Stellar Metallicities from SkyMapper Photometry. II. Precise Photometric Metallicities of ∼280,000 Giant Stars with [Fe/H] < −0.75 in the Milky Way

We queried the entire SkyMapper catalog to retrieve photometry of all sources brighter than g = 17 using the Virtual Observatory Access (TAP) protocol ⁶ with the TapPlus class in the astroquery Python package (Ginsburg et al. 2019). To ease computing, individual queries were performed on 15° by 15° regions that, when combined, tiled the full southern hemisphere. The photometry was then dereddened using maps from Schlegel et al. (1998) with bandpass absorption coefficients listed on the SkyMapper website ⁷ In all analyses, we used the Petrosian magnitudes, which were denoted in the catalog by, e.g., g_petro. We also only retained objects with the keys flags=0 and class_star>0.9 in the SkyMapper DR2 catalog. This initial cut ensured that our sample was composed of stars with no obvious issues, e.g., blending affecting their photometry.

The photometric metallicities of our stars were derived using the methods in Chiti et al. (2020), which we briefly outline here. First, we generated a grid of flux-calibrated synthetic spectra over a range of stellar parameters (see Table 1) using the Turbospectrum software (Alvarez & Plez 1998; Plez 2012), MARCS model atmospheres (Gustafsson et al. 2008), and a line list from the VALD database (Piskunov et al. 1995; Ryabchikova et al. 2015) supplemented by carbon molecular lines from Brooke et al. (2013, 2014), Masseron et al. (2014), Ram et al. (2014), and Sneden et al. (2014). The [α/Fe] values was set to match the "standard" MARCS model atmospheres, in which [α/Fe] = 0.4 when [Fe/H] < −1.0, [α/Fe] = 0 when [Fe/H] = 0, and [α/Fe] decreases linearly between the two values when −1 < [Fe/H] < 0. This behavior matches the general [α/Fe] trend in the Milky Way halo. Then, we derived a grid of synthetic photometry by calculating the expected flux that each of our synthetic spectra would produce through each of the SkyMapper filters (Bessell et al. 2011).

To derive photometric metallicities, we then matched the magnitudes in SkyMapper DR2 photometry to those in our grid of synthetic photometry and found the associated metallicity. Specifically, stars with distinct metallicities separate in a well-behaved manner in the color–color plot v − g × 0.9(g − i) versus g − i (see Figure 1). Consequently, we overlaid our synthetic photometry on this plot and interpolated between the contours of constant metallicity using the scipy.interpolate.griddata to map each location in that plot to a metallicity. Then, simply by overlaying the observed SkyMapper photometry onto this plot, we were able to determine metallicities.

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We note that the metallicity contours in the color–color plot v − g × 0.9(g − i) versus g − i are dependent on surface gravity (see Figure 3 in Chiti et al. 2020), so we iteratively determined photometric metallicities to account for this fact. As such, we first derived photometric metallicities assuming $\mathrm{log}g$ = 2.0. Then, we derived photometric surface gravities using the fact that stars with distinct surface gravities separate in a well-behaved manner in the color–color plot u − v × 0.9(g − i) versus g − i (see Figure 1). As such, we could simply replicate the procedure described for photometric metallicities to derive photometric surface gravities using the first-pass metallicity estimates as inputs to generate contours for each star. Then, we used these photometric surface gravity measurements as inputs to adjust the photometric metallicity contours and derive updated, final photometric metallicities.

We note that stars may have stellar parameters or metallicities beyond our grid of synthetic spectra, and we outline how we account for those situations here. In the case of metallicity, stars with SkyMapper photometry consistent with [Fe/H] > −0.5 or [Fe/H] < −4.0 would be beyond the edge of our grid. To avoid the spurious presence of such stars in our catalog, we exclude stars with photometric [Fe/H] > −0.75 or photometric [Fe/H] < −3.75. We exclude all stars with $\mathrm{log}\,g$ beyond the upper edge of our grid ($\mathrm{log}\,g$ = 3.0), but do retain stars with $\mathrm{log}\,g$ below the lower range of our grid ($\mathrm{log}\,g$ = 1.0) as the effect on the photometric metallicity contours from $\mathrm{log}\,g$ is not hugely significant below that value. Finally, we account for stars with T_eff beyond the range of our grid by excluding stars with g − i < 0.35 and g − i > 1.2.

We derived uncertainties on our photometric metallicities by adding sources of random uncertainty and an estimate of the systematic uncertainty in quadrature. We derived random uncertainties by varying the v − g × 0.9(g − i) and g − i colors for each star by propagating the photometric uncertainties in SkyMapper DR2. After each term was varied, photometric metallicities were rederived, and the differences between the rederived metallicity and the original metallicity were added in quadrature to derive the total random uncertainty. The intrinsic systematic uncertainty from this method was taken as 0.16 dex, following Chiti et al. (2020). The random and systematic uncertainties were then added in quadrature for each star to derive a final uncertainty on the photometric metallicity.

Due to the large size and broad spatial coverage of the SkyMapper catalog, it was necessary to test for systematic effects in our metallicities as a function of sky location, color, and reddening. To accomplish this, we compared our photometric metallicities to metallicities derived in three large spectroscopic surveys: APOGEE DR16 (Eisenstein et al. 2011; Blanton et al. 2017; Majewski et al. 2017), GALAH DR3 (Buder et al. 2021), and LAMOST DR6 (Zhao et al. 2006, 2012; Cui et al. 2012). A full description of the cross-matching procedure and quality criteria that were applied to compile a comparison sample from these large spectroscopic surveys is detailed in Section 3.1. For the investigations in this section, we only included stars from those surveys in the metallicity range of our sample (−3.75 < [Fe/H] < −0.75) to ensure a consistent comparison sample.

We first checked for any trends in the residuals of our photometric metallicities with respect to the metallicities from GALAH DR3 as a function of R.A., decl., Galactic longitude (l), and Galactic latitude (b). The GALAH survey was chosen for the comparison sample due to its broad overlap in spatial coverage and magnitude range with our catalog of photometric metallicities (see Figure 2). We find no trends with respect to R.A. and Galactic longitude but find statistically significant trends as a function of decl. and Galactic latitude (see Figure 3). The trend with respect to decl. likely arises from residual effects on the photometry from the airmass. Similarly, the trend with respect to Galactic latitude likely arises from residual effects of reddening on the photometry, which would become more notable at lower Galactic latitudes. We fit the trends in the top panels of Figure 3 with the displayed linear equations and subtracted the trends from our metallicities to account for these systematic effects.

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We then investigated the behavior of the metallicity residuals as a function of the metallicity-sensitive color v − g to calibrate for possible imperfections in our grid of synthetic photometry. We used LAMOST, GALAH, and APOGEE metallicities as comparison samples to investigate such effects. We find that the residuals of the photometric metallicities with respect to metallicities in those surveys show systematic trends with respect to the v − g color (see Figure 4), suggesting slight imperfections in our method of deriving metallicities. We alleviated this imperfection by reducing our photometric surface gravities by 0.55 dex before deriving final photometric metallicities. This adjustment to the surface gravities reduces these systematic trends (see bottom panels of Figure 4) and also brings our surface gravity scale in agreement with that used in large high-resolution spectroscopic studies of metal-poor stars (e.g., Ezzeddine et al. 2020).

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We further find no strong systematics in the residuals of our photometric metallicities with respect to metallicities from GALAH DR3 as a function of reddening values from Schlegel et al. (1998) out to E(B−V) ∼ 0.35. This is shown in Figure 5.

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We performed additional tests using Gaia EDR3 data (Gaia Collaboration et al. 2016, 2021) to flag two cases of contaminants in our catalog. First, while we aim for our catalog to be limited to giant stars by limiting to photometric surface gravities $\mathrm{log}\,g\lt 3.0$, there may still be main-sequence interlopers due to, e.g., stars with high uncertainties on their $\mathrm{log}\,g$ values. Second, given the large number of stars in the Milky Way in the metallicity regime right above our sample (−0.75 < [Fe/H] < 0.0), it is possible for some stars in that metallicity regime to contaminate the more metal-rich end ([Fe/H] ≳ −1.25) of our sample. We thus performed two checks to identify such stars in our catalog.

We first cross-matched our sample with Bailer-Jones et al. (2021) to compile their photogeometric distances. We then derived a distance modulus and absolute magnitude for each star from these distances to generate a color–magnitude diagram of our entire sample of stars. We identified stars that had an 84% percentile value in their distance posterior that led to absolute SkyMapper g magnitude < 5.0 as plausible main-sequence interlopers because such magnitudes easily exclude stars from the giant branch (see Figure 6). Further, we then overlaid a Dartmouth isochrone (Dotter et al. 2008) with [Fe/H] = −0.75, 10 Gyr on our color–magnitude diagram to identify plausible metal-rich stars in our catalog. We identified stars that had an 84% percentile in their distance posterior that placed them redward of the isochrone and that had photometric [Fe/H] > −2.0 as plausible metal-rich interlopers. Stars that satisfy either of these criteria have flag_msmr=1 in our catalog (see Table 2).

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Our full catalog of photometric metallicities is composed of 728,712 stars after the implementation of a number of cuts for quality control purposes that we briefly describe here. First, we applied an initial photometric quality cut, as outlined in Section 2.1. Second, to ensure a basic quality of our compiled photometric metallicities, we excluded stars with a random uncertainty in their photometric metallicity (e.g., the propagated uncertainty from the photometry) of ≥ 0.75 dex. Third, we applied cuts discussed in Section 2.2 to avoid keeping stars with stellar parameters near the edge of our photometry grid. Fourth, we excluded stars at Galactic latitudes ∣b∣ < 10° or with E(B − V) > 0.35 to excise regions of extreme reddening. This ultimately resulted in our final sample of stars, which we refer to as our catalog in the following discussions. The distribution of magnitudes and metallicity uncertainties of our catalog are shown in Figure 7. Our catalog is shown in Table 2, which is published in its entirety in machine-readable format. Of the 728,712 stars in our catalog, 282,351 stars pass the checks in Section 2.4.

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Due to the large size of our data set and sky coverage, there is significant overlap with several large spectroscopic surveys. To test the validity of our metallicities, for stars in common, we compared our photometric metallicities with metallicities presented in LAMOST DR6 (Zhao et al. 2006, 2012; Cui et al. 2012), GALAH DR3 (Buder et al. 2021), and APOGEE DR16 (Eisenstein et al. 2011; Blanton et al. 2017; Majewski et al. 2017). Data from these surveys were downloaded ^{8 , 9 , 10} and cross-matched to our catalog using the TOPCAT software (Taylor 2005). The results of these comparisons are presented in Figure 8 and are discussed further in this section.

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We find 6409 stars in our catalog that have stellar parameters in LAMOST DR6. We applied several cuts to the LAMOST catalog ($\mathrm{log}\,g\lt 3.0$ and 4000 < T_eff < 5700) to ensure the stellar parameters of stars in the LAMOST sample were comparable to those of stars in our catalog. Then, we excluded stars in LAMOST and our catalog that have metallicity uncertainties greater than 0.3 dex and stars in LAMOST with $\mathrm{log}\,g$ uncertainties >0.30 to compare stars with high-quality stellar parameters. This resulted in a sample of 2262 stars, which are plotted in the leftmost panel of Figure 8 as hollow squares. Of those stars, 1835 pass the Gaia-based quality checks in Section 2.4 and are plotted as solid squares. We find that our metallicities that pass the quality checks are on average 0.05 dex lower than the LAMOST metallicities, and the standard deviation of the residuals between metallicities is 0.24 dex. This is great agreement, given that typical best metallicity precisions achievable with medium-resolution spectroscopy are ∼0.15 dex and the systematic floor on the metallicity precision from our photometric method is ∼0.16 dex.

There are 14,362 stars in our catalog that have stellar parameters in GALAH DR3. We applied the same cuts to the GALAH catalog that we applied to the LAMOST sample to ensure a high-quality stellar parameter comparison. We also applied some cuts using flags in the GALAH catalog (qcr flag_sp=0, flag_fe_h==0) to further increase the quality of the comparison sample. This resulted in a sample of 6957 stars, of which 4312 passed all the checks outlined in Section 2.4. The comparison between the metallicities is plotted in the middle panel of Figure 8. We find that these metallicities are on average 0.24 dex lower than those metallicities presented in GALAH, and the standard deviation of the residuals between our metallicities is 0.25 dex.

The same cuts were applied to the APOGEE DR16 catalog as for the previous catalogs to ensure a high-quality reference sample. Additionally, we only retained APOGEE stars with ASCAPFLAG=0 which indicated no warnings or errors were raised by the APOGEE stellar parameter pipeline (García Pérez et al. 2016). This led to a sample of 1307 stars in total and 959 stars passing the checks in Section 2.4, all of which are plotted in the right panel of Figure 8. Our photometric metallicities that pass the quality checks are on average 0.11 dex lower than the APOGEE metallicities, and the residuals of metallicities between the two data sets have a standard deviation of 0.23 dex.

There are a number of stars in our catalog that have metallicities previously determined by high-resolution spectroscopic studies. Metallicity comparisons are particularly useful to test the behavior of our photometric values in the very low-metallicity regime (−3.5 < [Fe/H] < −2.5). We thus compared our metallicities to those derived by the high-resolution studies of Barklem et al. (2005), Jacobson et al. (2015), Marino et al. (2019), and Ezzeddine et al. (2020) that are within the metallicity range of our grid ([Fe/H] > −4.0), as well as a sample of stars that was specifically observed for comparison purposes with the high-resolution MIKE spectrograph (Bernstein et al. 2003) on the Magellan/Clay Telescope in January, October, and December 2020. Detailed results will be presented in X. Ou et al., (2021 in preparation) but we compare to their derived metallicities here. For completeness, we refer the reader to Section 3 of Ezzeddine et al. (2020), which comprehensively details the methodology (e.g., line list, analysis software) used in X. Ou et al. (2021, in preparation) for deriving stellar metallicities.

Results of the various metallicity comparisons are shown in Figure 9. The top-left panel displays the comparisons to both X. Ou et al. (2021, in preparation) and Marino et al. (2019). The following panels, in clockwise order, show the comparisons to Barklem et al. (2005), Ezzeddine et al. (2020), and Jacobson et al. (2015), respectively. The orange data points in the panels correspond to the warmer stars in our sample (g − i < 0.65), and the black data points correspond to the cooler stars (g − i > 0.65). For reference, g − i = 0.65 corresponds to an effective temperature of ∼5000 K.

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The agreement of photometric metallicities for all 55 stars in common with those of the combined sample of Marino et al. (2019) and X. Ou et al. (2021, in preparation) is excellent. Our metallicities are marginally higher (0.15 dex) on average but the standard deviation of the residuals is 0.29 dex. Note that in Figure 9 we list a slightly different standard deviation that refers to stars with g − i > 0.65.

We find worse agreement (mean offset of 0.24 dex with a standard deviation of 0.45 dex) for the metallicities of our stars in common with the three other studies (Barklem et al. 2005; Jacobson et al. 2015; Ezzeddine et al. 2020) combined but there are hints that this is the case because our photometric metallicities are biased high when g − i < 0.65. If we only include the 87 cooler stars with g − i > 0.65, the average offset drastically reduces to 0.08 dex, and the standard deviation of the residuals reduces to 0.36 dex. Finally, combining all five high-resolution samples and restricting the comparison to −4.0 < [Fe/H] < −2.5 (as measured on our metallicity scale), metallicities agree reasonably well (mean offset of 0.03 dex with a standard deviation of 0.30 dex), with a roughly similar scatter when g − i > 0.65 (mean offset on 0.02 dex with a standard deviation of 0.31 dex).

To further gauge precision in the lowest-metallicity regime (−3.5 ≲ [Fe/H] ≲ −2.5), we investigated the contamination rate of stars with [Fe/H] < −4.0 in our catalog by cross-matching our catalog to the sample of ultra-metal-poor stars listed in Ezzeddine et al. (2017). We recover only 3 of their 16 stars, CD −38° 245, HE 2139−5432, and SMSSJ0313−6708, suggesting a negligible presence of stars below [Fe/H] < −4.0 in our catalog. Furthermore, the presence of HE 2139−5431 and SMSSJ0313−6708 in our catalog is not altogether surprising, given their extremely large relative carbon abundances ([C/Fe] = 2.59; Yong et al. 2013 and [C/Fe] > 4.8; Keller et al. 2014), which significantly upscatters their photometric metallicities (see Section 3.3). Our recovery of CD −38° 245 ([Fe/H] = −4.12 ± 0.10; Ezzeddine et al. 2020) cannot be explained this way as it has no strong overabundance of [C/Fe], but we note an [Fe/H] = −3.05 ± 0.48 for this star in our catalog. In general, anomalously high or low [α/Fe] values, unresolved interstellar Ca absorption, significant CH absorption, or other issues may mask stellar Ca and are known to result in systematic overestimates for stars when the signal from the Ca ii K line has become incredibly weak (e.g., when [Fe/H] ≲ −3.5). This highlights the difficulty in extending this technique to derive precise metallicities at the very lowest [Fe/H] regime (e.g., ultra-metal-poor stars).

This comparison exercise with results from high-resolution spectroscopy principally validates our analysis technique and confirms that our photometric metallicities are reliable down to [Fe/H] ∼ −3.3 for the cooler subsample of our catalog (g − i > 0.65). It also suggests that the photometric metallicities presented in this catalog could feasibly be used for targeted searches for the most metal-poor stars in our Galaxy, especially among the cooler stars. The use of metallicities of warmer stars with g − i < 0.65 is less accurate due to some evidence of systematic metallicity offsets when compared to Barklem et al. (2005), Jacobson et al. (2015), and Ezzeddine et al. (2020), but we still report their metallicities because (1) of the overall good agreement with the X. Ou et al. (2021, in preparation) and Marino et al. (2019) studies, and (2) even if these metallicities were somewhat biased high, they would still be useful for targeted spectroscopic follow-up campaigns for low-metallicity stars.

As extensively discussed in, e.g., Da Costa et al. (2019) and Chiti et al. (2020), stars with a prominent CN spectral feature at ∼3870 Å may have photometric metallicities from SkyMapper photometry that are biased high. This is because that absorption feature is located within the wavelength region covered by the SkyMapper v filter and thus affects the observed flux and will make the star appear more metal rich. Such an effect could be particularly pronounced at lower metallicities where carbon-rich stars become more frequent.

At face value, this effect implies that carbon-enhanced metal-poor (CEMP) stars in this catalog will appear to have higher metallicities than their true metallicity. For reference, a star with T_eff = 4700 K, [Fe/H] = −2.5, and [C/Fe] = 0.50 will have a metallicity biased upward by ∼0.40 dex compared with a similar star with [C/Fe] = 0 (Chiti et al. 2020). This means that for the majority of stars in our catalog, this effect will be below that t the ∼0.40 dex level because most stars with −3.0 < [Fe/H] < −1.0 do not reach that level of carbon enhancement (Figure 2 in Placco et al. 2014). Obvious exceptions to this would be, e.g., CEMP-s stars (typically with [Fe/H] ≳ −2.5) that display extreme carbon enhancements due to mass transfer from a binary companion but those numbers are expected to be comparably small. We also emphasize that if variations in the carbon abundance were greatly influencing our metallicity determinations for a bulk of stars in this catalog, this effect would have manifested as a much larger scatter in our comparisons to the metallicities obtained by the LAMOST, GALAH, and APOGEE surveys (see also Section 3.1), which is not observed. Hence, for the bulk of stars in this catalog, we regard the effect of carbon abundance on the metallicity as likely not significant.

We also attempt to quantify the extent to which our catalog is biased in selecting or deselecting stars as a function of metallicity. We test for any such effect among stars with −2.0 < [Fe/H] < −1.0 by deriving the fraction of stars that we recover in the southern hemisphere coverage of the LAMOST DR6, GALAH DR3, and APOGEE DR16 catalogs with comparable stellar parameters ($\mathrm{log}\,g\lt 3.0$, −2.50 < [Fe/H] < −0.75, 4000 K < T_eff < 5700 K, and σ_[Fe/H] < 0.3) and spatial distribution (∣b∣ > 10°), over a magnitude range 11 ≲ g ≲ 16.5.

We note that our recovery rate with respect to the combined sample of LAMOST, GALAH, and APOGEE stars is between 40% and 50%, but this apparently low value is largely driven by our initial photometric quality cut on the SkyMapper DR2 catalog (flags=0). After that initial cut, a significantly higher 70% of stars in the LAMOST, GALAH, and APOGEE catalogs are retained in our photometric metallicity catalog, suggesting that the majority of the loss is driven by photometric quality and not anything particular to our subsequent analysis technique. However, we still present the recovery fraction below including the loss of stars in our catalog due to photometric quality, in order to test whether such losses could plausibly have an effect on the metallicity selection. Because SkyMapper imaging covers the entire southern sky, we note that our catalog includes a significant number of stars that are in neither the LAMOST, GALAH, nor APOGEE catalogs.

We determined that for −1.5 < [Fe/H] < −1.0, 42% of stars were retained in our catalog. For −2.0 < [Fe/H] < −1.5, 47% were retained. At face value, this suggests that we are slightly more sensitive to accurately selecting stars with −2.0 < [Fe/H] < −1.5 than −1.5 < [Fe/H] < −1.0. This difference in recovered stars is robust given the large sample size of 8270 reference stars from LAMOST, GALAH, and APOGEE.

To test whether any potential selection effects extend into the [Fe/H] < −2.0 regime, we performed the same exercise, except this time using the combined sample of stars from Barklem et al. (2005), Jacobson et al. (2015), Marino et al. (2019), Ezzeddine et al. (2020), and X. Ou et al. (2021 in preparation) as references, as they extend to lower metallicities than the APOGEE/LAMOST/GALAH comparison. In this case, we find no strong dependency of the recovery fraction with metallicity, with recovery fractions of 58%, 51%, 45%, and 25% for the respective 0.5 dex increments ranging from [Fe/H] = −1.5 to [Fe/H] = −3.5. Unfortunately, the smaller sample size of 417 stars in this combined sample is too small to resolve differences below a ∼7% level (set by Poisson statistics) in each of these bins. For that reason, it is particularly difficult to assess the completeness in the extremely metal-poor regime with [Fe/H] < −3.0 at this time, although indications suggest that our catalog is preferentially incomplete in that regime. This is not surprising, as the selection is likely to decrease due to a loss of metallicity precision because the color–color separation between stars of different metallicities significantly narrows in this regime (see Figure 1). We note that including/excluding stars that fail the quality checks in Section 2.4 negligibly changes these recovery fractions.