satellites unusually light. The 90% C.L. for Hydra II is ${M}_{1/2}\lt 1.0\times {10}^{6}\;{M}_{\odot }$, which is less than a factor of 2 smaller than Pisces II. The 90% C.L. mass limit for Segue 2, the least massive galaxy, is 7 times more stringent than Hydra II. The limit for Laevens 1 is slightly more stringent than Hydra II, but we argue below that Laevens 1 is not a galaxy.

Willman & Strader (2012) proposed that a "galaxy" should be defined as a stellar system that cannot be explained by a combination of baryons and Newton's laws of gravity. The M/L for Pisces II is ${370}_{-240}^{+310}\;{M}_{\odot }/{L}_{\odot }$. This value is far too large to be explained by baryons alone, even for the oldest stellar populations in the universe. In fact, $99\%$ of the successful MCMC trials have ${\text{}}M/L\gt 10\;{M}_{\odot }/{L}_{\odot }$. Hence, Pisces II satisfies the definition of a galaxy. However, upper limits on the M/Ls on Hydra II and Laevens 1 do not help in deciding if they are galaxies. In Section 6, we use chemical evidence to resolve the nature of these two satellites.

One of the reasons dwarf galaxies are interesting is that they are targets for the detection of gamma rays due to dark matter self-annihilation. Pisces II has similar structural properties (r_h and ${\sigma }_{v}$) and distance to Canes Venatici II. Hence, the two galaxies' potential for the detection of the gamma-ray signal is about the same. Bonnivard et al. (2015) found that Canes Venatici II is not the most promising dwarf galaxy to search for self-annihilation, but it would contribute significantly to an analysis that stacks the Fermi gamma-ray telescope observations of all of the dwarfs (e.g., Ackermann et al. 2014, 2015).