Stellar Metallicities from SkyMapper Photometry I: A Study of the Tucana II Ultra-faint Dwarf Galaxy

Observations of the Tucana II UFD were taken between 2015 July 19 and 2015 December 15 with the 1.35 m SkyMapper telescope at Siding Springs Observatory, Australia, as part of an auxiliary program to obtain deep photometry of UFDs. Table 1 summarizes our photometric observations. The SkyMapper camera has 32 4k × 2k CCD chips covering a 234 by 240 field of view, which enabled the imaging of the entire Tucana II UFD (r_1/2 ∼ 10'; Bechtol et al. 2015; Koposov et al. 2015) in each frame. Images were taken with the custom SkyMapper u, v, g, and i filters (Bessell et al. 2011).

We developed a data reduction pipeline for these data separately from the one used by the SkyMapper collaboration (Wolf et al. 2018), because no pipeline existed when the data for this project were collected in late 2015. The reduction procedure for SkyMapper data is nontrivial due to the presence of systematic pattern-noise signatures in the raw data that, if not properly removed, would impair any photometric measurements, as can be seen in Figure 1. We therefore explicitly outline each step of our data reduction procedure in Section 2.1.1, and describe our handling of the pattern-noise removal process in Section 2.1.2. We then discuss the precision and completeness of our photometry in Section 2.1.3.

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2.1.1. Data Reduction

2.1.2. Pattern-noise Removal

2.1.3. Completeness and Photometric Precision

We used the Turbospectrum synthesis code (Alvarez & Plez 1998; Plez 2012), MARCS model atmospheres (Gustafsson et al. 2008), and a line list composed of all lines between 3000 and 9000 Å available in the VALD database (Piskunov et al. 1995; Ryabchikova et al. 2015) to generate our grid of flux-calibrated synthetic spectra. We replaced the lines of the CN molecule in the VALD line list with those from Brooke et al. (2014) and Sneden et al. (2014), those of CH with lines from Masseron et al. (2014) and Brooke et al. (2013), and those of C₂ with lines from Ram et al. (2014). This resulted in a line list with ∼800,000 lines. An example of two synthetic spectra with different metallicities is shown in Figure 2. The ¹²C/¹³C isotope ratio was assumed following the relation presented in Kirby et al. (2015), which is based on Figure 4 in Keller et al. (2001). We note that solar abundances for the MARCS model atmospheres are adopted from Grevesse et al. (2007).

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For the analysis of RGB stars, we generated a grid of spectra with stellar parameters ranging from T_eff = 4000 to 5700 K, $\mathrm{log}g=1.0$ to 3.0, and [Fe/H] = −4.0 to −0.5. We opted to use the "standard" spherical model geometry within the MARCS model atmospheres. We used a microturbulence of 2 km s⁻¹. The α-enhancement was set to [α/Fe] = 0.4 for stars with [Fe/H] < −1.0, and linearly decreased between $-1\lt {\rm{[Fe/H]}}\lt 0$ such that [α/Fe] = 0 when [Fe/H] = 0.

For the analysis of MSTO stars, we generated a grid of spectra with stellar parameters ranging from T_eff = 5600 to 6700 K, $\mathrm{log}g=3.0$ to 5.0, and [Fe/H] = −4.0 to −0.5. We opted to use plane-parallel model geometries as part of the MARCS model atmospheres, and used the same microturbulence value and [α/Fe] trends as for the RGB grid.

For each synthetic spectrum, we calculated the absolute magnitude from the flux through each of the SkyMapper u, v, g, and i filters. First, we retrieved the bandpasses of each of the SkyMapper filters (Bessell et al. 2011) from the Spanish Virtual Observatory (SVO) Filter Profile Service (Rodrigo et al. 2012).⁴ We then closely followed the methodology in Casagrande & VandenBerg (2014) to generate synthetic magnitudes for each of our synthetic spectra. We computed synthetic AB magnitudes, in which a flux density of ${F}_{\nu }=3.63\times {10}^{-20}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}$ is defined as having m_AB = 0, through each filter by applying the following formula

$$\begin{eqnarray}&&{m}_{\mathrm{AB}}=-2.5\mathrm{log}\displaystyle \frac{{\int }_{{\nu }_{i}}^{{\nu }_{f}}{\nu }^{-1}\,{F}_{\nu }\,{T}_{\eta }\,d\nu }{{\int }_{{\nu }_{i}}^{{\nu }_{f}}{\nu }^{-1}\,{T}_{\eta }\,d\nu }-48.60,\end{eqnarray} \tag{ 1 }$$

where F_ν is the flux from a flux-calibrated synthetic spectrum as a function of wavelength, T_η is the system response function over the bandpass of the filter, and ν_i and ν_f are the lowest and highest wavelengths of the bandpass filter. We note that small zero-point offsets on the order of ∼0.02 are possible in this formalism, as briefly mentioned in Casagrande & VandenBerg (2014). However, we find that we need to apply a zero-point correction of +0.06 mags to our synthetic v magnitudes to derive accurate metallicities, as described in the penultimate paragraph of Section 4.4.

The SkyMapper v filter has been designed to be sensitive to stellar metallicity (e.g., Keller et al. 2007). This sensitivity arises from the presence of the strongest metal absorption line, Ca ii K, at 3933.7 Å in the bandpass. Since the strength of the Ca ii K line scales with the overall metallicity of the star, the overall flux measured through the filter is thus governed by the stellar metallicity. An example is illustrated in Figure 2, where synthetic spectra of stars with [Fe/H] = −1.0 and −3.0 are juxtaposed, and the bandpass of the v filter is overplotted.

Making use of the relation between Ca ii K absorption and metallicity, previous work by Keller et al. (2012) suggested that metal-poor stars can be discriminated from metal-rich ones in the v−g − 2 × (g−i) versus g − i space. Inspired by this, we instead choose to utilize v−g − 0.9 × (g−i) versus g − i as a discriminator, which we have already successfully used to identify metal-poor dwarf galaxy stars using our custom SkyMapper data and SkyMapper DR1.1 (Chiti et al. 2018; Chiti & Frebel 2019).

As part of this work, we plotted v−g − 0.9 × (g−i) versus g − i of the photometry from the synthetic spectra (described in Section 3) on the left panels of Figure 3. We did so for four different $\mathrm{log}g$ values, from 1 to 4. As can be seen, stars of a given metallicity form well-behaved contours, allowing us to easily interpolate between these contours to derive quantifiable stellar metallicities. Hence, we interpolated between these metallicity contours with a piecewise 2D cubic spline interpolator using the scipy.interpolate.griddata function, and thereby derived photometric metallicities for every star with v, g, and i photometry. We flagged each of the stars with photometry placing them beyond the upper (most metal-poor) bounds given these contours, and set their metallicity to the boundary value (i.e., [Fe/H] = −4.0).

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As is shown on the left panel in Figure 3, the contours used for measuring metallicity depend on the surface gravity $\mathrm{log}g$. It is thus necessary to assume an initial $\mathrm{log}g$ before attempting any metallicity calculations. We initially assume $\mathrm{log}g=2$, which should roughly correspond to the surface gravity of stars on the RGB of Tucana II.

Upon obtaining these initial metallicities, photometric surface gravities were then derived as described in Section 4.2. After that, the photometric surface gravities were used to determine our final photometric metallicities. The average change in the photometric metallicities upon updating the surface gravity is marginal (∼0.02 dex for stars with $\mathrm{log}g\lt 3.0$), suggesting that one iteration is sufficient for convergence. Section 4.7 discusses our final adopted metallicity uncertainties.

The SkyMapper u and v filters can be used to discriminate the surface gravities of stars. These filters bracket the Balmer Jump at 3646 Å, which is sensitive to the H⁻ opacity—which, in turn, is a function of the $\mathrm{log}g$ of the star (e.g., Murphy et al. 2009). Similar to the method outlined in Section 4.1 for deriving photometric metallicities, plotting u−v − 0.9 × (g−i) versus g − i can discriminate stellar surface gravities. This behavior is illustrated in the right panels in Figure 3, based on the synthetic spectra described in Section 3. We then use the same interpolation technique described in Section 4.1 to derive photometric surface gravities from the u−v − 0.9 × (g−i) contours.

We use the first-pass synthetic metallicities from Section 4.1 to choose the corresponding set of $\mathrm{log}g$ contours from which to derive surface gravities. Since we use surface gravities solely to remove foreground main-sequence stars from our sample, we opt not to iteratively remeasure $\mathrm{log}\,g$ with updated photometric metallicity values.

Since a CN molecular absorption feature is located at ∼3870 Å in the bandpass of the SkyMapper v filter (encompassing ∼3600 to ∼4100 Å), its spectral morphology can become strong enough to systematically affect the flux through the filter. The strength of the CN feature significantly depends on the carbon abundance and effective temperature of the star: a higher carbon abundance and a lower effective temperature lead to a stronger CN absorption feature—which, in turn, leads to an artificially higher photometric metallicity. This could systematically skew photometric metallicity results, since a significant fraction of metal-poor stars tend to be enhanced in carbon ([C/Fe] > 0.7) and are known as carbon-enhanced metal-poor (CEMP) stars. Eighty percent of stars with [Fe/H] < −4.0 and even 24% of stars with [Fe/H] < −2.5 have [C/Fe] > 0.7 (Placco et al. 2014). We thus attempt to quantify these effects in order to gauge how our photometric metallicities derived from the v filter are influenced by the carbon abundance.

We test the effect of the strength of the CN feature on the flux through the SkyMapper v filter by regenerating our grid of synthetic spectra, as described in Section 3. We do so by varying the carbon abundances of the synthetic spectra between [C/Fe] = −0.5 and [C/Fe] = 1.0 in intervals of 0.5. We then derived the v − g − 0.9 × (g−i) index and g − i colors for these synthetic spectra, and obtained the corresponding photometric metallicities following the procedure described in Section 4.1.

In Figure 4, we plot the changes in the resulting photometric metallicity, relative to a baseline of [C/Fe] = 0, for four different carbon abundances as a function of surface gravity and effective temperature, corresponding to our RGB grid in Table 2. The [C/Fe] = 0 baseline, however, is temperature-dependent because the strength of the CN band is temperature-sensitive. Decreasing the carbon abundance by 0.5 dex to gauge the corresponding effect on the photometric metallicity leads minimal effects of ∼0.1 dex, as seen in Figure 4. However, among the cooler stars (T_eff < 4700 K) with [C/Fe] > 0.5, we find significant changes (the ultimately measured [Fe/H] of a CEMP star gets artificially increased by Δ[Fe/H] ∼ 0.5). Accordingly, some true CEMP stars may always remain "hidden" in our samples, especially among the cooler stars. No significant effects are apparent otherwise, because the CN feature is relatively weak for all these stars, meaning the feature does not influence the overall flux through the v filter. Therefore, our analysis suggests that we would still select moderately cool (T_eff ∼ 4700 K) CEMP stars as very metal-poor candidates. This result is supported by the fact that we can reidentify all three members of Tucana II that are CEMP stars, all of which are warmer than 4600 K (Chiti et al. 2018) but are not greatly enhanced in carbon ([C/Fe] < 1.0 before applying the carbon correction following Placco et al. (2014)).

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Overall, we conclude that, while our derived photometric metallicities are dependent on the carbon abundance and effective temperature of stars, we can select stars with (uncorrected) $[{\rm{C}}/\mathrm{Fe}]\lesssim 0.5$ that also have [Fe/H] ∼ −2.5 and have T_eff ≳ 4800 K with sufficient precision (within +0.3 dex). Stars that turn out to have, e.g., [C/Fe] ∼ 0.35, if on the RGB ($\mathrm{log}\,g\sim 1.5$), would likely become CEMP stars after applying a correction for the evolutionary status of the star following Placco et al. (2014). Correspondingly, a star with a carbon abundance of up to [C/Fe] ∼ 1 and [Fe/H] ∼ −2.5 could principally still be identified as a candidate member of a UFD (${\rm{[Fe/H]}}\lesssim -1.5)$ when it has T_eff ≳ 5000 K, because its photometric metallicity would be shifted by Δ[Fe/H] ≲ 1.0.

CEMP-s stars tend to be the most carbon-enhanced ([C/Fe] ≳ 1.25 at ${\rm{[Fe/H]}}\gtrsim -2.8$) subclass of CEMP stars, and would thus systematically have among the strongest CN bands (Yoon et al. 2016), somewhat irrespective of temperature. Consequently, CEMP-s stars would appear as much more metal-rich stars (we estimate by about 1 dex or more), supposing they were on the RGB. Hence, any CEMP-s star with, e.g., [Fe/H] = −2.5 would be measured as having a metallicity of −1.5 dex or higher. These metallicities tend to be excluded from our selection, as we are focused on more metal-poor stars, so our sample could thus be regarded as mostly free of CEMP-s stars.

At lower metallicities, the effect of the CN absorption on the measured [Fe/H] is somewhat mitigated. After repeating our procedure for [Fe/H] = −4.0, a star with [C/Fe] = 1.0 will affect the measured [Fe/H] by ∼0.3 dex when it has T_eff ≳ 4500 K. When [C/Fe] is increased to 2.0, moderately cool (T_eff ∼ 4800 K) stars will be affected by up to 0.75 dex due to the highly nonlinear growth of the CN feature. Nevertheless, we note that, to first order, the CN feature of a star with [Fe/H] = −5.0 and [C/Fe] = 2.0 should be similar to that of a star with [Fe/H] = −4.0 and [C/Fe] = 1.0, assuming similar stellar parameters. This implies that most CEMP stars with ${\rm{[Fe/H]}}\lt -4.0$ should be identifiable (except, perhaps, for very extreme cases).

In general, these results suggests that any MDF derived from SkyMapper photometry will likely be upscattered to some degree. According to our models, the most metal-poor ([Fe/H] ∼ −4.0), moderately cool (T_eff ∼ 4800 K) stars with a significant carbon enhancement ([C/Fe] ∼ 2.0) will be affected by up to 0.75 dex. High-resolution spectroscopic follow-up observations of stars in the SkyMapper data set can confirm the extent of these CN feature-induced changes.

Globular clusters are old (∼10 Gyr) and metal-poor ([Fe/H] < −1.0) star clusters. The dispersion of the metallicities of their member stars is generally small (${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}\sim 0.05$), as discussed in, e.g., Carretta et al. (2009). The stellar population of individual globular clusters therefore provides a useful test of the precision of deriving photometric metallicities, since most of the dispersion in the photometric metallicities of member stars can be ascribed to the uncertainty in our SkyMapper data and broader methodology.

While we did not observe any globular clusters as part of our observing program, a number of globular clusters are located within the footprint of the first data release (DR1.1) of the SkyMapper Southern Survey (Wolf et al. 2018). Thus, we retrieved SkyMapper u, v, g, and i photometry from the DR1.1 catalog for member stars of all globular clusters in the southern hemisphere with a distance less than 10 kpc. Specifically, we used the Harris (2010) catalog of globular clusters, an update to the older Harris (1996) catalog, and retrieved all stars within three times the tidal radius of each globular cluster. This resulted in the retrieval of 17 globular clusters with metallicities ranging from [Fe/H] = −2.27 to [Fe/H] = −0.99 as measured in Carretta et al. (2009).

Upon retrieving SkyMapper u, v, g, i photometry from the public catalog, we selected likely member stars of each globular cluster. We first overlaid 13 Gyr Dartmouth isochrones (Dotter et al. 2008) with metallicities and distance moduli matching those from Carretta et al. (2009), and then selected all stars with g − i within 0.3 mag of the isochrone. Next, we computed the photometric metallicities and surface gravities of these candidate members, using the methods described in Sections 4.1 and 4.2.

We used proper motion measurements from the second data release from the Gaia mission (DR2; Gaia Collaboration et al. 2016, 2018; Salgado et al. 2017) as an additional avenue to exclude nonmembers, since members of a globular cluster should have similar proper motions. To identify the systemic proper motion of each cluster, we generated 2D histograms of the proper motions with a bin size of 0.2 mas yr⁻¹ in μ_α and μ_δ. We then fitted a 2D elliptical Gaussian to the overdensity in each proper motion histogram, and selected all stars enclosed within the 3σ bounds of the Gaussian.

We then chose to only retain stars with photometric surface gravities of $\mathrm{log}\,g\lt 3$, as the depth of the public SkyMapper photometry with usable photometric metallicity precision (g ∼ 16) does not extend to the main sequences in our sample of globular clusters. We also only retained stars with photometric metallicity uncertainties below 0.5 dex and photometric surface gravity uncertainties below 0.75 dex. The determination of the uncertainties is described in Section 4.7. Each step of our selection of likely member stars of globular clusters is shown in Figure 5. We finally derive an overall metallicity of each globular cluster by taking the average of the photometric metallicities, weighted by the inverse-squared photometric metallicity uncertainties, of each remaining sample of likely member stars. Two histograms of the photometric metallicities of likely member stars for NGC 6254 and NGC 6809 are shown as examples in Figure 5.

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For all clusters for which we identify N > 1 member stars, we plotted the residuals of our derived cluster metallicities with respect to spectroscopically derived metallicities of each cluster from Carretta et al. (2009). We found that applying an offset of 0.06 mags to our synthetic v magnitudes removed a ∼0.1 dex systematic offset between our metallicities and those in Carretta et al. (2009). Thus, we applied this offset to our contours and rederived our cluster metallicities. We note that all photometric metallicities and $\mathrm{log}\,g$ values presented in this paper are calculated with this offset of +0.06 mags in the synthetic v magnitudes.

The final residuals of our cluster metallicities with respect to Carretta et al. (2009) are shown in Figure 6. A negligible final offset of −0.02 dex is found, with a standard deviation of 0.16 dex with respect to the values from Carretta et al. (2009). We thus take 0.16 dex as an estimate of the intrinsic uncertainty from our method as further discussed in Section 4.7. Table 3 lists our measured photometric metallicities as well as spectroscopic metallicities from Carretta et al. (2009).

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Seven stars in Tucana II have high-resolution spectroscopic metallicities presented in Chiti et al. (2018). We compare our photometric metallicities and surface gravities for those seven stars to the spectroscopically determined values. The results are shown in the left panel of Figure 7 and in Figure 8.

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For the metallicities, we find a mean offset between our values of 0.09 dex (in which we measure a higher [Fe/H]) with a standard deviation of 0.34 dex. This is excellent agreement, given that all but one photometric metallicity is within 1σ agreement of the metallicities derived from high-resolution spectroscopy (see Section 4.7 for a discussion of the derivation of these uncertainties). Additionally, the mean carbon abundance of these stars is $[{\rm{C}}/\mathrm{Fe}]=0.35$ and their mean T_eff is 4870 K. According to Figure 4, this would suggest that we should overestimate the photometric metallicity by ∼0.1 dex.

We also find generally excellent agreement between our photometric $\mathrm{log}g$ values and those in Chiti et al. (2018), as shown in Figure 8. The mean offset is −0.09 dex, meaning we measure a lower $\mathrm{log}g$ relative to those derived from high-resolution spectroscopy. The standard deviation of the residual between our $\mathrm{log}g$ measurements is 0.22 dex. The standard deviation and mean offset are almost entirely driven by the one outlier, labeled as TucII-078 in Chiti et al. (2018), at $\mathrm{log}g\sim 1.9$ in Figure 8. Excluding it would change the offset to +0.02 dex and the standard deviation to 0.11 dex. However, the presence of this outlier is not entirely surprising, given that Chiti et al. (2018) derive a correspondingly large uncertainty of 0.67 dex in the $\mathrm{log}\,g$ of TucII-078.

We also compare our photometric metallicities to [Fe/H] values from Walker et al. (2016), who derived these values from R ∼ 18,000 and R ∼ 10,000 spectra of the Mg b region (∼5150 Å) for 137 candidate member stars in the vicinity of Tucana II. We chose to only compare with stars in Walker et al. (2016) that had metallicity uncertainties <0.20 dex, in order to ensure a high-quality comparison. We further only compared to stars with [Fe/H] < −1.0 in Walker et al. (2016), as our grid of synthetic photometry only extends to [Fe/H] = −0.5. We find good agreement between our photometric metallicity measurements and those in Walker et al. (2016), with a mean offset of −0.12 dex, meaning we measure a lower [Fe/H], and a standard deviation between our measurements of 0.23 dex.

We assume that the uncertainty in each photometric [Fe/H] value is a combination of (1) intrinsic uncertainty from our methodology and (2) random uncertainty that is propagated from uncertainties in the photometry. The intrinsic uncertainty in our methodology is assumed to be 0.16 dex, which is the standard deviation of the residuals of our photometric metallicities for globular clusters (see Section 4.4). We thus take into account that the mean photometric [Fe/H] value for each cluster is usually derived from a large number of stars (N > 10), suggesting that the standard error in each of these values is generally small. We therefore assume that the 0.16 dex scatter in the residuals is mostly driven by the intrinsic uncertainty in our method, which we adopt as such when calculating the final uncertainty in our photometric [Fe/H] values. The random uncertainty is derived by adding in quadrature the difference in photometric [Fe/H] obtained after varying each the v, g, and i magnitudes by their 1σ photometric uncertainties and redetermining final values. If the variation of any of the magnitudes by their 1σ photometric uncertainties takes them beyond the bounds of the grid of synthetic photometry, then a conservative uncertainty of 0.75 dex is adopted.

The intrinsic and random uncertainties are then added in quadrature to derive final uncertainties on our photometric [Fe/H] values. Our final photometric metallicity uncertainties appear to be reasonable, as the medians of the uncertainties of the photometric metallicities in the left and right panels of Figure 7 are 0.31 dex and 0.21 dex, respectively. These uncertainties are similar to the standard deviations of the data points in each of these panels of 0.34 dex and 0.23 dex, respectively. For another estimate of the precision of our method, we can thus pool together the residuals in Figure 6 and 7 and compute their standard deviation. Upon doing this, we find that the standard deviation of the residuals is 0.20 dex for data points with [Fe/H] > −2.5 and 0.34 dex for those with [Fe/H] < −2.5.

The uncertainty in the photometric $\mathrm{log}g$ is calculated in a similar manner. The random uncertainty is derived by adding in quadrature the difference in photometric $\mathrm{log}g$ after varying the u, v, g, and i magnitudes by their 1σ photometric uncertainties. The intrinsic uncertainty is assumed to be 0.20 dex, since this leads to the median uncertainty of the photometric $\mathrm{log}g$ values in Figure 8 agreeing with the standard deviation of the residuals.

We performed several preliminary steps to prepare our source catalog for analysis. We first removed galaxies by crossmatching our sources with those in the DES Y1A1 gold catalog (Drlica-Wagner et al. 2018). Following the criteria and procedure described in Desai et al. (2012) and Bechtol et al. (2015), we excluded all sources from the DES catalog with the parameter SPREAD_MODEL_I > 0.003 (Desai et al. 2012), in order to retain only stars. We then measured photometric metallicities and surface gravities of every star within the parameters of our grid of synthetic photometry, and compiled their proper motion measurements from the Gaia DR2 catalog (Gaia Collaboration et al. 2016, 2018). Next, we compiled a list of confirmed member stars of Tucana II from Walker et al. (2016) and Chiti et al. (2018), and confirmed nonmember stars in the vicinity of Tucana II from Walker et al. (2016). Walker et al. (2016) derived membership probabilities for 137 stars in the vicinity of the Tucana II UFD. Two new confirmed member stars of Tucana II had already been identified by Chiti et al. (2018) from the data presented in this paper.

We consider all stars with a membership probability >95% in Walker et al. (2016) to be likely members in our subsequent analysis. Of particular interest in this regard is whether likely member stars could be separated from nonmember stars using our photometric stellar parameter measurements and Gaia proper motion data. In Figure 9, we illustrate several tests to qualitatively separate the nonmembers and likely members from Walker et al. (2016) and Chiti et al. (2018). The top two panels demonstrate that the majority of likely members separate from nonmembers in the color–color plots we employ to measure photometric stellar parameters. The bottom two panels of Figure 9 show that, when combining metallicity, $\mathrm{log}g$, and proper motion information, the confirmed members are largely distinct from foreground stars. However, three members from Walker et al. (2016) do not separate as cleanly. One of these stars is fairly metal-rich ([Fe/H] ∼ −1.3), about 1 dex more so than the other member stars. It is likely a metal-rich or carbon-enhanced (see Section 4.3) member of the UFD, given its separation from the foreground in $\mathrm{log}g$ and proper motion. The other two stars may indeed be nonmembers, given our measurements of their photometric metallicity ([Fe/H] > −1) and surface gravities ($\mathrm{log}\,g\gt 2.5$). Furthermore, the slight separation of these two stars from the other confirmed member stars in proper motion space, as shown in the bottom right panel of Figure 9, supports this notion. However, since these two stars are faint (g > 20) and their measurements are correspondingly less precise, firm arguments about their membership status cannot be made.

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In conclusion, however, we demonstrate that photometric metallicities and surface gravities, especially in the case of high-quality measurements, can clearly separate UFD member stars from foreground stars. Furthermore, the Gaia proper motion data is useful in identifying likely members that may otherwise be metal-rich (i.e., the one star at [Fe/H] ∼ −1.3 in the bottom left plot of Figure 9).

In order to quantitatively derive properties (i.e., MDF) of the Tucana II UFD, member stars need to be selected well despite the presence of large numbers of foreground stars. Given that we derive photometric $\mathrm{log}\,g$ and [Fe/H] values, we can immediately remove foreground metal-rich, and main sequence stars from our sample to alleviate the issue of significant foreground contamination. Then, as previously demonstrated in, e.g., Pace & Li (2019), we use a combination of the spatial location of each star and its Gaia DR2 proper motion measurements to derive quantitative membership probabilities for each star. The bottom panels of Figure 9 already qualitatively show that using photometric metallicity, $\mathrm{log}g$, and proper motions enable adequate membership identification.

To quantify the membership likelihood of each star, we then proceed with several steps. First, we remove stars that are either metal-rich ([Fe/H] > −1.0), not on the RGB ($\mathrm{log}g\geqslant 3.0$), or fainter than g = 20. We apply the brightness cut to ensure that our stars have reliable photometric $\mathrm{log}g$ and [Fe/H] values. We apply the metallicity cut since no metal-rich stars are known as members of UFDs (see i.e., Frebel & Norris 2015; Simon 2019 for reviews), and we apply the $\mathrm{log}g$ cut as stars in Tucana II down to g = 20 are at the base of the RGB or higher up.

We model the remaining set of metal-poor giants using a mixture model with the following likelihood function:

$$\begin{eqnarray}\begin{array}{rcl}{{ \mathcal L }}_{\mathrm{Total}} & = & {f}_{\mathrm{mem}}{{ \mathcal L }}_{\mathrm{sp},\mathrm{mem}}{{ \mathcal L }}_{\mathrm{pm},\mathrm{mem}}\\ & & +(1-{f}_{\mathrm{mem}}){{ \mathcal L }}_{\mathrm{sp},\mathrm{nonmem}}{{ \mathcal L }}_{\mathrm{pm},\mathrm{nonmem}}\end{array}\end{eqnarray} \tag{ 2 }$$

where f_mem denotes the fraction of member stars of Tucana II. The spatial distribution of member stars of Tucana II is assumed to follow an exponential profile, following Martin et al. (2008) and Longeard et al. (2020), with a likelihood function given by

$$\begin{eqnarray}&&{{ \mathcal L }}_{\mathrm{sp},\mathrm{mem}}=\displaystyle \frac{\exp \left(-\tfrac{R}{{R}_{e}}\right)}{2\pi {R}_{e}(1-\epsilon )}/{\int }_{S}\displaystyle \frac{\exp \left(-\tfrac{R}{{R}_{e}}\right)}{2\pi {R}_{e}(1-\epsilon )}\,{dS},\end{eqnarray} \tag{ 3 }$$

where is the ellipticity, R_e is the exponential radius, and R is the elliptical radius, given by

$$\begin{eqnarray}\begin{array}{rcl}R & = & \left({\left(\displaystyle \frac{1}{1-\epsilon }\left((x-{x}_{0})\cos \theta -(y-{y}_{0})\sin \theta \right)\right)}^{2}\right.\\ & & +{\left.{\left((x-{x}_{0})\sin \theta +(y-{y}_{0})\cos \theta \right)}^{2}\right)}^{1/2},\end{array}\end{eqnarray} \tag{ 4 }$$

where x₀ and y₀ are the R.A. and decl. of the center of Tucana II, as measured in Koposov et al. (2015), and θ is the position angle of the elliptical distribution. x and y are the distances from the center of Tucana II along the direction of R.A. and decl., respectively. The spatial distribution of nonmembers, ${{ \mathcal L }}_{\mathrm{sp},\mathrm{nonmem}}$ is assumed to be uniform.

The likelihood functions for the proper motions of members and nonmembers, ${{ \mathcal L }}_{\mathrm{pm},\mathrm{mem}}$ and ${{ \mathcal L }}_{\mathrm{pm},\mathrm{nonmem}}$ are assumed to be bivariate Gaussians, following the formalism presented in, e.g., Longeard et al. (2020). We use a standard bivariate Gaussian to model the foreground stars, but use the following probability density to model the members of Tucana II:

$$\begin{eqnarray}&&\begin{array}{l}p=\displaystyle \frac{{\left(2\pi \right)}^{-1}}{{\sigma }_{{\mu }_{\alpha }}\,{\sigma }_{{\mu }_{\delta }}}\times \exp \\ \times \left[-\displaystyle \frac{{\left({\mu }_{\alpha }-{\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{TII}}\right)}^{2}}{2{\sigma }_{{\mu }_{\alpha }}^{2}}-\displaystyle \frac{{\left({\mu }_{\delta }-{\left\langle {\mu }_{\delta }\right\rangle }_{\mathrm{TII}}-k\left({\mu }_{\alpha },-,{\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{TII}}\right)\right)}^{2}}{2{\sigma }_{{\mu }_{\delta }}^{2}}\right]\end{array}\end{eqnarray} \tag{ 5 }$$

where μ_α is Gaia proper motion in the direction of R.A., μ_δ is the proper motion is the direction of decl., ${\sigma }_{{\mu }_{\alpha }}$ and ${\sigma }_{{\mu }_{\delta }}$ are their corresponding uncertainties, ${\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{TII}}$ and ${\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{TII}}$ denote the systemic proper motion of the Tucana II UFD, and k adds the analog of a position angle to the bivariate Gaussian. Identically to Pace & Li (2019), we assume that the intrinsic proper motion uncertainties are much smaller than the observational uncertainties in proper motion, and thus the width of the bivariate Gaussian for the UFD members is solely determined by the uncertainties in proper motions.

We sample the likelihood function using the emcee package (Foreman-Mackey et al. 2013), which uses the ensemble sampler from Goodman & Weare (2010). There were eight free parameters in our sampling, namely f_mem, k, ${\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{TII}}$, ${\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{TII}}$, ${\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{MW}}$, ${\left\langle {\mu }_{\alpha }\right\rangle }_{\mathrm{MW}}$, ${\sigma }_{{\mu }_{\alpha ,\mathrm{MW}}}$, and ${\sigma }_{{\mu }_{\delta ,\mathrm{MW}}}$. The parameters R_e, , θ were fixed to the values provided in Koposov et al. (2015). We initialized the sampler with 200 walkers, with 2000 steps after a burn-in period of 500 steps to ensure a good sampling of the posterior distributions. The membership probability was then simply assumed to be the ratio of the membership terms to the total likelihood in Equation (2).

In Table 4, Figure 10, and the top panels of Figure 11, we present our final membership probability for each star. As expected, we find a number of likely members near the nominal center of Tucana II. However, interestingly, we also find several stars well-separated from the center of the galaxy that also have a likelihood of being members.

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Table 4.  Photometric Metallicities of Stars with Tucana II Membership Probability p_mem > 0.50

R.A. (deg) (J2000)	Decl. (deg) (J2000)	${g}_{\mathrm{SM}}$	iSM	pmem	[Fe/H]phot	σ([Fe/H]phot)
342.671075	−58.518976	18.58	17.94	1.00	−2.66	0.26
342.959507	−58.627823	18.17	17.42	1.00	−2.40	0.19
343.136343	−58.608469	19.42	18.77	1.00	−3.56	0.75
342.929412	−58.542702	18.73	18.06	1.00	−2.89	0.31
343.089087	−58.518710	19.51	18.97	1.00	−1.16	0.21
342.753839	−58.537255	19.37	18.81	0.99	−1.21	0.20
342.784619	−58.552258	18.57	17.90	0.99	−2.27	0.21
342.715112	−58.575714	18.76	18.10	0.99	−2.92	0.32
343.652659	−58.616101	18.71	18.10	0.99	−3.08	0.41
342.537105	−58.499739	18.72	18.02	0.96	−3.73	0.75
341.916360	−58.402040	19.09	18.47	0.75	−1.05	0.19
342.352876	−58.346508	18.83	18.13	0.73	−1.39	0.18
342.687905	−58.939023	18.98	18.33	0.64	−3.44	0.75

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To ensure that our identification of likely members is accurate, we investigated whether we recovered the known sample of Tucana II members from Walker et al. (2016) and Chiti et al. (2018). We only considered stars with DES g < 20 in Walker et al. (2016), as this is comparable to the initial magnitude cut for our sample. We consider stars that have membership probability p > 0.95 in Walker et al. (2016) and the two additional members presented in Chiti et al. (2018) to be likely members, and stars with membership probability p < 0.50 in Walker et al. (2016) to be likely nonmembers. Results of our comparison are shown in Figure 11.

As an additional check, we also compared our catalog of likely members with that of Pace & Li (2019), who identified likely members based on Gaia DR2 proper motions and DES photometry. We find that we recover their entire sample of 10 likely (p > 0.50) members of the RGB of Tucana II brighter than g ∼ 19.6. We additionally identify three likely member stars not found as having membership probability greater than 0.50 in their catalog. We note that two of our likely members that appear to be more metal-rich ([Fe/H] > −1.5) also appear as likely members in Pace & Li (2019), further supporting that they are indeed members.

We find that our initial exclusion of stars with photometric [Fe/H] > −1.0 and $\mathrm{log}g\gt 3.0$ removes all but five likely nonmembers from Walker et al. (2016). Furthermore, the five remaining likely nonmembers are identified as likely nonmembers from our method, since we derive membership probabilities p < 0.10 for all those stars. We reidentify all likely members of the RGB from Walker et al. (2016) and Chiti et al. (2018) as highly likely members in our sample (all p > 0.99). The one likely member we are not recovering from Walker et al. (2016) is on the horizontal giant branch, since we exclude stars not on the RGB from our sample. In addition to reidentifying all the known likely members on the RGB, we here identify likely members both in the core of Tucana II and several half-light radii away from it. This result demonstrates that SkyMapper photometry and Gaia proper motions very efficiently identify likely member stars of UFDs—and by extension, alleviate the problem of foreground contamination when studying these systems.

We further note that our selection procedure excludes all known nonmembers in the core of Tucana II. This fact implies that it may be possible to identify members of Tucana II, agnostic of the spatial distribution of stars. Purely as an exercise, we recompute membership probabilities after excluding the spatial terms in Equation (2) and present the result in the bottom panels of Figure 11. We find, as expected, that we still exclude all known nonmembers in the core of Tucana II and reidentify the likely members on the RGB. We additionally find a number of candidate members that are many half-light radii from the center of the system. In upcoming work, we indeed confirm the membership status of a handful of these distant stars (A. Chiti et al. 2020, in preparation), which is suggestive of a more spatially extended population of stars, some tidal disturbance, or a need to revisit the structural parameters of the system.

Given the membership probabilities obtained using Equation (2) in Section 5.2, we can now derive an MDF for Tucana II including spatial priors. We compile the photometric metallicity values and uncertainties derived in Section 4, together with our membership probabilities (see Section 5.2). We then generate a Gaussian for each star in which the mean is the photometric metallicity, with one σ being equal to the uncertainty in the photometric metallicity, and the amplitude being equal to the membership probability. We then simply sum these Gaussians to generate an MDF. The result is shown in Figure 12.

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We find a population of extremely metal-poor stars in this distribution, which makes Tucana II one of the most metal-poor galaxies, with an MDF peaking at [Fe/H] ∼ −2.9. This result follows earlier investigations that also yielded overall low metallicities for the system (Ji et al. 2016b; Chiti et al. 2018). However, we also find a more metal-rich component around [Fe/H] ∼ −1.25. If these photometric [Fe/H] values are taken at face value, this higher-metallicity component would suggest an extended formation history for the system. Any indications for an extended star formation history might, however, suggest that even more stars at higher metallicity are present in the system. This has not been found by other studies, as all other UFDs have been shown to not contain stars with ${\rm{[Fe/H]}}\gt -1.0$ (Simon 2019). It is thus unlikely that the apparent bump at [Fe/H] ∼ −1.25 represents a truly metal-rich component. As discussed in detail in Section 4.3, the absorption features around the Ca ii K line (most importantly, the CN feature) artificially increase the measured metallicity of each star in accordance with their carbon abundance. Thus, the high-metallicity population may instead be indicative of the presence of strongly carbon-enhanced CEMP stars in Tucana II. Given that the metal-poor halo population contains a significant fraction of CEMP stars (Placco et al. 2014) and that UFDs have not yielded many strongly enhanced CEMP stars ([C/Fe] > 1.0), this is an interesting option to explore further with spectroscopic follow-up observations.