adopted to track and ensure accumulated signal over multiple visits. Delivered performance in this area is demonstrated by Figure 19, which shows the distribution of S/N measured in three-visit spectra of all stars (main science and ancillary targets, amounting to ~1600 stars) in a narrow range of (undereddeden) magnitudes ($12.15 < H < 12.20$) at the three-visit plate limit of $H = 12.2$.$^{75}$ The distribution is nearly Gaussian (despite the long tail toward very low S/N), with a peak at S/N ~ 93. The FWHM spread in S/N is about 30 or $\sigma \sim 13$, which, for $\bar{S}/\bar{N} = 93$ translates into a $\pm 0.32$ mag ($1\sigma$) dispersion in flux. A small fraction of this spread can be ascribed to photometric uncertainties in the 2MASS catalog ($\sigma_H \sim 0.02$ mag at $H = 12.2$),$^{76}$ but most of it is likely due to variable seeing and extinction due to clouds, since conditions during data collection were often non-photometric. The latter reflects the realities of accommodating variable weather conditions within a semi-rigid observing plan structured on gathering set numbers of paired 500 s standard exposures for each plugplate (nominally a dozen pairs for each three-visit plugplate). Assuming that the whole of the scatter is due to weather and seeing variations, one finds that for the best observing conditions, represented by those observations more than $1\sigma$ ($2\sigma$) above the median of the distribution, the S/N achieved was about 106 (118), indicating that the spectrograph delivered, and probably exceeded, the throughput needed to meet the S/N requirement established at the survey outset.

### 7.3. Derived Parameters

More important than achieving a nominal S/N requirement is the ability to achieve the desired uncertainties on higher level survey data products, and in this regard APOGEE has generally succeeded. A good estimate of RV precision can be obtained from analysis of repeat measurements of single stars. In DR12, the RV residuals for stars with multiple visits and S/N $\ge 20$ peak at $\sim 70$ m s$^{-1}$ (Nidever et al. 2015). Uncertainties in the cross-correlation method tend to be smaller for spectra with lots of sharp absorption lines. Therefore, RVs are more accurate for cooler and/or metal-rich giants than for metal-poor and/or hotter/high surface gravity stars, whose spectra are characterized by fewer and/or broader absorption lines, respectively. In any case, the precision achieved surpasses the stated requirement (Section 2.4). The absolute RV zeropoint of APOGEE is estimated to be $\sim 350 \pm 30$ m s$^{-1}$, from comparison with data from other sources for stars in common (Nidever et al. 2015).

Even though no technical requirements were specified for the stellar parameters $T_{\text{eff}}$ and $\log g$, they drive the accuracy of derived chemical abundances and spectroscopic parallaxes. Figure 20 shows the final DR12 values (Holtzman et al. 2015) for APOGEE stars in a “spectroscopist’s HR diagram.” The final stellar parameters adopted and shown in this plot result from calibration of the raw parameters delivered by ASPCAP against photometry and abundance data from the literature, and asteroseismological surface gravities from APOKASC (Pinsonneault et al. 2014), as described by Holtzman et al. (2015). There is very good agreement between stellar parameters from APOGEE spectra and independent theoretical predictions,

<figure><img src="image_22.png" /><figcaption>**Figure 20.** Final, calibrated, ASPCAP-derived DR12 parameters for main survey stars in the nominal temperature range of the APOGEE main sample. Colors show the metallicities derived for the stars according to the scale on the right. The lines show Padova PARSEC (Bressan et al. 2012) isochrones for 5 Gyr populations at metallicities of $[\text{M/H}] = -1.5, -1.0, -0.5, 0.0$, and $+0.3$, against which the calibrated spectral metallicities for individual stars may be compared. The apparent mismatch of the isochrones to the derived stellar parameters for more metal-poor stars is partly due to the use of 5 Gyr isochrones, whereas those metal-poor stars are likely older. In addition, the isochrones shown are for solar-scaled abundances, whereas metal-poor stars tend to be $\alpha$-enhanced.</figcaption></figure>

shown by the isochrones. Of course, some scatter of the data about the isochrones is expected given the dispersion of the sample in age and $[\alpha/\text{Fe}]$ at any metallicity. Moreover, some unresolved issues remain. The most important example happens for red clump stars, which should be distinctly separated from the red giant branch. Stellar evolution models, which are confirmed independently by accurate gravities from asteroseismology for a subsample of APOGEE stars in the Kepler field (e.g., see Figure 18 of Pinsonneault et al. 2014), predict a narrow range of surface gravities for red clump stars. Such a feature is not seen in APOGEE data, which instead show a correlation between $T_{\text{eff}}$ and $\log g$. Another unresolved issue is the slightly too warm APOGEE temperatures at the cool end. These are areas where refinements in ASPCAP will bring improvements in the future. For a further discussion of these issues, see Holtzman et al. (2015) and García Pérez et al. (2016).

The precision and accuracy of the derived elemental abundances are reviewed in detail by Holtzman et al. (2015). To achieve the goals in probing GCE specified in Section 1.3, APOGEE had a specification for a precision in measured chemical abundances of 0.1 dex, and an accuracy of 0.2 dex. The precision of the actually derived APOGEE elemental abundances was established by measuring the dispersion of the measurements at fixed $T_{\text{eff}}$ in clusters stars, where the abundances are expected to be constant. Precisions were found to be better than 0.1 dex for all top and medium priority elements, thus formally meeting the original requirement. For many elements, precisions are better than 0.05 dex and for only one low priority element (vanadium) is the precision worse than 0.1 dex.

Comparison of APOGEE [Fe/H] with mean literature abundances of cluster stars based on HR optical spectroscopy shows that the 0.2 dex accuracy requirement is met everywhere, except perhaps for [Fe/H] lower than $\sim -1.5$. In view

<footnote>$^{75}$ We quote the median S/N per pixel in the combined spectrum, as given in DR12.</footnote>

<footnote>$^{76}$ http://www.ipac.caltech.edu/2mass/releases/allsky/doc/figures/secii2f9.gif</footnote>
<figure><img src="image_23.png" /><figcaption>**Figure 21.** Time series data of a double-lined spectroscopic binary, illustrating the variation in the position of the lines for both the primary (lines marked by blue arrows) and secondary (red arrows) stars in the system.</figcaption></figure>

of the presence of clear systematic differences between “raw” derived APOGEE values via ASPCAP and literature values (where APOGEE values are higher by up to 0.2 dex), a calibration to convert APOGEE [Fe/H] into the literature scale was derived (Holtzman et al. 2015). For some of the other elements, abundance ratios—i.e., [X/Fe], computed by adopting the non-calibrated [Fe/H]—compare well with the literature, in spite of some scatter, which is likely due to the heterogeneity and uncertainties in the literature data. For a few elements, such as Ca and Ti, trends with $T_{eff}$ are found. In the absence of a statistically significant homogeneous sample of optical data from the literature, it is difficult at this stage to draw firm conclusions regarding the APOGEE accuracy for some of the elemental abundances. Nevertheless, while the original requirements are met for most of the elements, more work is required, on one hand, to refine the elemental abundances delivered by ASPCAP and, on the other, to more firmly establish the systematic differences that will inevitably be present between the APOGEE abundance scales and those of other large observational programs (typically performed at optical wavelengths).

## 7.4. Science Demonstrations of Data Capabilities

The achieved performance and capabilities of APOGEE are perhaps most eloquently demonstrated by examples of how the collected data may be used in a wide variety of science applications. In this section, we briefly discuss a few examples of published and in preparation research based on APOGEE data, with an eye toward illustrating the breadth of potential APOGEE science, both within the confines of Galactic astronomy and beyond. The order of presentation of these science examples roughly tracks the degree of processing of the APOGEE data, as described in Section 6—i.e., from direct analyses of the spectral character of sources, to analyses of derived stellar velocities, to explorations of bulk metallicity and then more detailed chemical abundance patter data, to even higher level results made possible by inclusion of derived stellar ages, and concluding with analyses incorporating the former information for the analysis of star clusters and the interstellar medium.

<figure><img src="image_24.png" /><figcaption>**Figure 22.** Close-up view of the variation in the Brackett 11 (16811 Å) line in one of the Be stars discovered by APOGEE (HD 232940, with $V = 9.45$, $H = 8.62$).</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>**Figure 23.** (Re-)discovery of the hot Jupiter around HD 114762 using 11 epochs of APOGEE data.</figcaption></figure>

### 7.4.1. Time Series Spectral Data

The time series data that are available from multi-epoch observations of the majority of APOGEE targets (e.g., Figure 18) lend themselves to a number of useful applications. These include, e.g., the identification of binary stars that partly motivated this survey strategy (Section 2.8). For instance, Figure 21 shows an example of a double-lined spectroscopic binary made evident through the multi-epoch spectroscopy). As another example of the interesting phenomena that a detailed exploration of APOGEE’s time series spectral data might uncover, Figure 22 shows the strong variation in a Brackett series line for one of the numerous Be stars discovered by APOGEE (Chojnowski et al. 2015) within the sample of hot stars observed for telluric absorption correction.

### 7.4.2. Time Series Precision Velocity Data

The high precision of the APOGEE radial velocity measurements, made possible by the tightly controlled environmental conditions (gravity vector, temperature, vacuum) of the APOGEE spectrograph combined with the
<figure><img src="image_26.png" /><figcaption>**Figure 24.** Star-by-star APOGEE heliocentric velocities as a function of Galactic X–Y position and projected on an artist’s conception image of the Milky Way. The points represent main APOGEE survey stars (i.e., excluding those in the *Kepler* field) having projected $|Z_{GC}| < 2$ kpc and log g ≥ 1. Only stars with no “bad” flags in the database are used. (Background image credit, R. Hurt, NASA/JPL-Caltech.)</figcaption></figure>

availability of multi-epoch visits, makes the survey sensitive to not only stellar, but also substellar mass companions. The opportunity for large-scale statistical explorations of brown dwarfs and even hot Jupiters is illustrated by Figure 23, which shows one of a number of exoplanet candidates identified within the APOGEE database. In this case, the star, HD 114762, has a known $11M_{Jup}$ companion in an 83.9 day period (Latham et al. 1989). Before recognizing that this was a previously known exoplanet, the APOGEE team, through a project to automatically fit multi-epoch APOGEE velocity data, determined this source to have a $14M_{Jup}$ companion in a 77.9 day period. This result, based on only 11 APOGEE spectra, is not far from that already determined by Latham et al. The rms of the best fit to this relatively bright star system yields a residual of only 33 m s⁻¹; further refinements in the velocity measurement pipeline may bring similar rms precisions to fainter stars and perhaps enable further improvements in velocity precision for brighter stars.

### 7.4.3. Radial Velocities Across the Galaxy

While not all stars in the APOGEE database will have more than several radial velocity measurements (see Figure 18), almost all of them will have mean radial velocities measured with an accuracy greater than is typically found in previous large spectroscopic surveys of Milky Way stars. Combined with its systematic probe of all stellar populations, APOGEE’s radial velocity database makes possible new large-scale explorations of Galactic dynamics (e.g., see Figure 24). Because APOGEE was designed to include extensive and deep probes of the low-latitude Milky Way, including the highly extinguished regions of the disk and bulge, previously

<figure><img src="image_27.png" /><figcaption>**Figure 25.** Same as Figure 24, but with points color-coded by metallicities [M/H] and using stars with projected $|Z_{GC}| < 2$ kpc. (Background image credit, R. Hurt, NASA/JPL-Caltech.)</figcaption></figure>

poorly studied regions of the Galaxy have now been opened up to extensive kinematical canvassing. As a result, a number of Galactic dynamical phenomena have already been discovered or reexamined with unprecedented statistical significance, including the discovery of a kinematically extreme population in the bulge (Nidever et al. 2012), likely associated with the Galactic bar (Aumer & Schönrich 2015; Molloy et al. 2015); a comprehensive analysis of the dynamics of the bulge (Ness et al. 2016b); a new derivation of the circular velocity of the Sun afforded by the more global APOGEE view of disk kinematics (Figure 24; Bovy et al. 2012, 2015); and finally, an assessment of the power spectrum of non-axisymmetric velocity perturbations of the disk, of which most can be attributed to the action of the central bar (Bovy et al. 2015).

### 7.4.4. Metallicities Across the Galaxy

A primary goal of the APOGEE survey is to probe the large-scale distribution of stellar chemical compositions across the Galaxy. Typical results are demonstrated by the [M/H] metallicity gradients shown in Figure 25, where the distribution of APOGEE targets projected onto the *XY* plane is displayed. Accurate measurements of gradients across a range of distances, both Galactocentric and away from the Galactic plane, provide strong constraints on models for the formation of the thick and thin Galactic disks (for further details on the application of APOGEE to these problems, see Bovy et al. 2014; Anders et al. 2014; Hayden et al. 2014, 2015; Nidever et al. 2014).

### 7.4.5. Multi-element Abundance Variations

The power of APOGEE to deliver similar information for multiple chemical elements and with great statistical power is illustrated by Figure 26, a representation of the metallicity
<figure><img src="image_28.png" /><figcaption>**Figure 26.** Direct spectral representation of the Milky Way disk's metallicity gradient. This figure displays median-stacked normalized APOGEE spectra of RC stars in bins of Galactocentric radius of width 0.1 kpc and normalized by the spectrum at the solar circle (assumed to be *R* = 8 kpc, indicated by the dashed line). Redder/ bluer colors represent more/less absorption compared to that at the solar circle. Only about one-sixth of the full APOGEE spectral range is shown here, primarily regions containing strong, clean lines and representing all of the elements whose abundances can be determined from APOGEE spectra. Some of the interesting lines of neutral-atomic and molecular species as well as their central wavelengths are labeled at the top. Because RC stars span a narrow range of stellar parameters, absorption line strengths translate into rough elemental abundances directly. All elements display a clear abundance gradient from the inner to the outer disk. The only exception perhaps is vanadium, which is based on a very weak line at 15929 Å that becomes vanishingly weak beyond the solar circle.</figcaption></figure>

gradient in the Milky Way's disk using APOGEE spectra directly. We stack the pseudo-normalized spectra of RC stars in the DR12 APOGEE-RC catalog (Bovy et al. 2014) as a function of Galactocentric radius in bins of width 0.1 kpc and normalize by the stacked spectrum at the solar circle (*R* = 8 kpc). Because the RC occupies a small region in (log g, *T*<sub>eff</sub>), the *T*<sub>eff</sub> and log g values for RC stars are all very similar, so that spectrum-to-spectrum differences in absorption line strengths are mostly due to star-to-star elemental abundance variations. This figure clearly demonstrates that metal absorption increases toward the center of the disk and decreases toward the outskirts for every element with transitions in the APOGEE spectral region (except for vanadium, which has such a weak line that absorption disappears almost completely around the solar circle). A quantitative measurement of the overall radial [M/H] gradient of the RC sample is −0.09 ± 0.01 dex kpc<sup>-1</sup> (Bovy et al. 2014).<sup>77</sup>

### 7.4.6. Analysis of Abundance Patterns

A central rationale for APOGEE's sensitivity to the abundances of multiple chemical elements is to access the information contained in variations of chemical abundance patterns, particularly for patterns containing elements synthesized on different evolutionary timescales within populations. The power of APOGEE to probe GCE in this way is demonstrated by Figure 27, which shows the spatial distribution of [Mg/Fe] with [Fe/H] in different spatial zones of the Galactic disk. Figure 27 is a more elemental-specific example of the more general [α/Fe] distributions explored in Anders et al. (2014), Nidever et al. (2014), and Hayden et al. (2015), and shows that APOGEE not only confirms the existence of a bimodal distribution of [α/Fe] at fixed [Fe/H], but that this bimodality exists over a large extent of the disk, including for previously uncharted Galactocentric distances for |z| < 0.5 kpc (see Hayden et al. 2015 for an even more extensive coverage of

<figure><img src="image_29.png" /><figcaption>**Figure 27.** Spatial variation of [Mg/Fe] vs. [Fe/H] distributions across the Galactic disk, from Nidever et al. (2014).</figcaption></figure>

the disk). These results pose important constraints on disk formation models, in particular calling for the presence of two stellar populations with different chemical enrichment histories in the outer Galactic disk. That APOGEE data can provide such data across a large multidimensional space of elements probing different nucleosynthetic pathways is further demonstrated by the results shown in Figure 30 below.

### 7.4.7. Stellar Ages

Collaboration between the APOGEE and the *Kepler* and *CoRoT* asteroseismology teams has greatly increased the power of APOGEE data to shed light on Galaxy formation scenarios. The combination of APOGEE chemical compositions with

<footnote n="77">⁷⁷ While some radii do not follow the overall radial trend (e.g., the stacked spectrum at *R* = 7 kpc is almost exactly that at the solar circle), this is most likely due to first-ascent RGB contamination in the APOGEE-RC catalog.</footnote>
<figure><img src="image_30.png" /><figcaption>**Figure 28.** Chemical abundance patterns informed by individual stellar ages, derived from the combination of *Kepler* asteroseimology and APOGEE chemistry (see Martig et al. 2016).</figcaption></figure>

asteroseismological data makes possible the determination of accurate masses, and thus ages, for a large sample of APOGEE field giants (Pinsonneault et al. 2014). Demonstrations of the power of analyzing combined detailed chemical compositions and ages from these APOGEE subsamples are starting to emerge (e.g., Epstein et al. 2014; Chiappini et al. 2015; Martig et al. 2015); one example is demonstrated in Figure 28, which shows the unexpected discovery (Martig et al. 2015) of a small sample of stars with high [α/Fe] and relatively low ages (~3–5 Gyr). The mere existence of intermediate-age stars with such high [α/Fe] constitutes a serious challenge to existing chemical evolution models and is, as yet, not fully explained.

### 7.4.8. Open Clusters

The APOGEE database has made the targeting of star clusters a priority, not only because they provide reliable abundance calibration references, but because they are extremely useful stellar population components of great interest in their own right. Open clusters, in particular, provide a powerful, independent means by which to explore the chemistry, kinematics, and extinction of the Galactic disk because cluster distances can be precisely gauged via isochrone fitting, made all the more accurate when the variable of metallicity can be removed using spectroscopic metallicities. An important output of such isochrone fits are cluster ages, which provide critical and confident timestamps for benchmarking evolutionary studies across the disk. Fortunately, apart from a set of key open clusters that drove specific plugplate pointings, the vast majority of the large APOGEE sample of over 150 open clusters was a natural product of its extensive canvassing of the Galactic plane, and only required attention to the allocation of fibers on already overlapping plugplates from the APOGEE grid to known or suspected members of these clusters. As part of the Open Cluster Chemical Analysis and Mapping (OCCAM) survey (Frinchaboy et al. 2013), these data have already been used to study disk metallicity gradients and abundance patterns as a function of both space and time; an example of the opportunities opened up with this kind of analysis is demonstrated in Figure 29.

### 7.4.9. Globular Clusters

Unlike the open clusters, where spectra of large samples of cluster members are easily generated as part of APOGEE's systematic coverage of the Galactic disk, considerable investment of effort, planning, and survey time was needed to ensure ample attention to globular clusters. Many globular clusters are distant,

<figure><img src="image_31.png" /><figcaption>**Figure 29.** APOGEE-derived metallicity and [α/Fe] (using the reliable individual DR12 elements O+Ca+Si as α) as a function of Galactocentric radius for 29 clusters in two age regimes: blue (orange) points denote clusters younger (older) than 1 Gyr. The light gray region in the upper panel shows a gradient in [Fe/H] of −0.06 dex kpc⁻¹ within R<sub>GC</sub> = 15 kpc and hints at a flat distribution (admittedly based on very few data points) beyond with a spread of 0.2 dex. A shallower, positive gradient, of +0.007 kpc⁻¹ dex, is seen in [α/Fe] (lower panel), consistent with previous literature-based open cluster studies (e.g., Yong et al. 2012). Additional individual element abundance gradients are explored in P. M. Frinchaboy et al. (2017, in preparation).</figcaption></figure>

which makes even their giant stars relatively faint and means that the stars are densely packed on the sky relative to the fiber-to-fiber collision radius (see Section 2). These two facts typically necessitated many visits to specialized fields (see Figure 10), with multiple plugplate designs to accumulate long integrations on fainter targets and to overcome the collision radius limitations to generate reasonable sample sizes. Nevertheless, the globular cluster visits were deemed high priority both because the member stars are extremely useful calibration targets and because the chemistry of globular clusters is itself interesting and relevant to understanding the evolution of Milky Way stellar populations.

The study of globular cluster formation is undergoing a revolution since the discovery of the commonality of multiple populations in these systems (e.g., Piotto et al. 2007; Milone et al. 2008; Gratton et al. 2012), which has been established predominantly on the basis of observations collected from the Southern Hemisphere. APOGEE is already making important contributions to the study of globular cluster evolution through the determination of accurate multi-element abundances of relatively large samples of northern cluster members. This is illustrated in Figure 30, which, for the majority of the 10 clusters shown (eight that were never previously studied in this way), gives evidence for strong internal Al abundance variations—in some cases anti-correlated with Mg—a feature commonly interpreted as the signature of the presence of multiple stellar populations. Interestingly, APOGEE has shown that some globular clusters (M3, M53) display apparently discrete Al–Mg distributions (i.e., Al-rich and Al-poor groups), while others (e.g., M13, M5) may show a more continuous distribution in the Al abundances (Mészáros et al. 2015). APOGEE data have also been used to test previous claims of the presence of multiple populations in the well-known, unusually large, old but super-metal-rich open cluster, NGC 6791 (Cunha et al. 2015).

A distinct advantage afforded by these APOGEE studies of globular clusters is that the inferred chemistry of the member stars may be directly compared to those of the numerous field
<figure><img src="image_32.png" /><figcaption>**Figure 30.** Abundance spreads and anti-correlations as seen for 428 giant star members in 10 northern hemisphere globular clusters. Figure from Mészáros et al. (2015).</figcaption></figure>

stars surveyed in precisely the same way. An example of the power of such comparisons, with interesting implications for our understanding of both globular cluster and galaxy bulge formation, is the discovery of remnants of globular cluster destruction in the Galactic bulge—long predicted by theoretical arguments (Tremaine et al. 1975)—through the identification of chemical signatures typical of globular cluster stars in an APOGEE sample of field bulge stars (Schiavon et al. 2017).

### 7.4.10. Mapping Interstellar Extinction

The combination of APOGEE spectroscopy with available photometric databases, such as those provided by 2MASS or the *Spitzer* IRAC surveys, increases the scope of approachable astrophysical problems. For example, comparison of spectroscopically derived atmospheric properties with measured broadband colors can give key, star-by-star measurements of the distribution of interstellar reddening, and therefore a powerful means by which to explore the three-dimensional distribution of dust. For example, Figure 31 shows the distribution of derived $K_s$-band extinction across the Galactic plane, with the extinctions derived by comparing observed colors to the intrinsic colors expected from theoretical isochrones matched to the ASPCAP-derived values of $T_{eff}$, log g, and [M/H] (see Schultheis et al. 2014), and distances derived from comparing apparent and associated isochrone absolute magnitudes. Apart from showing global trends in dust properties, studies such as this can help calibrate or highlight inadequacies in extinction maps derived by other means.

### 7.4.11. Mapping Diffuse Interstellar Bands

The accuracy with which the APOGEE spectral library matches the intrinsic spectra of typical giant stars makes possible further explorations of interesting astrophysics that is unrelated to the stars themselves. For instance, disagreements between spectral synthesis and observations may reveal the presence of absorbers/emitters along the line of sight. A compelling example of this is shown in Figure 32, where the difference between an observed spectrum and its best-matching synthetic template reveals the presence of a relatively strong diffuse interstellar band (DIB; Herbig 1995). Using the fact that this same DIB feature is seen in the vast majority of APOGEE spectra along disk and bulge sight lines, Zasowski et al. (2015)

<figure><img src="image_33.png" /><figcaption>**Figure 31.** Distribution of extinction across the Galactic plane, as measured by comparing star-by-star photometric and spectroscopic data to derive $A_{K_s}$, according to the isochrone matching method discussed in Schultheis et al. (2014). Point positions correspond to the projected locations of the stars against which the extinction was measured. Only stars from DR12 with $|Z_{GC}| < 500$ pc are shown. Note the substantial increase in extinction at the spiral arm toward the outer disk and also toward the Galactic center. (Background image credit, R. Hurt, NASA/JPL-Caltech.)</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Figure 32.** (Left) Comparison of synthetic (red lines) to observed (black lines) APOGEE spectra for two late-type giant stars (panels a and b) and a hotter star (panel c). (Right) The difference spectra (blue points) clearly show the DIB feature at 15272 Å, which can be fit with simple Gaussians (black lines) to measure column density and varying Doppler velocities (Zasowski et al. 2015).</figcaption></figure>

for the first time thoroughly mapped the spatial distribution and velocity field of a DIB carrier over many kiloparsecs of the Galactic disk (Figure 33). Comparison of these properties to those of other components of the ISM (dust, atomic and molecular gas) will yield critical evidence toward the identification of the carriers of these mysterious spectroscopic signatures—a longstanding puzzle in Galactic astrophysics.

## 8. Data Products, Distribution, and Documentation

### 8.1. Data Products

There are two main sets of APOGEE data products. The first consists of wavelength-calibrated, normalized, 1D rest-frame
<figure><img src="image_35.png" /><figcaption>**Figure 33.** Same as Figure 31, but for the distribution of measured $\lambda$ 15272 Å DIB strength (Zasowski et al. 2015). As with Figure 31, the plotted points correspond to the projected locations of the stars against which the DIB absorption was observed. Only stars from DR12 having $|Z_{GCl}| < 500$ pc are shown. (Background image credit, R. Hurt, NASA/JPL-Caltech.)</figcaption></figure>

spectra, and the radial velocities resulting from analysis of visit spectra. These data products are the outputs of the data reduction and radial velocity pipelines, described in Sections 6.1–6.4. The second set of data products contains the stellar parameters ($T_{\text{eff}}$, log g, [M/H]) and the abundances of up to 15 elements, namely, C, N, O, Na, Mg, Al, Si, S, K, Ca, Ti, V, Fe, Mn, and Ni. The latter set results from application of ASPCAP (Section 6.5) to the spectra. To ensure that the high-level data can be reproduced by the community, ingredients that are crucial for the stellar parameter and elemental abundance determinations—such as the adopted model atmospheres (Mészáros et al. 2012), line list (Shetrone et al. 2015), and grids of synthetic spectra (Zamora et al. 2015)—are also publicly available.

## 8.2. Data Releases

The data products from the three-year APOGEE survey have been included in several SDSS-III data releases (DRs). In Data Release 10 (DR10, announced 2013 July), calibrated APOGEE spectra, radial velocities, stellar parameters, and a limited set of elemental abundances were made available for 57,454 stars (Ahn et al. 2014). DR12 (made available in 2015 January) includes the data described in Section 8.1 for all ~136,000 primary science targets in the SDSS-III/APOGEE sample (Alam et al. 2015; Holtzman et al. 2015). In addition, radial velocities for the ~17,000 hot stars<sup>78</sup> used as telluric standards, as well as spectra and derived parameters for approximately 900 bright stars observed using the APOGEE feed from the NMSU 1 m telescope (Section 5.3.3), are also included in DR12. In 2016, a further data release, DR13 (SDSS

Collaboration et al. 2016), was made that included new reductions of these same APOGEE spectra but with improved telluric subtraction, upgraded pipelines, and grids of synthetic spectra (including rotational broadening for dwarf star spectra and extension to cooler stars, to $T_{\text{eff}}$ = 3500 K) and updated abundance determinations, including the addition of several atomic species (C I, P, Ti II, Co, Cu, Ge, and Rb) previously not analyzed or newly found to have lines in the APOGEE spectra. Further improvements in the pipelines and data will be found in DR14, to be released in the summer of 2017.

## 8.3. Data Access

APOGEE data can be accessed in a number of different ways through the http://www.sdss.org Web site. The SDSS-III Catalog Archive Server (CAS) contains the high-level APOGEE data products, namely, radial velocities, radial velocity dispersion, $T_{\text{eff}}$, log g, [M/H], and elemental abundances, as well as information relevant to target selection, including, e.g., coordinates, 2MASS, WISE, Spitzer/IRAC, and Washington+DDO51 photometry, proper motions, where available, and assumed interstellar extinction. These data can be accessed via low-level SQL scripts, which allow users to select subsamples according to suitable criteria in the CasJobs link. Lower level data products, including the visit and combined spectra of sources searchable via standard, basic, or advanced online forms, can be accessed with the SAS. The SAS also provides access to the directory tree containing the full data set (for expert users), as well as a summary FITS file containing all of the catalog information listed above. The SkyServer offers another way of interfacing with the data, through a “quick look” tool that makes possible non-interactive visualization of images and spectra of sources that are searchable by position and ID, via an online form. Finally, both the SAS and SkyServer link to a Web tool that allows for a quick assessment of data and model quality, through interactive viewing of the (final) observed spectra overplotted with the best-fitting synthetic spectrum.

## 8.4. Documentation

The primary source of in-depth information for users of APOGEE data are the technical papers listed in Table 1. Additional, often less detailed, information can be obtained in the Web pages associated with each data release. Users of APOGEE are strongly urged to peruse those Web pages or technical papers for a complete understanding of the data quality, limitations, and caveats that are specific to each data release (Ahn et al. 2014; Holtzman et al. 2015). Users of high-level data products should pay particular attention to the documentation pertaining to ASPCAP (Mészáros et al. 2012, 2013; Smith et al. 2013; Shetrone et al. 2015; Zamora et al. 2015; García Pérez et al. 2016), where the limitations and known systematics in the APOGEE stellar parameters and elemental abundances are described. On the other hand, users of APOGEE spectra will be interested in information about possible systematics induced by instrument features and reduction procedures (Nidever et al. 2015; J. C. Wilson et al. 2017, in preparation). A good grasp of the possible biases introduced by APOGEE’s target selection procedure and field placement strategy (Zasowski et al. 2013) is encouraged for those exploring global properties, trends, and correlations for stars across the Galaxy, and for those comparing these empirical results to chemical and/or chemodynamical models of stellar populations.

<footnote n="78"><sup>78</sup> This number includes both survey-quality and commissioning data.</footnote>
# 9. Future Efforts

## 9.1. Software Development and Future Data Releases

As part of APOGEE-2 (Section 9.2), we continue to develop our data reduction and analysis capability. In addition, it is expected that our understanding of the atomic and molecular physics related to the relevant line transitions will continue to evolve. Therefore, to maintain consistency across the integrated APOGEE-1 and APOGEE-2 efforts, future APOGEE data releases will be expected to include updated analyses of the APOGEE-1 data.

## 9.2. APOGEE-2 in SDSS-IV

In 2012, the APOGEE team proposed to continue with an APOGEE-2 program in Sloan Digital Sky Survey IV. Beyond an immediate continuation of operations on the Sloan Telescope, a key feature of this proposal is the extension of the APOGEE-2 program into the Southern Hemisphere, in a collaboration with the Observatories of the Carnegie Institution for Science (OCIS) to use the du Pont 2.5 m telescope for this purpose. The du Pont is very much a forerunner of the Sloan Telescope, having been designed with a wide FOV (Babcock 1977) and with a heritage in fiber plugplate spectroscopy (Shectman et al. 1996) that influenced the subsequent design of the SDSS system. APOGEE-2 was approved as an SDSS-IV program in 2012, and APOGEE-2 began observing at APO in 2014 September. The current instrument at APO is the same as that described in Section 3 with one important modification in that the blue detector with “superpersistence” has been replaced with a cosmetically cleaner array free of this problem.

While initially it was unclear whether APOGEE-2 would operate with two spectrographs working on the Sloan and du Pont Telescopes in parallel or whether the existing spectrograph would be moved to the du Pont after an initial two-year campaign on the Sloan Telescope, by 2014 November complete funding was secured to build a second APOGEE spectrograph to make parallel operations possible. With the active participation of OCIS, Chilean universities, and other SDSS-IV collaborators, the southern infrastructure development, including the creation of a scaled-down version of the Sloan fiber plugplate system (cartridges, plugging station, mapping system, cartridge transport and loading system), is underway, as is the construction of an infrastructure “mock-up and training facility” in a special laboratory at the University of La Serena, Chile. The second APOGEE spectrograph, which is planned as a near duplicate of the original with only minor alterations (e.g., to include seismic mitigation and to incorporate various other “lessons learned”), is currently planned to begin operations on the du Pont Telescope in mid-2015.

When it is necessary to distinguish it from the APOGEE-2 survey, the original “APOGEE” survey will in the future be referred to as “APOGEE-1.” Henceforth, the term “APOGEE” will generally be intended to refer to the combined APOGEE-1 and APOGEE-2 surveys, which together will provide a fully comprehensive, all-sky view of the Milky Way.

We thank the referee for thorough comments that helped improve the paper. We are also grateful to Whitney Richardson for assistance with Figure 13.

S.R.M. acknowledges support from National Science Foundation grant AST-1109178 and AST-1616636.

R.P.S. acknowledges support from the Gemini Observatory, which is operated by the Association of Universities for

Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, and the United States of America.

D.A.G.H. and O.Z. acknowledge the support provided by the Spanish Ministry of Economy and Competitiveness under grant AYA-2011-27754. S.M. acknowledges support from the NASA grant NNX12AE17G.

Sz.M. has been supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the Premium Postdoctoral Research Program of the Hungarian Academy of Sciences, and by the Hungarian NKFI Grants K-119517 of the Hungarian National Research, Development and Innovation Office.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III Web site is http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofísica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

# Appendix A

## H-band Line Maps for Individual Molecules and Atoms

Winnowing to the desired APOGEE wavelength range initially involved inspection of the Hinkle et al. (1995) atlas of the infrared spectrum of Arcturus (Section 2.2), followed by use of synthetic spectra, to assess the potentially useful atomic lines. Figure 34 shows a telluric absorption spectrum as well as examples of these element line maps that guided the selection of the specific wavelengths within the H-band used for APOGEE.

# Appendix B

## Calculations Used in Estimates of the APOGEE S/N Requirements

To quantify the survey S/N requirements, we performed the following exercise: a series of H-band spectra for RGB stars with $T_{\text{eff}} = 4000$ K and $\log g = 1$, with $[\text{Fe}/\text{H}] = -2, -1$, and 0 were calculated. For each case, we computed two spectra, one with scaled-solar metal abundances ($F(0.0)$), and a second one in which the abundance of a particular element was increased by 0.1 dex ($F(0.1)$). From these, we derived the minimum S/N required as the inverse of $\min|F_i(0.1)/F_i(0.0) - 1|$, where the index *i* runs through all the pixels in the spectra. The elements modeled were: C, N, O, Na, Mg, Al, Si, S, K, Ca, Ti, V, Mn, Fe, and Ni, and they are listed in Table 3 from the most to least challenging, based on this analysis.

Table 3 summarizes some of these S/N per (0.15 Å) pixel requirements for 0.1 dex abundance accuracies from the spectral synthesis described for three resolutions spanning the
<figure><img src="image_36.png" /></figure>

Wavelength (Å)

<figure><img src="image_37.png" /></figure>

Wavelength (Å)

<figure><img src="image_38.png" /></figure>

Wavelength (Å)

<figure><img src="image_39.png" /></figure>

Wavelength (Å)

**Figure 34.** Line maps of specific molecules and elements having lines/bands expressed in the *H*-band. Generally, these are C, N, O, Na, Mg, Al, Si, S, K, Ca, Ti, V, Cr, Mn, Fe, Co, and Ni. This is a useful subset of elements with which to probe most types of nucleosynthesis and chemical evolutions. The vertical lines in each plot indicate the ranges of the strong telluric absorption features near 1.6 µm.
<table><caption>**Table 3**
Required S/N for Detection of 0.1 dex Abundance Variations</caption><thead><tr><th>R= [Fe/H] = Element</th><th>15k</th><th>21k</th><th>30k</th><th>15k</th><th>21k</th><th>30k</th><th>15k</th><th>21k</th><th>30k</th><th>Priority</th></tr></thead><tbody><tr><td>Na</td><td>3648.0</td><td>2673.7</td><td>2050.3</td><td>430.6</td><td>309.8</td><td>230.0</td><td>78.7</td><td>56.0</td><td>41.4</td><td>medium</td></tr><tr><td>S</td><td>1498.4</td><td>1067.2</td><td>802.0</td><td>232.4</td><td>167.2</td><td>125.9</td><td>144.0</td><td>104.8</td><td>81.6</td><td>medium</td></tr><tr><td>V</td><td>2089.3</td><td>1504.7</td><td>1124.0</td><td>231.0</td><td>164.4</td><td>121.4</td><td>61.0</td><td>42.4</td><td>30.5</td><td>lower</td></tr><tr><td>K</td><td>697.5</td><td>505.6</td><td>384.4</td><td>105.6</td><td>75.3</td><td>56.6</td><td>65.0</td><td>44.6</td><td>33.1</td><td>medium</td></tr><tr><td>Mn</td><td>260.0</td><td>184.9</td><td>136.2</td><td>73.0</td><td>50.9</td><td>36.9</td><td>64.8</td><td>46.9</td><td>34.9</td><td>medium</td></tr><tr><td>Ni</td><td>142.0</td><td>101.6</td><td>76.7</td><td>64.9</td><td>45.7</td><td>34.3</td><td>55.3</td><td>46.4</td><td>35.4</td><td>top</td></tr><tr><td>Ca</td><td>126.1</td><td>89.5</td><td>66.0</td><td>60.2</td><td>42.7</td><td>31.5</td><td>57.7</td><td>41.0</td><td>30.3</td><td>top</td></tr><tr><td>Al</td><td>66.2</td><td>47.2</td><td>35.1</td><td>59.6</td><td>41.8</td><td>30.4</td><td>60.3</td><td>42.1</td><td>31.5</td><td>top</td></tr><tr><td>Si</td><td>51.0</td><td>35.2</td><td>25.3</td><td>53.4</td><td>38.6</td><td>28.6</td><td>43.1</td><td>35.7</td><td>29.6</td><td>top</td></tr><tr><td>N</td><td>199.7</td><td>147.3</td><td>113.4</td><td>52.5</td><td>41.7</td><td>32.2</td><td>25.4</td><td>21.4</td><td>18.1</td><td>top</td></tr><tr><td>Ti</td><td>154.1</td><td>110.0</td><td>81.8</td><td>51.7</td><td>36.5</td><td>26.7</td><td>53.7</td><td>38.9</td><td>29.3</td><td>medium</td></tr><tr><td>Mg</td><td>46.4</td><td>33.1</td><td>24.7</td><td>48.9</td><td>36.7</td><td>27.7</td><td>34.7</td><td>26.4</td><td>20.4</td><td>top</td></tr><tr><td>Fe</td><td>57.1</td><td>41.6</td><td>31.2</td><td>38.9</td><td>34.3</td><td>25.5</td><td>25.9</td><td>21.3</td><td>18.4</td><td>top</td></tr><tr><td>C</td><td>56.2</td><td>40.4</td><td>29.9</td><td>19.5</td><td>14.8</td><td>11.3</td><td>10.2</td><td>8.3</td><td>6.8</td><td>top</td></tr><tr><td>O</td><td>34.5</td><td>24.5</td><td>18.1</td><td>18.8</td><td>14.6</td><td>10.8</td><td>11.9</td><td>9.1</td><td>7.4</td><td>top</td></tr></tbody></table>

nominal range originally considered for APOGEE, R = 14,990, 21,414 and 29,979 (as shown in Figure 3, more resolutions than this were sampled), and for stars with [Fe/H] = −2, −1, and 0. The numbers in Table 3 are based on the single most sensitive feature in the spectrum for each element. From these numbers, one can see that the S/N requirements are higher for lower resolution and lower metallicity, which is associated with the difficulty of measuring variations in poorly resolved and weak lines, respectively. According to this initial estimate, for the required abundance accuracy to be reached for all top priority elements from Section 2.2, an S/N of at least ~100–150 pixel⁻¹ must be achieved, depending on the spectral resolution of the APOGEE spectrograph.

The analysis above did not account for the throughput variations expected along the APOGEE spectra, nor did it allow for the fact that for some elements, more lines can be used in the analysis than others. The latter effect is particularly important, as more lines lead to a relative decrease in the S/N requirement. To include those effects in the estimates, we defined the following metric for each element X:

$$FC(X) = \sum_{i=1}^{N} \left[ \left( \frac{F_i(0.1)}{F_i(0.0)} - 1 \right) \times t_i \right]^2, \quad (3)$$

where N is the total number of pixels and tᵢ the expected spectrograph throughput, as estimated a priori by the hardware team and normalized to 1.600 µm. These computations were performed for synthetic spectra simulated at the expected APOGEE sampling and resolution, including their dependence on wavelength, as provided by the hardware team.

In most cases, one finds for the ratio spectrum that F(0.1)/F(0.0) < 1 due to strengthened line absorption, but for some elements and some wavelengths, we find F(0.1)/F(0.0) > 1 due to interactions between species through molecular dissociation equilibrium (e.g., an increase in C when C/O < 1 will cause increased CO strengths but reduced OH absorption).

To avoid lots of pixels with very small changes from influencing the result, a series of cutoffs were imposed, setting the fractional changes to zero if they were smaller (in absolute

value) than 0.005, 0.01, 0.015, 0.02, and 0.025. Obviously, the numbers on the high end are fairly extreme; if one ignores all lines that change the flux by less than 2%–2.5%, there are some elements that become entirely lost. The estimated required S/N is then given by

$$S/N = 1/\sqrt{FC}. \quad (4)$$

Because the synthetic spectra are sampled at half the pixel size (i.e., as combined from two dithered exposures), these are S/N required in half the total observing time. This can be seen as the required S/N being √2 times larger. Note this exercise only takes into consideration the impact of elemental abundance on line opacities. Therefore, the results are somewhat inaccurate for those elements that affect continuum opacity, which is dominated by H⁻ and therefore fairly sensitive to the abundances of important electron donors.

The formal results are shown in Table 4. Note that S/N = ∞ means that the element is undoable, i.e., no signal above the cutoff is detected. From these numbers, one can see that the overall required S/N is much lower than those from Table 3. This is because the metric in Equation (3) is roughly proportional to the number of pixels that are sensitive to a given abundance, whereas the metric used to generate the numbers in Table 3 is sensitive to the pixels contained in a few prominent features only. That explains why C, N, and O require such low S/N, due to the many thousands of CN, CO, and OH transitions that overlap in the H-band.

Interestingly, the dependence of the required S/N on [Fe/H] is much stronger than in Table 3. This is probably due to the combined effect of sensitivity per line getting lower and lines vanishing as one goes toward lower metallicity. The latter effect does not affect the numbers in Table 3, which are only based on the single most sensitive feature. Even though these exercises provided a first assessment of the S/N needs of the survey, the conclusions from these tests were relatively limited, since important effects such as line blending and limitations of models to reproduce real spectra were not considered. Another factor ignored in this analysis was the availability of continuum points either for equivalent width measurements or to guide the
<table><caption>**Table 4**
Required S/N for Detection of 0.1 dex Abundance Variations</caption><thead><tr><th colspan="5">Cutoff at 0.005</th></tr><tr><th>S/N/pixel<br>[Fe/H]</th><th>0</th><th>-1</th><th>-2</th><th>Priority</th></tr></thead><tbody><tr><td>Na</td><td>28.8</td><td>∞</td><td>∞</td><td>medium</td></tr><tr><td>S</td><td>42.8</td><td>120.9</td><td>∞</td><td>medium</td></tr><tr><td>V</td><td>15.0</td><td>94.8</td><td>∞</td><td>lower</td></tr><tr><td>K</td><td>28.1</td><td>53.7</td><td>∞</td><td>medium</td></tr><tr><td>Mn</td><td>12.1</td><td>25.2</td><td>276.9</td><td>medium</td></tr><tr><td>Ni</td><td>7.3</td><td>13.7</td><td>58.4</td><td>top</td></tr><tr><td>Ca</td><td>9.8</td><td>12.3</td><td>38.6</td><td>top</td></tr><tr><td>Al</td><td>16.0</td><td>16.5</td><td>24.6</td><td>top</td></tr><tr><td>Si</td><td>2.6</td><td>5.8</td><td>10.8</td><td>top</td></tr><tr><td>N</td><td>1.6</td><td>4.4</td><td>96.5</td><td>top</td></tr><tr><td>Ti</td><td>8.0</td><td>13.3</td><td>55.0</td><td>medium</td></tr><tr><td>Mg</td><td>1.3</td><td>1.9</td><td>4.1</td><td>top</td></tr><tr><td>Fe</td><td>1.2</td><td>1.9</td><td>6.9</td><td>top</td></tr><tr><td>C</td><td>0.6</td><td>1.7</td><td>8.0</td><td>top</td></tr><tr><td>O</td><td>1.2</td><td>2.0</td><td>3.1</td><td>top</td></tr></tbody><thead><tr><th colspan="5">Cutoff at 0.02</th></tr><tr><th>S/N/pixel<br>[Fe/H]</th><th>0</th><th>-1</th><th>-2</th><th>Priority</th></tr></thead><tbody><tr><td>Na</td><td>63.0</td><td>∞</td><td>∞</td><td>medium</td></tr><tr><td>S</td><td>∞</td><td>∞</td><td>∞</td><td>medium</td></tr><tr><td>V</td><td>21.5</td><td>∞</td><td>∞</td><td>lower</td></tr><tr><td>K</td><td>45.5</td><td>∞</td><td>∞</td><td>medium</td></tr><tr><td>Mn</td><td>21.8</td><td>∞</td><td>∞</td><td>medium</td></tr><tr><td>Ni</td><td>10.7</td><td>25.8</td><td>∞</td><td>top</td></tr><tr><td>Ca</td><td>12.9</td><td>14.3</td><td>∞</td><td>top</td></tr><tr><td>Al</td><td>27.6</td><td>20.2</td><td>35.7</td><td>top</td></tr><tr><td>Si</td><td>6.9</td><td>8.8</td><td>15.2</td><td>top</td></tr><tr><td>N</td><td>2.1</td><td>18.2</td><td>∞</td><td>top</td></tr><tr><td>Ti</td><td>11.2</td><td>16.2</td><td>∞</td><td>medium</td></tr><tr><td>Mg</td><td>4.8</td><td>8.3</td><td>11.9</td><td>top</td></tr><tr><td>Fe</td><td>1.7</td><td>3.5</td><td>12.7</td><td>top</td></tr><tr><td>C</td><td>0.7</td><td>2.4</td><td>∞</td><td>top</td></tr><tr><td>O</td><td>1.4</td><td>2.4</td><td>3.9</td><td>top</td></tr></tbody></table>

comparison with synthetic spectra. At lower temperatures and higher metallicity, continuum points are expected to be fewer, posing a stronger requirement on the minimum S/N needed to determine the continuum accurately. These issues make it very difficult for one to make definitive a priori estimates of both the overall sensitivity of the spectra to abundance variations and the effects of line blending.

A primary conclusion obtained from this early analysis was that a precise estimate of the S/N mandated by the abundance accuracy requirement of the APOGEE survey depends on variables whose effects could not be simulated accurately enough at the time. However, it is clear that the ideal S/N is nicely bracketed by the two extremes resulting from the exercises above, being most likely closer to the numbers in Table 3, given that the metric in Equation (3) tends to strongly overestimate the contribution by lines that are either too weak or cannot be resolved. Therefore, prudence dictated a conservative approach in this case, and therefore we stipulated a minimum S/N requirement of 100 pixel⁻¹, which is closer to the numbers provided in Table 3 and was expected to meet the abundance accuracy requirements for at least all of the top priority elements.

## Appendix C
### Simulations of the Sensitivity of Cadenced APOGEE Observations to Binary Stars

To assess the cadencing requirements to optimize the sensitivity of APOGEE observations to the presence of binary stars, a suite of simulations of APOGEE observations of parent distributions of stellar populations with binaries was performed. Binary systems were generated for three representative lines of sight in the APOGEE survey, at Galactic coordinates of (l, b) = (0, 2.5), (45, 2.5), and (90, 0) degrees. The distribution of primary masses was generated using the TRILEGAL model (Girardi et al. 2005). For each line of sight, we generated 300 binary systems and ran 1000 simulated APOGEE surveys to observe these stars for each tested cadence. The period distribution of the binaries were adopted from Duquennoy & Mayor (1991, “DM91” hereafter), excluding systems with log P (days) ≤0. Note that the Griffin (1985) data on red giants presented in DM91 generally follow this period distribution, but with a deficiency at low log P. This difference suggests that the simulations may have slightly overestimated the fraction of short-period binaries. We did compensate somewhat by discarding physically impossible binary systems with the simple constraint that the stellar radius cannot exceed the orbital separation, but we did not consider more sophisticated schemes such as the plausibility of systems that would be undergoing (or have undergone) tidal interactions. The eccentricity distribution also follows that in DM91, which includes circularization of orbits having P < 100 days. (These simulations pre-dated the Duchêne & Kraus 2013 finding that the DM91 eccentricity distribution is a much poorer fit to observed eccentricities of binaries than a simple uniform distribution of eccentricities.) The adopted distribution of secondary mass ratios is uniform between 0.1 and 1.0. The orientation of the binary orbital axis is isotropic, and the longitude of periastron is uniformly distributed. The time of periastron passage was randomized uniformly between zero and the length of the period.

To simulate the observations, we defined a three-visit observing cadence of $O_1$, $O_2$, and $O_3$ days, where the time of the first visit $O_1$ is always 0 and $O_2$ and $O_3$ are the times of the second and third visit observation with respect to the first observation. To avoid perfect integer spacing of the simulated observations, we added random offsets to $O_1$, $O_2$, and $O_3$. Once the observation times and orbital parameters were defined for each binary system, we used the IDL code helio_rv in the IDL Astronomy User's Library to calculate the radial velocity at each observation date and then added measurement noise drawn from a Gaussian distribution with σ of 0.5 km s⁻¹. We then calculated the average RV of each binary system. Since we adopted 0 km s⁻¹ for the systemic RV of each system, this average RV corresponds to ΔRV, the difference between the measured and true velocity of the system. Binaries with large ΔRV have the largest detrimental effect on kinematical measurements of the stellar populations.

We explored cadences ($O_1$, $O_2$, $O_3$) over a number of possible baselines spanning one week (0, 1, 7.1), one month (0, 7.2, 30.4), three months (0, 15.2, 91.2), and one year (0, 30.4, 365.25). The detectability of each binary is defined as the maximum RV difference between the three RV observations. Figure 35 shows the cumulative distribution functions (CDF) of the ΔRV of binary systems that would be unidentified or “missed” when observed with the four different model three-
<figure><img src="image_40.png" /></figure>

**Figure 35.** Normalized cumulative distribution functions (CDFs) of the fraction of stars having a given APOGEE-measured radial velocity offset from the true systemic radial velocity for the four different observing cadences described in the text. Note that these are shown only for the binaries that are not flagged as a “likely binary” using the >4 km s⁻¹ pairwise-difference criterion described in Section 2.8. In the left-hand plots, the normalizations are to the total number of binaries missed for that cadence. In the right-hand plot, the distributions are normalized to the total number of simulated binaries; thus, the difference in the maximum CDF value between each cadence corresponds to the different fractions of “missed binaries.”

<figure><img src="image_41.png" /></figure>

visit cadences. The figure shows two normalizations, one to the total number of missed binary systems for each cadence and the other to the total number of binary systems in the simulation. The simulations showed that in the case of three observations, the longer the baseline, the fewer binary systems that are missed (right panel) and, more importantly, the fewer binaries with large ΔRV that are missed (left panel). However, the improvement in the number of large ΔRV binaries identified between one cadence and the next longest cadence diminished as the baseline increased. We also explored the effects of the timing of the second observation in the one-month cadence by varying O₂ between 1 and 5 days and found that there was little change in results.

## Appendix D
### Simulations of the Expected Galactic Distribution of APOGEE Targets

Section 4.1.1 describes the main philosophy that was adopted for the APOGEE field targeting plan, while Section 4.1.2 describes the four major phases through which the targeting plan evolved to the final targeting configuration (Section 4.1.3). This evolution was guided by application of Galactic stellar population models—namely the TRILEGAL (Girardi et al. 2005) and Besançon (Robin et al. 2003) Galaxy models—to multiple strawman field placement designs for each of the three principal field star survey regions: disk ($|b| \sim 0°$), bulge ($|b| < 20°$ and $|b| < 20°$), and halo ($|b| > 20°$). This modeling was essential to the task of optimizing not only the specific locations of fields but also the cohort distributions, and color and magnitude limits/numbers of visits employed. Figures 36(a) and (b) illustrate some example results of this modeling, which was used to address a number of specific issues—e.g., ensuring that each Galactic component was well sampled across the greatest possible distance ranges, that the stellar samples were optimized to target predominantly giant stars so as to make the largest distances most accessible, and that each major Galactic population would be amply represented within APOGEE.

These competing priorities were frequently revisited and rebalanced, with reference to the Galactic models, as the APOGEE targeting plan evolved in response to the changing considerations described in Section 4.1.2—especially the evolving co-observing relationship with MARVELS, but further amended mid-survey by the addition of both the twilight observing (Section 5.3.1) and dark time observing (Section 5.3.2) campaigns, and modified further, of course, by prevailing weather conditions during the APOGEE survey. Over time (and even while APOGEE observing was underway), no less than a half dozen different global disk + bulge field placement plans were considered. Less effort was invested in modeling halo targeting, because it was realized early on that a large fraction of the available relevant observing hours would already be needed to probe globular clusters and known halo streams, although eventually additional simple “picket fence” distributions of predominantly 3 hr fields were added to these deep halo fields along $b = 30°, 45°, 60°, \text{ and } 75°$. In the end, the final adopted field plan (Figure 10) while ultimately achieving the objectives for APOGEE targeting (Section 4.1.1), nevertheless contains some vestiges of earlier field plan strategies designed to accomplish this.

It is worth pointing out that, throughout the modeling efforts conducted to shape the APOGEE targeting plan, large variations in expected distributions were seen when comparing the results of the TRILEGAL and Besançon models. These differences in results were, in part, due to differences between the codes in the adopted prescriptions for the thick disk structure as well as in the adopted prescriptions to account for reddening. While tweaking of model parameters could bring the results of the two models into better agreement and make more consistent projections, systematic discrepancies of one sort or another in the results of the two modeling codes typically remained. Such discrepancies between the models illustrated the lack of strong observational constraints, particularly in the direction of the Galactic midplane, that were available to calibrate them—a problem that can now be at least partly remedied by the application of APOGEE results.
<figure><img src="image_42.png" /></figure>

**Figure 36.** Example of TRILEGAL modeling of the expected distributions of different properties of sampled stars. Each field position is represented by a pie chart describing target distributions of Galactic component membership (panel a) and evolutionary stage (panel b). In both panels, symbol size is proportional to number of visits. (a) Expected distributions of stars from each of the major Galactic stellar populations on a field-by-field basis. This same distribution is shown in an alternative, Cartesian format in Figures 11 and 12. According to the simulation, thin disk (bulge) fields would be expected to be dominated by thin disk (bulge) stars. However, in halo fields, the modeled contribution by thin disk stars is overestimated in this particular simulation, for several reasons. Many halo fields were placed on known overdensities (which increases the relative halo contribution) and globular clusters, where targets were selected to maximize cluster membership. These strategies are not taken into account in the TRILEGAL simulation, which is based on a Galactic model composed of symmetrical thin and thick disks, halo, and bulge. Moreover, the simulation does not include the effect of the additional halo field selection criterion based on Washington+DDO photometry (Section 4.2.2), which was designed to minimize (predominantly disk) dwarf contamination, and, indeed, was motivated by model results like that shown here. (b) Example of TRILEGAL modeling of the expected giant/dwarf ratio on a field-by-field basis, for the final, approved APOGEE plan (after MARVELS descope). This model shows that the disk fields were expected to be dominated by giants (as borne out by the survey); on the other hand, the modeled dwarf/giant ratio in halo fields is much higher than found in the actual survey, because of the additional implemented strategies explained in the text.

# Appendix E

## Laboratory Astrophysics Efforts and Development of the APOGEE Line List

Physical data (line identifications, wavelengths, transition probabilities, excitation potentials, damping constants) for line transitions in NIR stellar spectra are not as mature as those for optical spectra. Because such data are critical inputs to the ASPCAP processing of APOGEE spectra, significant effort was put into canvassing the literature and collating previously published data, whether theoretically derived or empirically measured in the laboratory or through astrophysical observations. In addition, it was found necessary to collaborate with laboratory atomic physicists (primarily at the University of Wisconsin and Imperial College, London) to supplement and improve the line list database. To ensure consistency across these multi-sourced data and reduce their uncertainties, the catalogs of data were used to generate synthetic spectra which were then compared to very high resolution, Fourier Transform Spectroscopy data on well-known stars, μ Leo, β And, δ Oph,

Arcturus, and the Sun (Smith et al. 2013; Shetrone et al. 2015) to create improved “astrophysical” line lists. The result of this enterprise has been the creation of catalogs of data for as many as 134,000 atomic and molecular features, meticulously checked against the cataloged and APOGEE-observed (Section 5.3.3) spectra of the Sun and Arcturus (Shetrone et al. 2015).

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