Modeling disc non-axisymmetries: multiple patterns, radial migration, and thick discs
Ivan Minchev, Benoit Famaey, Alice C. Quillen, Walter Dehnen
备注：
6 pages, 3 figures, to appear in the proceedings of "Assembling the Puzzle of the Milky Way", Le Grand Bornand (Apr. 17-22, 2011), C. Reyle, A. Robin, M. Schultheis (eds.)
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 cannot be thickened sufficiently to match observed thick discs. We relate this to the adiabatic cooling as stars migrate radially outwards. We also find that the bulge contribution to a thick-disc component for an Sa-type galaxy at ~2.5 disc scale-lengths is less than 1% and zero in the case of a Milky Way-like, Sb-type. Our findings cast doubt on the plausibility of thick disc formation via stellar radial migration.
We perform controlled N-body simulations of disc galaxies growing within live dark matter (DM) haloes to present-day galaxies that contain both thin and thick discs. We consider two types of models: a) thick-disc initial conditions to which stars on near-circular orbits are continuously added over ~10 Gyr and b) models in which the birth velocity dispersion of stars decreases continuously over the same time-scale. We show that both schemes produce double-exponential vertical profiles similar to that of the Milky Way (MW). We indicate how the spatial age structure of galaxies can be used to dis…
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 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…
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…
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…
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 simulati…
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…
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…
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…
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…
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 investigate the evolution of galactic disks in N-body Tree-SPH simulations. We find that disks, initially truncated at three scale-lengths, can triple their radial extent, solely driven by secular evolution. Both Type I (single exponential) and Type II (down-turning) observed disk surface-brightness profiles can be explained by our findings. We relate these results to the strong angular momentum outward transfer, resulting from torques and radial migration associated with multiple patterns, such as central bars and spiral waves of different multiplicity. We show that even for stars ending u…
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…
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 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 …
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…
We performed a spectroscopic survey of nearly 700 stars probing the galactic thick disc far from the solar neighbourhood towards the galactic coordinates (l~277, b~47). The derived effective temperatures, surface gravities and overall metallicities were then combined with stellar evolution isochrones, radial velocities and proper motions to derive the distances, kinematics and orbital parameters of the sample stars. The targets belonging to each galactic component (thin disc, thick disc, halo) were selected either on their kinematics or according to their position above the galactic plane, and…
We present {complexity} of the Galactic outer disc {by fitting the stellar volume densities of the red giant branch stars with a two-disc component model}. {The discs are confirmed to} extend to $R\sim19$\,kpc. The radial density profile of the discs shows {two breaks at $R\sim11$ and $\sim14$\,kpc, respectively, which} separate the radial profile into three segments with different scale lengths of $2.12\pm0.26$, $1.18\pm0.08$, and $2.72$\,kpc at $R<11$, $11\leq R\leq14$, and $R>14$\,kpc, respectively. The first {break} is likely due to the sudden drop in the radial profile of the thin disc, w…
In recent years star formation has been discovered in the Milky Way's warp. These stars formed in the warp (warp stars) must eventually settle into the plane of the disc. We use an $N$-body$+$smooth particle hydrodynamics model of a warped galaxy to study how warp stars settle into the disc. By following warp stars in angular momentum space, we show that they first tilt to partially align with the main disc in a time scale of $\sim1$ Gyr. Then, once differential precession halts this process, they phase mix into an axisymmetric distribution on a time scale of $\sim 6$ Gyr. The warp stars end u…
Correlations between stellar chemistry and kinematics have long been used to gain insight into the evolution of the Milky Way Galaxy. Orbital angular momentum is a key physical parameter and it is often estimated from three-dimensional space motions. We here demonstrate the lower uncertainties that can be achieved in the estimation of one component of velocity through selection of stars in key directions and use of line-of-sight velocity alone (i.e. without incorporation of proper motion data). In this first paper we apply our technique to stars observed in the direction of Galactic rotation i…
We search for the existence of chemically-distinct stellar components in the solar neighbourhood using published data. Extending earlier work, we show that when the abundances of Fe, alpha elements, and the r-process element Eu are considered, stars separate neatly into two groups that delineate the traditional thin and thick disk of the Milky Way. The group akin to the thin disk is traced by stars with [Fe/H]>-0.7 and alpha/Fe<0.2. The thick disk-like group overlaps the thin disk in [Fe/H] but has higher abundances of alpha elements and Eu. Stars in the range -1.5<[Fe/H]<-0.7 with low [alpha/…
Within a cosmological hydrodynamical simulation, we form a disc galaxy with sub- components which can be assigned to a thin stellar disc, thick disk, and a low mass stellar halo via a chemical decomposition. The thin and thick disc populations so selected are distinct in their ages, kinematics, and metallicities. Thin disc stars are young (<6.6 Gyr), possess low velocity dispersion (σU,V,W = 41, 31, 25 km/s), high [Fe/H], and low [O/Fe]. The thick disc stars are old (6.6<age<9.8 Gyrs), lag the thin disc by \sim21 km/s, possess higher velocity dispersion (σU,V,W = 49, 44, 35 km/s), relatively l…
We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit de…
We present a set of self-consistent chemo-dynamical simulations of MW-type galaxies formation to study the origin of the bimodality of $α$-elements in stellar populations. We explore how the bimodality is related to the geometrically and kinematically defined stellar discs, gas accretion and radial migration. We find that the two $α$-sequences are formed in quite different physical environments. The high-$α$ sequence is formed early from a burst of star formation (SF) in a turbulent, compact gaseous disc which forms a thick disc. The low-$α$ stellar populations is the result of quiescent SF su…
We investigate the properties of the double sequences of the Milky Way discs visible in the [$α$/Fe] vs [Fe/H] diagram. In the framework of Galactic formation and evolution, we discuss the complex relationships between age, metallicity, [$α$/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 [$α$/Fe]-[Fe/H] diagram into 3 stellar populations: the thin disc, the high-$α$ metal-poor thick disc and the high-$α$ metal-rich thick disc and characterise each o…
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 …
The aim of this paper is to characterise the abundance patterns of five iron-peak elements (Mn, Fe, Ni, Cu, and Zn) for which the stellar origin and chemical evolution are still debated. We automatically derived iron peak (Mn, Fe, Ni, Cu, and Zn) and alpha element (Mg) chemical abundances for 4666 stars. We used the bimodal distribution of [Mg/Fe] to chemically classify sample stars into different Galactic substructures: thin disc, metal-poor and high-alpha metal rich, high-alpha and low-alpha metal-poor populations. High-alpha and low-alpha metal-poor populations are fully distinct in Mg, Cu,…
We examine the origin of radial and vertical gradients in the age/metallicity of the stellar component of a galaxy disc formed in the APOSTLE cosmological hydrody- namical simulations. Some of these gradients resemble those in the Milky Way, where they have sometimes been interpreted as due to internal evolution, such as scattering off giant molecular clouds, radial migration driven by spiral patterns, or orbital reso- nances with a bar. Secular processes play a minor role in the simulated galaxy, which lacks strong spiral or bar patterns, and where such gradients arise as a result of the grad…
We perform a series of controlled N-body simulations of growing disc galaxies within non-growing, live dark matter haloes of varying mass and concentration. Our initial conditions include either a low-mass disc or a compact bulge. New stellar particles are continuously added on near-circular orbits to the existing disc, so spiral structure is continuously excited. To study the effect of combined spiral and giant molecular cloud (GMC) heating on the discs we introduce massive, short-lived particles that sample a GMC mass function. An isothermal gas component is introduced for a subset of the mo…
The observed radial and vertical metallicity distribution of old stars in the Milky Way disk provides a powerful constraint on the chemical enrichment and dynamical history of the disk. We present the radial metallicity gradient, Δ[Fe/H]/ΔR, as a function of height above the plane, |Z|, using 7010 main sequence turnoff stars observed by the Sloan Extension for Galactic Understanding and Exploration (SEGUE) survey. The sample consists of mostly old thin and thick disk stars, with a minimal contribution from the stellar halo, in the region 6 < R < 16 kpc, 0.15 < |Z| < 1.5 kpc. The data reveal th…
