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 outflow-to-infall ratio of metals in our simulated halo shows a time-independent profile scaling with the disc growth. The simulated disc undergoes two modes of gas inflow: (i) an infall of metal-poor and relatively low-[$α$/Fe] gas, and (ii) a radial flow where already chemically-enriched gas moves inwards with an average velocity of $\sim0.7$ km/s. Moreover, we find that stellar migrations mostly happen outwards, on typical time scales of $\sim5$ Gyr. Our predicted radial metallicity gradients agree with the observations from APOGEE-DR16, and the main effect of stellar migrations is to flatten the radial metallicity profiles by 0.05 dex/kpc in the slopes. We also show that the effect of migrations can appear more important in [$α$/Fe] than in the [Fe/H]-age relation of thin-disc stars.
The gradient of the gravitational redshift in the potential of the Milky-Way induces an apparent spurious radial migration. I show that this effect is simply related to the local acceleration, which was measured recently by Gaia eDR3, implying a spectroscopic shift of $[-2.4x10^{-2}/(r/8kpc)] km/s/kpc. The transverse Doppler effect yields a comparable contribution. The spurious radial velocity from both relativistic effects amounts to crossing a major portion of the Milky-Way disk during the age of the universe, and must be corrected for in any future measurement of the actual radial migration…
Stellar migration is an important dynamical process in Galactic disk. Here we model the radial stellar migration in the Galactic disk with an analytical method, then add it to detailed Galactic chemical evolution model to study the influence of radial stellar migration on the chemical evolution of the Milky Way, especially for the abundance gradients. We found that the radial stellar migration in the Galactic disk can make the profile of the G-dwarf metallicity distribution of the solar neighborhood taller and narrower, thus it becomes another solution to the "G-dwarf problem". It can also sca…
We develop and apply a model to quantify the global efficiency of radial orbit migration among stars in the Milky Way disk. This model parameterizes the possible star formation and enrichment histories, radial birth profiles, and combines them with a migration model that relates present-day orbital radii to birth radii through a Gaussian probability, broadening with age $τ$ as $σ_\mathrm{RM8}~\sqrt{τ/8{~\mathrm{Gyr}}}$. Guided by observations, we assume that stars are born with an initially tight age--metallicity relation at given radius, which becomes subsequently scrambled by radial orbit mi…
Recent analysis of the SDSS-III/APOGEE Data Release 12 stellar catalogue has revealed that the Milky Way's metallicity distribution function (MDF) changes shape as a function of radius, transitioning from being negatively skewed at small Galactocentric radii to positively skewed at large Galactocentric radii. Using a high resolution, N-body+SPH simulation, we show that the changing skewness arises from radial migration - metal-rich stars form in the inner disk and subsequently migrate to the metal-poorer outer disk. These migrated stars represent a large fraction (> 50%) of the stars in the ou…
Influence of Bar Formation on Star Formation Segregation and Stellar Migration: Implications for Variations in the Age Distribution of Milky Way Disk Stars
We show that in N-body simulations of isolated spiral discs, spiral arms appear to transient, recurring features that co-rotate with the stellar disc stars at all radii. As a consequence, stars around the spiral arm continually feel a tangential force from the spiral and gain/lose angular momentum at all radii where spiral structure exists, without gaining significant amounts of random energy. We demonstrate that the ubiquitous radial migration in these simulations can be seen as outward (inward) systematic streaming motions along the trailing (leading) side of the spiral arms. We characterise…
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…
The determination of the birth radius of the Sun is important to understand the evolution and consequent disruption of the Sun's birth cluster in the Galaxy. Motivated by this fact, we study the motion of the Sun in the Milky Way during the last 4.6 Gyr in order to find its birth radius. We carried out orbit integrations backward in time using an analytical model of the Galaxy which includes the contribution of spiral arms and a central bar. We took into account the uncertainty in the parameters of the Milky Way potential as well as the uncertainty in the present day position and velocity of t…
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…
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…
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…
We develop a hybrid model of galactic chemical evolution that combines a multi-ring computation of chemical enrichment with a prescription for stellar migration and the vertical distribution of stellar populations informed by a cosmological hydrodynamic disc galaxy simulation. Our fiducial model adopts empirically motivated forms of the star formation law and star formation history, with a gradient in outflow mass loading tuned to reproduce the observed metallicity gradient. With this approach, the model reproduces many of the striking qualitative features of the Milky Way disc's abundance str…
Recent observations show that the Milky Way's metallicity distribution function (MDF) changes its shape as a function of radius. This new evidence of radial migration within the stellar disc sets additional constraints on Galactic models. By performing controlled test particle simulations in a very detailed, observationally motivated model of the Milky Way, we demonstrate that, in the inner region of the disc, the MDF is shaped by the joint action of the bar and spiral arms, while at outer radii the MDF is mainly shaped by the spiral arms. We show that the spiral arms are able to imprint their…
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 …
Evidence of radial-migration driven Galactic disc expansion with the U-shape stellar age profile
South-Western Institute for Astronomy Research, Yunnan University（西南天文研究所，云南大学）；Yunnan Key Laboratory of Survey Science, Yunnan University（云南省测绘科学重点实验室，云南大学）
Radial migration is defined as the change in guiding centre radius of stars and gas caused by gains or losses of angular momentum that result from gravitational interaction with non-axisymmetric structure. This has been shown to have significant impact on the metallicity distribution in galactic discs, and therefore affects the interpretation of Galactic archeology. We use a simulation of a Milky Way-sized galaxy to examine the effect of radial migration on the star and gas radial metallicity distribution. We find that both the star and gas component show significant radial migration. The stel…
Albeit radial migration must be a ubiquitous process in disc galaxies, its significance in the evolution of stellar discs is not always reflected through global trends. However, there are other key observables, such as the metallicity distribution function (MDF), that may shed some light in this matter. We argue that the shape of the MDF not only tells us whether the stellar disc experienced radial migration, but it also contains important clues on the structure that triggered it. Specifically, the MDF contains information about the dynamics and morphology of the spiral pattern. To constrain t…
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…
Modelling the broken age-[Fe/H] relation and metallicity distribution function of mono-age populations
South-Western Institute for Astronomy Research, Yunnan University（西南天文研究所，云南大学）；Yunnan Key Laboratory of Survey Science, Yunnan University（云南省测绘科学重点实验室，云南大学）
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…
The present-day Age-Metallicity Relation (AMR) is a record of the star formation history of the Galaxy, as this traces the chemical enrichment of the gas over time. We use a zoomed-in cosmological simulation that reproduces key signatures of the Milky Way (MW), g2.79e12 from the NIHAO-UHD project, to examine how stellar migration and satellite infall shape the AMR across the disk. We find in the simulation, similar to the MW, the AMR in small spatial regions (R, z) shows turning points that connect changes in the direction of the relations. The turning points in the AMR in the simulation, are …
It is widely accepted that stars in a spiral disk, like the Milky Way's, can radially migrate on order a scale length over the disk's lifetime. With the exception of cold torquing, also known as "churning," processes that contribute to the radial migration of stars are necessarily associated with kinematic heating. Additionally, it is an open question whether or not an episode of cold torquing is kinemically cold over long radial distances. This study uses a suite of analytically based simulations to investigate the dynamical response when stars are subject to cold torquing and are also resona…
The redistribution of stars in galactic disks is an important aspect of disk galaxy evolution. Stars that efficiently migrate in such a way that does not also appreciably heat their orbits can drastically affect the stellar populations observed today and therefore influence constraints derived from such observations. Unfortunately, while the theoretical understanding of the migration process is becoming increasingly robust, there are currently few specific observable predictions. As a result, we do not yet have a clear handle on whether the process has been important for the Milky Way in the p…
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…
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…
We study the role of radial motions of stars and gas on the evolution of abundance profiles in the Milky Way disk. We investigate, in a parametrized way, the impact of radial flows of gas and radial migration of stars induced mainly by the Galactic bar and its iteraction with the spiral arms. We use a model with several new or up-dated ingredients (atomic and molecular gas phases, star formation depending on molecular gas, recent sets of metallicity-dependent stellar yields from H to Ni, observationally inferred SNIa rates), which reproduces well most global and local observables of the Milky …
We investigate the formation history of the stellar disk component in the Milky Way (MW) based on our new chemical evolution model. Our model considers several fundamental baryonic processes, including gas infall, re-accretion of outflowing gas, and radial migration of disk stars. Each of these baryonic processes in the disk evolution is characterized by model parameters, which are determined by fitting to various observational data of the stellar disk in the MW, including the radial dependence of the metallicity distribution function (MDF) of the disk stars, which has recently been derived in…
We attempt to determine the relative fraction of stars that have undergone significant radial migration by studying the orbital properties of metal-rich ([Fe/H]$>0.1$) stars within 2 kpc of the Sun using a sample of more than 3,000 stars selected from iDR4 of the Gaia-ESO Survey. We investigate the kinematic properties, such as velocity dispersion and orbital parameters, of stellar populations near the sun as a function of [Mg/Fe] and [Fe/H], which could show evidence of a major merger in the past history of the Milky Way. This was done using the stellar parameters from the Gaia-ESO Survey alo…
Enhanced rates of stellar radial migration in gas-rich discs at high redshift
University of Cambridge（剑桥大学）；University of Sydney（悉尼大学）；Kavli Institute for the Physics and Mathematics of the Universe（宇宙物理与数学柯尔菲研究所）；University College London（伦敦大学学院）；Lund University（隆德大学）
We investigate the influence of stellar migration caused by minor mergers (mass ratio from 1:70 to 1:8) on the radial distribution of chemical abundances in the disks of Milky Way-like galaxies during the last four Gyr. A GPU-based pure N-body tree-code model without hydrodynamics and star formation was used. We computed a large set of mergers with different initial satellite masses, positions, and orbital velocities. We find that there is no significant metallicity change at any radius of the primary galaxy in the case of accretion of a low-mass satellite of 10$^9$ M$_{\odot}$ (mass ratio 1:7…
We study the presence and importance of stellar migration in the evolution of 17 Milky-Way like disk galaxies with stellar mass $10 < \textrm{log}(M_{*}/{\rm M}_\odot) < 11$ from the Auriga suite of zoom-in cosmological hydrodynamical simulations. We compare the birth radii of the stars to their radii at $z=0$ for each system and present mean values of the strength of stellar migration as a function of radius and stellar age which vary between 1-4 kpc. We also investigate the effect of migration on age and metallicity radial profiles in the disks. We find several cases of age gradient flatteni…
Physics of the gravitational effect of the galactic bar and spiral structure is presented. Physical equations differ from the conventionally used equations. Application to the motion of the Sun is treated. The speed of the Sun is taken to be consistent with the Oort constants. Galactic radial migration of the Sun is less than +- 0.4 kpc for the four-armed spiral structure. The Sun remains about 75 % of its existence within galactocentric distances (7.8 - 8.2) kpc and the results are practically independent on the spiral structure strength. Thus, the radial distance changes only within 5 % from…
We have recently identified a previously unknown radial migration mechanism resulting from the overlap of spiral and bar resonances in galactic discs (Minchev & Famaey 2010, Minchev et al. 2010). This new mechanism is much more efficient than mixing by transient spirals and its presence is unavoidable in all barred galaxies, such as our own Milky Way. The consequences of this are a strong flattening in the metallicity gradient in the disc, an extended disc profile, and the formation of a thick disc component, all taking place in only a couple of Gyr. This timescale is drastically shorter than …
Multi-object spectrographs have opened a new window on the analyses of the chemo-dynamical properties of old Milky Way stars. These analyses allow us to trace back the internal mechanisms and the external factors that have influenced the evolution of our Galaxy, and therefore understand fundamental aspects of galaxy evolution in general. Here, we present recent results from the RAdial Velocity Experiment (RAVE) and the Gaia-ESO survey. These surveys explore the Milky Way properties in different ways, in terms of sample size and selection, magnitude range, and spectral resolution. We focus here…
[Abridge] In the first paper of this series (paper I) we presented a new approach for studying the chemo-odynamical evolution in disk galaxies, focusing on the Milky Way. Here we extend these results to different distances from the Galactic center, looking for variations of observables that can be related to on-going and future spectroscopic surveys. By separating the effects of kinematic heating and radial migration, we show that migration is much more important, even for the oldest and hottest stellar population. The distributions of stellar birth guiding radii and final guiding radii (signi…
Metallicity gradients derived from planetary nebulae (PNe) using O, Ne, and Ar abundances are studied and compared to those from HII regions in the galaxies M31, M33, NGC 300 and the Milky Way. Galactocentric radii and chemical abundances were collected from the literature, carefully selecting a homogeneous sample for each galaxy. Metallicity gradients shown by PNe are flatter than those of HII regions in all cases. The extreme case is M31 where PN abundances are not related to galactocentric distances and the gradients are consistent with zero. To analyze the evolution of gradients with time …
Rediscovering the Milky Way with an orbit superposition approach and APOGEE data V. The disc growth and history of star formation
Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦阿基米德天体物理研究所）；Department of Astrophysics, University of Vienna（维也纳大学天体物理系）；BIFOLD, Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究所）；LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台LIRA实验室，巴黎文理研究大学，索邦大学，巴黎西岱大学，CY塞尔吉巴黎大学，法国国家科学研究中心）；Universität Potsdam, Institut für Physik und Astronomie（波茨坦大学物理与天文学研究所）；Friedrich-Schiller Uni（弗里德里希·席勒大学）
We live in an age where an enormous amount of astrometric, photometric, asteroseismic, and spectroscopic data of Milky Way stars are being acquired, many orders of magnitude larger than about a decade ago. Thanks to the Gaia astrometric mission and followup ground-based spectroscopic surveys in the next 5-10 years about 10-20 Million stars will have accurate 6D kinematics and chemical composition measurements. KEPLER-2, PLATO, and TESS will provide asteroseismic ages for a good fraction of those. In this article we outline some outstanding problems concerning the formation and evolution of the…
Effective radial migration and mixing of orbits throughout the stellar disk has been definitively established in the Milky Way, but not in any other galaxy. We show how such radial mixing can be measured (or strongly constrained) in M31 using a combination of existing data and readily available facilities.
We identify migrating stars in an N-body simulation of a Milky-Way-like disk. Outward migration can occur when a star in a low eccentricity orbit lags a short-lived local spiral arm density peak. We interpret short lived local density peaks, that appear and fade on approximately an orbital period, as arising from positive interference between spiral density wave patterns. Stars near such a peak can migrate over a significant distance in galactocentric radius during the peak lifetime, providing that the peak is sufficiently dense. Using a Gaussian bar model for the potential perturbation associ…
By means of N-body simulations, we show that radial migration in galaxy disks, induced by bar and spiral arms, leads to significant azimuthal variations in the metallicity distribution of old stars at a given distance from the galaxy center. Metals do not show an axisymmetric distribution during phases of strong migration. Azimuthal variations are visible during the whole phase of strong bar phase, and tend to disappear as the effect of radial migration diminishes, together with a reduction in the bar strength. These results suggest that the presence of inhomogeneities in the metallicity distr…
The best way to trace back the history of star formation and mass assembly of the Milky Way disc is by combining chemical compositions, ages and phase-space information for a large number of disc stars. With the advent of large surveys of the stellar populations of the Galaxy, such data have become available and can be used to pose constraints on sophisticated models of galaxy formation. We use SDSS-III/APOGEE data to derive the first detailed 3D map of stellar density in the Galactic disc as a function of age, [Fe/H] and $\mathrm{[α/Fe]}$. We discuss the implications of our results for the fo…
The aim of Galactic Archaeology is to recover the evolutionary history of the Milky Way from its present day kinematical and chemical state. Because stars move away from their birth sites, the current dynamical information alone is not sufficient for this task. The chemical composition of stellar atmospheres, on the other hand, is largely preserved over the stellar lifetime and, together with accurate ages, can be used to recover the birthplaces of stars currently found at the same Galactic radius. In addition to the availability of large stellar samples with accurate 6D kinematics and chemica…
We use a high resolution cosmological zoom simulation of a Milky Way-sized halo to study the observable features in velocity and metallicity space associated with the dynamical influence of spiral arms. For the first time, we demonstrate that spiral arms, that form in a disc in a fully cosmological environment with realistic galaxy formation physics, drive large-scale systematic streaming motions. In particular, on the trailing edge of the spiral arms the peculiar galacto-centric radial and azimuthal velocity field is directed radially outward and azimuthally backward, whereas it is radially i…
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…
Large-scale stellar surveys coupled with recent developments in magneto-hydrodynamical simulations of the formation of Milky Way-mass galaxies provide an unparalleled opportunity to unveil the physical processes driving the evolution of the Galaxy. We developed a framework to compare a variety of parameters with their corresponding predictions from simulations in an unbiased manner, taking into account the selection function of a stellar survey. We applied this framework to a sample of over 7000 stars with asteroseismic, spectroscopic, and astrometric data available, together with 6 simulation…
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…
Radial stellar migration in galactic discs has received much attention in studies of galactic dynamics and chemical evolution, but remains a dynamical phenomenon that needs to be fully quantified. In this work, using a Tree-SPH simulation of an Sb-type disc galaxy, we quantify the effects of blurring (epicyclic excursions) and churning (change of guiding radius). We quantify migration (either blurring or churning) both in terms of flux (the number of migrators passing at a given radius), and by estimating the population of migrators at a given radius at the end of the simulation compared to no…
Using a sample of 69,919 red giants from the SDSS-III/APOGEE Data Release 12, we measure the distribution of stars in the [$α$/Fe] vs. [Fe/H] plane and the metallicity distribution functions (MDF) across an unprecedented volume of the Milky Way disk, with radius $3<R<15$ kpc and height $|z|<2$ kpc. Stars in the inner disk ($R<5$ kpc) lie along a single track in [$α$/Fe] vs. [Fe/H], starting with $α$-enhanced, metal-poor stars and ending at [$α$/Fe]$\sim0$ and [Fe/H]$\sim+0.4$. At larger radii we find two distinct sequences in [$α$/Fe] vs. [Fe/H] space, with a roughly solar-$α$ sequence that sp…
