The Most Metal-poor Stars in Omega Centauri (NGC 5139)¹¹1This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile.

For consistency with the Johnson & Pilachowski (2010) temperature/gravity scale, model atmosphere parameters were determined for each star using dereddened B, V, and K_S-band photometry from van Leeuwen et al. (2000) and the Two Micron All Sky Survey (2MASS; Skrutskie et al., 2006). Although several authors note the existence of minor ($\Delta$ $\sim$ 0.02 mag.) differential reddening near the cluster core (e.g., Calamida et al., 2005; van Loon et al., 2007; McDonald et al., 2009), we assumed a constant E(B$-$V) = 0.11 (Calamida et al., 2005) across the cluster and also utilized the relation E(V$-$K_S)/E(B$-$V) = 2.70 from McCall (2004). For target stars with clear 2MASS matches, effective temperatures (T_eff) were determined using the V$-$K_TCS color-temperature relation from Alonso et al. (1999)⁵⁵5Note that the 2MASS K_S-band photometry were transformed onto the K_TCS system using the transformations listed in Johnson et al. (2005).. In the few cases where clear 2MASS matches could not be obtained we used the B$-$V color-temperature relation from Alonso et al. (1999) to derive T_eff values. The estimated T_eff uncertainty is approximately 30 K for temperatures derived from V$-$K_TCS and 130 K for B$-$V, based on the scatter of the empirical color-temperature relations in Alonso et al. (1999, see their Table 2).

Similar to T_eff, surface gravity (log g) values were determined for each star using photometric temperatures and absolute bolometric magnitudes (M_bol.). The bolometric magnitude values were calculated using the corrections provided by Alonso et al. (1999) and a distance modulus of (m$-$M)_V = 13.7 (van de Ven et al., 2006). Final surface gravity values were determined using the relation,

where we assumed a mass of 0.8 M_⊙ for all stars. Although a mass of 0.8 M_⊙ is a reasonable assumption for most cluster RGB stars, Figure 1 shows that some of our targets may be lower mass AGB or red HB stars. McDonald et al. (2011) showed that $\omega$ Cen RGB stars lose $\sim$ 25$\%$ of their mass between the RGB and AGB sequences so a significant fraction of our targets may have masses closer to 0.6 M_⊙. Fortunately, the photometric surface gravity estimate shown above is only sensitive to the log of the mass difference, and we have restricted the present analysis to only include Fe I lines, which are not strongly pressure sensitive in the stars targeted here. Assuming the difference between RGB and AGB masses does not exceed $\sim$0.2 M_⊙, we adopt a log(g) uncertainty of 0.15 (cgs).

For most stars in our analysis, the available Fe I lines are too strong to tightly constrain the microturbulence ($\xi$_mic.). Therefore, we determined an empirical relation between T_eff and $\xi$_mic. as,

using data from Johnson & Pilachowski (2010) that spanned the same T_eff range as the stars presented here. The adopted microturbulence calibration has a dispersion of 0.17 km s^-1.

Since the photometric color-temperature relation is dependent on metallicity and the surface gravity and microturbulence estimates require accurate temperature measurements, generating a global model atmosphere solution for each star is an iterative process. Therefore, we initially determined T_eff, log(g), and $\xi$_mic. for each star assuming [Fe/H] = $-$1.7, and iteratively solved for all four parameters as the metallicity determination improved (see also $\S$3.3). We interpolated within the ATLAS9 grid of model atmospheres from Castelli & Kurucz (2003), and in general a stable solution was reached after $\sim$ 3 iterations. The adopted model atmosphere parameters, [Fe/H] values, photometry, star identifiers, and coordinates are provided in Table 1.

Although cluster membership probabilities were provided by van Leeuwen et al. (2000) based on proper motion measurements, we verified membership using radial velocity measurements as well. Radial velocities were determined using the first exposure of each configuration and comparing it with a synthetic reference spectrum at rest velocity that matched the resolution and sampling of the data. The observed radial velocity values were determined using the XCSAO routine from Kurtz & Mink (1998), and heliocentric corrections were calculated using IRAF’s rvcor routine. The final heliocentric radial velocities and XCSAO error measurements for each star are provided in Table 1.

We found a mean heliocentric radial velocity of $+$232.5 km s^-1 for $\omega$ Cen with a dispersion of 12.8 km s^-1. These values are in good agreement with previous work (e.g., Reijns et al., 2006; Sollima et al., 2009). A direct comparison of stars in common between this work and Reijns et al. (2006) gives a mean velocity difference, in the sense of the present work minus the literature, of $+$1.0 km s^-1 with a dispersion of 1.7 km s^-1 (55 stars). A similar comparison with Sollima et al. (2009) gives a mean difference of $+$2.2 km s^-1 and a dispersion of 2.9 km s^-1 (215 stars). The data presented in Table 1 indicate a radial velocity range spanning $+$186.7 to $+$271.1 km s^-1; however, given the cluster’s high radial velocity relative to the background and its large velocity dispersion, we designate all stars in our sample as cluster members⁶⁶6We reiterate that the targets have already been selected to have membership probabilities $>$ 70$\%$, based on the van Leeuwen et al. (2000) proper motion analysis..

Given the modest S/N ratios of the spectra and the small number of available Fe II lines, all iron abundance determinations were made using synthetic spectrum fits to Fe I features. We first selected a subset of 14 Fe I lines between 5140 and 5390 Å that were visible in a majority of our spectra but had typical equivalent widths lower than about 150 mÅ. The spectrum synthesis line lists were augmented to include significant lines within 5 Å of each Fe I feature listed in Table 2. Due to a paucity of high accuracy experimental log gf values for the features given in Table 2, empirical log gf values were determined for all lines by first adopting atomic data from the Vienna Atomic Line Database (Ryabchikova et al., 2015) compilation and then adjusting the log gf values until a satisfactory fit to an M2FS daylight solar spectrum was achieved. We adopted the Anders & Grevesse (1989) solar abundances for all elements⁷⁷7Note that the Anders & Grevesse (1989) solar abundances were used for consistency with Johnson & Pilachowski (2010).. Although MgH lines may be present at wavelengths bluer than $\sim$ 5200 Å, the roughly 4800 K temperatures and low metallicities of our stars inhibited significant molecular contamination. Furthermore, we only selected Fe I lines that were at least $\sim$ 0.5 Å away from significant molecular blends. As a result, the adopted line list only included atomic features. The adopted atomic parameters for all Fe I lines of interest are provided in Table 2.

As mentioned previously, an initial estimate of T_eff, log(g), and $\xi$_mic. was made for each star assuming [Fe/H] = $-$1.7. For the first iteration, the T_eff, log(g), and $\xi$_mic. values were held fixed while model atmospheres and synthetic spectra were generated for [Fe/H] values ranging from $-$2.75 to $-$0.5, in 0.01 dex steps, using the LTE line analysis code MOOG (Sneden, 1973). The fits for each line were visually inspected to identify and remove lines affected by spectrum flaws, to set appropriate smoothing/broadening parameters, and to remove extreme outliers ($\gtrsim$ 0.3 dex from the mean). The [Fe/H] abundance that minimized the fitting residuals between the synthetic and observed spectra was selected as the new metallicity parameter, which enabled an update to the T_eff, log(g), and $\xi$_mic. values. This process was repeated until the difference in mean [Fe/H] between consecutive runs decreased to $<$ 0.03 dex, and then a final iteration was performed. The adopted [Fe/H] abundances for each star are provided in Table 1 and also summarized as a histogram in Figure 3.

The targets were selected to have minimal overlap with other high resolution spectroscopic studies; however, the present sample does have 8 stars in common with Marino et al. (2011). A comparison between the two studies indicates good agreement with a mean offset in [Fe/H] of 0.0 dex and a dispersion of 0.13 dex, which is comparable to the mean line-to-line [Fe/H] dispersion reported in Table 1 for our analysis. We also have 52 stars in common with the low resolution (R $\sim$ 2000) spectroscopic analysis by An et al. (2017) that shows a mean offset, in the sense of the present work minus the literature value, of $+$0.12 dex and a dispersion of 0.15 dex. We attribute the worse agreement to the order of magnitude lower resolution in the An et al. (2017) data.

The [Fe/H] error values ($\Delta$[Fe/H]) provided in Table 1 take into account several factors added in quadrature, including the standard error of the mean [Fe/H] value and uncertainties related to temperature ($\Delta$T_eff = 100 K), surface gravity ($\Delta$log(g) = 0.15 cgs), model atmosphere metallicity ($\Delta$[M/H] = 0.15 dex), and microturbulence ($\Delta$$\xi$_mic. = 0.13 km s^-1) errors. However, since we exclusively used Fe I lines the error budget is dominated by the T_eff, $\xi$_mic., and measurement uncertainties, which also includes log gf and continuum normalization and/or fitting errors. Typical uncertainties are approximately 0.14 dex in [Fe/H]. Since corrections for departures from local thermodynamic equilibrium (LTE) are not available for several of the lines used here, all [Fe/H] measurements assume LTE. Fortunately, calculations from several authors (Bergemann et al., 2012; Lind et al., 2012; Mashonkina et al., 2016) indicate that absolute Fe I non-LTE corrections should be $\lesssim$ 0.05-0.10 dex in magnitude for the parameter space analyzed here. Relative differences between stars with similar temperatures should be even smaller.

In Figure 3 we compare the biased metallicity distribution function derived here against the relatively unbiased distribution found by Johnson & Pilachowski (2010). The new observations clearly confirm the presence of the dominant metal-poor population near [Fe/H] $\sim$ $-$1.7 and the intermediate metallicity group at [Fe/H] $\sim$ $-$1.5, and as expected from our selection procedure we find far fewer stars with [Fe/H] $\gtrsim$ $-$1.3. Figure 4 further shows that our [Fe/H] determinations follow the expected correlation between metallicity and RGB color, and that most of the stars in our sample with [Fe/H] $\gtrsim$ $-$1.3 lie on the AGB or red HB sequences.

We find a possible metal-poor population near [Fe/H] $\sim$ $-$2.1 that appears separate from the dominant group at [Fe/H] $\sim$ $-$1.7 (see also $\S$ 4.1.1), and we suspect that these RGB stars are part of the same metal-poor faction identified by Pancino et al. (2011b) on the SGB. Interestingly, we also find a new population of 11 stars with metallicities below the [Fe/H] = $-$2.26 limit set by Johnson & Pilachowski (2010). These stars represent 2.8$\%$ of our sample and span from [Fe/H] = $-$2.30 to $-$2.52. Figure 4 further shows that these very metal-poor stars generally fall on the blue edge of the cluster RGB, as expected, but 2-3 of the targets could be AGB or HB stars. The very metal-poor stars identified here are close to the empirically determined globular cluster metallicity floor noted in Beasley et al. (2019).

The existence of a metal-poor tail in $\omega$ Cen is already a unique trait among iron-complex clusters. The metallicity distribution functions for all iron-complex clusters except $\omega$ Cen possess a sharp rise at low metallicity, one or more populations at higher metallicity, and occasionally a metal-rich tail. The only other compelling case for a cluster hosting a metal-poor tail or a minor population at low metallicity is Terzan 5, which has a dominant population near [Fe/H] $\sim$ $-$0.3, a secondary population at [Fe/H] $\sim$ $+$0.25, and a minority ($\lesssim$ 6$\%$) metal-poor group at [Fe/H] $\sim$ $-$0.8 (Origlia et al., 2013; Massari et al., 2014). However, the various Terzan 5 sub-populations do not possess the complex light element variations observed in $\omega$ Cen.

Other than metallicity, do the most metal-poor stars in $\omega$ Cen possess any unusual properties? Figure 5 compares the radial and spatial distributions, radial velocities, and Gaia DR2 proper motions for the stars analyzed in the present study. Visual inspection of the two left panels in Figure 5 indicate that: (1) stars with [Fe/H] $<$ $-$2 span a broad range in right ascension but only populate a narrow range in declination and (2) the most metal-poor stars may be very centrally concentrated. First addressing the spatial distribution, we note that the dispersion in declination for stars with [Fe/H] $>$ $-$2 is 0.128 degrees while the dispersions for stars with $-$2.25 $\leq$ [Fe/H] $\leq$ $-$2 and [Fe/H] $<$ $-$2.25 are 0.023 and 0.029 degrees, respectively. Similarly, two-sided Kolmogorov-Smirnov (KS) tests comparing the declination distributions of all stars versus first those with [Fe/H] $<$ $-$2 and then those with [Fe/H] $<$ $-$2.25 returned $p$-values⁸⁸8We adopt the common convention that a $p$-value $<$ 0.05 is sufficient to reject the null hypothesis. of 0.002 and 0.095, respectively. From these data we can conclude that there is marginal evidence indicating that the most metal-poor $\omega$ Cen stars may be confined to a more narrow plane than the majority of cluster stars. However, a larger sample size is required to draw any strong conclusions.

Regarding the radial distributions, Figure 5 shows that nearly all of the stars with [Fe/H] $<$ $-$2 are projected within 12$\arcmin$ of the cluster core and 84$\%$ are within 3$\arcmin$. Similarly, all of the stars with [Fe/H] $<$ $-$2.25 are within 10$\arcmin$ and 81$\%$ are inside of 3$\arcmin$. These results match previous observations by Johnson & Pilachowski (2010) who noted that 88$\%$ of the stars in their sample with [Fe/H] $<$ $-$2 were found within 5$\arcmin$ of the cluster core. The combination of the present work with the larger sample of Johnson & Pilachowski (2010) hints that the most metal-poor stars in $\omega$ Cen may be mostly confined to within a half-light radius (5$\arcmin$). A two-sided KS test comparing the radial distributions of stars with [Fe/H] $>$ $-$2 against those with [Fe/H] $<$ $-$2 returned a $p$-value of 2.91$\times$10^-10 while a similar test comparing the radial distributions of stars with [Fe/H] $>$ $-$2 and [Fe/H] $<$ $-$2.25 returned a $p$-value of 8.66$\times$10^-5. The extremely low $p$-values indicate a low probability that stars with [Fe/H $<$ $-$2 follow the same radial distribution as their higher metallicity counterparts. We did not detect any further differences between the most metal-poor stars and any other populations when examining radial velocity or proper motion distributions; however, larger sample sizes are required to draw any firm conclusions.

If the stars in $\omega$ Cen with [Fe/H] $<$ $-$2, and especially those with [Fe/H] $<$ $-$2.25, are truly distinct from the other cluster populations, then their presence may reveal important details about the cluster’s early formation history. The available evidence suggests several possible origins for $\omega$ Cen’s very metal-poor stars, including: (1) early star formation in the unenriched primordial cloud, (2) the capture of surrounding field stars, assuming the cluster formed in a dwarf galaxy, or (3) an early merger between $\omega$ Cen and a pre-existing but metal-poor sub-structure.