Ships Passing in the Night: Spectroscopic Analysis of Two Ultra-faint Satellites in the Constellation Carina^{* † ‡}

We obtained multi-slit spectroscopy of Car II and Car III with the IMACS spectrograph (Dressler et al. 2006) on the Magellan Baade telescope on 2017 January 24–25. The observing setup was the same as for the spectroscopy of the Tucana III (Simon et al. 2017) and Eridanus II (Li et al. 2017) dwarf galaxies. We used the f/4 camera on IMACS, which provides a full field-of-view of $15\buildrel{\,\prime}\over{.} 4\times 15\buildrel{\,\prime}\over{.} 4$. The spectrograph was configured with the 1200 ℓ/mm grating and a tilt angle of 324, producing a spectral resolution of R ∼ 11,000 for a 07 slit width and a wavelength range of at least 7550–8750 Å for each slit. This wavelength range covers the calcium triplet (CaT) lines around 8500 Å, used for measuring radial velocities and metallicities of candidate member stars, as well as the telluric absorption lines (Fraunhofer A-band) around 7600 Å used for the correction of velocity errors caused by mis-centering of the stars within the slits (see Sohn et al. 2007 for details).

The target selection and mask design for Magellan/IMACS (hereafter IMACS) were performed using the photometry from the original MagLiteS catalog. Based on the knowledge of confirmed members of the DES-discovered dwarf galaxies Reticulum II from Simon et al. (2015) and Tucana III from Simon et al. (2017), we used similar selection criteria as described in the latter paper. Target selection and mask design used a preliminary estimate for the distance modulus for Car II (Car III) of $m-M=17.5$ ($m-M=17.1$). For Car II, the red giant branch (RGB) candidate members were selected to be redder than the fiducial sequence of the metal-poor globular cluster M92 from An et al. (2008), bluer than a 12 Gyr, ${\rm{[Fe/H]}}=-2.2$ theoretical PARSEC isochrone³¹ from Bressan et al. (2012), and brighter than g = 20.8. Several candidate blue horizontal branch (BHB) stars were selected at $17.7\lt g\,\lt 18.8$ and $g-r\lt 0.1;$ a handful of candidate red horizontal branch (RHB) stars were selected at $17.9\lt g\lt 18.6$ and $0.1\lt g-r\lt 0.3$. Potential main sequence turnoff (MSTO) stars were selected using a 0.1 mag wide window in g − r around the PARSEC isochrone for $20.8\lt g\lt 22$ (although because of the observing conditions, we did not get any useful spectra for MSTO candidates).

For Car III, we used the same selection criteria as for Car II, with the exception of shifting all sequences 0.4 mag brighter according to the difference in distance moduli. Based on these targets, we designed two slitmasks (IMACS-Car2Mask1 and IMACS-Car2Mask2) near the center of Car II and one slitmask (IMACS-Car3Mask1) near the center of Car III, using the maskgen program.³² Stars were placed on the slit masks in a category prioritization descending order of BHB, RGB, RHB, and MSTO. Within each category, priorities were based on brightness and distance from the center of Car II or Car III. Finally, any remaining mask space was filled by stars with photometry that made them unlikely to be members. IMACS-Car2Mask1 contains 72 slits, IMACS-Car2Mask2 contains 48 slits, and IMACS-Car3Mask1 contains 67 slits. All the targets, observed with IMACS and other instruments described in later sections, are presented in Figure 1.

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We obtained a 1.7 hr exposure with IMACS-Car2Mask2 and a 3.7 hr exposure with IMACS-Car3Mask1 on 2017 January 24, and a 1.25 hr exposure on IMACS-Car2Mask1 on 2017 January 25. One of the BHB candidates, MAGLITES J073834.84−575211.2, on IMACS-Car3Mask1 happened to fall in a gap between CCDs, so we also obtained a 30 minute exposure on this star with a 07-wide long slit (IMACS-Car3LongSlit) on 2017 January 25. The observing conditions on both nights were relatively poor, with high humidity and $\sim 1^{\prime\prime} \mbox{--}3^{\prime\prime}$ seeing.

We reduced the IMACS spectra following the procedures described by Simon et al. (2017) for Tucana III. We first performed the bias subtraction and removal of read-out pattern noise, then we used the Cosmos pipeline (Dressler et al. 2011; Oemler et al. 2017) to derive an initial wavelength solution and performed the slit mapping, followed by a refined wavelength calibration and spectral extraction using an IMACS pipeline derived from the DEEP2 data reduction pipeline for Keck/DEIMOS (Cooper et al. 2012). For each mask, the extracted spectra from multiple exposures were combined using inverse-variance weighting. The combined spectra reach a signal-to-noise ratio (S/N) ∼ 5 pixel⁻¹ at r = 19.0 for Car II and at r = 19.3 for Car III.

The details of the instrument setup, observing information, mask information, etc., for IMACS and other instruments described in later sections, are summarized in Table 1.

Table 1.  Observations

Mask/Run	α (J2000)	δ (J2000)	Slit PA	λ/Δλ	disp.	# of	Σ${t}_{\exp }$	Seeing	MJDa	# of	# of Useful
Name	(h m s)	(° ' '')	(deg)		Å/pix	Exp	(s)	('')		Slits/Fibers	Spectra
IMACS-Car2Mask1	07:36:36.00	−57:57:20.0	172.0	11,000	0.19	2	4500	12	57779.3	72	32
IMACS-Car2Mask2	07:36:26.00	−58:02:00.0	248.0	11,000	0.19	3	6000	15	57778.3	48	33
IMACS-Car3Mask1	07:38:28.00	−57:53:30.0	317.0	11,000	0.19	6	13200	25	57778.2	67	40
IMACS-Car3LongSlit	07:38:34.84	−57:52:11.2	180.0	11,000	0.19	1	1800	12	57779.3	1	1
AAT-Jan	07:36:33.60	−58:01:12.0	⋯	10,000	0.24	5	13200	13	57777.6	388	131
AAT-May	07:36:33.60	−58:01:12.0	⋯	10,000	0.24	2	4800	20	57902.4	309	55
VLT-Feb	07:37:32.40	−57:57:16.0	⋯	6,000	0.20	1	2775	03	57811.1	116	116

Note.

^aThe date listed here is the weighted mean observation date over multiple exposures. For AAT-Jan observations, the date is the weighted mean over multiple nights.

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We observed Car II and Car III with the AAOmega Spectrograph (Sharp et al. 2006), a fiber-fed multi-object spectrograph on the 3.9 m AAT at the Australian Astronomical Observatory (AAO). The AAOmega Spectrograph is fed by the Two Degree Field ("2dF") multi-object system, allowing acquisition of up to 392 simultaneous spectra of objects within a 2° field on the sky.

AAOmega is a dual-beam spectrograph, which feeds a blue arm and a red arm with a beam splitter at 5700 Å. For the red arm, we utilized the 1700D grating, providing a spectral resolution of R = 10,000 and wavelength coverage of 8400–8810 Å, which enabled us to target the spectral region of the CaT absorption lines for velocity and metallicity measurements. For the blue arm, we chose the 580V grating with resolution of R = 1300 and wavelength coverage of 3750–5750 Å, which allowed us to study additional elements (e.g., carbon) in the blue. This paper focuses on the kinematics and metallicities of the Carina systems, and therefore the spectra from the blue arm will be discussed in a future paper.

Observations with AAT/AAOmega+2dF (hereafter AAT) were taken on 2017 January 23 and May 29 through the service observing program, and on 2017 January 25 through classical observing time. We obtained three 40 minute exposures on January 23, one 40 minute exposure and one 60 minute exposure on January 25, and two 40 minute exposures on May 29. To ensure accurate velocity determination, the arc frames were taken right before the science exposures at the same position. During the January run, the seeing was around 1''–15 with intermittent clouds. During the May run, the weather was clear with seeing around 16–22. Among the 392 fibers, 25 of them were assigned to sky positions, eight were assigned to guide stars selected from the UCAC4 catalog (Zacharias et al. 2013), and the remaining fibers were assigned to target stars.

The targets for the AAT run were mostly selected using the photometry from the original MagLiteS catalog. The RGB and RHB candidates were selected using the best-fit PARSEC isochrone for Car II ($\mathrm{log}\,\mathrm{age}=10.0$, ${\rm{[Fe/H]}}=-1.7$, $m-M=17.5$) and Car III ($\mathrm{log}\,\mathrm{age}=9.75$, ${\rm{[Fe/H]}}=-0.9$, $m-M=17.1$) at the time of the observations.³³ The BHB candidates were selected using a fiducial M92 BHB isochrone placed at the distance modulus of Car II and Car III.

In addition to MagLiteS photometry, we also used photometry from time-series follow-up observations (to search for RR Lyrae stars) acquired with DECam during Blanco 4 m Director's Discretionary and engineering time. The exposure times for these follow-up studies were shorter than the original MagLiteS exposures and therefore brighter stars could be observed. In addition, u-band measurements were performed in the follow-up observations, and a handful of K/M giant candidates were selected based on the u − g and g − i color (e.g., see Figure 2 of Yanny et al. 2009). Furthermore, we included some RR Lyrae candidates from the preliminary analysis of time-series follow-up studies. Thanks to the proximity of Car II and Car III on the sky, as well as the large field of view (FOV) of AAT+2dF, both systems were targeted in a single pointing. We assigned RR Lyrae candidates the highest priority, followed by the BHB and K/M giant candidates. Stars in two remaining categories (RGB, RHB) were prioritized based on their brightness in the r-band. Note that the target spacing of 2dF is typically 30''–40'' due to fiber collisions, and therefore some targets located close to the centers of Car II and Car III were missed where the target density is high.

The candidate stars were then allocated according to the priorities described above using the fiber configuration program configure³⁴ provided by the AAO. Flexibility in target allocation with 2dF allowed us to identify bright (S/N > 20 per pixel) non-member stars in the January 23 data, leading to re-allocation of those fibers to alternative targets during the January 25 observations. A total of 388 candidates were targeted from the two nights of observations in the January run; 309 of them were targeted again in the May run.

The data reduction was performed using the 2dfdr³⁵ v6.28 data reduction program of the AAO. The reduction includes bias subtraction, scattered light subtraction, flat-fielding, optimal spectral extraction, wavelength calibration, sky subtraction, and frame combination with cosmic ray rejection. Wavelength calibration was first performed using the arc frames taken immediately before or after each science exposure, followed by a recalibration with a second-order polynomial fit using sky emission lines. As the observations were taken from different nights, the reduced spectra were corrected for the heliocentric motion of the Sun at each exposure, before the spectra from multiple exposures were combined using inverse-variance weighting. To detect possible binary stars, we combined the spectra from the January run (AAT-Jan) and May run (AAT-May) separately for the velocity measurements. The combined spectra had S/N ∼5 pixel⁻¹ at r = 18.7 for AAT-Jan and at r = 18.0 for AAT-May.

After the observations with AAT and Magellan, we also observed Car II and Car III with the GIRAFFE+FLAMES spectrograph (Pasquini et al. 2000) on the 8.2 m Kueyen telescope (UT2) based at the ESO-VLT through Director's Discretionary time. Observations were taken in MEDUSA mode, which allows the simultaneous observation of up to 132 objects, with a minimum target separation of 11'' due to fiber collisions. On the night of 2017 February 26, one 2775 s exposure was taken under excellent seeing conditions ($\sim 0\buildrel{\prime\prime}\over{.} 3)$. The LR8 grating was used for this observation, which covers the wavelength range from 8206 to 9400 Å at a resolution of R ∼ 6000. The calibration frames, including biases, flats and ThAr arcs, were taken at the end of the night.

Target selection for VLT/GIRAFFE+FLAMES (hereafter VLT) was done in a similar way as for the AAT, with the exception that we manually shifted the best-fit PARSEC isochrone $g-r\sim 0.07$ bluer, based on the confirmed Car II members identified by IMACS and AAT.³⁶ As the FOV of FLAMES is about 25' in diameter, we centered the exposure field in between Car II and Car III and therefore missed some of the BHB members found in the AAT data (see Section 3). A total of 116 targets were selected to feed to FLAMES, with 13 fibers assigned to blank sky positions.

As only a single exposure was obtained with VLT, we first removed cosmic rays using L.A.Cosmic (van Dokkum 2001). We then reduced the data with the GIRAFFE Gasgano pipeline (v2.4.8) provided by ESO for bias subtraction, flat-fielding, wavelength calibration, and spectral extraction of individual objects. We performed a wavelength re-calibration using sky emission lines and a sky subtraction with our own code. For details, we refer to the spectroscopic analysis of the Horologium I dwarf galaxy (T. S. Li et al. 2018, in preparation). In summary, a first-order wavelength correction derived from sky lines was applied to every spectrum to compensate for the wavelength shift likely caused by the temperature changes between the science observing during the night and the calibration frames taken at the end of the night. We then combined the 13 sky fibers into a master sky spectrum. To compensate for fiber-to-fiber throughput and resolution variations, for each target spectrum we degraded the resolution of either the target spectrum or the master sky spectrum (whichever had the higher resolution) and then scaled the master sky spectrum to match the intensity of the sky lines in the target spectrum before the subtraction. The final reduced spectra (referred to as VLT-Feb) had S/N ∼ 7 pixel⁻¹ at $r\sim 19.8$.

The reduced spectra from IMACS, AAT, and VLT were used for radial velocity measurements following the method described in Li et al. (2017). We measured the heliocentric radial velocities (v_hel) by fitting the reduced spectra with velocity templates using a Markov chain Monte Carlo (MCMC) sampler and finding the best-fit velocity that maximizes the likelihood defined by Equation (1) in Li et al. (2017). Instead of using only one velocity template per spectrum, we defined a set of templates for each instrument and used the template that gave the largest likelihood at the best-fit velocity as the best template for each star. The template set for each instrument included at least one metal-rich RGB, one metal-poor RGB, and one BHB star. The velocity templates for AAT and IMACS were observed using the same instrument setting as the science observation and were constructed following the description in Simon et al. (2017). We were not able to obtain any velocity template spectra during the VLT run. Instead, we used the Keck/DEIMOS templates from Kirby et al. (2015a), as the Keck/DEIMOS spectra have a much wider wavelength coverage and a similar resolution ($R\sim 6000)$ as our VLT spectra. For the IMACS spectra, we also applied a telluric correction derived using a telluric template to correct for the mis-centering of spectroscopic targets within each slit (see Li et al. 2017 for more details).

The statistical uncertainty on each velocity measurement is calculated as the standard deviation of the posterior velocity distribution from the MCMC sampler. This error is related primarily to the S/N of the spectra, with stellar temperature and metallicity also playing a role. Other systematic effects, such as instrument flexure, uncertainties in the wavelength calibration, uncertainties in the template velocity, and template mismatching should also be considered in the final velocity uncertainty budget. We estimated the systematic uncertainty as the quadrature difference between repeat measurements and the statistical uncertainty (see Li et al. 2017; Simon & Geha 2007; Simon et al. 2017). We adopted the systematic floor of 1.0 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for IMACS from Simon et al. (2017). For AAT, we determined the systematic floor to be 0.5 $\mathrm{km}\,{{\rm{s}}}^{-1}$ using repeat measurements of 18 bright stars (S/N $\gt 8$) from the January run and the May run. Since only one exposure was taken with VLT, we were not able to derive a systematic floor with this data set. We adopted a systematic floor of 0.9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from the VLT observations of Horologium I (T. S. Li et al. 2018, in preparation), which has the same instrument setup as this data set. We added these systematic uncertainties in quadrature with the statistical uncertainties to obtain the final reported velocity uncertainties ${\delta }_{v}$.

In order to combine the velocities derived from three different spectrographs to produce the final data set for the velocity dispersion determination in Section 3.3, we need to verify that there is no systematic offset between these three data sets. We compare the repeated measurements from different instruments as shown in the top panels of Figure 2 and find no obvious systematic offset between any given pair of instruments. In order to confirm that our error estimation is reasonable for each instrument, we again use these repeated measurements from each pair of instruments and compute the distribution of velocity differences between the two independent measurements (v₁, v₂), divided by the quadrature sum of their uncertainties ($\sqrt{{\delta }_{1}^{2}+{\delta }_{2}^{2}}$). The resulting distributions, shown in the bottom panels of Figure 2, are well-described by normal distributions with zero mean and unit variance, as shown by red dashed curves in the same plots. From this comparison, we conclude that there is no significant zero-point shift between the various spectrographs, and that combining the three data sets will not introduce additional velocity uncertainties.

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In order to study the kinematics of Car II and Car III, as well as the spectroscopic membership in each system, we combined the velocity measurements from the three different instruments into a single data set. With this combined sample, we successfully determined the velocities of 283 stars. The heliocentric velocities and the associated uncertainties are reported in Table 4. Note that, although the results reported in the table are from each observing run or each mask, we use the weighted average ($w=1/{\delta }^{2}$) for stars with more than one measurement for the remainder of this paper.

Figure 1 shows the CMD, spatial distribution, and velocity distribution of the observed stars in both systems. We identified a total of 18 members in Car II and four members in Car III from the combined sample (see below).

The 18 members in Car II form a coherent velocity peak near 480 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in the heliocentric velocity distribution (lower right panel), including six BHB members, two RR Lyrae members, and ten RGB members. Since the heliocentric velocity of Car II is quite high relative to the mean velocity and velocity dispersion of the Milky Way halo, there are no foreground contaminants anywhere near the velocity of Car II. Furthermore, all stars within this velocity peak fall on the Car II isochrone, making the membership of this system unambiguous. The BHB members are all far from the center of Car II (r > 10') and therefore four of them are only observed with AAT. The velocity uncertainties of these BHB members are relatively large as a result of their broad lines and the low S/N of their spectra. The brightest RGB member, MAGLITES J073621.25−575800.3, was observed both in January (AAT and IMACS) and in May (AAT). The difference between the January and May observations is ∼30 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Another RGB member, MAGLITES J073646.47−575910.2, was observed both in January (AAT and IMACS) and February (VLT), and the difference is ∼25 $\mathrm{km}\,{{\rm{s}}}^{-1}$. We therefore conclude that these two stars are binaries. The two RR Lyrae members of Car II also show velocity variability, and are discussed in more detail in Section 3.2.2.

We find a second narrow peak in the velocity distribution, containing four stars, centered at 280 $\mathrm{km}\,{{\rm{s}}}^{-1}$. All four stars are located within the Car III half-light radius and we therefore identify them as Car III members. While it is difficult to confirm an association based on only four stars, two of the four are BHB stars at the distance of Car III (m − M = 17.22, see the upper left panel in Figure 1). The brighter of the two RGB stars lies exactly on the expected Car III isochrone, while the fainter one is slightly redder than expected. Nevertheless, the combination of the spatial coincidence between these stars and their position in the CMD strongly suggests that this group is related to Car III.

Finally, seven candidate stars have velocities in the range 260–400 $\mathrm{km}\,{{\rm{s}}}^{-1}$ and are displayed in blue in Figure 1. Given their velocities, these stars are clearly not members of Car II. Their CMD positions and large distance away from Car III also indicate that they are not Car III members. We used the Besançon Galactic stellar model (Robin et al. 2003) to estimate the expected number of foreground Milky Way stars in our spectroscopic sample. We selected simulated stars within 0.2 mag of the PARSEC isochrone and with $r\lt 19.5$. We found that in an area of 1 deg² centered on Car II there are ∼15 simulated stars that have a velocity larger than 260 $\mathrm{km}\,{{\rm{s}}}^{-1}$, with a majority at $g-r\lt 0.4$ (i.e., foreground main-sequence stars). The surface density of non-Car II and Car III members in our spectroscopic sample is similar to this value. The small number of contaminants from the Besançon model further supports the conclusion that the two peaks are associated with Car II and Car III members. Given that Car II is relatively close to the LMC on the sky, some of these non-member stars might also belong to the LMC, which is discussed further in Section 3.2.1.

3.2.1. LMC Contamination

3.2.2. RR Lyrae Stars

Car II contains three RR Lyrae stars (Paper I). Our spectroscopic runs targeted two of those stars, namely MAGLITES J073637.00–580114.5 and MAGLITES J073645.86–575154.1 (or V1 and V2 in Paper I), which are the two innermost of the RR Lyrae stars, with projected distances from the center of Car II of 21 and 77. The derivation of the center-of-mass velocity, or systemic velocity, of RR Lyrae stars requires special treatment since the radial velocity for these stars changes significantly (up to ∼100 km s⁻¹ for RRab stars) during their pulsation cycle. A model of a radial velocity curve must be fitted to the spectroscopic data. To do this, we followed the procedure developed in Vivas et al. (2008). The observational data and the fitted model for each star are shown in Figure 3. As the period of RR Lyrae stars is usually less than a day, we measured the velocities from the January 23 and 25 AAT observations separately. For other measurements, we used the velocity measured over one to three combined exposures from that night, as reported in Table 4. We therefore have five independent velocity measurements for V1 and three for V2.

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For V1, an RRab star, we used the radial velocity model of the star X Arietis, which was parameterized by Layden (1994) based on observations made by Oke (1966). The radial velocity curve of the ab-type RR Lyrae stars (the type of our star V1) has a large discontinuity near maximum light. Thus, it is advisable not to measure radial velocities near that phase in the pulsation cycle ($\phi \lt 0.05$ or $\phi \gt 0.9$). However, at the time of the spectroscopic observations we had not obtained final light curves of the RR Lyrae stars, and thus spectra were taken at random phases. Phases were calculated later once the light curves were characterized by Paper I. One of our observations for V1 was indeed not useful since the spectrum was acquired at phase ϕ = 0.93. Thus, the radial velocity curve was fitted using four observations with phases ranging from 0.08 to 0.58. As seen in Figure 3, all the individual observations follow very nicely the model of X Arietis, which was shifted in velocity to match the observations. The best match was produced when the systemic velocity was 491 $\mathrm{km}\,{{\rm{s}}}^{-1}$. The rms of the fit is 2.8 $\mathrm{km}\,{{\rm{s}}}^{-1}$. However, to obtain a more realistic error we followed Vivas et al. (2005) and included uncertainties due to star-to-star variations of the amplitude of the radial velocity curve as well as possible differences on the exact phase of the systemic velocity. We determined a final systemic (heliocentric) velocity for V1 of 491 ± 7 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

For V2, which is an RRc star, we used a template constructed by Duffau et al. (2006) based on observations of T Sex and DH Peg. The amplitude of the radial velocity curve of RRc stars is not as large as for RRab variables, nor is there a discontinuity at maximum light. Thus, all three spectra available for this star can be used to determine its velocity. We measured a heliocentric velocity for V2 of 474 ± 5 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

The systemic radial velocities obtained for these two RR Lyrae stars confirm that they are members of Car II.

We used eight RGB stars (excluding the two binaries mentioned in Section 3.2) and six BHB stars (hereafter the 14 star sample) to calculate the systemic velocity and the velocity dispersion of Car II using the two-parameter Gaussian likelihood function defined in Walker et al. (2006) and an MCMC to sample the distributions of the systemic velocity v_hel and the velocity dispersion ${\sigma }_{v}$. We used a flat prior for the systemic velocity with range (455, 495) $\mathrm{km}\,{{\rm{s}}}^{-1}$ and a non-informative Jeffreys prior for the velocity dispersion with range (0.01, 100) $\mathrm{km}\,{{\rm{s}}}^{-1}$ (or equivalent to a flat prior in log(${\sigma }_{v}$) space with range (−2, 2)). The probability distribution from the MCMC is shown in Figure 4. We find a systemic velocity of ${v}_{\mathrm{hel}}=477.2\pm 1.2$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ and a velocity dispersion of ${\sigma }_{v}={3.4}_{-0.8}^{+1.2}$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, where we report the median of the posterior and the uncertainty calculated from the 16th and 84th percentiles.

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In order to test the effects of our input assumptions, we also calculated the systemic velocity and velocity dispersion with different priors and different data sets. A summary of these comparisons is presented in Table 3. With a flat prior for velocity dispersion and the same 14 star sample, the velocity dispersion is ${3.8}_{-0.9}^{+1.3}\,\mathrm{km}\,{{\rm{s}}}^{-1}$, which is slightly higher than the value determined using the Jeffreys prior with same data set. This result is similar to what was seen in Kim et al. (2015). If we expand our sample to 16 stars by including the two RR Lyrae stars using the velocities derived in Section 3.2.2, both the systemic velocity and the velocity dispersion are very similar to what we determined with the 14 star sample (default sample). We then run similar calculations with only RGB members and only BHB members. The result with eight RGB members is again very similar to our default sample, suggesting that the results are mostly constrained by the RGB members (which have smaller velocity uncertainties). The six BHB members give a smaller dispersion, but with larger uncertainties so that the results are statistically consistent, mainly due to the large velocity uncertainties (${\delta }_{v}\gtrsim 4$ $\mathrm{km}\,{{\rm{s}}}^{-1}$) on the BHB stars.

Table 3.  Systemic Velocity and Velocity Dispersion with Different Data Sets

Name	Data Set	Prior	vhel	${\sigma }_{v}$
			$(\mathrm{km}\,{{\rm{s}}}^{-1})$	$(\mathrm{km}\,{{\rm{s}}}^{-1})$
14 star sample (default)	8 RGB + 6 BHB	Jeffreys	477.2 ± 1.2	${3.4}_{-0.8}^{+1.2}$
14 star sample	8 RGB + 6 BHB	flat	477.2 ± 1.3	${3.8}_{-0.9}^{+1.3}$
16 star sample	8 RGB + 6 BHB + 2 RRL	Jeffreys	477.4 ± 1.2	${3.5}_{-0.9}^{+1.2}$
RGB only	8 RGB	Jeffreys	476.6 ± 1.2	${3.5}_{-0.9}^{+1.3}$
BHB only	6 BHB	Jeffreys	478.8 ± 2.2	${0.9}_{-0.9}^{+3.7}$
IMACS only	4 RGB	Jeffreys	475.8 ± 2.1	${4.0}_{-1.7}^{+2.7}$
VLT only	4 RGB + 2 BHB	Jeffreys	477.1 ± 1.5	${3.3}_{-1.1}^{+1.7}$
AAT only	5 BHB	Jeffreys	480.9 ± 2.5	${0.2}_{-0.2}^{+2.4}$
one-epoch	10 RGB (incl. 2 Binary) + 6 BHB	Jeffreys	477.8 ± 2.2	${7.7}_{-1.4}^{+1.8}$

Note. All values reported here (and in this paper) are from the 50th percentile of the posterior probability distributions. The uncertainties are from the 16th and 84th percentiles of the posterior probability distributions.

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We also calculated the systemic velocity and velocity dispersion using the results from each instrument to see if there is any instrumental bias. We obtained very consistent results using the VLT data or IMACS data alone, while the AAT data show much smaller dispersion as the members found by AAT are mostly BHBs (plus RR Lyraes and binaries). We additionally calculated the velocity dispersion using the velocity measurements from only one epoch. We included the 14 stars in addition to the two binaries. For each star the measurement with highest S/N was chosen. The derived velocity dispersion was more than doubled compared to that derived from the 14 star sample. This exercise mimics a case in which only single-epoch velocity measurements are made for each star and therefore no binary information is available. Because of the large velocity amplitudes of the two binary stars, observations made near the velocity extrema of the binary orbits can substantially inflate the apparent velocity dispersion of Car II.

Finally, we performed a jackknife test (MacQueen 1967) to assess the robustness of the measured velocity dispersion with the 14 star sample, in particular, to check whether the results are driven by any single star. We removed one star out of the 14 star sample and recomputed the average velocity and velocity dispersion. In the jackknife runs, the average velocity had a median difference of 0.0 $\mathrm{km}\,{{\rm{s}}}^{-1}$, a standard deviation of 0.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$, and a minimum and maximum difference of −0.5 and 0.6 $\mathrm{km}\,{{\rm{s}}}^{-1}$. For the velocity dispersion the median difference was 0.1 $\mathrm{km}\,{{\rm{s}}}^{-1}$, the standard deviation 0.2 $\mathrm{km}\,{{\rm{s}}}^{-1}$, and the minimum and maximum −0.5 and 0.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$. We conclude that, apart from the binaries, there are no individual stars whose inclusion or exclusion from the sample significantly affects the kinematics of Car II.

We checked if Car II contains a velocity gradient following the method in Li et al. (2017). We calculated a best-fit velocity gradient of $0.0\pm 0.3\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{arcmin}}^{-1}$, consistent with the null model. We computed the Bayes factor comparing the velocity gradient and constant velocity dispersion models and found $\mathrm{lnB}=-2.2$, which favors the constant velocity dispersion model (we follow Wheeler et al. 2017 to interpret the Bayes' factor value). We conclude that there is no evidence for a velocity gradient in Car II.

For Car III, we determined a systemic velocity of ${284.6}_{-3.1}^{+3.4}$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ and velocity dispersion of ${5.6}_{-2.1}^{+4.3}$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ using the four identified members. We caution that the small number of stars may not lead to a reliable estimate for the velocity dispersion of Car III. Furthermore, a single binary star can easily inflate the velocity dispersion. We give a more detailed discussion of the implications of the measurements and the nature of Car III in Section 4.1.

We measured the metallicity of the red giant member stars in both systems using the equivalent widths (EWs) of the CaT lines. Following the procedure described by Simon et al. (2015) and Li et al. (2017), we fitted all three of the CaT lines with a Gaussian plus Lorentzian function and then converted the summed EWs of the three CaT lines to metallicity using the calibration relation from Carrera et al. (2013) with absolute V magnitude. We first performed the color-transformation from DES-g and DES-r to apparent V magnitude using Equation (5) in Bechtol et al. (2015) and then adopted distance moduli of $(m-M)=17.86$ for Car II members and $(m-M)=17.22$ for Car III members to calculate absolute magnitudes. The statistical uncertainties on the EWs were calculated from the Gaussian and Lorentzian fit. We added a systematic uncertainty of 0.2 Å (as determined in Li et al. 2017) in quadrature with the statistical uncertainties to obtain the final EW uncertainties. The metallicity uncertainties shown in Table 4 are dominated by the uncertainties on the CaT EWs, with small contributions from the uncertainties on the heliocentric distances, the stellar photometry, and the uncertainties on the calibration parameters from Carrera et al. (2013).

Table 4.  Velocity and Metallicity Measurements

ID	${\alpha }_{2000}$	${\delta }_{2000}$	g0a	r0a	Masks/	MJD	S/N	v	$\mathrm{EW}$	$[\mathrm{Fe}/{\rm{H}}]$	Comment
	(deg)	(deg)	(mag)	(mag)	Instruments			($\mathrm{km}\,{{\rm{s}}}^{-1}$)	(Å)
Carina II
MAGLITES J073504.92−575646.9	113.77049	−57.94636	18.18	18.35	AAT-Jan	57777.7	7.9	482.80 ± 3.38	⋯	⋯	BHB
					AAT-May	57902.4	3.3	487.20 ± 12.63	⋯	⋯
MAGLITES J073546.15−574911.6	113.94231	−57.81988	18.68	19.02	AAT-Jan	57777.7	4.4	484.66 ± 6.53	⋯	⋯	BHB
MAGLITES J073558.28−580328.2	113.99285	−58.05784	19.25	18.81	IMACS-Car2Mask2	57778.3	4.8	475.96 ± 2.47	1.78 ± 0.28	−2.74 ± 0.18
MAGLITES J073558.39−581227.7	113.99329	−58.20769	18.36	18.61	AAT-Jan	57777.7	4.1	485.43 ± 13.64	⋯	⋯	BHB
MAGLITES J073559.15−575918.2	113.99644	−57.98838	18.93	18.45	IMACS-Car2Mask2	57778.3	7.3	470.93 ± 1.62	2.45 ± 0.24	−2.43 ± 0.13
MAGLITES J073601.33−575843.8	114.00552	−57.97885	18.26	17.76	VLT-Feb	57811.1	32.9	472.34 ± 1.03	2.99 ± 0.28	−2.32 ± 0.14
MAGLITES J073611.87−581228.6	114.04945	−58.20796	18.23	18.46	AAT-Jan	57777.7	6.0	478.94 ± 8.75	⋯	⋯	BHB
MAGLITES J073621.25−575800.3	114.08852	−57.96675	16.98	16.30	AAT-Jan	57777.7	40.7	492.70 ± 0.51	4.30 ± 0.26	−2.07 ± 0.12	Binary
					IMACS-Car2Mask2	57778.3	42.4	494.30 ± 1.03	4.66 ± 0.22	−1.92 ± 0.10
					AAT-May	57902.4	20.1	464.92 ± 0.83	4.44 ± 0.32	−2.01 ± 0.14
MAGLITES J073624.62−575922.1	114.10256	−57.98948	18.89	18.36	IMACS-Car2Mask2	57778.3	7.3	479.46 ± 2.10	⋯	⋯
					IMACS-Car2Mask1	57779.3	8.3	481.56 ± 1.90	2.24 ± 0.90	−2.56 ± 0.48
MAGLITES J073624.98−575714.3	114.10408	−57.95397	18.43	17.97	VLT-Feb	57811.1	31.5	477.75 ± 1.11	2.01 ± 0.20	−2.77 ± 0.12
MAGLITES J073637.00−580114.5	114.15416	−58.02069	18.56	18.36	AAT-Jan	57777.7	9.0	489.30 ± 1.84	⋯	⋯	RR Lyrae
					IMACS-Car2Mask2	57778.3	9.3	457.03 ± 2.25	⋯	⋯
					IMACS-Car2Mask1	57779.3	8.1	498.71 ± 1.63	⋯	⋯
					AAT-May	57902.4	4.6	440.82 ± 14.58	⋯	⋯
MAGLITES J073645.86−575154.1	114.19109	−57.86503	17.97	18.02	AAT-Jan	57777.7	8.3	484.83 ± 2.01	⋯	⋯	RR Lyrae
					IMACS-Car2Mask1	57779.3	10.4	457.63 ± 2.06	⋯	⋯
MAGLITES J073646.47−575910.2	114.19362	−57.98617	19.39	18.93	AAT-Jan	57777.7	3.6	485.57 ± 4.42	⋯	⋯	Binary
					IMACS-Car2Mask2	57778.3	5.4	484.15 ± 3.17	⋯	⋯
					IMACS-Car2Mask1	57779.3	5.0	486.62 ± 2.59	2.62 ± 0.29	−2.26 ± 0.15
					VLT-Feb	57811.1	17.5	460.69 ± 1.37	2.82 ± 0.30	−2.16 ± 0.16
MAGLITES J073655.60−580049.8	114.23168	−58.01383	18.99	18.52	IMACS-Car2Mask2	57778.3	7.2	475.21 ± 1.92	⋯	⋯
MAGLITES J073729.30−580447.8	114.37206	−58.07993	19.14	18.68	VLT-Feb	57811.1	19.6	479.53 ± 1.32	2.42 ± 0.33	−2.40 ± 0.18
MAGLITES J073737.04−574925.5	114.40434	−57.82375	19.09	19.46	VLT-Feb	57811.1	6.0	481.13 ± 8.25	⋯	⋯	BHB
MAGLITES J073739.81−580507.0	114.41589	−58.08528	17.80	17.25	VLT-Feb	57811.1	46.8	480.22 ± 0.97	2.52 ± 0.26	−2.64 ± 0.13
MAGLITES J073745.86−580406.7	114.44108	−58.06853	18.28	18.52	AAT-Jan	57777.7	4.1	467.44 ± 8.43	⋯	⋯	BHB
					VLT-Feb	57811.1	16.9	474.10 ± 2.80	⋯	⋯
Carina III
MAGLITES J073823.68−575150.8	114.59866	−57.86412	20.21	19.71	VLT-Feb	57811.1	6.4	290.56 ± 4.99	⋯	⋯
MAGLITES J073834.84−575211.2	114.64516	−57.86977	17.60	17.77	AAT-Jan	57777.7	8.5	277.14 ± 3.93	⋯	⋯	BHB
					IMACS-Car3LongSlit	57779.3	6.9	282.26 ± 2.99	⋯	⋯
MAGLITES J073834.94−575705.4	114.64558	−57.9515	17.70	17.18	IMACS-Car3Mask1	57778.2	29.9	280.19 ± 1.29	3.73 ± 0.25	−1.97 ± 0.12
					VLT-Feb	57811.1	43.8	280.36 ± 1.00	3.73 ± 0.28	−1.97 ± 0.13
MAGLITES J073835.54−575622.3	114.64808	−57.93952	17.53	17.68	IMACS-Car3Mask1	57778.2	15.6	288.25 ± 1.56	⋯	⋯	BHB
					VLT-Feb	57811.1	23.8	291.92 ± 1.86	⋯	⋯
					AAT-May	57902.4	4.4	288.25 ± 4.92	⋯	⋯
Non Memberb
MAGLITES J073507.41−574725.4	113.78087	−57.79038	18.13	17.89	AAT-Jan	57777.7	13.5	291.13 ± 1.80	3.56 ± 0.56	⋯
					AAT-May	57902.4	7.3	298.29 ± 2.30	⋯	⋯
MAGLITES J073613.95−580641.2	114.05814	−58.11145	18.31	17.92	AAT-Jan	57777.7	10.0	396.63 ± 1.81	2.64 ± 0.63	⋯
					AAT-May	57902.4	6.9	388.58 ± 2.72	⋯	⋯
MAGLITES J073629.58−574940.0	114.12327	−57.82777	18.21	17.96	AAT-Jan	57777.7	8.9	309.01 ± 2.19	3.55 ± 0.36	⋯
MAGLITES J073634.86−580340.6	114.14526	−58.06127	18.51	18.70	AAT-Jan	57777.7	5.5	329.64 ± 3.85	⋯	⋯	BHB
					IMACS-Car2Mask2	57778.3	4.0	327.09 ± 3.91	⋯	⋯
					VLT-Feb	57811.1	14.4	335.29 ± 2.87	⋯	⋯
MAGLITES J073651.54−580247.8	114.21475	−58.04662	18.07	17.79	IMACS-Car2Mask2	57778.3	11.8	294.38 ± 1.41	4.29 ± 0.39	⋯
MAGLITES J073710.30−575819.3	114.29293	−57.97202	19.92	19.55	VLT-Feb	57811.1	9.5	261.93 ± 3.18	4.20 ± 0.59	⋯
MAGLITES J073727.87−574421.9	114.36613	−57.73943	18.21	17.93	AAT-Jan	57777.7	11.3	266.26 ± 1.66	5.17 ± 0.44	⋯
					AAT-May	57902.4	5.2	294.10 ± 4.91	⋯	⋯

Notes.

^a(a) Quoted magnitudes represent the weighted-average point-spread function magnitude derived from the original MagLiteS survey (rather than the photometry from time-series follow-up observations that were used to search for RR Lyrae stars). The photometry provided here is the dereddened photometry using the extinction map from Schlegel et al. (1998). At the location of Car II and Car III, the average color excess is $E(B-V)\sim 0.19$. ^bFor non-members, only stars with ${v}_{\mathrm{hel}}\gt 220\,\mathrm{km}\,{{\rm{s}}}^{-1}$ are presented here. The remaining non-members are available in the online version in machine readable format.

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

Download table as:  DataTypeset images: 1 2

Among the 10 confirmed spectroscopic RGB members in Car II, we successfully measured metallicities for nine stars. The metallicities of the Car II members range from ${\rm{[Fe/H]}}=-2.7$ to ${\rm{[Fe/H]}}=-1.9$. We used a Gaussian likelihood model as described above for the velocities to calculate the mean metallicity and metallicity dispersion of Car II. We found a mean metallicity of ${\rm{[Fe/H]}}=-2.44\pm 0.09$, with a dispersion of ${\sigma }_{{\rm{[Fe/H]}}}\,={0.22}_{-0.07}^{+0.10}$. The probability distribution from the MCMC is shown in Figure 5.

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For Car III, we measured the metallicity of the brightest RGB member, MAGLITES J073834.94−575705.4, and obtained ${\rm{[Fe/H]}}=-1.97\pm 0.12$ for this star. If this RGB member represents the mean metallicity of Car III, then the metallicities of Car II and Car III are different at 3-σ level. Note that in Paper I we obtained ${\rm{[Fe/H]}}=-1.8\pm 0.1$ for Car II and ${\rm{[Fe/H]}}\,=-1.8\pm 0.2$ for Car III from the isochrone fitting using photometry alone. While this metallicity estimate for Car III is consistent with that of the brightest RGB member from the spectroscopic measurements, for Car II the metallicity derived from isochrone fitting is more metal-rich than its spectroscopic mean metallicity.

We calculated the mass of Car II contained within the half-light radius according to the mass estimator from Wolf et al. (2010) (see also Walker et al. 2009b), using the velocity dispersion determined in Section 3.3 and the half-light radius of Car II from Paper I. We found a dynamical mass of ${M}_{1/2}={1.0}_{-0.4}^{+0.8}\,\times {10}^{6}$ ${M}_{\odot }$ and a mass-to-light ratio of ${369}_{-161}^{+309}$ ${M}_{\odot }$/${L}_{\odot }$ for Car II. The reported uncertainties on the dynamical mass and mass-to-light ratio include the uncertainties on the velocity dispersion from this paper, and the uncertainties on the half-light radius and luminosity from Paper I. The mass of Car II is much larger than its stellar mass, and the mass-to-light ratio is similar to those of other dwarf galaxies with comparable luminosities. The low average metallicity ($-2.44\pm 0.09$) and large metallicity dispersion (${0.22}_{-0.07}^{+0.10}$) also match observations of other dwarf galaxies with similar luminosities (Kirby et al. 2013). We therefore conclude that Car II is a dark-matter-dominated dwarf galaxy.

Because we have only identified four members of Car III, neither its mass nor its metallicity distribution is significantly constrained. We therefore cannot determine whether Car III is a dwarf galaxy. If the metallicity of the brightest confirmed member star (${\rm{[Fe/H]}}=-1.97$) represents the average metallicity of the system, then Car III is more metal-rich than most of the dwarf galaxies with similar luminosities, but still much more metal-poor than all known star clusters at a similar luminosity. If the velocity dispersion calculated from the four confirmed members is close to the true dispersion of the system, then Car III is likely to be a dark-matter-dominated dwarf galaxy. Given the small sample, though, a single binary star could easily inflate the velocity dispersion, and therefore this dispersion shall be used with caution. Interestingly, among the four member stars, MAGLITES J073834.94−575705.4, the brightest RGB member, was observed in both January (IMACS) and February (VLT), and MAGLITES J073835.54−575622.3, a BHB member, was observed in January (IMACS), February (VLT), and May (AAT). The differences in velocities are consistent with the measurement uncertainties (see Table 4) and therefore we do not see any strong evidence for binarity of these two stars from our observations across 1–3 month baselines. However, the velocities of these two stars are about 8 $\mathrm{km}\,{{\rm{s}}}^{-1}$ apart (and are the source of the large velocity dispersion on Car III). This large difference, if indeed not caused by binary motion, could provide a hint that Car III should be classified as a dwarf galaxy. Identifying more members with deeper observations will be necessary to confirm the nature of Car III. Observing these bright members at one or two additional epochs will also help determine whether or not they are in binary systems.

We note that the mass estimator from Wolf et al. (2010) is only valid for dispersion-supported stellar systems in dynamical equilibrium. It is possible that Car II has had a tidal interaction with the Milky Way ($d\sim 36$ kpc), LMC ($d\sim 20$ kpc), or Car III ($d\sim 10$ kpc) due to their close proximity. Either a velocity gradient or an increasing velocity dispersion at large radii could be potential signs of tidal disruption. In Section 3.3, we conclude that we are not able to detect a velocity gradient with our current data. In Figure 6, we show the velocity as a function of distance to the center of Car II. Interestingly, the six BHB stars are also the outermost members. As shown in Table 3, the velocity dispersion from the BHB sample alone is small due to the large velocity uncertainties and, therefore, we also do not see a larger velocity dispersion at large radii. However, we note that both null results could result from the large velocity uncertainties of these BHB stars. Further studies that either identify more RGB stars at large radii or improve the velocity precision for the known BHB members will be necessary to completely rule out a velocity gradient or other tidal effects.

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The fact that all six BHB members are the outermost stars (Figure 6) implies a possible non-uniform spatial distribution of the stellar populations in Car II. However, we also caution that this distribution is likely caused by a selection bias from the observations. Note that the four outermost BHB members are uniquely identified by AAT, which has the largest FOV among three instruments. However, the target selection for AAT was performed with an older version of PARSEC isochrones and therefore may have missed a few RGB members with $r\gt {r}_{h}$, as explained in the Appendix. Further observations, including a more comprehensive search for bright RGB members outside of the half-light radius, may be necessary to fully understand the possible stellar population dependent spatial distribution in Car II.

To check whether the observed kinematics of Car II and Car III are consistent with their being gravitationally bound systems, we have computed their tidal radii (r_t) with the Milky Way as the host via Equation (18) in Bonnivard et al. (2015a), using the Milky Way mass model presented in Eadie & Harris (2016). To set a lower limit on r_t, we used the Car II ${M}_{1/2}$ value for the total mass and found ${r}_{t}\sim 500$ pc. This lower limit on r_t is already significantly larger than the observed size of the system. With a mass profile based on a Navarro et al. (1996) profile, the total mass of Car II (with r = 300 pc) is estimated to be 5–10 times larger than ${M}_{1/2}$ (with ${r}_{s}=0.1\mbox{--}0.5$ kpc), implying ${r}_{t}\sim 0.9\mbox{--}1.1\,\mathrm{kpc}$. The mass profile of Car III is more uncertain due to the small number of stars and the unknown nature of the object. If we assume conservatively that Car III is a dwarf galaxy with dispersion $\sigma =1\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and $M({r}_{\max })=10\times {M}_{1/2}$, then we find ${r}_{t}\sim 250$ pc, again much larger than the observed size of Car III. If the true dispersion of Car III is close to the measurement from a sample of four members, then the tidal radius will be even larger. We additionally computed r_t assuming that the LMC is the host instead of the Milky Way. For Car II, the LMC host r_t values are 5%–10% larger than the Milky Way host values while for Car III they are $\sim 50 \%$ larger. Although a complete analysis of the Car II tidal radius should include the LMC+Milky Way system, we still expect the tidal radius to be larger than the observed size of Car II. Therefore, we conclude that Car II is likely to be a bound system based on its current location in the Milky Way, though it is still possible that it had a smaller tidal radius if it approached closer to the Milky Way or LMC in the past.

The small projected separation ($\sim 18^{\prime}$) of Car II and Car III and their similar distances naturally lead to the question of whether the two are (or were) a bound pair of satellites. Similar speculation has occurred for the satellite pairs Leo IV–Leo V (${\rm{\Delta }}{d}_{3{\rm{D}}}\sim 20.6\,\mathrm{kpc}$ and ${\rm{\Delta }}v\sim 47\,\mathrm{km}\,{{\rm{s}}}^{-1};$ Belokurov et al. 2008; Walker et al. 2009a; de Jong et al. 2010) and Pisces II–Pegasus III (${\rm{\Delta }}{d}_{3{\rm{D}}}\sim 43\,\mathrm{kpc}$ and ${\rm{\Delta }}v\sim 10\,\mathrm{km}\,{{\rm{s}}}^{-1};$ Kim et al. 2015, 2016). While Car II and Car III have the smallest known physical separation to date, ${\rm{\Delta }}{d}_{3{\rm{D}}}\sim 10\,\mathrm{kpc}$, their separation in velocity is quite large ${\rm{\Delta }}v\sim 193\,\mathrm{km}\,{{\rm{s}}}^{-1}$.

We applied the method presented in Evslin (2014) to estimate the minimum halo mass for the Car II–Car III system to be bound and found an unrealistically large halo mass of $\sim {10}^{11}\,{M}_{\odot }$ (similar to the halo mass of the LMC; van der Marel & Kallivayalil 2014). Based on the observed kinematics of Car II, the escape velocity at the distance of Car III is between $15\,\mathrm{and}\,25\,\mathrm{km}\,{{\rm{s}}}^{-1}$, significantly smaller than the observed velocity difference. Car II and Car III are therefore highly unlikely to be a bound pair of satellites.

Assuming the pair have similar proper motions, the two satellites would have had a close encounter and sailed past one another $\sim 53\,\mathrm{Myr}$ ago. Based on this trajectory and the observed separation they would have passed within 200 pc of one another ($\sim 2\times ({r}_{1/2,\mathrm{Car}\mathrm{II}}+{r}_{1/2,\mathrm{Car}\mathrm{III}})$). At the point of closest encounter, the Car III tidal radius would have been no more than a few tens of parsecs. Regardless of the nature of Car III, a close encounter between the satellites could have disrupted Car III. While there is no reason to expect Car II and Car III to have similar proper motions given the large difference in their radial velocities, it will be interesting to explore this scenario further when proper motions are available. We note that the brightest spectroscopic members in both Car II and Car III are brighter than the faint limit for Gaia proper motion measurements.

The properties of Car II and Car III derived in this paper are summarized in Table 2.

As discussed in Section 1, the MagLiteS survey was designed to search for satellites of the Magellanic Clouds. Having searched in the vicinity of the LMC and SMC, it is therefore unsurprising that Car II and Car III are physically close to the Magellanic Clouds. The newly measured velocities of the Carina pair can now be used to test whether a physical association with the Clouds is likely.

To aid comparison with models, we first transform the line-of-sight velocities of Car II and Car III from the heliocentric frame to the Galactic Standard of Rest frame³⁷ and obtain ${v}_{\mathrm{GSR},\mathrm{Car}\mathrm{II}}=235$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ and ${v}_{\mathrm{GSR},\mathrm{Car}\mathrm{III}}=42$ $\mathrm{km}\,{{\rm{s}}}^{-1}$. Next, we compare these measurements with the dynamical model of Magellanic satellites presented in Jethwa et al. (2016). Assuming an association with the LMC, this model predicts a velocity of ${v}_{\mathrm{GSR}}={118}_{-80}^{+142}({149}_{-114}^{+142}$ $\mathrm{km}\,{{\rm{s}}}^{-1}$) at the position of Car II (Car III). For an association with the SMC, the predicted velocities are higher, at ${v}_{\mathrm{GSR}}={350}_{-70}^{+50}$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ for both Car II and Car III. According to this model, both Carinas therefore have velocities consistent with an LMC association. In Figure 7, we show the comparison between the observed phase-space distribution of dwarf galaxies/dwarf galaxy candidates and the simulated probability distribution of LMC satellites from the Jethwa et al. (2016) model, and the neutral hydrogen gas column density from Nidever et al. (2010). According to the Jethwa et al. model, both Car II and Car III are consistent with having originated with the LMC.

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As pointed out in Section 3.2.1, the non-rotating LMC halo population and the LMC rotating disk both have ${v}_{\mathrm{hel}}\,\sim 380\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at the location of Car II and Car III, which differs by ∼100 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from the heliocentric velocities of Car II and Car III. According to van der Marel & Kallivayalil (2014), the enclosed LMC mass out to a radius of 8.7 kpc is M($\lt 8.7\,\mathrm{kpc})=1.7\times {10}^{10}{M}_{\odot }$. The corresponding escape velocity is $\sim 90\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at the distance of Car II (∼18 kpc from the LMC) and $\sim 75\,\mathrm{km}\,{{\rm{s}}}^{-1}$ at the distance of Car III (∼25 kpc from the LMC). Because these values are based on a lower limit to the enclosed mass of the LMC, the actual escape velocities are likely to be somewhat larger. Therefore, we tentatively suggest that one or both of Car II and Car III are likely to be bound satellites of the LMC, although proper motion measurements will be needed to confirm this hypothesis.

We also note that all three newly discovered MagLiteS satellite candidates (Car II, Car III, and Pictor II) fall along a linear sequence on the sky as defined by the positions of the LMC, SMC, and seven of the DES satellite candidates. This configuration is shown by the dashed black line in Figure 7. This linear sequence was first pointed out in Jethwa et al. (2016), prior to any MagLiteS discoveries. As discussed in Paper I, it is unclear whether this linear sequence corresponds to a planar distribution of satellites around the Magellanic Clouds, or simply a satellite distribution that is elongated along the LMC–SMC separation vector. Once dynamical models of both scenarios are available, the velocities we have measured may provide a useful discriminant.

Milky Way satellite galaxies are among the most promising targets for indirect dark matter searches due to their substantial dark matter content, proximity, and dearth of conventional non-thermal emission (e.g., Baltz et al. 2008; Winter et al. 2016). In particular, analyses of γ-ray data from the Fermi Large Area Telescope (LAT) around previously known Milky Way satellites are now sensitive to dark matter annihilating at the canonical thermal relic cross section for particle masses up to 100 GeV (e.g., Ackermann et al. 2015a; Geringer-Sameth et al. 2015b). The discovery of additional Milky Way satellites, especially nearby objects such as Car II and Car III, can improve the sensitivity of such searches (He et al. 2015; Charles et al. 2016), as demonstrated by Drlica-Wagner et al. (2015a) and Albert et al. (2017).

In this subsection, we compute the astrophysical component of the dark matter annihilation and decay fluxes, the so-called J- and D-factors, for both Car II and Car III. The J-factor is the line-of-sight integral of the dark matter density squared: $J(\theta )=\int {\rho }_{\mathrm{DM}}^{2}d{\rm{\Omega }}{dl}$. The D-factor is the linear analog: $D(\theta )=\int {\rho }_{\mathrm{DM}}d{\rm{\Omega }}{dl}$. Here, ${\rho }_{\mathrm{DM}}$ is the dark matter density and the integral is performed over a solid angle ${\rm{\Delta }}{\rm{\Omega }}$ with radius θ. The standard approach for computing ${\rho }_{\mathrm{DM}}$ in dwarf spheroidal galaxies uses the spherical Jeans equation (e.g., Strigari et al. 2008; Bonnivard et al. 2015b).

The three main ingredients of a spherical Jeans analysis are: the stellar density profile, which we modeled as a Plummer profile (Plummer 1911); the gravitational potential, assumed to be dark matter dominated and modeled with a Navarro–Frenk–White profile (Navarro et al. 1996); and the stellar anisotropy, modeled with a constant profile.³⁸ Jeffreys priors are assumed for the dark matter halo parameters: $-2\lt {\mathrm{log}}_{10}({r}_{s}/\mathrm{kpc})\lt 1$ and $4\,\lt {\mathrm{log}}_{10}({\rho }_{s}/{M}_{\odot }\ \,\ {\mathrm{kpc}}^{-3})\lt 14$ for the scale radius, r_s, and scale density, ${\rho }_{s}$, respectively. Additionally, a prior of ${r}_{s}\gt {r}_{1/2}$ is imposed, where ${r}_{1/2}$ is the azimuthally averaged stellar half-light radius. We adopted the ${r}_{s}\gt {r}_{1/2}$ prior for several reasons: in our posterior distributions there are no trends between J and r_s except for ${r}_{s}\lt {r}_{1/2}$ where J is systematically higher, the J-factor tends to be overestimated in mock data sets without this cut (see Section 4.1 of Bonnivard et al. 2015b), and small r_s values are disfavored in ΛCDM N-body simulations (based on Garrison-Kimmel et al. 2014, a halo with ${V}_{\max }\sim 5\mbox{--}10\,\mathrm{km}\,{{\rm{s}}}^{-1}$ has a ${r}_{s}\sim 100\mbox{--}300$ pc). For the anisotropy prior, we assumed a flat symmetrized anisotropy parameter; $-0.95\lt \tilde{\beta }\lt 1.0$ (see Equation (8) in Read et al. 2006). A flat prior was used for the average velocity ($470\lt \overline{v}\lt 490\,\mathrm{km}\,{{\rm{s}}}^{-1}$) and Gaussian priors were assumed for the distance and structural parameters.³⁹ We used an unbinned likelihood function (Strigari et al. 2008; Martinez et al. 2009; Geringer-Sameth et al. 2015a) and determined posterior distributions with the MultiNest sampling routine (Feroz & Hobson 2008; Feroz et al. 2009). We estimated the dark matter r_t (required to compute the J- and D-factors) at each point in the posterior distribution by iteratively computing the enclosed mass and solving for r_t as described in Section 4.1. We find the Car II r_t posterior to be roughly Gaussian, centered at 1 kpc but containing a substantial tail to larger values.

We calculated the Car II integrated J-factor enclosed within solid angles of radii $\theta ={\alpha }_{c},0.1,0.2,0\buildrel{\circ}\over{.} 5$ to be ${\mathrm{log}}_{10}(J/{\mathrm{GeV}}^{2}\ \,\ {\mathrm{cm}}^{-5})={18.1}_{-0.5}^{+0.5},{17.9}_{-0.5}^{+0.6},{18.0}_{-0.5}^{+0.5},{18.2}_{-0.5}^{+0.5}$, respectively, using the 14 star sample. ${\alpha }_{c}$ is the angle within which the J-factor errors are minimized (Walker et al. 2011); ${\alpha }_{c}=2{r}_{1/2}/d\approx 0\buildrel{\circ}\over{.} 23$ for Car II. The equivalent radius for the D-factor occurs at ${\alpha }_{c}/2$. We determined the D-factor within $\theta ={\alpha }_{c}/2,0.1,0.2,0\buildrel{\circ}\over{.} 5$ to be ${\mathrm{log}}_{10}(D/\mathrm{GeV}\ \,\ {\mathrm{cm}}^{-2})$ = ${17.1}_{-0.3}^{+0.3},{16.9}_{-0.3}^{+0.3},{17.4}_{-0.3}^{+0.3},{18.0}_{-0.4}^{+0.4}$. These values agree with the simple J-factor estimator (Equation (13) of Evans et al. 2016). This value is an order of magnitude smaller than the simple empirical J-distance scaling relations (Drlica-Wagner et al. 2015a; Albert et al. 2017). The J-factor contains a large velocity dispersion scaling ($J\propto {M}^{2}\propto {\sigma }^{4}$) and an increase of only ${\rm{\Delta }}\sigma \sim 1.5\,\mathrm{km}\,{{\rm{s}}}^{-1}$ would move Car II onto the J-distance scaling relation (Pace & Strigari 2018). There are multiple ultra-faint satellites with larger J-factors (6–8 are larger depending on the J-factor compilation; Bonnivard et al. 2015a; Geringer-Sameth et al. 2015a). The D-factor at $0\buildrel{\circ}\over{.} 1$ is smaller than most of the other dwarf spheroidals (Bonnivard et al. 2015a). Though Car II has similar heliocentric distance and velocity dispersion to Ret II, its J-factor is smaller because it has a larger ${r}_{1/2}$ (Pace & Strigari 2018). Car II is therefore not the most promising individual target for a dark matter annihilation signal but will be a useful addition in stacked analyses.

We applied the same methodology to the four star sample of Car III. We find the integrated J-factor within solid angles of radii $\theta ={\alpha }_{c},0.1,0.2,0\buildrel{\circ}\over{.} 5$ to be ${\mathrm{log}}_{10}(J/{\mathrm{GeV}}^{2}\,{\mathrm{cm}}^{-5})$ = ${19.8}_{-0.9}^{+1.0},{19.9}_{-0.9}^{+1.0},{20.1}_{-0.9}^{+1.0},{20.2}_{-0.9}^{+1.0}$, respectively. ${\alpha }_{c}=0\buildrel{\circ}\over{.} 08$ for Car III. The D-factor for Car III within $\theta ={\alpha }_{c}/2,0.1,0.2,0\buildrel{\circ}\over{.} 5$ is ${\mathrm{log}}_{10}(D/\mathrm{GeV}\ \,\ {\mathrm{cm}}^{-2})$ = ${17.2}_{-0.4}^{+0.5},{17.8}_{-0.5}^{+0.5},{18.3}_{-0.5}^{+0.6},{18.8}_{-0.7}^{+0.6}$. The J-factor estimation of Car III is larger than that of Car II due to its proximity, smaller size, and larger (but uncertain) velocity dispersion. From our analysis, Car III potentially has one of the largest J-factors. However, given the very small stellar kinematic sample and the uncertain classification of Car III, it is premature to draw strong conclusions about the suitability of Car III as a dark matter annihilation target. As discussed in Section 4.1, the large velocity dispersion could result from binary star motions, small number statistics, or possible tidal effects. As a cautionary case in point, the Triangulum II ultra-faint dwarf galaxy has recently had its J-factor values revised downward due to the identification of previously unsolved binary stars (Genina & Fairbairn 2016; Kirby et al. 2017). In addition, the velocity dispersion of Boötes II has likely been overestimated in past determinations due to the presence of one binary star (Koch et al. 2009; Ji et al. 2016).

We searched for excess γ-ray emission coincident with Car II and Car III using eight years of LAT data (2008 August 4 to 2016 August 5) passing the P8R2_SOURCE event class selection from 500 MeV to 500 GeV. The low-energy bound of 500 MeV was selected to mitigate the impact of leakage from the bright limb of the Earth because the LAT point-spread function broadens considerably below that energy. The high-energy bound of 500 GeV is chosen to mitigate the effect of the increasing residual charged-particle background at higher energies (Ackermann et al. 2015b). To remove γ-rays produced by cosmic-ray interactions in the Earth's limb, we rejected events with zenith angles greater than 100^◦. To analyze data coincident with Car II and Car III, we used $10^\circ \times 10^\circ$ regions of interest (ROIs) centered on each object. Data reduction was performed using ScienceTools version 11-05-03.⁴⁰

We used the maximum-likelihood analysis pipeline described by Ackermann et al. (2014) to test for γ-ray emission coincident with Car II and III in excess of the known astrophysical backgrounds. The background model for the ROI includes Galactic interstellar emission (Acero et al. 2016), isotropic emission,⁴¹ and point sources from a catalog derived from four years of data (3FGL; Acero et al. 2015). Car II and Car III reside in a region of the sky where the diffuse γ-ray background is relatively smooth (Galactic latitude of $\sim \,15^\circ$), and the nearest 3FGL catalog source is $\sim 2^\circ$ away.

We first created a detection significance map for the entire $10^\circ \times 10^\circ$ ROI by rastering a putative point source with fixed power-law spectrum (${dN}/{dE}\sim {E}^{-2}$) across the ROI in $0\buildrel{\circ}\over{.} 1$ steps and computing the improvement in the delta log-likelihood test statistic (TS; Mattox et al. 1996). This procedure led to the identification of three additional point-like source candidates in the region, none of which is within $3^\circ$ of Car II or III (Figure 8). The TS values obtained at the locations of Car II and Car III are 0.16 and 4.2, respectively, both consistent with the background-only hypothesis. We note that Car II and Car III would not be resolvable as independent sources given the resolution of the LAT instrument, which is $\sim 1^\circ$ at 1 GeV and asymptotes to ∼01 above 10 GeV. The TSs associated with Car II and Car III are thus correlated, and can be attributed to a single excess of counts located $\sim \,0\buildrel{\circ}\over{.} 7$ from Car III at ($\alpha ,\delta$) = (1145, −579).

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To search for γ-ray emission consistent with the annihilation of a dark matter particle into standard model products, we fit the γ-ray data coincident with Car II and Car III using a variety of spectral models generated by DMFit (Jeltema & Profumo 2008; Ackermann et al. 2014). We scan a range of dark matter masses spanning from 2 GeV to 10 TeV and annihilating through the $b\bar{b}$ and ${\tau }^{+}{\tau }^{-}$ channels. The most significant excess has TS = 6.2 and occurs for a dark matter particle with mass 35.4 GeV annihilating through the ${\tau }^{+}{\tau }^{-}$ channel. Given that the statistical significance of this excess is well below the typical point-source detection criteria of the LAT (TS = 25), we calculate limits on the dark matter annihilation cross section, $\langle \sigma v\rangle$, using the J-factors derived in Section 4.3. We find that Car II (Car III) can be used to constrain $\langle \sigma v\rangle \lt 2.2\times {10}^{-24}$ cm³ s⁻¹ (3.3 × 10⁻²⁵ cm³ s⁻¹) for 100 GeV dark matter particles annihilating through the $b\bar{b}$ channel. These constraints are ∼100 (∼10) times larger than the thermal-relic cross section (i.e., Steigman et al. 2012). We again caution against overinterpreting the constraints derived from Car III because the J-factor value of Car III is derived from a very small stellar kinematic sample.