BRIGHT METAL-POOR STARS FROM THE HAMBURG/ESO SURVEY. II. A CHEMODYNAMICAL ANALYSIS

Broadband V magnitudes and B − V colors for the majority of our program objects were obtained from the APASS database (Henden et al. 2015), supplemented by photometry from a number of sources as described in Paper I (primarily stars that were re-discoveries of metal-poor candidates from the HK survey; Beers et al. 1985, 1992). For stars that are of particular interest, i.e., those found in Paper I to have $[\mathrm{Fe}/{\rm{H}}]\lt -2.0$ or to exhibit enhanced carbon, we also make use of photometry reported by Beers et al. (2007). In a number of cases, we have also used photometry from the SIMBAD database. For stars with photometry available from multiple sources, we either use the data judged to be superior, or else average data expected to be of similar precision. Near-IR JHK photometry from the 2MASS catalog (Skrutskie et al. 2006) is available for all but a few stars in our sample.

Column (1) of Table 1 lists the star names, while columns (2) and (3) list other common names for the star and the HK Survey star name, respectively. The full set of coordinates for our program stars are provided in Paper I. Columns (4) and (5) list the Galactic longitude and latitude for our program stars. The adopted V magnitude and B − V colors are provided in columns (6) and (7). The 2MASS J magnitude and J − K colors (including only stars without flags indicating potential problems in the listed values) are listed in columns (8) and (9).

Table 1.  Photometric Information and Adopted Reddening

Star Name	Other Name	HK Survey	LON	LAT	V	B − V	J	J − K	$E{(B-V)}_{S}$	$E{(B-V)}_{A}$
			(${}^{\circ }$)	(${}^{\circ }$)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
HE 0000-3017	CD-30:19801		14.8	−79.1	10.36	0.40	9.546	0.275	0.015	0.02
HE 0000-4401	CD-44:15435		330.2	−70.7	10.66	0.55	9.717	0.302	0.010	0.01
HE 0000-5703	HD 225032		315.9	−59.1	9.40	0.24	9.001	0.109	0.010	0.01
HE 0001-4157	CD-42:16578		333.7	−72.5	10.52	0.67	9.385	0.376	0.012	0.01
HE 0001-4449	CD-45:15231		328.4	−70.2	11.14	0.49	10.192	0.296	0.012	0.01
HE 0001-5640	CD-57:8943		315.9	−59.5	10.50	0.41	9.571	0.285	0.011	0.01
HE 0002-3233		CS 22961-023	2.9	−78.8	12.00	0.41	11.068	0.323	0.016	0.02
HE 0002-3822	CD-38:15729		341.8	−75.3	10.79	0.53	9.808	0.335	0.016	0.02
HE 0002-5625			315.9	−59.8	12.60	0.69	11.425	0.424	0.010	0.01
HE 0003-0503	BD-05:6112		95.0	−65.2	10.70	0.74	8.990	0.602	0.030	0.03

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.

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In order to obtain absorption- and reddening-corrected estimates of the magnitudes and colors, respectively, we initially adopted the Schlegel et al. (1998) estimates of reddening listed in column (10) of Table 1. We have applied corrections to these estimates for stars with reddening greater than $E{(B-V)}_{S}$ = 0.10, as described by Beers et al. (2000). The corrected reddening estimates, $E{(B-V)}_{A}$, are listed in column (11).

Radial velocities were (re-)measured for our program stars using the line-by-line and cross-correlation techniques described in detail by Beers et al. (1999) and references therein. In the process of carrying out this exercise, we found that many of the new measurements differ (in some cases by large amounts) from those originally reported in Paper I, which apparently suffered from transcription difficulties during file exchanges between the authors. The current measurements supersede those values. The spectral resolution of our data is similar to that obtained for the majority of the HK Survey follow-up; thus we expect that the measured radial velocities should be precise to the same level (or better, given the higher signal-to-noise of our present spectra), on the order of 7–10 km s⁻¹ (one sigma). Column (1) of Table 2 is the star name, while column (2) lists notes on the nature of a small number of stars that deviate from the majority (e.g., hot stars, sdB and WD stars, known variable stars, stars with emission lines, extremely late-type stars), which precludes their use in later analysis. We conservatively estimate that our medium-resolution velocities, RV_M, listed in column (3) of Table 2, are precise to 10 km s⁻¹ (as validated below).

Roughly one-third of our program objects (614 stars) have had radial velocities determined from the RAVE survey, based on moderate-resolution (R ∼ 7500) spectroscopy in the region of the Ca triplet from Data Release 4 (Kordopatis et al. 2013). The RAVE velocities should be more precise than those we obtained from our lower-resolution spectra (Kordopatis et al. 2013 demonstrate that the majority of the RAVE radial velocities are precise to better than 2 km s⁻¹, with a tail going out to ∼5 km s⁻¹, and have small zero-point offsets relative to external catalogs). For our purpose we conservatively assume a precision of 5 km s⁻¹ for the RAVE velocities (validated below). We adopt the RAVE velocities for our subsequent analysis, except in cases where flags were raised in the DR4 database indicating potential problems (including possible binary membership). The available RAVE velocities are listed as RV_R in column (4) of Table 2. In order to weed out stars with inaccurate RAVE velocities, we have indicated stars with flags suggesting potential problems with parentheses around them. We still adopt these radial velocities for our analysis if they are within 20 km s⁻¹ of the listed RV_M value. If the RAVE velocities differ by more than this amount and had flags raised, we assume that the RV_M estimates are superior. We indicate such cases by brackets around the listed RV_R values. In some instances, there are no flags raised, but the RAVE radial velocities differ from our medium-resolution results by more than 20 km s⁻¹; in such cases, we assume the RAVE estimates are superior, and adopt them.

There are 148 stars in our sample (mostly VMP stars and stars of interest for other reasons, such as carbon enhancement) for which radial velocities based on high-resolution spectroscopy are available, either in the published literature or based on more recent unpublished observations we are aware of. These are listed as RV_H in column (5) of Table 2. We adopt these measurements (when available), with assumed errors of 2 km s⁻¹, even in the few cases where they disagree by more than 20 km s⁻¹ with either RV_M or RV_R. Unrecognized binarity may be responsible for a number of these discrepancies.

Figure 1 (left column) compares the medium-resolution velocities, RV_M, with the high-resolution radial velocities, RV_H, while the middle column of panels compares RV_M with the moderate-resolution RAVE velocities, RV_R (excluding the rejected cases). The right column of panels compares the RAVE velocities with the high-resolution velocities. As can be appreciated from inspection of this figure, there is generally very good agreement between the different sources of radial velocity. The middle row of panels shows the residuals in radial velocity for each comparison, with dark gray and light gray regions indicating the 1σ and 2σ ranges, respectively. Maximum-likelihood fits to the residuals in radial velocity for each comparison are shown in the lower panels of each column. The RV_M versus RV_H residuals exhibit a scatter of 10.7 km s⁻¹ and a small zero-point offset; the RV_M versus RV_R residuals exhibit a scatter of 8.8 km s⁻¹ and a similarly small offset. The RV_R versus RV_H residuals exhibit a scatter of 4.7 km s⁻¹ and a small offset. Assuming our adopted estimate of the 2 km s⁻¹ precision for the high-resolution radial velocities, our results indicate that the RAVE radial velocities are precise to 4.2 km s⁻¹ (note that this comparison emphasizes metal-poor stars, for which the RAVE velocities are expected to be somewhat less precise than for more metal-rich stars). Adopting this value for the scatter in the RAVE velocities, we estimate that the medium-resolution velocities have a precision of 7.7 km s⁻¹. Compared to the high-resolution velocities, the medium-resolution velocities are estimated to have a precision of 10.5 km s⁻¹. These values justify our adopted estimates for the kinematic analysis carried out below—${\sigma }_{{\mathrm{RV}}_{R}}$ = 5 km s⁻¹ and ${\sigma }_{{\mathrm{RV}}_{M}}=10$ km s⁻¹ for the RAVE and medium-resolution velocities, respectively.

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For each star, the measured (geocentric) radial velocities are used to place a set of fixed bands for the derivation of line-strength indices, which are the pseudo-equivalent widths of prominent spectral features. We employ a subset of the bands listed in Table 1 of Beers et al. (1999).⁸ Although we do not make use of them in the present analysis, others may choose to, so we list line indices for prominent spectral features in each of our program stars in columns (6)–(8) of Table 2. A number of our stars have had more than one spectrum obtained during the course of our follow-up observations. From a comparison of the stars with repeated measurements, we estimate that errors in the line indices on the order of 0.1 Å are achieved. Note that our line indices are identical to those reported in Paper I.

In a series of papers, Lee et al. (2008a, 2008b, 2011a), Allende Prieto et al. (2008), and Smolinski et al. (2011) describe the development, testing, and validation of the SSPP software, which has been used to determine atmospheric parameter estimates for over 500,000 stars from the SDSS and its extensions. Although the spectra of our program stars do not reach as far red as SDSS spectra (and hence we cannot use as many of the independent methods as the SSPP enables), they are of similar resolving power. We have thus modified the SSPP to accept input from our program spectra, which span a range of 3600–4400 Å, 3600–4800 Å, or 3600–5250 Å, depending on the telescope/spectrograph that was used to acquire them. We have also implemented the use of input $V,B-V$ (and/or 2MASS $J,J-K$) photometric information rather than requiring SDSS ugriz inputs. This new approach, known as the n-SSPP (for non-SEGUE Stellar Parameter Pipeline), makes use of a subset of previously calibrated methods from the SSPP (those that apply to the available wavelength range of the input spectra) to obtain estimates of the fundamental stellar parameters ${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, and [Fe/H]. For spectra that extend sufficiently redward to include the CH G-band at ∼4300 Å and/or the Mg i feature at ∼5175 Å, the n-SSPP can obtain estimates of [C/Fe] and [α/Fe]⁹ as well (if the spectra are of sufficiently high signal-to-noise, S/N). The n-SSPP has already been applied by Beers et al. (2014) to medium-resolution spectra of stars from the sample of Bidelman & MacConnell (1973) stars studied by Norris et al. (1985). The interested reader should consult that paper for additional information on the operation of the n-SSPP.

We apply the n-SSPP to the sample of 1777 stars from Paper I. Unfortunately, the S/Ns for the spectra of our program stars that extend to wavelength regions that include the Mg i feature are not generally high enough to enable confident estimation of this abundance ratio (Lee et al. 2011a recommend S/N > 20 or 25, the latter applying to stars with $[\mathrm{Fe}/{\rm{H}}]\lt -1.4$); hence we do not report [α/Fe] for our program stars.

The n-SSPP estimates of stellar atmospheric parameters are listed in columns (9)–(11) of Table 2 as Teff_S, log g_S, and [Fe/H]_S. Although according to the tests described by Lee et al. (Lee et al. 2008a, 2008b) and Allende Prieto et al. (2008) the external accuracy of SSPP parameter estimates is expected to be on the order of 150 K, 0.30 dex, and 0.25 dex for ${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, and [Fe/H], respectively, these are based on the availability of SDSS ugriz and the full spectral coverage associated with SDSS spectroscopy, neither of which applies to the present data. We provide an independent test of our expected parameter errors below.

Lee et al. (2013) describes the procedures adopted to estimate [C/Fe] for SDSS/SEGUE spectra, based on spectral matching against a dense grid of synthetic spectra; these techniques, with different input photometric information, also apply to the n-SSPP. We have recently expanded the carbon grid to reach as low as $[{\rm{C}}/\mathrm{Fe}]=-1.5$, rather than the limit of $[{\rm{C}}/\mathrm{Fe}]=-0.5$ employed by Lee et al. (2013). According to Lee et al., the precision of [C/Fe] estimates is better than 0.35 dex for the parameter space and S/Ns explored by SDSS/SEGUE spectra. We expect improved results for the application of the n-SSPP to our program spectra, based on their generally higher signal-to-noise (which typically exceeds S/N ∼50 in the region of the CH G-band). We note that Beers et al. (2014) concluded that the n-SSPP determination of [C/Fe] for spectra with S/N similar to that of our current program achieved a precision (based on empirical comparisons with high-resolution spectroscopic analyses) of ∼0.20 dex.

Table 3 lists the medium-resolution estimates of the [C/Fe] abundance ratios ("carbonicity") for our program stars in column (3), indicated as [C/Fe]_S. For convenience, we have also listed the n-SSPP estimate of [Fe/H]_S in column (2). Column (4) indicates whether the listed measurement is considered a detection, DETECT = "D"; a lower limit, "L"; an upper limit, "U"; or a non-detection, "X," which indicates either that the star is too hot (or cool) for carbon to be measured from the CH G-band or that the star does not have a reference metallicity determination. Column (5) provides the correlation coefficient, CC, obtained between the observed spectrum and the best-matching [C/Fe] from the model grids, and column (6) lists the equivalent width of the CH G-band, EQW. For an acceptable measurement of this ratio, we require DETECT = "D," CC $\geqslant \,0.7$, and EQW $\geqslant \,1.2$. The latter restriction ensures that stars with very weak carbon features are not spuriously assigned values by the grid search procedure. See Lee et al. (2013) for a further discussion of these quantities. Stars for which either the CC or the EQW does not meet the minimum value are indicated by a colon attached to the DETECT parameter in column (4). There are 1491 stars listed in Table 3 for which acceptable measurements of [C/Fe] are obtained—1422 are listed as detections, 58 as upper limits, and 11 as lower limits.

There are external measurements of stellar atmospheric parameter estimates for 707 stars in our sample from the RAVE DR4 catalog (Kordopatis et al. 2013) and another 104 stars for which atmospheric parameter estimates based on high-resolution analyses are available from a variety of sources, including the SAGA database (Suda et al. 2008, 2011; Yamada et al. 2013) and Frebel (2010), as well as the references listed in the PASTEL catalog (Soubiran et al. 2010),¹⁰ supplemented by determinations that have appeared in more recent studies, or unpublished results from co-authors of this paper. We either adopted the parameter estimates we judged to be superior or, in some cases, took a straight average of the available estimates.

The external parameter estimates from RAVE are listed in columns (12)–(14) of Table 2 as Teff_R, log g_R, and [Fe/H]_R. The high-resolution estimates are listed in columns (15)–(17) of that table as Teff_H, log g_H, and [Fe/H]_H.

Before carrying out comparisons with our own estimates, based on medium-resolution spectra, we first check for external parameter estimates that grossly differ from the estimates determined by the n-SSPP. For the external estimates to be considered commensurate with the n-SSPP estimates, reasonable agreement with the effective temperature, ${T}_{\mathrm{eff}}$, is required, at a minimum. To implement this pre-filter, we require that the estimated effective temperatures from the external comparisons are within 500 K of the n-SSPP estimates and (in the case of RAVE) that there be no other indication of potential problems, such as flags raised in the RAVE DR4 catalog listing. This results in a total of 80 stars with RAVE estimates marked as suspect, indicated in Table 2 with brackets around the individual parameter estimates. Only 9 stars with available high-resolution spectroscopic parameter estimates are suspect by this criterion, and these are marked with parentheses around the individual parameter estimates in the table.

Beers et al. (2014) presented a similar analysis for the sample of 302 metal-poor candidates from Bidelman & MacConnell (1973) studied by Norris et al. (1985), roughly one-third of which had external estimates of stellar atmospheric parameters based on high-resolution spectroscopic analyses. Beers et al. used the sample of stars in common to derive empirical corrections to the n-SSPP parameter estimates, which they applied in order to place these estimates on a scale commensurate with that of the high-resolution work. For the convenience of the reader, these corrections are listed below:

$$\begin{eqnarray}&&{[\mathrm{Fe}/{\rm{H}}]}_{C}={[\mathrm{Fe}/{\rm{H}}]}_{S}-(-0.232\cdot {[\mathrm{Fe}/{\rm{H}}]}_{S}-0.428),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&T{\mathrm{eff}}_{C}=T{\mathrm{eff}}_{S}-(-0.1758\cdot T{\mathrm{eff}}_{S}+1062),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\mathrm{log}\,{g}_{C}=\mathrm{log}\,{g}_{S}-(-0.237\cdot \mathrm{log}\,{g}_{S}+0.523).\end{eqnarray} \tag{ 3 }$$

The corrected n-SSPP estimates (Teff_C, log g_C, and [Fe/H]_C) for our program stars are listed in columns (18)–(20) of Table 2. Column (21) of this table lists our adopted type classifications, obtained as described below.

Figure 2 illustrates comparisons of Teff_C, log g_C, and [Fe/H]_C for our program stars with the adopted high-resolution results. Note that, with the exception of a few individual stars lying outside the 2σ bands shown on the left panels, their agreement is quite satisfactory. Maximum-likelihood fits to the distributions of residuals between these various estimates are shown on the right panels. Both the mean offsets (Δ Teff_C = 117 K, Δ log g_C = 0.34 dex, Δ [Fe/H]_C = 0.05 dex) and the scatter in the estimates (σ Teff_C = 179 K, σ log g_C = 0.65 dex, σ [Fe/H]_C = 0.27 dex) are reasonably small. Taking into account the expected errors in the high-resolution estimates of these parameters (125 K, 0.4 dex, and 0.2 dex, respectively), we conclude that the external precision of the n-SSPP estimates of Teff_C, log g_C, and [Fe/H]_C is on the order of 125 K, 0.5 dex, and 0.2 dex, respectively.

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Figure 3 shows that a comparison with the (non-suspect) RAVE determinations is significantly worse for Teff_C but commensurate with the comparisons to the high-resolution results for log g_C and [Fe/H]_C. There are too few stars in common between the stars with RAVE parameter estimates and those with high-resolution estimates to make meaningful comparisons.

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Beers et al. (2014) also used literature values of [C/Fe], based on high-resolution spectroscopic analyses, to derive corrections for the n-SSPP estimates of [C/Fe], as follows:

$$\begin{eqnarray}&&{[{\rm{C}}/\mathrm{Fe}]}_{C}={[{\rm{C}}/\mathrm{Fe}]}_{S}-(-0.068\cdot {[{\rm{C}}/\mathrm{Fe}]}_{S}+0.273).\end{eqnarray} \tag{ 4 }$$

The corrected values are listed as [C/Fe]_C in column (8) of Table 3. This table also lists, in column (9), the absolute value of the carbon abundance, A(C) = log (C).¹¹ We assume, following Beers et al., that external errors for [C/Fe]_C are on the order of ∼0.20 dex.

The parameter CEMP, shown in column (10) of Table 3, indicates whether the star is considered carbon enhanced (CEMP = "C," satisfying ${[{\rm{C}}/\mathrm{Fe}]}_{C}\gt +0.7$, $\mathrm{CC}\geqslant 0.7$, and $\mathrm{EQW}\geqslant 1.2$), of intermediate carbon enrichment (CEMP =  "I," satisfying $+0.5\lt {[{\rm{C}}/\mathrm{Fe}]}_{C}\leqslant +0.7$, $\mathrm{CC}\geqslant 0.7$, and $\mathrm{EQW}\geqslant 1.2$), or carbon normal (CEMP = "N," satisfying ${[{\rm{C}}/\mathrm{Fe}]}_{C}\leqslant +0.5$, $\mathrm{CC}\geqslant +0.7$, and $\mathrm{EQW}\geqslant 1.2$). Stars with upper limits on their carbon ratios are indicated by CEMP = "U" (these include stars with DETECT = "U," $\mathrm{CC}\geqslant +0.7$, and DETECT = "D" but $\mathrm{CC}\lt +0.7$). Stars without carbon measurements are listed as CEMP = "X." There are 48 stars listed with CEMP = "C," 29 with CEMP = "I," 1362 with CEMP = "N," and 116 with CEMP = "U."

Distances to individual stars in our sample are estimated using the M_V versus ${(B-V)}_{0}$ relationships described by Beers et al. (2000). These relationships require that the likely evolutionary stage of a star be given. Assignments to the evolutionary stage, based on the derived (corrected) stellar atmospheric parameters, are as follows: dwarf, ${\rm{D}}(\mathrm{log}\,{g}_{C}\geqslant 4.0$); turnoff, TO ($3.5\leqslant \mathrm{log}\,{g}_{C}\lt 4.0$); and subgiant or giant, ${\rm{G}}\,(\mathrm{log}\,{g}_{C}\lt 3.5$). Note that refinements to this scheme, designed to resolve the possible incorrect assignments of TO stars at cooler temperatures, are adopted as described in Beers et al. (2012). Following Santucci et al. (2015), stars with effective temperature $T{\mathrm{eff}}_{C}\geqslant 6000$ K and $\mathrm{log}\,{g}_{C}\leqslant 3.5$ are classified as field horizontal-branch (FHB) stars.

Based on previous tests of this approach, we expect the distances assigned as described above to be accurate on the order of 15%. Fortunately, there are a small number of stars (24) in our sample with reliable distance estimates available from Hipparcos parallax measurements, listed in Table 4, using the van Leeuwen (2007) reduction. Column (1) lists the star names, column (2) the assigned evolutionary type, column (3) the Hipparcos parallax ${\pi }_{\mathrm{HIP}}$, column (4) the error on the parallax ${\sigma }_{{\pi }_{\mathrm{HIP}}}$, and column (5) the ratio ${\sigma }_{{\pi }_{\mathrm{HIP}}/{\pi }_{\mathrm{HIP}}}$. In order to be considered a reliable estimate of the parallax, this ratio should be less than 0.20. The parallax distance estimate and its error are listed as ${D}_{\mathrm{HIP}}$ and ${\sigma }_{{{\rm{D}}}_{\mathrm{HIP}}}$ in columns (6) and (7), respectively. The estimated photometric distances ${D}_{\mathrm{pho}}$ and their errors ${\sigma }_{{D}_{\mathrm{pho}}}$ are provided in columns (8) and (9), respectively.

Table 4.  Parallaxes and Distance Estimates for Stars with Hipparcos Measurements

Star Name	Type	πHIP	${\sigma }_{{\pi }_{\mathrm{HIP}}}$	${\sigma }_{{\pi }_{\mathrm{HIP}}}/{\pi }_{\mathrm{HIP}}$	${D}_{\mathrm{HIP}}$	${\sigma }_{{{\rm{D}}}_{\mathrm{HIP}}}$	Dpho	${\sigma }_{{{\rm{D}}}_{\mathrm{pho}}}$
		(mas)	(mas)		(kpc)	(kpc)	(kpc)	(kpc)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
HE 0035-0834	D	9.51	1.11	0.12	0.105	0.012	0.084	0.013
HE 0115-5135	G	6.67	1.30	0.19	0.150	0.029	0.285	0.043
HE 0134-2142	D	7.57	1.55	0.20	0.132	0.027	0.150	0.023
HE 0246-5114	D	4.31	0.66	0.15	0.232	0.036	0.199	0.030
HE 0422-4205	D	5.61	1.13	0.20	0.178	0.036	0.158	0.024
HE 0429-4149	D	13.80	0.95	0.07	0.072	0.005	0.064	0.010
HE 0435-4121	D	5.33	1.06	0.20	0.188	0.037	0.181	0.027
HE 0455-3157	D	10.05	1.31	0.13	0.100	0.013	0.076	0.011
HE 0457-3209	D	6.42	1.18	0.18	0.156	0.029	0.134	0.020
HE 0511-4835	D	11.23	0.92	0.08	0.089	0.007	0.099	0.015
HE 0520-5617	D	4.55	0.50	0.11	0.220	0.024	0.142	0.021
HE 1108-3217	D	6.80	0.60	0.09	0.147	0.013	0.049	0.007
HE 1120-0858	D	8.32	1.49	0.18	0.120	0.022	0.177	0.027
HE 1211-3038	D	13.81	1.50	0.11	0.072	0.008	0.100	0.015
HE 1223-0133	TO	9.05	1.11	0.12	0.110	0.014	0.125	0.019
HE 1349-1827	FHB	4.57	0.76	0.17	0.219	0.036	...	...
HE 1411-0542	TO	23.33	0.53	0.02	0.043	0.001	0.022	0.003
HE 1450-1808	D	25.31	1.85	0.07	0.040	0.003	0.027	0.004
HE 2231-0149	D	9.38	0.47	0.05	0.107	0.005	0.283	0.042
HE 2255-1758	D	5.14	0.88	0.17	0.195	0.033	0.175	0.026
HE 2307-4543	D	22.13	1.31	0.06	0.045	0.003	0.046	0.007
HE 2327-4203	D	10.17	1.19	0.12	0.098	0.012	0.145	0.022
HE 2332-4431	D	10.06	1.78	0.18	0.099	0.018	0.127	0.019
HE 2333-4047	D	8.67	1.65	0.19	0.115	0.022	0.110	0.017
HE 2333-4325	TO	6.47	1.31	0.20	0.155	0.031	0.149	0.022

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Figure 4 presents a comparison of the distances calculated on the basis of the photometric estimates and Hipparcos parallaxes. From inspection of this figure, a great majority of the stars have commensurate distance estimates; the one-sigma scatter of the residuals varies between 10% and 20%, on the order of our adopted distance error of 15%. The most deviant stars include one giant and one dwarf.

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Table 5 lists star names in column (1) and the assigned type classifications, photometric distance estimates, and their errors in columns (2)–(4), respectively.

Table 5.  Distance Estimates and Proper Motions

Star Name	Type	Dpho	${\sigma }_{{{\rm{D}}}_{\mathrm{pho}}}$	μα	μδ	${\sigma }_{{\mu }_{\alpha }}$	${\sigma }_{{\mu }_{\delta }}$	PM Source
		(kpc)	(kpc)	(mas yr−1)	(mas yr−1)	(mas yr−1)	(mas yr−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
HE 0000-3017	D	0.249	0.037	20.0	1.3	1.1	0.8	U
HE 0000-4401	D	0.174	0.026	23.6	11.5	1.0	2.9	U
HE 0000-5703	D	0.253	0.038	13.9	2.6	0.9	1.0	U
HE 0001-4157	D	0.107	0.016	−19.9	−54.8	0.8	0.8	U
HE 0001-4449	TO	0.223	0.033	−1.0	0.7	1.1	1.0	U
HE 0001-5640	D	0.249	0.037	40.2	−13.0	1.0	1.2	U
HE 0002-3233	TO	0.430	0.065	57.4	−31.6	1.3	1.5	U
HE 0002-3822	D	0.158	0.024	−36.2	−8.9	1.0	1.5	U
HE 0002-5625	D	0.258	0.039	11.8	−4.9	1.4	1.4	U
HE 0003-0503	G	0.163	0.024	9.5	−1.5	1.8	1.3	U

Note. Sources of proper motions: U = UCAC4, S = SPM4, H = Hipparcos or Tycho II.

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.

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The great majority of our program stars (1732 stars) have reasonably high-quality proper motions available from the UCAC4 catalog (Zacharias et al. 2013), the SPM4 catalog (Girard et al. 2011; 321 stars), or the Hipparcos (van Leeuwen 2007) and Tycho II catalogs (Høg et al. 2000; 66 stars). We have chosen to adopt, where possible, the UCAC4 proper motions, since they exist for almost all of our stars and generally have very small errors. The only exception is that when proper motions are available from the Hipparcos or Tycho II catalogs, we adopt those. The final results are listed as ${\mu }_{\alpha }$ and ${\mu }_{\delta }$ for the proper motions in the R.A. and decl. directions, respectively, in columns (5) and (6) of Table 5. Their associated errors are listed in columns (7) and (8). The source of the adopted proper motion is listed in column (9). Note that, for a small number of stars for which some ambiguity exists as to which star of a listed pair is the one intended (generally those with "A," "B," or "F" appended to their names), we do not adopt any proper motions.

The derivation of space motions and orbital parameters of our program stars from Paper I follows the procedures described by Carollo et al. (2010), which for convenience are summarized below. Similar procedures were employed by Beers et al. (2014) for the supplemental stars; results are listed in Table 5 of that paper.

Corrections for solar motion with respect to the local standard of rest (LSR) are applied during the course of the calculation of the full space motions; here we adopt the values (U, V, W) = (9, 12, 7) km s⁻¹ (Mihalas & Binney 1981). We follow the convention that U is positive in the direction away from the Galactic center, V is positive in the direction of Galactic rotation, and W is positive toward the north Galactic pole. It is also convenient to obtain the rotational component of a star's motion about the Galactic center in a cylindrical frame, denoted as ${V}_{\phi }$ and calculated assuming that the LSR is in a circular orbit with a value of 220 km s⁻¹ (Kerr & Lynden-Bell 1986). Our assumed values of the solar radius (${R}_{\odot }$ = 8.5 kpc) and the circular velocity of the LSR are both consistent with two recent independent determinations of these quantities by Ghez et al. (2008) and Koposov et al. (2009). Bovy et al. (2012) obtained an estimate of the Milky Way's circular velocity at the position of the Sun of V_c(${R}_{\odot }$) = 218 ± 6 km s⁻¹, based on an analysis of high-resolution spectroscopic determinations from APOGEE, which is also consistent with our adopted value.

The orbital parameters of the stars, including the perigalactic distance ${r}_{\mathrm{peri}}$(the closest approach of an orbit to the Galactic center), the apogalactic distance ${r}_{\mathrm{apo}}$ of each stellar orbit (the farthest extent of an orbit from the Galactic center), and the orbital eccentricity e = (${r}_{\mathrm{apo}}$ − ${r}_{\mathrm{peri}}$)/(${r}_{\mathrm{apo}}$ + ${r}_{\mathrm{peri}}$), as well as ${Z}_{\max }$ (the maximum distance that a stellar orbit achieves above or below the Galactic plane), are derived by adopting an analytic Stäckel-type gravitational potential (which consists of a flattened, oblate disk and a nearly spherical massive dark-matter halo; see the description given by Chiba & Beers 2000, Appendix A) and integrating their orbital paths based on the starting point obtained from the observations.

Table 6 provides a summary of the above calculations. Column (1) provides the star names. Columns (2) and (3) list the positions of the stars in the meridional (R, Z)-plane. The derived U, V, and W velocity components are provided in columns (4)–(6); their associated errors are listed in columns (7)–(9). Column (10) lists the velocity projected onto the Galactic plane (V_R, positive in the direction away from the Galactic center), while column (11) lists the derived rotation velocity ${V}_{\phi }$. The derived ${r}_{\mathrm{peri}}$ and ${r}_{\mathrm{apo}}$ are given in columns (12) and (13), respectively. Columns (14) and (15) list the derived ${Z}_{\max }$ and orbital eccentricity e, respectively. The INOUT parameter listed in column (16) is set to 1 if the star is considered in our kinematic analysis, and set to 0 if not.

Errors on our derived estimates of the individual components of the space motions take into account an estimated 15% error in the photometric distances, as well as the individual errors in the proper motions (the average error on our adopted proper motions is 1.3 mas yr⁻¹ in each of the R.A. and decl. component directions) and in the adopted radial velocities (2 km s⁻¹ for the high-resolution determinations, 5 km s⁻¹ for the moderate-resolution determinations, and 10 km s⁻¹ for the medium-resolution determinations). Figure 6 shows the distributions of these errors. After removing the 145 stars that are missing one or more of the input quantities used for the determination of their space motions or have individual estimated errors larger than 50 km s⁻¹ in any one of the three components of space motion, we obtain for our program sample average errors of $\sigma (U,V,W)$ = (5.9, 6.3, 6.9) km s⁻¹. These are slightly smaller errors than were acquired (after the removal of stars having errors in U, V, or W greater than 50 km s⁻¹) for the supplemental stars from Beers et al. (2014), who reported $\sigma (U,V,W)$ = (7.9, 9.1, 6.5) km s⁻¹, presumably due to the inclusion of more distant stars with less certain distances and proper motions.

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For the remaining analysis, we combine our program stars from Paper I with the supplemental sample based on the Beers et al. (2014) analysis of the "weak metal" stars from Bidelman & MacConnell (1973). For the purpose of the kinematic analysis, both samples have had stars with errors in excess of 50 km s⁻¹ in any of the $U,V,W$ velocity components removed from consideration.

Figure 7 presents the individual components of the space motions as a function of [Fe/H] for our combined sample with accepted kinematic estimates; the program stars from Paper I are shown as black dots, while the supplemental sample stars are indicated as red squares. From inspection of this figure, the two samples cover similar ranges of [Fe/H], although in different proportions—the Paper I sample dominates above [Fe/H] = −1.0, the supplemental sample stars exceed the Paper I stars in the metallicity interval $-2.0\lt [\mathrm{Fe}/{\rm{H}}]\lt -1.0$ by about a factor of two, and the Paper I stars dominate the combined sample of stars with $[\mathrm{Fe}/{\rm{H}}]\lt -2.0$, in particular for $[\mathrm{Fe}/{\rm{H}}]\lt -3.0$. The combined sample is heavily populated by stars in the thin-disk and thick-disk stellar populations. Some low-metallicity stars with V velocities in the interval −40 to −80 km s⁻¹ are also present and are likely to be associated with the MWTD.

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Figure 8 is a plot of ${Z}_{\max }$ as a function of [Fe/H] for the combined sample of stars. From inspection of this figure, it is clear that both the Paper I and supplemental samples explore similar regions of this space, further justifying a joint kinematic analysis. For the remainder of our analysis, we thus choose to suppress identification of the individual samples.

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As seen in Figure 8, only a handful of stars with metallicities above [Fe/H] = −1.5 are found to have ${Z}_{\max }$ > 3 kpc. Following previous results from, e.g., Carollo et al. (2010), stars with ${Z}_{\max }$ ≤ 3 kpc and $-1.8\leqslant [\mathrm{Fe}/{\rm{H}}]\leqslant -0.8$ are likely to be associated with the MWTD, although some overlap with the inner-halo population is not precluded, especially at the low end of this metallicity range. Further interpretation of the nature of the MWTD as an individual component is limited by the relatively small numbers of stars, even in the combined sample, that are available in the pertinent metallicity interval.

Figure 9 shows a plot of [Fe/H] as a function of orbital eccentricity for the combined sample of stars. As seen previously (e.g., Norris et al. 1985; Chiba & Beers 2000; Carollo et al. 2007, 2010; Beers et al. 2014), the orbital eccentricity for these non-kinematically selected stars exhibits a very broad metallicity distribution, outside of the region of the metal-richest stars with $e\leqslant 0.2\mbox{--}0.3$, as expected from the currently favored hierarchical assembly model for the formation of the Milky Way.

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The so-called Toomre diagram (a plot of (${U}^{2}+{W}^{2}{)}^{1/2}$, the quadratic addition of the U and W velocity components as a function of the rotational component V), the distribution of orbital rotation velocity ${V}_{\phi }$ for cuts in orbital eccentricity and [Fe/H], plots of the perpendicular angular momentum component ${L}_{\perp }$ as a function of the vertical angular momentum component L_Z, and the Lindblad diagram (a plot of the integral of motion representing the total energy E as a function of L_Z) are commonly used to investigate the nature of the kinematics of stellar populations in the Galaxy. Given the high quality of the estimated kinematics for our combined sample of stars, it is worthwhile to investigate what can be learned from inspection of these diagrams, as discussed individually below.

4.4.1. The Toomre Diagram

Figure 10 shows the Toomre diagram for the combined sample of stars; the legend indicates the metallicity intervals chosen to roughly separate stars expected to belong to the thick (or thin) disk ($[\mathrm{Fe}/{\rm{H}}]\gt -0.8$), the MWTD ($-1.8\lt [\mathrm{Fe}/{\rm{H}}]\leqslant -0.8$), and the halo system ($[\mathrm{Fe}/{\rm{H}}]\leqslant -1.8$) in accordance with Carollo et al. (2010). As expected, the more metal-rich stars in both samples are primarily found in the region with low (${U}^{2}+{W}^{2}{)}^{1/2}$ and high orbital rotation velocities, ${({U}^{2}+{W}^{2})}^{1/2}\lesssim 100$ km s⁻¹ and $-100\lt V\lt 50$ km s⁻¹, while stars with intermediate metallicities are divided between those inside and outside this region. We expect that many of the intermediate-metallicity stars inside this region are associated with the MWTD component. It is also clear from inspection of this figure that the lowest-metallicity stars, with $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.8$, are the dominant contributors to the distribution of stars in the higher-energy regions (those beyond the circle that intersects V = −300 km s⁻¹), as might be expected if they are primarily comprised of members of the outer-halo population, with some overlap from members of the inner-halo population. The stars with energies that place them between the V = −300 km s⁻¹ and V = −200 km s⁻¹ surfaces exhibit a broader range of metallicity, as expected from overlapping inner- and outer-halo populations.

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Figure 10 also indicates two subsets of (newly identified) stars in the combined sample that may belong to previously identified structures in phase-space: (1) likely members of the stream/trail of stars first identified by Helmi et al. (1999) and further populated by stars in the sample considered by Chiba & Beers (2000), indicated by light-green squares, and (2) possible members of the debris stream associated with the globular cluster ω Cen, following the work of Dinescu (2002), Klement et al. (2009), and Majewski et al. (2012), indicated by light-blue circles. Justification for the selection of these stars is provided below.

4.4.2. Distribution of ${V}_{\phi }$

Figure 11 is a stripe-density diagram of the distribution of ${V}_{\phi }$ for our combined sample of stars for metallicity intervals chosen to emphasize the various kinematic components of the Milky Way, split into two regions of orbital eccentricity, $e\leqslant 0.3$ (upper panels, expected to be dominated by members of the disk system) and $e\gt 0.3$ (lower panels, expected to be dominated by members of the halo system). For each interval in metallicity, the black stripes indicate the mean ${V}_{\phi }$ for that sub-sample of stars. The light-green and light-blue stripes indicate stars that we argue below are candidate members of the Helmi et al. stream/trail and the ω Cen debris streams, respectively.

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Inspection of Figure 11 generally meets expectation based on previous work. The low-eccentricity stars for all three sub-panels with $[\mathrm{Fe}/{\rm{H}}]\gt -1.8$ exhibit rotational properties consistent with those of the disk system of the Milky Way (thin disk, thick disk, and MWTD), while those with $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.8$ appear to be primarily members of the inner- and outer-halo populations. The high-eccentricity stars preferentially populate the sub-panels with $-1.8\lt [\mathrm{Fe}/{\rm{H}}]\leqslant -0.8$ and $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.8$, consistent with membership in the inner- and outer-halo populations, with overlapping contributions from each.

It is worth noting that the presence of putative members of the two debris streams has a potentially large impact on interpretation of the distribution of ${V}_{\phi }$ among the high-eccentricity stars with $[\mathrm{Fe}/{\rm{H}}]\lt -1.8$, with these members populating both the central region of the stripe plot (the Helmi et al. stream/trail) and the high-velocity tail (the ω Cen debris stream).

4.4.3. L_⊥ versus L_Z

The left panel of Figure 12 shows the distribution of stars in angular momentum space (L_⊥, L_Z), where L_⊥ = (L_X² + L_Y²) and L_Z is the vertical angular momentum. The three different ranges of metallicity are identified with different colors, shown in the figure legend.

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Two interesting features are seen in this diagram: (1) a clump of stars with $[\mathrm{Fe}/{\rm{H}}]\lt -1.8$ (with the exception of two stars with higher metallicity) located at L_⊥ ∼ 2000– 2900 kpc km s⁻¹ and L_Z ∼ 800–1600 kpc km s⁻¹ (indicated by the solid black box in the figure) and (2) an elongated distribution of stars with $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.8$ located at L_⊥ > 1500 km s⁻¹ and −400 ≲ L_Z ≲ 300 kpc km s⁻¹ (indicated by the orange box).

The first feature was identified by Helmi et al. (1999), comprising 7 stars with $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.6$ and 12 stars with $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.0$. Chiba & Beers (2000) detected the same stream among their sample of 1203 stars over similar ranges in metallicity. They also identified a possible trail in angular momentum space located at 1250 kpc km s⁻¹ < L_⊥ < 2000 kpc km s⁻¹ and 1200 kpc km s⁻¹ < L_Z < 2000 kpc km s⁻¹ and covering similar metallicity ranges (their Figure 15). This is similar to the trail identified in Figure 12, occupying the region defined by the dotted black box and covering angular momentum ranges of L_⊥ = [1300, 2000] kpc km s⁻¹ and L_Z = [1000, 1600] kpc km s⁻¹, but at lower metallicities $[\mathrm{Fe}/{\rm{H}}]\leqslant -1.8$. Note that a few stars with metallicities above [Fe/H] = −1.8 are also within the areas delimited by the two boxes associated with the Helmi et al. stream/trail.

The second feature (orange box) is similar to the excess of stars located in the phase-space noted by Dinescu (2002) within the Chiba & Beers (2000) data set. Dinescu argued that these stars may be part of a debris stream associated with the globular cluster ω Cen. Dinescu (2002) found that most of the stars in this region possessed slightly retrograde orbits, as is also the case for ω Cen, and discovered another two clusters (NGC 362 and NGC 6779) that present similar retrograde orbits. The author also suggested that the cluster ω Cen (shown as a large orange star in the figure), as well as the two other globular clusters, may have been stripped, along with numerous other stars, from a proposed parent dwarf galaxy now dissolved into the halo-system population.

4.4.4. The Lindblad Diagram, E versus L_Z