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Dynamical model of the Milky Way using APOGEE and Gaia data

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 Publication date 2021
  fields Physics
and research's language is English




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We construct a dynamical model of the Milky Way disk from a data set, which combines Gaia EDR3 and APOGEE data throughout Galactocentric radii between $5.0leq Rleq19.5$ kpc. We make use of the spherically-aligned Jeans Anisotropic Method to model the stellar velocities and their velocity dispersions. Building upon our previous work, our model now is fitted to kinematic maps that have been extended to larger Galactocentric radii due to the expansion of our data set, probing the outer regions of the Galactic disk. Our best-fitting dynamical model suggests a logarithmic density slope of $alpha_{rm DM}=-1.602pm0.079_{rm syst}$ for the dark matter halo and a dark matter density of $rho_{rm DM}(R_{odot})=(8.92pm0.56_{rm syst})times 10^{-3}$ M$_{odot}$ pc$^{-3}$ ($0.339pm0.022_{rm syst}$ GeV cm$^{3}$). We estimate a circular velocity at the solar radius of $v_{rm circ}=(234.7pm1.7_{rm syst})$ km s$^{-1}$ with a decline towards larger radii. The total mass density is $rho_{rm tot}(R_{odot})$=$(0.0672pm0.0015_{rm syst})$ M$_{odot}$ pc$^{-3}$ with a slope of $alpha_{rm tot}$=$-2.367pm0.047_{rm syst}$ for $5leq Rleq19.5$ kpc and the total surface density is $Sigma(R{_odot}, |z|leq$ 1.1 kpc)=$(55.5pm1.7_{rm syst})$ M$_{odot}$ pc$^{-2}$. While the statistical errors are small, the error budget of the derived quantities is dominated by the 3 to 7 times larger systematic uncertainties. These values are consistent with our previous determination, but systematic uncertainties are reduced due to the extended data set covering a larger spatial extent of the Milky Way disk. Furthermore, we test the influence of non-axisymmetric features on our resulting model and analyze how a flaring disk model would change our findings.



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The kinematics of the Milky Way disc as a function of age are well measured at the solar radius, but have not been studied over a wider range of Galactocentric radii. Here, we measure the kinematics of mono-age, mono-$mathrm{[Fe/H]}$ populations in the low and high $mathrm{[alpha/Fe]}$ discs between $4 lesssim R lesssim 13$ kpc and $|z| lesssim 2$ kpc using 65,719 stars in common between APOGEE DR14 and $it{Gaia}$ DR2 for which we estimate ages using a Bayesian neural network model trained on asteroseismic ages. We determine the vertical and radial velocity dispersions, finding that the low and high $mathrm{[alpha/Fe]}$ discs display markedly different age--velocity-dispersion relations (AVRs) and shapes $sigma_z/sigma_R$. The high $mathrm{[alpha/Fe]}$ disc has roughly flat AVRs and constant $sigma_z/sigma_R = 0.64pm 0.04$, whereas the low $mathrm{[alpha/Fe]}$ disc has large variations in this ratio which positively correlate with the mean orbital radius of the population at fixed age. The high $mathrm{[alpha/Fe]}$ disc components flat AVRs and constant $sigma_z/sigma_R$ clearly indicates an entirely different heating history. Outer disc populations also have flatter radial AVRs than those in the inner disc, likely due to the waning effect of spiral arms. Our detailed measurements of AVRs and $sigma_z/sigma_R$ across the disc indicate that low $mathrm{[alpha/Fe]}$, inner disc ($R lesssim 10,mathrm{kpc}$) stellar populations are likely dynamically heated by both giant molecular clouds and spiral arms, while the observed trends for outer disc populations require a significant contribution from another heating mechanism such as satellite perturbations. We also find that outer disc populations have slightly positive mean vertical and radial velocities, likely because they are part of the warped disc.
We summarise recent results from analysis of APOGEE/Gaia data for stellar populations in the Galactic halo, disk, and bulge, leading to constraints on the contribution of dwarf galaxies and globular clusters to the stellar content of the Milky Way halo. Interpretation of the extant data in light of cosmological numerical simulations suggests that the Milky Way has been subject to an unusually intense accretion history at z >~ 1.5.
We investigate the chemo-kinematic properties of the Milky Way disc by exploring the first year of data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE), and compare our results to smaller optical high-resolution samples in the literature, as well as results from lower resolution surveys such as GCS, SEGUE and RAVE. We start by selecting a high-quality sample in terms of chemistry ($sim$ 20.000 stars) and, after computing distances and orbital parameters for this sample, we employ a number of useful subsets to formulate constraints on Galactic chemical and chemodynamical evolution processes in the Solar neighbourhood and beyond (e.g., metallicity distributions -- MDFs, [$alpha$/Fe] vs. [Fe/H] diagrams, and abundance gradients). Our red giant sample spans distances as large as 10 kpc from the Sun. We find remarkable agreement between the recently published local (d $<$ 100 pc) high-resolution high-S/N HARPS sample and our local HQ sample (d $<$ 1 kpc). The local MDF peaks slightly below solar metallicity, and exhibits an extended tail towards [Fe/H] $= -$1, whereas a sharper cut-off is seen at larger metallicities. The APOGEE data also confirm the existence of a gap in the [$alpha$/Fe] vs. [Fe/H] abundance diagram. When expanding our sample to cover three different Galactocentric distance bins, we find the high-[$alpha$/Fe] stars to be rare towards the outer zones, as previously suggested in the literature. For the gradients in [Fe/H] and [$alpha$/Fe], measured over a range of 6 $ < $ R $ <$ 11 kpc in Galactocentric distance, we find a good agreement with the gradients traced by the GCS and RAVE dwarf samples. For stars with 1.5 $<$ z $<$ 3 kpc, we find a positive metallicity gradient and a negative gradient in [$alpha$/Fe].
We investigate the properties of the double sequences of the Milky Way discs visible in the [$alpha$/Fe] vs [Fe/H] diagram. In the framework of Galactic formation and evolution, we discuss the complex relationships between age, metallicity, [$alpha$/Fe], and the velocity components. We study stars with measured chemical, seismic and astrometric properties from the APOGEE survey, the Kepler and Gaia satellites, respectively. We separate the [$alpha$/Fe]-[Fe/H] diagram into 3 stellar populations: the thin disc, the high-$alpha$ metal-poor thick disc and the high-$alpha$ metal-rich thick disc and characterise each of these in the age-chemo-kinematics parameter space. We compare results obtained from different APOGEE data releases and using two recent age determinations. We use the Besanc{c}on Galaxy model (BGM) to highlight selection biases and mechanisms not included in the model. The thin disc exhibits a flat age-metallicity relation while [$alpha$/Fe] increases with stellar age. We confirm no correlation between radial and vertical velocities with [Fe/H], [$alpha$/Fe] and age for each stellar population. Considering both samples, V$_varphi$ decreases with age for the thin disc, while it increases with age for the h$alpha$mp thick disc. Although the age distribution of the h$alpha$mr thick disc is very close to that of the h$alpha$mp thick disc between 7 and 14 Gyr, its kinematics seems to follow that of the thin disc. This feature, not predicted by the hypotheses included in the BGM, suggests a different origin and history for this population. Finally, we show that there is a maximum dispersion of the vertical velocity, $sigma_Z$, with age for the h$alpha$mp thick disc around 8 Gyr. The comparisons with the BGM simulations suggest a more complex chemo-dynamical scheme to explain this feature, most likely including mergers and radial migration effects
We employ Gaia DR2 proper motions for 151 Milky Way globular clusters from Vasiliev (2019) in tandem with distances and line-of-sight velocities to derive their kinematical properties. To assign clusters to the Milky Way thick disk, bulge, and halo we follow the approach of Posti et al. (2018) who distinguished among different Galactic stellar components using starss orbits. In particular, we use the ratio $L_{z}/e$, the $Z$ projection of the angular momentum to the eccentricity, as population tracer, which we complement with chemical abundances extracted from the literature and Monte-Carlo simulations. We find that 20 globular clusters belong to the bar/bulge of the Milky Way, 35 exhibit disk properties, and 96 are members of the halo. Moreover, we find that halo globular clusters have close to zero rotational velocity with average value $<Theta>$ =1$pm$ 4 km s$^{-1}$. On the other hand, the sample of clusters that belong to the thick disk possesses a significant rotation with average rotational velocity 179 $pm$ 6 km s$^{-1}$. The twenty globular clusters orbiting within the bar/bulge region of the Milky Way galaxy have average rotational velocity of 49 $pm$ 11 km s$^{-1}$.
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