We study how migration affects stars of a galaxy with a thin stellar disc and thicker stellar components. The simulated galaxy has a strong bar and lasting spiral arms. We find that the amplitude of the churning (change in angular momentum) is similar for thin and thick components, and of limited amplitude, and that stars of all components can be trapped at the corotation of the bar. At the exception of those stars trapped at the corotation, we find that stars that are far from their initial guiding radius are more likely so due to blurring rather than churning effects. We compare the simulation to orbits integration with a fixed gravitational potential rotating at a constant speed. In the latter case, stars trapped at corotation are churned periodically outside and inside the corotation radius, with a zero net average. However, as the bar speed of the simulated galaxy decreases and its corotation radius increases, stars trapped at corotation for several Gyrs can be churned outwards on average. We study the location of extreme migrators (stars experimenting the largest churning) and find that extreme migrators come from regions on the leading side of the effective potential local maxima.
We present a study of the extent to which the Sellwood & Binney radial migration of stars is affected by their vertical motion about the midplane. We use both controlled simulations in which only a single spiral mode is excited, as well as slightly more realistic cases with multiple spiral patterns and a bar. We find that rms angular momentum changes are reduced by vertical motion, but rather gradually, and the maximum changes are almost as large for thick disc stars as for those in a thin disc. We find that particles in simulations in which a bar forms suffer slightly larger angular momentum …
We present evidence that isolated growing discs, subject to internal spiral perturbations, thicken due to both heating \emph{and} radial migration. We show this by demonstrating that the thickness and vertical velocity dispersions of coeval stars depend on their age as well as the change in their radii. While the disc thickens due to internal processes, we find that this induces only a minor amount of flaring. We further demonstrate the consequences of such thickening on the structural properties of stellar populations and find that they qualitatively agree with recent studies of the Milky Way…
We analyse disc heating and radial migration in N-body models of growing disc galaxies with thick and thin discs. Similar to thin-disc-only models, galaxies with appropriate non-axisymmetric structures reproduce observational constraints on radial disc heating in and migration to the Solar Neighbourhood (Snhd). The presence of thick discs can suppress non-axisymmetries and thus higher baryonic-to-dark matter fractions are required than in models that only have a thin disc. Models that are baryon-dominated to roughly the Solar radius R_0 are favoured, in agreement with data for the Milky Way. F…
The separation of the Milky Way disk into a thin and thick component is supported by differences in the spatial, kinematic and metallicity distributions of their stars. These differences have led to the view that the thick disk formed early via a cataclysmic event and constitutes fossil evidence of the hierarchical growth of the Milky Way. We show here, using N-body simulations, how a double-exponential vertical structure, with stellar populations displaying similar dichotomies can arise purely through internal evolution. In this picture, stars migrate radially, while retaining nearly circular…
Disc non-axisymmetrc components, such as spirals and central bars, are nowadays known to play an important role in shaping galactic discs. Here we use Tree-SPH N-body simulations to examine the effect of these perturbers on two aspects: the occurrence of multiple patterns in discs and the effects of radial migration on disc thickening. We find that, in addition to a central bar, multiple spiral patterns and lopsided modes develop in all models. Interaction among these asymmetric features results in a large scale stellar migration. However, we show that, despite the strong radial mixing, discs …
Non-axisymmetric components, such as spirals and central bars, play a major role in shaping galactic discs. An important aspect of the disc secular evolution driven by these perturbers is the radial migration of stars. It has been suggested recently that migration can populate a thick-disc component from inner-disc stars with high vertical energies. Since this has never been demonstrated in simulations, we study in detail the effect of radial migration on the disc velocity dispersion and disc thickness, by separating simulated stars into migrators and non-migrators. We apply this method to thr…
We combine the estimated metallicities [Fe/H], abundances [α/Fe], positions and motions of a sample of 27,500 local (7<R/kpc<9, 0.5<|z|/kpc<2.5) SDSS/SEGUE G-type dwarf stars to investigate the chemo-orbital properties of the Milky Way's disk around the Sun. When we derive the orbital properties reflecting angular momentum, circularity, and thickness as function of [α/Fe] vs. [Fe/H], we find that there is a smooth variation with [α/Fe], a proxy for age. At the same time, the orbital properties of the old stars with [α/Fe]$\gtrsim$0.25 do show a transition with [Fe/H]: below [Fe/H]$\simeq$-0.6 …
We study the role of radial migration of stars on the chemical evolution of the Milky Way disk. In particular, we are interested in the impact of that process on the local properties of the disk (age-metallicity relation and its dispersion, metallicity distribution, evolution of abundance ratios) and on the morphological properties of the resulting thick and thin disks.We use a model with several new or up-dated ingredients: atomic and molecular gas phases, star formation depending on molecular gas, yields from the recent homogeneous grid provided by Nomoto et al. (2013), observationally infer…
We use numerical simulations to examine the effects of radial migration on the vertical structure of galaxy disks. The simulations follow three exponential disks of different mass but similar circular velocity, radial scalelength, and (constant) scale height. The disks develop different non-axisymmetric patterns, ranging from feeble, long-lived multiple arms to strong, rapidly-evolving few-armed spirals. These fluctuations induce radial migration through secular changes in the angular momentum of disk particles, mixing the disk radially and blurring pre-existing gradients. Migration affects pr…
We study the radial metallicity gradient $Δ[M/H]/ΔR_g$ as a function of [Mg/Fe] and $|Z|$ with the help of a guiding radius based on the Apache Point Observatory Galactic Evolution Experiment and Gaia and then analyze the radial migration effect on the radial metallicity gradient and metallicity-rotation gradient between the Galactic thin and thick disks. The derived trend of gradient $Δ[M/H]/ΔR_g$ versus [Mg/Fe] shows a transition at [Mg/Fe] $\sim 0.18$ dex, below which the gradient is negative and varies a little as [Mg/Fe] increases; however, it changes sharply in [Mg/Fe] ranges of 0.16-0.1…
We study the kinematics of the Galactic thin and thick disk populations using stars from the RAVE survey's second data release together with distance estimates from Breddels et al. (2009). The velocity distribution exhibits the expected moving groups present in the solar neighborhood. We separate thick and thin disk stars by applying the X (stellar-population) criterion of Schuster et al. (1993), which takes into account both kinematic and metallicity information. For 1906 thin disk and 110 thick disk stars classified in this way, we find a vertical velocity dispersion, mean rotational velocit…
We test competing models that aim at explaining the nature of stars in the Milky Way that are well away (|z|$\gtrsim$ 1kpc) from the midplane, the so-called thick disk: the stars may have gotten there through orbital migration, through satellite mergers and accretion, or through heating of pre-existing thin disk stars. Sales et al. (2009) proposed the eccentricity distribution of thick disk stars as a diagnostic to differentiate between these mechanisms. Drawing on SDSS DR7, we have assembled a sample of 34,223 G-dwarfs with 6-D phase-space information and metallicities, and have derived orbit…
Recent observations suggest a "double-branch" behaviour of Li/H versus metallicity in the local thick and thin discs. This is reminiscent of the corresponding O/Fe versus Fe/H behaviour, which has been explained as resulting from radial migration in the Milky Way disc. We use a semi-analytical model of disc evolution with updated chemical yields and parameterised radial migration. We explore the cases of long-lived (red giants of a few Gy lifetime) and shorter-lived (Asymptotic Giant Branch stars of several 10$^8$ yr) stellar sources of Li, as well as those of low and high primordial Li. We sh…
The $([α/{\rm Fe}],[{\rm Fe/H}])$ distribution of Milky Way stars shows at least two distinct sequences, which have traditionally been associated with the thin and thick disc components. The abundance distribution varies systematically with location $R$ and $|z|$ across the Galaxy. Using an analytical chemodynamical model that includes the effects of radial migration and kinematic heating, we show that it is possible to reproduce the observed abundance distribution at different locations. Unlike some earlier models, our scheme does not require a distinct thick disc component emerging from a se…
(Abridged) We analyze chemical and kinematical properties of about 850 FGK solar neighborhood long-lived dwarfs observed with the HARPS high-resolution spectrograph. The stars in the sample have logg > 4 dex, 5000 < Teff < 6500 K, and -1.39 < [Fe/H] < 0.55 dex. We apply a purely chemical analysis approach based on the [alpha/Fe] vs. [Fe/H] plot to separate Galactic stellar populations into the thin disk, thick disk and high-alpha metal-rich (hamr). Our analysis shows a negative gradient of the rotational velocity of the thin disk stars with [Fe/H] (-17 km s^-1 dex^-1), and a steep positive gra…
We study the orbital properties of stars in four (published) simulations of thick disks formed by: i) accretion from disrupted satellites, ii) heating of a pre-existing thin disk by a minor merger, iii) radial migration and iv) gas rich mergers. We find that the distribution of orbital eccentricities are predicted to be different for each model: a prominent peak at low eccentricity is expected for the heating, migration and gas-rich merging scenarios, while the eccentricity distribution is broader and shifted towards higher values for the accretion model. These differences can be traced back t…
The Gaia mission, with its unprecedented astrometric and photometric precision, combined with its Radial Velocity Spectrometer, will provide to the astronomical community a wealth of necessary constraints to disentangle between the different formation scenarios of the Galactic thick disc. The aim of this review is to present some of the recent results obtained spectroscopically concerning this Galactic structure, and highlight the open questions that still remain to be answered under the Gaia era. These concern mainly the measurement of the chemo-dynamical properties of the Milky Way at the in…
We determined the chemical and kinematic properties of the Galactic thin and thick disk using a sample of 307,246 A/F/G/K-type giant stars from the LAMOST spectroscopic survey and Gaia DR2 survey. Our study found that the thick disk globally exhibits no metallicity radial gradient, but the inner disk ($R \le 8$ kpc) and the outer disk ($R>8$ kpc) have different gradients when they are studied separately. The thin disk also shows two different metallicity radial gradients for the inner disk and the outer disk, and has steep metallicity vertical gradient of d[Fe/H]/d$|z|$ $=-0.12\pm0.0007$ dex k…
The GALAH survey targets one million stars in the southern hemisphere down to a limiting magnitude of V = 14 at the Anglo- Australian Telescope. The project aims to measure up to 30 elemental abundances and radial velocities (~1 km/s accuracy) for each star at a resolution of R = 28000. These elements fall into 8 independent groups (e.g. alpha, Fe peak, r-process). For all stars, Gaia will provide distances to 1% and transverse velocities to 1 km/s or better, giving us a 14D set of parameters for each star, i.e. 6D phase space and 8D abundance space. There are many scientic applications but he…
We study the radial migration of stars driven by recurring multi-arm spiral features in an exponential disk embedded in a dark matter halo. The spiral perturbations redistribute angular momentum within the disk and lead to substantial radial displacements of individual stars, in a manner that largely preserves the circularity of their orbits and that results, after 5 Gyr (~40 full rotations at the disk scalelength), in little radial heating and no appreciable changes to the vertical or radial structure of the disk. Our results clarify a number of issues related to the spatial distribution and …
We use a suite of numerical simulations to investigate the mechanisms and effects of radial migration of stars in disk galaxies like the Milky Way (MW). An isolated, collisionless stellar disk with a MW-like scale-height shows only the radial "blurring" expected from epicyclic orbits. Reducing the disk thickness or adding gas to the disk substantially increases the level of radial migration, induced by interaction with transient spiral arms and/or a central bar. We also examine collisionless disks subjected to gravitational perturbations from a cosmologically motivated satellite accretion hist…
We study the radial migration of stars as a function of orbital action as well as the structural properties of a large suite of N-body simulations of isolated disc galaxies. Our goal is to establish a relationship between the radial migration efficiency of stars and their vertical action. We aim to describe how that relationship depends on the relative gravitational dominance between the disc and the dark matter halo. By changing the mass ratio of our disc and dark matter halo we find a relationship between disc dominance, number and strength of spiral arms, and the ensuing radial migration as…
Based on high-resolution spectra obtained with the MIKE spectrograph on the Magellan telescopes we present detailed elemental abundances for 20 red giant stars in the outer Galactic disk, located at Galactocentric distances between 9 and 13 kpc. The outer disk sample is complemented with samples of red giants from the inner Galactic disk and the solar neighbourhood, analysed using identical methods. For Galactocentric distances beyond 10 kpc, we only find chemical patterns associated with the local thin disk, even for stars far above the Galactic plane. Our results show that the relative densi…
By selecting in the RAVE-DR4 survey the stars located between 1 and 2 kpc above the Galactic plane, we question the consistency of the simplest three-component model (thin disc, thick disc, halo) for the Milky Way. We confirm that the metallicity and azimuthal velocity distribution functions of the thick disc are not Gaussian. In particular, we find that the thick disc has an extended metallicity tail going at least down to [M/H]=-2 dex, contributing roughly at 3% of the entire thick disc population and having a shorter scale-length compared to the canonical thick disc. The mean azimuthal velo…
We investigate the role of radial migration history of stars in chemical evolution of a disk galaxy, in particular in understanding the origin of their bimodal distribution on the [alpha/Fe]-[Fe/H] plane. For this purpose, we examine the three different models with no, continuous, and discontinuous radial migration, respectively. We find that for the model with radial migration, the [alpha/Fe] ratios of stars in outer disk regions decrease more rapidly with time than the model without radial migration, because the associated net transfer of intermediate and old disk stars from inner to outer d…
We study the eccentricity distribution of a thick disc sample of stars observed in the Radial Velocity Experiment (RAVE) and compare it to that expected in four simulations of thick disc formation in the literature (accretion of satellites, heating of a primordial thin disc during a merger, radial migration, and gas-rich mergers), as compiled by Sales et al. (2009). We find that the distribution of our sample is peaked at low eccentricities and falls off smoothly and rather steeply to high eccentricities. This distribution is fairly robust to changes in distances, thin disc contamination, and …
We estimate the age for the individual stars located at the lower part of the red giant branch from the LAMOST DR2 K giant sample. Taking into account the selection effects and the volume completeness, the age--metallicity map for the stars located between 0.3 and 1.5 kpc from the Sun is obtained. A significant substructure (denoted as the \it{narrow stripe}) located from (age, [Fe/H])$\sim$(5, 0.4) to (10 Gyr, -0.4 dex) in the age--metallicity map is clearly identified. Moreover, the \it{narrow stripe} stars are found the dominate contributors to several velocity substructures, including the …
We present a kinematic analysis of a sample of 23,908 G- and K-type dwarfs in the Galactic disk. Based on the $α$-abundance ratio, [$α$/Fe], we separated our sample into low-$α$ thin-disk and high-$α$ thick-disk stars. We find a $V_{\rm ϕ}$ gradient of $-$28.2 km s$^{-1}$ dex$^{-1}$ over [Fe/H] for the thin disk, and an almost flat trend of the velocity dispersions of $V_{\rm R}$, $V_{\rm ϕ}$, and $V_{\rm Z}$ components with [Fe/H]. The metal-poor (MP; [Fe/H] $<$ $-$0.3) thin-disk stars with low-$V_{\rm ϕ}$ velocities have high eccentricities ($e$) and small perigalacticon distances ($r_{\rm p…
Revisiting the Radial Metallicity Gradient-Age Relation in the Milky Way's Thin and Thick Disks
Shanghai Jiao Tong University（上海交通大学）；University of Chinese Academy of Sciences（中国科学院大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Tianjin Normal University（天津师范大学）
Since thin disc stars are younger than thick disc stars on average, the thin disc is predicted by some models to start forming after the thick disc had formed, around 10 Gyr ago. Accordingly, no significant old thin disc population should exist. Using 6-D coordinates from Gaia-DR2 and age estimates from Sanders & Das (2018), we select $\sim 24000$ old stars (${τ> 10}$ Gyr, with uncertainties $\lesssim 15\%$) within 2 kpc from the Sun (full sample). A cross-match with APOGEE-DR16 ($\sim 1000$ stars) reveals comparable fractions of old chemically defined thin/thick disc stars. We show that the f…
We study the chemical evolution of the thick and thin discs of the Galaxy by comparing detailed chemical evolution models with recent data from the AMBRE Project. The data suggest that the stars in the thick and thin discs form two distinct sequences with the thick disc stars showing higher [α/Fe] ratios. We adopt two different approaches to model the evolution of thick and thin discs. In particular, we adopt: i) a two-infall approach where the thick disc forms fast and before the thin disc and by means of a fast gas accretion episode, whereas the thin disc forms by means of a second accretion…
Stars born on near-circular orbits in spiral galaxies can subsequently migrate to different orbits due to interactions with non-axisymmetric disturbances within the disc such as bars or spiral arms. This paper extends the study of migration to examine the role of external influences using the example of the interaction of the Sagittarius dwarf galaxy (Sgr) with the Milky Way (MW). We first make impulse approximation estimates to characterize the influence of Sgr disc passages. The tidal forcing from Sgr can produce changes in both guiding radius ($ΔR_g$) and orbital eccentricity, as quantified…
In order to understand the roles of metal flows in galaxy formation and evolution, we analyse our self-consistent cosmological chemo-dynamical simulation of a Milky Way like galaxy during its thin-disc phase. Our simulated galaxy disc qualitatively reproduces the variation of the dichotomy in [$α$/Fe]-[Fe/H] at different Galactocentric distances as derived by APOGEE-DR16, as well as the stellar age distribution in [$α$/Fe]-[Fe/H] from APOKASC-2. The disc grows from the inside out, with a radial gradient in the star-formation rate during the entire phase. Despite the radial dependence, the outf…
In the last years, stellar migration in galactic discs has been the subject of several investigations. However, its impact on the chemical evolution of the Milky Way still needs to be fully quantified. In this paper, we aim at imposing some constraints on the significance of this phenomenon by considering its influence on the chemical evolution of the Milky Way thin disc. We do not investigate the physical mechanisms underlying the migration of stars. Rather, we introduce a simple, heuristic treatment of stellar migration in a detailed chemical evolution model for the thin disc of the Milky Wa…
Planets form in the discs of gas and dust that surround young stars. It is not known whether gas giant planets on wide orbits form the same way as Jupiter or by fragmentation of gravitationally unstable discs. Here we show that a giant planet, which has formed in the outer regions of a protostellar disc, initially migrates fast towards the central star (migration timescale ~10,000 yr) while accreting gas from the disc. However, in contrast with previous studies, we find that the planet eventually opens up a gap in the disc and the migration is essentially halted. At the same time, accretion-po…
Stellar radial migration plays an important role in reshaping a galaxy's structure and the radial distribution of stellar population properties. In this work, we revisit reported observational evidence for radial migration and quantify its strength using the age--[Fe/H] distribution of stars across the Milky Way with APOGEE data. We find a broken age--[Fe/H] relation in the Galactic disc at $r>6$ kpc, with a more pronounced break at larger radii. To quantify the strength of radial migration, we assume stars born at each radius have a unique age and metallicity, and then decompose the metallici…
The gravitational interaction between a protoplanetary disc and planetary sized bodies that form within it leads to the exchange of angular momentum, resulting in migration of the planets and possible gap formation in the disc for more massive planets. In this article, we review the basic theory of disc-planet interactions, and discuss the results of recent numerical simulations of planets embedded in protoplanetary discs. We consider the migration of low mass planets and recent developments in our understanding of so-called type I migration when a fuller treatment of the disc thermodynamics i…
Despite the recent advancements in the field of galaxy formation and evolution, fully self-consistent simulations are still unable to make the detailed predictions necessary for the planned and ongoing large spectroscopic and photometry surveys of the Milky Way disc. These difficulties arise from the very uncertain nature of sub-grid physical energy feedback within models, affecting both star formation rates and chemical enrichment. To avoid these problems, we have introduced a new approach which consists of fusing disc chemical evolution models with compatible numerical simulations. We demons…
[Abridged] In this first paper of this series, we present a new approach for studying the chemo-dynamical evolution in disk galaxies, which consists of fusing disk chemical evolution models with compatible numerical simulations of galactic disks. This method avoids known star formation and chemical enrichment problems encountered in simulations. Here we focus on the Milky Way, by using a detailed thin-disk chemical evolution model and a simulation in the cosmological context, with dynamical properties close to those of our Galaxy. We show that, due to radial migration from mergers at high reds…
