Spectroscopic-astrometric surveys show that the Milky Way's thick disk has a positive azimuthal-velocity–metallicity correlation, ∂Vϕ/∂[M/H]\partial V_\phi/\partial[\mathrm{M/H}], whose strength grows with Galactocentric radius (about +21+21 km s−1^{-1} dex−1^{-1} at R=6R=6 kpc to +60+60 km s−1^{-1} dex−1^{-1} at R=12R=12 kpc), while the present-day thick-disk radial metallicity gradient is almost flat. N-body models tuned to reproduce the positive correlation sign (Kawata et al. 2018, models C1 and C2-thick1, assuming a positive initial interstellar-medium metallicity gradient) instead predict a constant-to-decreasing correlation with radius. The open problem is to identify the physical mechanism — or combination of initial ISM gradient sign, inside-out/upside-down formation, radial migration and blurring, and early gas-rich mergers — that reproduces simultaneously the flat metallicity gradient, the positive correlation sign, and its radially increasing trend.

Background

The Milky Way has two dominant stellar disk components: a cold, thin disk and a hotter, older, α\alpha-enhanced thick disk (α\alpha-enhanced meaning rich in α\alpha-process elements such as oxygen and magnesium relative to iron, a sign of formation from gas enriched mainly by short-lived massive stars), whose origin is still debated. Candidate scenarios include heating of a pre-existing thin disk by minor mergers, accretion of stars from disrupted satellites, turbulent gas-rich mergers at high redshift, and secular radial migration combined with inside-out disk growth. Each scenario predicts distinct correlations between stellar chemistry and orbital motion, so chemo-kinematic relations are a key discriminator.

Here VϕV_\phi is the azimuthal (rotational) velocity of a star about the Galactic center, RR the Galactocentric cylindrical radius, and [M/H][\mathrm{M/H}] the logarithmic overall metallicity relative to the Sun. The rotation–metallicity correlation ∂Vϕ/∂[M/H]\partial V_\phi/\partial[\mathrm{M/H}] measures how mean rotation changes with stellar metallicity. In the thin disk this correlation is negative (metal-rich stars rotate more slowly, at roughly −16-16 to −44-44 km s−1^{-1} dex−1^{-1}), which is understood as the combined effect of the negative interstellar-medium (ISM) metallicity gradient, epicyclic blurring (oscillation of a star's guiding radius along its eccentric orbit), and churning (migration of a star's guiding radius without orbital heating) by spiral arms. For the thick disk, Spagna et al. (2010) first detected a positive correlation in the solar neighborhood (about +30+30 to +50+50 km s−1^{-1} dex−1^{-1}), confirmed by Lee et al. 2011, Kordopatis et al. 2011–2013, Haywood et al. 2013, Allende Prieto et al. (2016) and others.

Theoretically, Curir et al. (2012) proposed that a positive thick-disk correlation is the fossil of an 'inverse' (positive) metallicity gradient in the early Galactic disk. Kawata et al. (2018) tested this with N-body simulations of Milky-Way-like disks chemically 'painted' via Markov Chain Monte Carlo, assuming an initially flat or positive radial metallicity gradient for the thick-disk progenitor, and concluded that the thick disk formed inside-out and upside-down, with radial migration subsequently flattening gradients. Independently, Schönrich & McMillan (2017) developed an analytical chemical-evolution model in which the positive thick-disk correlation arises from inside-out formation and encodes the relative timescales of disk growth, metal enrichment, and enrichment by Type Ia supernovae (SNIa); in their picture the correlation links the high-metallicity tail of the α\alpha-enhanced population to birth at larger guiding radii.

Using 58,882 thin- and thick-disk red giants (evolved low-mass stars) from Gaia Data Release 2 (DR2) astrometry — the European Space Agency's Gaia mission measuring stellar positions and space motions — and APOGEE DR14 spectroscopy (the Apache Point Observatory Galactic Evolution Experiment, a near-infrared stellar spectroscopic survey) over 5<R<135<R<13 kpc and ∣z∣<3|z|<3 kpc, Re Fiorentin, Lattanzi & Spagna (2019) measured, for the first time as a function of radius, thick-disk values of ∂Vϕ/∂[M/H]\partial V_\phi/\partial[\mathrm{M/H}] that are persistently positive over 8 kpc in radius and increase from about +21+21 km s−1^{-1} dex−1^{-1} at R=6R=6 kpc to about +60+60 km s−1^{-1} dex−1^{-1} at R=12R=12 kpc, despite an almost flat present-day thick-disk radial metallicity gradient. Comparing with Fig. 8 of Kawata et al. (2018), they noted that the N-body models C1 and C2-thick1, which assume positive cosmological chemical gradients, predict a constant or decreasing correlation with radius — an opposite trend to the observation — and that analytical scenarios like Schönrich & McMillan (2017) remained untested with fully realistic cosmological hydrodynamical simulations of Milky-Way-like galaxies (as in Murante et al. 2015). Subsequent observations have refined related thick-disk properties — Hu, Shao & Li (2023) measured angular-momentum gradients across the thick-disk mono-abundance plane (populations binned in metallicity and α\alpha-abundance) and found inside-out formation evidence, and Sun et al. (2024, 2026) confirmed a weakly positive, age- and height-invariant thick-disk radial metallicity gradient — but the mechanism behind the correlation's positive sign and radially increasing strength remains unexplained.

Problem Statement

Explain the physical origin of the Milky Way thick disk's rotation–metallicity correlation: identify the mechanism, or combination of mechanisms among the following candidates (sign of the thick-disk progenitor's initial interstellar-medium metallicity gradient, inside-out and upside-down formation, secular radial migration and blurring, early gas-rich mergers), that reproduces simultaneously (i) the thick disk's almost flat present-day radial metallicity gradient, (ii) the positive sign of the azimuthal-velocity–metallicity correlation ∂Vϕ/∂[M/H]\partial V_\phi/\partial[\mathrm{M/H}], and (iii) its observed increase with Galactocentric radius from roughly +21+21 km s−1^{-1} dex−1^{-1} at R=6R=6 kpc to roughly +60+60 km s−1^{-1} dex−1^{-1} at R=12R=12 kpc (Re Fiorentin et al. 2019, Gaia DR2 + APOGEE DR14 red giants; the slopes are measured in overall metallicity [M/H][\mathrm{M/H}] — the abundance of all elements with Z>2Z>2 relative to hydrogen — in 2-kpc-wide rings centred at R=6,8,10,12R=6,8,10,12 kpc), and also explains why the N-body models C1 and C2-thick1 of Kawata et al. (2018), which assume positive cosmological chemical gradients, instead predict a constant or decreasing correlation with radius.

References

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