Gaia Reveals a Metal-rich, in situ Component of the Local Stellar Halo

Gaia is a space-based mission that will map our Galaxy over the next several years (Perryman et al. 2001). The first data from the mission were released in 2016 September, and contain not only positions of all Gaia sources ($G\lt 20$), but also positions, parallaxes, and proper motions for ∼2 million of the brightest stars in the sky (Gaia Collaboration et al. 2016a, 2016b). Obtaining the 5D measurements after just a year of Gaia's operation was made possible by referencing the positions measured with Hipparcos (Michalik et al. 2015). The faintest stars observed by Hipparcos (ESA 1997; van Leeuwen 2007) and released as a part of the Tycho II catalog have $V\sim 12$ (Høg et al. 2000), which limits the size of the 5D sample in Gaia DR1 to $\approx 2$ million stars. A joint solution, known as the Tycho–Gaia Astrometric Solution (TGAS, Lindegren et al. 2016), is comparable in attained proper motions and parallaxes to the Hipparcos precision (typical uncertainty in positions and parallaxes is 0.3 mas and 1 mas yr⁻¹ in proper motions), but already on a sample that is more than an order of magnitude larger, making TGAS an unrivaled data set for precision exploration of the Galactic phase space.

Gaia is measuring radial velocities for ∼150,000 stars brighter than $G\lt 16$ (Gaia Collaboration et al. 2016b), but the first spectroscopic data will become available only in the second data release. Thus, we completed the phase-space information of TGAS sources by using radial velocities from ground-based spectroscopic surveys. We used two distinct spectroscopic data sets from the Radial Velocity Experiment (RAVE) and Apache Point Observatory Galactic Evolution Experiment (APOGEE) projects, and provide an overview below.

RAVE (Steinmetz et al. 2006) is a spectroscopic survey of the southern sky, with a magnitude range $9\lt I\lt 12$ well-matched to TGAS. The latest data release, RAVE DR5 (Kunder et al. 2017), contains ∼450,000 unique radial velocity measurements. Because RAVE avoided targeting regions of low galactic latitude, the actual overlap with TGAS is ∼250,000 stars—the largest of any spectroscopic survey. The survey was performed at the UK Schmidt telescope with the 6dF multi-object spectrograph (Watson et al. 2000), in the wavelength range 8410–8795 Å at a medium resolution of R ∼ 7500, so the typical velocity uncertainty is ∼2 km s⁻¹. Abundances of up to seven chemical elements are available for a subset of high signal-to-noise spectra. Casey et al. (2017) reanalyzed the RAVE DR5 spectra in a data-driven fashion with The Cannon (Ness et al. 2015), providing de-noised measurements of stellar parameters and chemical abundances in the RAVE-on catalog. In particular, the typical uncertainty in RAVE-on abundances is 0.07 dex, which is at least 0.1 dex better than the precision achieved using the standard spectroscopic pipeline. Therefore, we opted to use RAVE-on chemical abundances, focusing on metallicities, [Fe/H], and α-element abundances.

The Apache Point Observatory Galactic Evolution Experiment (APOGEE) is one of the programs in the Sloan Digital Sky Survey III (Alam et al. 2015; Majewski et al. 2015), which acquired ∼500,000 infrared spectra for ∼150,000 stars brighter than $H\sim 12.2$ (Holtzman et al. 2015). To capitalize on the infrared wavelength coverage, APOGEE mainly targeted the disk plane, but several high-latitude fields are included as well (Zasowski et al. 2013). Its higher resolution, R ∼ 22,500, provides more precise abundances for a larger number of elements (e.g., Ness et al. 2015). APOGEE targets are preferentially fainter than stars targeted by RAVE, so its overlap with TGAS is limited to a few thousand stars. APOGEE and RAVE have different footprints, targeting strategies, and observed wavelength windows. Thus, despite the smaller sample size, we found APOGEE to be a useful data set for validating conclusions that were reached by analyzing the larger RAVE sample.

After matching Gaia–TGAS to the spectroscopic surveys, we increase the quality of the sample by excluding stars with large observational uncertainties. However, the overlap between TGAS and spectroscopic surveys is limited, and the number density of halo stars in the solar neighborhood is low. To ensure that we have a sizable halo sample, we chose to use very generous cuts on observational uncertainties and propagate them when interpreting our results, rather than restricting our sample size by more stringent cuts. In particular, we included stars with radial velocity uncertainties smaller than 20 km s⁻¹, and relative errors in proper motions and parallaxes smaller than 1. In addition, we removed all stars with a negative parallax, to simplify the conversion to their distance. These criteria select 159,352 stars for the TGAS–RAVE-on data set, and 14,658 stars for the TGAS–APOGEE sample.

The spatial distribution of stars in our sample is entirely determined by the joint selection function of TGAS and the spectroscopic surveys, as we performed no additional spatial selection. Gaia is an all-sky survey, but the data is still being acquired, so completeness of the TGAS catalog varies across the sky. Ground-based spectroscopic surveys have geographically restricted target lists, in addition to the adopted targeting strategy. This results in a spatially non-uniform sample whose distribution of distances we provide in Appendix A. On the other hand, Wojno et al. (2016) have shown that the RAVE survey is both chemically and kinematically unbiased. Thus, focusing on kinematic properties of the sample will result in robust conclusions.

Access to the full 6D phase space information allows us to calculate Galactocentric velocities for all of the stars in the sample. We summarize the kinematic properties of the sample with a Toomre diagram (Figure 1), where the Galactocentric Y component on the velocity vector, V_Y (which points in the direction of the disk rotation), is on the x axis, whereas the perpendicular Toomre component, $\sqrt{{V}_{X}^{2}+{V}_{Z}^{2}}$, is on the y axis. This space has been widely used to identify major components of our Galaxy, such as the thin and thick disks, and the halo (e.g., Venn et al. 2004). Disk stars dominate a large overdensity at ${V}_{Y}\approx 220$ km s⁻¹, which corresponds to the circular velocity of the Local Standard of Rest (LSR, V_LSR). The density of stars (left panel of Figure 1) decreases smoothly for velocities that are progressively more different from V_LSR, extending all the way to retrograde orbits (${V}_{Y}\lt 0$).

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We distinguish between the disk and halo following Nissen & Schuster (2010): halo stars are identified with a velocity cut $| V-{V}_{\mathrm{LSR}}| \gt 220$ km s⁻¹, where ${V}_{\mathrm{LSR}}=(0,220,0)$ km s⁻¹ in the Galactocentric Cartesian coordinates. The dividing line between the components is marked with a black line in Figure 1, and both components are labeled in the left panel. The halo definition employed here is more conservative than similar cuts adopted by previous studies; e.g., Nissen & Schuster (2010) defined halo as stars with velocities that satisfy $| V-{V}_{\mathrm{LSR}}| \gt 180$ km s⁻¹. For example, Schönrich & Binney (2009a) have shown that the velocity distribution of a Galactic thick disk can be asymmetric, in which case the region $180\lt | V-{V}_{\mathrm{LSR}}| \lt 220$ km s⁻¹ could still contain many thick disk stars. A higher velocity cut ensures that the contamination of our halo sample with thick disk stars is minimized. In total, we identified 1376 halo and 157,976 disk stars, with the halo constituting $\sim 1 \%$ of our sample. This is in line with the expectations from number count studies in large-scale surveys (e.g., Jurić et al. 2008), although we do not expect an exact match, as TGAS is not volume complete.

In this section, we study the chemical composition of the solar neighborhood stars observed by both Gaia–TGAS and RAVE. The signal-to-noise ratio of 142,086 RAVE spectra was high enough to allow a measurement of metallicity [Fe/H]. Alpha-element abundances, [α/Fe], were obtained for a subset of 56,259 stars. All of the RAVE elemental abundances used in this work were measured by Casey et al. (2017). Right panel of Figure 1 shows the average metallicity in densely populated velocity bins of the Toomre diagram, whereas the points in the lower-density regions are individually colored-coded by [Fe/H]. As expected, the halo is poorer in metallicity than the disk (e.g., Gilmore et al. 1989; Ivezić et al. 2008). Within the disk itself, there is a smooth decrease in metallicity further from the V_LSR, starting from [Fe/H] ∼ 0 in the thin disk region, $({V}_{Y},{V}_{{XZ}})=(220,0)$ km s⁻¹, to $[\mathrm{Fe}/{\rm{H}}]\sim -0.5$ in the thick disk region, $({V}_{Y},{V}_{{XZ}})=(100,100)$ km s⁻¹. Surprisingly, however, there are many stars with thick disk-like metallicities found in the halo region of the Toomre diagram, and some of them are on very retrograde orbits.

Figure 2 (top) shows the metallicity distribution for the two kinematic components identified above: the disk in red and the halo in blue. The disk is richer in metallicity than the halo, and peaks at the approximately solar metallicity, $[\mathrm{Fe}/{\rm{H}}]=0$. The halo is relatively metal-poor, and exhibits a peak at $[\mathrm{Fe}/{\rm{H}}]\sim -1.6$, typical of the inner halo (e.g., Allende Prieto et al. 2006). However, the metallicity distribution of the halo has an additional peak at the metal-rich end, centered on $[\mathrm{Fe}/{\rm{H}}]\sim -0.5$ and extending out to the super-solar values.

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To corroborate the existence of metal-rich stars on halo orbits, we also show the metallicity distribution function for TGAS stars observed with APOGEE at the bottom of Figure 2. We used APOGEE elemental abundances provided as a part of the SDSS IV Data Release 13 (SDSS Collaboration et al. 2016). The disk-halo decomposition for the APOGEE sample was performed in a manner identical to that of RAVE-on. The metallicity distributions between the two surveys are similar: the disk stars are metal-rich, whereas the halo has a wide distribution ranging from $[\mathrm{Fe}/{\rm{H}}]\sim -2.5$ to $[\mathrm{Fe}/{\rm{H}}]\sim 0$. A bimodality is present in the metallicity distribution of APOGEE halo stars, although it is less prominent than in the RAVE-on sample due to the smaller sample size. The apparent bimodality in the metallicity distribution of RAVE-on halo stars is slightly more metal-poor, $[\mathrm{Fe}/{\rm{H}}]\approx -1.1$, than observed in the APOGEE sample, $[\mathrm{Fe}/{\rm{H}}]\approx -0.8$. In what follows, we compromise between these two values and split the halo sample at $[\mathrm{Fe}/{\rm{H}}]=-1$, into a metal-rich ($[\mathrm{Fe}/{\rm{H}}]\gt -1$) and a metal-poor component ($[\mathrm{Fe}/{\rm{H}}]\leqslant -1$). With 598 out of 941 RAVE-on halo stars (64%) and 22 out of 50 APOGEE halo stars (44%) having $[\mathrm{Fe}/{\rm{H}}]\gt -1$, approximately half of the halo sample is metal-rich.

Chemical abundances have been used to discern different components of the Galaxy (e.g., Gilmore et al. 1989). The abundance space of [α/Fe] versus [Fe/H] is particularly useful in tracing the origin of individual stars (e.g., Lee et al. 2015). Figure 3 shows this space for RAVE-on spectra on the top, and APOGEE on the bottom. The disk distribution is shown as a red density map, while the less numerous halo stars are shown individually in blue. Similarly to the overall metallicity distribution function, RAVE-on and APOGEE surveys are in qualitative agreement in terms of the more detailed chemical abundance patterns. At low metallicities, the halo is α-enhanced, but its [α/Fe] declines at high metallicities, following the disk abundance pattern, both in terms of the mean [α/Fe] and its range at a fixed [Fe/H]. In particular, thick-disk stars have higher α-element abundances at a given metallicity (e.g., Nidever et al. 2014) and follow a separate sequence visible in the more precise APOGEE data ([Fe/H]$\,\sim \,-0.2$, [α/Fe] ∼ 0.2), whereas the thin disk is generally more metal-rich and α-poor. Metal-rich halo stars in both samples span this range of high- and low-α abundances. At lower metallicities, Nissen & Schuster (2010) reported that halo stars follow two separate [α/Fe] sequences, with the high-α stars being on predominantly prograde orbits, whereas the low-α stars are mostly retrograde. We neither resolve the two sequences nor see any correlation between the orbital properties and [α/Fe] at a fixed [Fe/H]. However, the RAVE-on abundances are fairly uncertain (typical uncertainty is ∼0.07 dex, marked by a black cross on the top left in Figure 3), so the sequences seen in the higher-resolution data from Nissen & Schuster (2010) would not be resolved in this data set. In the APOGEE sample, where the typical uncertainty is smaller, ∼0.03 dex, the number of halo stars is too small to unambiguously identify multiple $[\alpha /\mathrm{Fe}]$ sequences.

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The evidence presented so far shows that the stellar halo in the solar neighborhood has distinct metal-poor and metal-rich components. Given that the metal-rich component follows the abundance pattern of the disk, we discuss possible contamination by the thick disk in Appendix B, and rule out the possibility that a sizable fraction of the metal-rich halo is attributable to the canonical thick disk. In the next section, we proceed to characterize the orbital properties of the two halo components.

Stellar orbits can be classified in terms of their integrals of motion. However, calculating these requires the knowledge of the underlying gravitational potential (Binney & Tremaine 2008). Furthermore, in a realistic Galactic environment, some stars are on chaotic orbits (e.g., Price-Whelan et al. 2016), where the integrals of motion do not exist. On the other hand, any star with a measured position in a 6D phase space has a well-defined angular momentum. In this section, we use angular momenta as empirical diagnostics of stellar orbits, and focus particularly on the orientation of the angular momentum vector with respect to the Galactocentric Z axis, quantified by the angle

$$\begin{eqnarray}&&{\theta }_{L}\equiv \arctan ({L}_{Z}/| {\boldsymbol{L}}| ),\end{eqnarray} \tag{ 1 }$$

where L_Z is the Z component of the angular momentum, and $| {\boldsymbol{L}}|$ its magnitude. Here, L_Z, and hence ${\theta }_{L}$, are conserved quantities in static, axisymmetric potentials, such as that of the Milky Way disk. This has already been utilized to identify coherent structures in the phase space of local halo stars (e.g., Helmi et al. 1999; Smith et al. 2009). In the adopted coordinate system, the disk orientation angle is ${\theta }_{L}=180^\circ$, such that prograde orbits are those with ${\theta }_{L}\gt 90^\circ$, and retrograde have ${\theta }_{L}\lt 90^\circ$. Figure 4 shows the distribution of angular momentum orientations ${\theta }_{L}$ for the Galactic components identified in the RAVE sample.

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As expected, most of the disk stars are indeed on orbits in the disk plane with ${V}_{Z}\approx 0$, and have ${\theta }_{L}\approx 180^\circ$ (red histogram in Figure 4). Angular momenta of both halo components span the entire range of $0^\circ \lt {\theta }_{L}\lt 180^\circ$. However, in detail, their distributions are significantly different from each other. The metal-poor halo has an almost flat distribution as a function of ${\theta }_{L}$, with a slight depression at very prograde angles (dark blue histogram in Figure 4). The metal-rich halo is predominantly prograde (63% of the stars have ${\theta }_{L}\gt 90^\circ$), but also has a long tail to retrograde orbits (light blue histogram in Figure 4). In the next section, we explore the origin of these distributions in terms of a toy model for the kinematic distribution of the Galaxy, as well as in comparison to a hydrodynamical simulation of a Milky Way-like galaxy.

To construct a toy model for our TGAS–RAVE-on sample, we assign stars to one of the three main components of the Milky Way galaxy: a thin disk, thick disk, or halo (e.g., Bland-Hawthorn & Gerhard 2016). The model is defined by the number of stars in each component, and their spatial and kinematic properties. To set the number of halo stars in the toy model, we assumed that the halo is isotropic. In that case, an equal number of halo stars are on prograde and retrograde orbits. Because we expect no contamination from the disk on retrograde orbits, we set the total size of the halo in the toy model to be twice the number of retrograde stars in our Milky Way sample. For the remaining disk stars, we vary the ratio of thin to thick disk stars to best match the distribution of prograde orbits.

Once the number of stars in each component is determined, we proceed to assign them their phase space coordinates. Our sample is spatially confined to within only several kpc from the Sun (see Appendix A), so we see no differences in spatial distributions of the kinematically defined components from Section 2.3. This allows us to take the spatial distribution of stars in our sample, and randomly designate them a component in the toy model, thus ensuring that the spatial selection function of both TGAS and RAVE-on is properly reproduced in the model. For each star in the model, we draw a 3D velocity from its component's velocity ellipsoid measured by Bensby et al. (2003) on a smaller sample of local stars with Hipparcos parallaxes and proper motions, which accounts for the asymmetric drift. With positions and velocities in place, we calculate the angular momenta and their orientation angles with respect to the Z axis, ${\theta }_{L}$, for all stars in the toy model.

The properties of our toy model are summarized in Figure 5. The top panel shows the components of the model in the Toomre diagram, with the disk stars in red, halo stars in blue, and the black line delineating our kinematic boundary between the halo and the disk. The velocity ellipsoids of these components overlap, so our kinematic definition of a halo produces a sample that is likely neither pure nor complete. This is illustrated in the toy model by several thick-disk stars that enter the halo selection box at $({V}_{Y},{V}_{{XZ}})\simeq (100,200)$ km s⁻¹, as well as halo stars on prograde orbits, which fall outside of the halo selection. As no simple kinematic cut will completely separate the different components, we opt to emphasize the purity of our halo sample. Based on the toy model, we estimate that the fraction of interloping disk stars in a kinematically defined halo is only $\sim 10 \%$, but this in turn makes the halo sample less complete at 75%. For a comparison, Nissen & Schuster (2010) define a halo that is $\sim 90 \%$ complete, but only $\sim 55 \%$ pure.

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The middle panel of Figure 5 shows the orientation of angular momenta, ${\theta }_{L}$, for the components of the toy model, with halo in blue and disk in red. As expected, the majority of disk stars are moving in the disk plane, and the distribution is sharply peaked at ${\theta }_{L}=180^\circ$. The nearly isotropic halo of the Bensby et al. (2003) model has a flat distribution in ${\theta }_{L}$. The sum of the two components is represented with a thick black line, which compares favorably to the distribution of ${\theta }_{L}$ observed in the Milky Way, and shown in dashed gray. The agreement between the toy model and the Milky Way is particularly good at very prograde or retrograde orbits. The abundance of stars on only slightly prograde orbits (${\theta }_{L}\approx 100^\circ$) is somewhat underestimated in the toy model, indicating that the transition between a disk and a halo component in the Milky Way is more gradual than what can be reproduced by a simple model that features only two disks and an isotropic halo.

The bottom panel of Figure 5 compares the modeled halo to the observed one. For a fair comparison, in this panel we only consider model stars that would satisfy our kinematic halo selection, which are a combination of some disk and the majority of halo stars, as discussed above. The distribution of ${\theta }_{L}$ for these kinematically-selected halo stars from a toy model is shown as a shaded histogram. Although the intrinsic distribution of an isotropic halo is flat (middle panel), kinematic selection introduces a suppression at the most prograde orbits (bottom panel). Kinematic selection excludes halo stars with $| V-{V}_{\mathrm{LSR}}| \leqslant 220$ km s⁻¹, all of which are on prograde orbits, which is manifested as a depression at ${\theta }_{L}\gtrsim 90^\circ$. The magnitude of this depression exactly matches the distribution of metal-poor halo stars in the Milky Way, overplotted with a dark blue line in the bottom panel of Figure 5. This suggests that the metal-poor halo in the solar neighborhood is intrinsically isotropic, and that at least some stars more metal-poor than $[\mathrm{Fe}/{\rm{H}}]\leqslant -1$, which are kinematically consistent with the disk, are in fact a part of the metal-poor halo. The distribution of metal-rich halo stars in the Milky Way, shown as light blue line in the bottom panel of Figure 5, shows the opposite behavior of an excess at prograde orbits, and is significantly different from the toy model prediction for an isotropic halo.

A simple toy model successfully explains the bulk properties of our sample: most of the stars are in a rotating disk, with a minority in an isotropic halo, which maps well to the metal-poor halo stars identified in our TGAS–RAVE-on sample. This toy model also highlights that the metal-rich halo stars are inconsistent with either of these components. Next, we analyze the origin of such a population using a hydrodynamical simulation.

The Latte simulation, first presented in Wetzel et al. (2016), comes from the Feedback In Realistic Environments (FIRE)⁸ project (Hopkins et al. 2014). Latte is fully cosmological, with baryonic mass resolution of $7000\,{M}_{\odot }$, and spatial softening/smoothing of $1\,\mathrm{pc}$ for gas and $4\,\mathrm{pc}$ for stars. The simulation uses the standard FIRE-2 implementation of gas cooling, star formation, stellar feedback, and metal enrichment described in Hopkins et al. (2017), including the numerical terms for turbulent diffusion of metals in gas described therein⁹ , and the GIZMO code (Hopkins 2015). FIRE simulations have been used to study galaxies ranging from ultra-faint dwarf galaxies (Wheeler et al. 2015) to small groups of galaxies (Feldmann et al. 2016). FIRE simulations successfully reproduce such features as: observed internal properties of dwarf galaxies (Chan et al. 2015; El-Badry et al. 2016); thin/thick disk structure, and both radial and vertical disk metallicity gradients in a Milky Way-like galaxy (Ma et al. 2016b); star-formation histories of dwarf and massive galaxies (Hopkins et al. 2014; Sparre et al. 2015); global galaxy scaling relations (Hopkins et al. 2014; Feldmann et al. 2016; Ma et al. 2016a); and satellite populations around Milky Way-mass galaxies (Wetzel et al. 2016).

To construct a sample of star particles in Latte analogous to the TGAS–RAVE-on sample, we first align the simulation coordinate system with the disk, and then select stars in a 3 kpc sphere located at a distance of 8.3 kpc from the center of the galaxy. We classify star particles as either disk or halo, using a kinematic cut in the Toomre diagram similar to the one employed for stars in the Milky Way (Section 3.1). Because the circular velocity in Latte is slightly different from the Galactic value, the definition of the local standard of rest is also different, but we keep the same conservative measure for the dispersion of 220 km s⁻¹ in the disk of Latte. The Toomre diagram for the sample in Latte is shown in the top panel of Figure 6. Qualitatively, it is similar to that of the Milky Way (Figure 1), with most of the stars rotating in the disk at ∼235 km s⁻¹, and the density of stars smoothly decreasing away from the local standard of rest. Quantitatively, the halo fraction in Latte is an order of magnitude higher at 10%. Its kinematic space is also more structured, compared to the Milky Way. This is partly because the Latte sample does not suffer from selection effects, so it effectively extends to larger distances, where the halo constitutes a larger mass fraction. Any kinematic structures are hence better sampled and more readily observable in Latte. Additionally, at least some of the structure present in the Milky Way sample is smoothed by the observational uncertainties (see, e.g., Sanderson et al. 2015), which are not present in Latte.

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Stars in the Toomre diagram of Figure 6 are color-coded by metallicity and show trends similar to those observed in the Milky Way. For a more quantitative analysis, we show metallicity distribution of Latte's disk and halo components in the central panel of Figure 6. To facilitate comparison, we also include metallicity distributions of the Milky Way components as empty histograms. The Latte halo is poorer in metallicity than its disk, and although there is no bimodality in the halo metallicity, the whole distribution is as wide as observed in the Milky Way—extending from [Fe/H] ≲ −2 to [Fe/H] ≃ 0. This agreement, in addition to $[\alpha /\mathrm{Fe}]$ abundance trends recovered in simulated disks (A.Wetzel et al. 2017, in preparation), demonstrates that the physics included in the FIRE simulations captures the most important ingredients for chemical evolution in galaxies. Following our analysis of the Milky Way sample, we proceed to divide the Latte halo into a metal-rich component with [Fe/H] > −1, and a metal-poor one with [Fe/H] ≤ −1. The ratio of metal-rich to metal-poor halo stars in Latte is not quite the same as in the Milky Way, but this does not seriously impede our goal of qualitatively understanding differences between the two populations.

Finally, we analyze orbital properties of stars in Latte by showing the orientation of their angular momenta with respect to the Z axis, ${\theta }_{L}$, as solid histograms in the bottom panel of Figure 6. The angular momenta of Latte disk stars are well-aligned with the z-axis, with ${\theta }_{L}\simeq 180^\circ$, similar to disk stars in the Milky Way (shown in Figure 6 as an empty histogram). The Latte halo shows a flatter distribution of ${\theta }_{L}$, but there is still an excess of metal-rich stars on prograde orbits (histogram shaded light blue) with respect to the metal-poor halo stars (dark blue). Overall, Latte stars have similar kinematic, chemical, and orbital properties to stars observed in the Milky Way, suggesting that it provides a reasonable analogue. We next trace Latte stars back to their birth location and suggest a possible scenario for the formation of halo stars in the solar neighborhood.

We define the formation distance of a star particle in Latte as its physical (not comoving) distance from the center of the primary (Milky Way-like) galaxy at the time that it formed. We inspect this formation distance as a function of the star's current (z = 0) age in Figure 7. Stars with disk kinematics (as defined by our Toomre-diagram cut in Figure 6) are shown in red, whereas those identified as halo stars are blue. The suppression of stars that formed at solar distances ∼7 Gyr ago coincides with the time of the last significant merger ($z\sim 0.7$). This event brought significant gas to the center of the galaxy, thus switching the star-forming conditions from those producing mainly stars on halo-like orbits (more than 95% of halo stars are older than 6 Gyr) to the orderly production of disk stars (more than 90% of disk stars were formed in the last 6 Gyr). The formation distances between the disk and halo components are equally dichotomous: most of the disk stars were formed close to their present-day distance from the galactic center ($5\mbox{--}11\,\mathrm{kpc}$, shaded gray in Figure 7), whereas halo stars originated from the extremes of the central 1 kpc to the virial radius and beyond (for reference, the virial radius 10 Gyr ago was $\approx 70$ kpc). The distribution of formation distances for the metal-rich and metal-poor halo components is shown on the right, with light and dark blue histograms, respectively. Metal-poor halo stars originate from a range of distances, with the median of the distribution at ∼45 kpc. On the other hand, the median formation distance of the metal-rich halo stars is ∼5 kpc, closer to the Galactic center than their current position. Overall, only ∼20% of Latte stars on halo orbits were formed within their present-day radial distance range, indicating that radial redistribution is an important phenomenon sculpting the inner Galaxy. We discuss the implications of the halo component undergoing radial migration/heating in Section 5.2.2.

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The formation distance of a star particle can also be used as a rudimentary diagnostic of its formation mechanism. From Figure 7, we see that almost none of the disk stars were formed beyond 20 kpc (indicated with a horizontal black line), so we adopt this distance as a delimiter between the in situ and accreted origin for stars in Latte. Most of the accreted stars are classified as halo, and were formed inside dwarf galaxies merging with the host galaxy. The tracks in the space of formation distance and age (Figure 7) delineate the orbits of these dwarf galaxies. All of the satellites are disrupted once they get within the central 20 kpc; for most of them, this happens on the first approach. In the process, they bring in gas that fuels in situ star formation. At early times, most of the stars that formed in situ also become a part of the halo, whereas the last significant merger starts the onset of the in situ formation of the disk. Although satellite accretion onto the host galaxy continues after the last significant merger, none of the accreted stars reach the solar circle, so effectively all of the halo stars in the solar neighborhood were formed prior to the last significant merger. This is in line with findings of Zolotov et al. (2009), who showed that late-time accretion predominantly builds outer parts of the stellar halo.

In summary, Latte stars born at late times formed in the disk, whereas old stars in Latte are predominantly part of the halo. One third of the halo in the solar neighborhood was accreted from the infalling satellites, whereas the majority of stars formed in situ in the inner galaxy and migrated to the solar circle. In this simplified depiction for the origin of the stellar halo, we do not account for the unlikely possibility that stars that formed within 20 kpc still could have been bound to a satellite galaxy, and hence accreted, nor do we distinguish between different modes of in situ halo formation—e.g., through a dissipative collapse (Samland & Gerhard 2003) or with stars being heated from the disk (Purcell et al. 2010). These are not serious short comings because satellites that entered the inner 20 kpc were disrupted soon thereafter, so any newly formed stars would have been only loosely bound to the satellite at the time. Furthermore, given that the median formation distance of all halo stars formed in situ is ∼4 kpc, we expect that dissipative collapse only marginally contributes to the census of halo stars at the solar circle, and ultimately, we draw conclusions that are insensitive to the particulars of their origin.

In Figure 8, we explore how the fraction of halo stars formed in situ depends on the angular momentum orientation (${\theta }_{L}$, left) and a combination of angular momentum and metallicity (right). On average, 40% of metal-poor halo stars have formed in situ (dark blue line in the left panel of Figure 8). Metal-rich halo stars are more likely to have formed in situ (light blue line), and this probability increases to 90% for stars whose orbits are aligned with the disk. Interestingly, when we investigate the dependence of the in situ fraction simultaneously as a function of metallicity and angular momentum orientation (right panel of Figure 8), we find only a weak dependence on the current angular momentum orientation of a star, but a strong correlation with metallicity. All of the lowest-metallicity stars, with [Fe/H] ≲ −2.5, were accreted (yellow), and all of the metal-rich halo stars, with [Fe/H] ≳ −0.5, formed in situ (purple). Given the similarities between the global chemical and orbital properties in Latte and the Milky Way, this result suggests that the metal-rich halo component identified in the TGAS–RAVE-on sample formed in the inner Galaxy, but was driven to the solar circle through subsequent evolution.

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Ages of individual stars are another important diagnostic of their origin, so we now explore correlations between metallicity and age for stars in the solar neighborhood, as predicted by the Latte simulation. Figure 9 shows how the metallicity of stars in Latte depends on their age for the disk (red), in situ halo (light blue), and accreted halo (dark blue). Shaded regions correspond to the 16–84th percentiles in the distribution of metallicities for stars of a given age. In general, metallicity increases with time. However, accretion of a significant amount of low-metallicity gas during the last significant merger 7 Gyr ago is evident as a decrease in the metallicity of stars formed in situ immediately following this event. Comparing the different populations in the simulation, we note that the metallicities of halo stars formed in situ closely follow the evolution of disk stars, while the accreted halo is more metal-poor at all ages. The bifurcation in the metallicity tracks for the in situ and accreted halo is a prediction of the Latte simulation, which, if confirmed observationally, can be used to directly differentiate between the accreted and in situ halo stars.

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Large-scale spectroscopic surveys have mapped the distribution of stellar metallicity in the Milky Way (e.g., Ivezić et al. 2008). Some of these stars have distance estimates, and can therefore be spatially identified with either the disk or the halo. Relevant to this discussion, halo stars in the outer Galaxy, ${R}_{G}\gt 15\,\mathrm{kpc}$, are very metal-poor, with median $[\mathrm{Fe}/{\rm{H}}]\,\sim -2.2$, whereas the typical metallicity of a halo star in the inner Galaxy is $[\mathrm{Fe}/{\rm{H}}]\sim -1.6$ (e.g., Carollo et al. 2007; de Jong et al. 2010; Fernández-Alvar et al. 2017), which agrees well with the metal-poor halo component identified in our sample. Also similar to our findings, metallicities of the inner halo extend to the solar value, even though these are the tail of the metallicity distribution (e.g., Allende Prieto et al. 2006) and not an additional component that is visible in Figure 2.

However, employing only spatial information makes it hard to distinguish between the halo and the thick disk, especially at high metallicity. The difference between the thick disk and the halo is more pronounced in kinematics, so Sheffield et al. (2012) selected outliers from the disk velocity field to study the halo. They identified eight metal-rich halo stars, whose α-abundances are consistent with the disk, and suggested these had been kicked out of the disk. Still, none of these stars have kinematics that could rule out a thick disk interpretation at a $3\sigma$ level.

To date, only one metal-rich star is known to have a high probability of being a halo star (Hawkins et al. 2015). This star has high velocity in the Galactic rest frame, ${V}_{\mathrm{GSR}}\simeq 430$ km s⁻¹, and is on an eccentric orbit, e = 0.72, that reaches ∼30 kpc above the Galactic plane. However, it has a metallicity of $[\mathrm{Fe}/{\rm{H}}]=-0.18$, so Hawkins et al. (2015) concluded that it had been ejected from the thick disk. This star is a valuable indicator of the processes governing the assembly of the Galaxy. Being only a single star, however, it cannot establish how ubiquitous these processes are.

The excess of metal-rich halo stars on prograde orbits indicates that they originate from within the Milky Way disk, but it is unclear at what Galactocentric distance these stars were formed. The bulk of similarly selected stars in Latte originated from the inner Galaxy, implying that a degree of radial migration and/or heating occurred. Alternatively, these stars could be runaway stars—stars kicked out of the disk at the solar radius during dynamical processes not captured within the Latte simulation. In this section, we explore implications of these opposing disk heating mechanisms, and assess how plausible they are in explaining metal-rich halo stars detected in RAVE-on-TGAS.

5.2.1. Runaway Stars

5.2.2. Radial Migration

In section Section 4.3, we showed that the metal-rich halo simulated in Latte was chemically enriched in a fashion similar to the Latte disk. When compared at a fixed age, these components have higher metallicity than the metal-poor halo at all times (see Figure 9). We can directly test this prediction by dating the stars in our TGAS–RAVE-on sample. Unfortunately, stellar ages are not obtained easily (for a recent review, see Soderblom 2010). A number of observables that correlate with age have been identified, such as stellar rotation (Barnes 2007), chromospheric activity (Mamajek & Hillenbrand 2008), and surface abundances (Ness et al. 2016), but none of these empirical relations are applicable to all of the field stars. Models of stellar evolution can relate the position of any star in the Hertzsprung–Russell diagram (HRD) and its internal structure to its age. The latter is inferred from asteroseismic studies of stellar pulsations, and has so far been employed to date a few dozen well observed stars (e.g., Silva Aguirre et al. 2015). In the coming decade, asteroseismic dating will be expanded, but still limited to the brightest stars (Rauer et al. 2014; Ricker et al. 2015). We expect the HRD age dating to be more easily applied to a larger sample of stars, and discuss it in more detail below.

Coeval stellar populations are routinely dated by comparison of their tracks in the HRD to theoretical isochrones (e.g., Sandage 1970; Chaboyer et al. 1998; Dotter et al. 2007), but isochrone dating of field stars is less straightforward. Intrinsically, without the HRD positions of coeval companions, age estimates of field stars are very uncertain in evolutionary stages that keep stars at an approximately constant position in the HRD, such as the main sequence phase. In addition, precisely measuring stellar distances (which are required to put a star on the HRD, as opposed to merely on a color–magnitude diagram) is observationally challenging. However, if distances are known, stellar ages can be measured for stars in pre- or post-main sequence evolutionary stages. Nordström et al. (2004) measured ages and other intrinsic stellar parameters for thousands of nearby field stars by obtaining their absolute magnitudes from Hipparcos parallaxes, effective temperatures, and metallicities from follow-up spectroscopy, and then reading off the age by interpolating theoretical isochrones in this three-dimensional space. TGAS has already increased the sample of stars with known distances by an order of magnitude, and several groups are modeling the multi-band stellar photometry (and including spectroscopy when available) to provide constraints on their ages. In such a procedure, ages of red giants are measured with a precision of $1\mbox{--}3\,\mathrm{Gyr}$ when only photometric data is available. Including spectroscopically derived stellar parameters reduces the uncertainty in recovered ages to 1 Gyr (P. Cargile 2017, private communication). Most of the halo stars in our sample are giants, so if the bifurcation in the age–metallicity relation of halo stars exists at the level suggested by the simulation studied here, we will soon be able to detect it observationally.