Particle tagging is an efficient, but approximate, technique for using cosmological N-body simulations to model the phase-space evolution of the stellar populations predicted, for example, by a semi-analytic model of galaxy formation. We test the technique developed by Cooper et al. (which we call STINGS here) by comparing particle tags with stars in a smooth particle hydrodynamic (SPH) simulation. We focus on the spherically averaged density profile of stars accreted from satellite galaxies in a Milky Way (MW)-like system. The stellar profile in the SPH simulation can be recovered accurately by tagging dark matter (DM) particles in the same simulation according to a prescription based on the rank order of particle binding energy. Applying the same prescription to an N-body version of this simulation produces a density profile differing from that of the SPH simulation by <10 per cent on average between 1 and 200 kpc. This confirms that particle tagging can provide a faithful and robust approximation to a self-consistent hydrodynamical simulation in this regime (in contradiction to previous claims in the literature). We find only one systematic effect, likely due to the collisionless approximation, namely that massive satellites in the SPH simulation are disrupted somewhat earlier than their collisionless counterparts. In most cases this makes remarkably little difference to the spherically averaged distribution of their stellar debris. We conclude that, for galaxy formation models that do not predict strong baryonic effects on the present-day DM distribution of MW-like galaxies or their satellites, differences in stellar halo predictions associated with the treatment of star formation and feedback are much more important than those associated with the dynamical limitations of collisionless particle tagging.
We establish a controlled comparison between the properties of galactic stellar halos obtained with hydrodynamical simulations and with `particle tagging'. Tagging is a fast way to obtain stellar population dynamics: instead of tracking gas and star formation, it `paints' stars directly onto a suitably defined subset of dark matter particles in a collisionless, dark-matter-only simulation.Our study shows that there are conditions under which particle tagging generates good fits to the hydrodynamical stellar density profiles of a central Milky-Way-like galaxy and its most prominent substructure…
Chemical tagging has great promise as a technique to unveil our Galaxy's history. Grouping stars based on their similar chemistry can establish details of the star formation and merger history of the Milky Way. With precise measurements of stellar chemistry, chemical tagging may be able to group together stars born from the same gas cloud, regardless of their current positions and kinematics. Successfully tagging these birth clusters requires high quality chemical space information and a good cluster-finding algorithm. To test the feasibility of chemical tagging on data from current and upcomi…
We use FIRE-2 simulations to examine 3-D variations of gas-phase elemental abundances of [O/H], [Fe/H], and [N/H] in 11 Milky Way (MW) and M31-mass galaxies across their formation histories at $z \leq 1.5$ ($t_{\rm lookback} \leq 9.4$ Gyr), motivated by characterizing the initial conditions of stars for chemical tagging. Gas within $1$ kpc of the disk midplane is vertically homogeneous to $\lesssim 0.008$ dex at all $z \leq 1.5$. We find negative radial gradients (metallicity decreases with galactocentric radius) at all times, which steepen over time from $\approx -0.01$ dex kpc$^{-1}$ at $z =…
A differentiable hydrodynamical approach to the Milky Way bar pattern speed with CO longitude--velocity data
Amanogawa Galaxy Astronomy Research Center, Graduate School of Science and Engineering, Kagoshima University（鹿儿大学理工学研究科天琴座星系天文学研究中心）；National Astronomical Observatory of Japan（日本国立天文台）；The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学）；The Institute of Statistical Mathematics（统计数学研究所）
A few rare halo giants in the range [Fe/H] $\simeq -2.9\pm0.3$ exhibit {\it r}-process element abundances that vary as a group by factors up to [$r$/Fe] $\sim80$, relative to those of the iron peak and below. Yet, the astrophysical production site of these {\it r}-process elements remains unclear. We report initial results from four years of monitoring the radial velocities of 17 {\it r}-process-enhanced metal-poor giants to detect and characterise binaries in this sample. We find three (possibly four) spectroscopic binaries with orbital periods and eccentricities that are indistinguishable fr…
Detailed chemical abundances are presented for seven M31 outer halo globular clusters (with projected distances from M31 greater than 30 kpc), as derived from high resolution integrated light spectra taken with the Hobby Eberly Telescope. Five of these clusters were recently discovered in the Pan-Andromeda Archaeological Survey (PAndAS)---this paper presents the first determinations of integrated Fe, Na, Mg, Ca, Ti, Ni, Ba, and Eu abundances for these clusters. Four of the target clusters (PA06, PA53, PA54, and PA56) are metal-poor ([Fe/H] < -1.5), alpha-enhanced (though they are possibly less…
Chemically tagging groups of stars born in the same birth cluster is a major goal of spectroscopic surveys. To investigate the feasibility of such strong chemical tagging, we perform a blind chemical tagging experiment on abundances measured from APOGEE survey spectra. We apply a density-based clustering algorithm to the eight dimensional chemical space defined by [Mg/Fe], [Al/Fe], [Si/Fe], [K/Fe], [Ti/Fe], [Mn/Fe], [Fe/H], and [Ni/Fe], abundances ratios which together span multiple nucleosynthetic channels. In a high quality sample of 182,538 giant stars, we detect twenty-one candidate cluste…
How well can we unravel the accreted constituents of the Milky Way stellar halo? A test on cosmological hydrodynamical simulations
Instituto de Astrofísica de Canarias（加那利天体物理研究所）；Universidad de La Laguna（拉各拉纳大学）；Astrophysics Research Institute, Liverpool John Moores University（利物浦约翰摩尔斯大学天体物理研究所）
We show that tagging RR Lyrae stars according to their location in the period-amplitude diagram can be used to shed light on the genesis of the Galactic stellar halo. The mixture of RR Lyrae of ab type, separated into classes along the lines suggested by Oosterhoff, displays a strong and coherent evolution with Galactocentric radius. The change in the RR Lyrae composition appears to coincide with the break in the halo's radial density profile at ~25 kpc. Using simple models of the stellar halo, we establish that at least three different types of accretion events are necessary to explain the ob…
We find that the relative contribution of satellite galaxies accreted at high redshift to the stellar population of the Milky Way's smooth halo increases with distance, becoming observable relative to the classical smooth halo about 15 kpc from the Galactic center. In particular, we determine line-of-sight-averaged [Fe/H] and [alpha/Fe] in the metal-poor main-sequence turnoff (MPMSTO) population along every Sloan Extension for Galactic Understanding and Exploration (SEGUE) spectroscopic line of sight. Restricting our sample to those lines of sight along which we do not detect elements of cold …
Environmental Dependence of Satellite Planarity and Orbital-Pole Coherence around Milky Way Analogues in a Hydrodynamical Cosmological Simulation
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Department of Physics, School of Physics and Electronics, Hunan Normal University（湖南师范大学物理科学与电子学院）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；Institute of Astronomy, School of physics, Zhejiang University（浙江大学物理学院天体物理研究所）；Institute of Astronomy and Physics, Inner Mongolia University（内蒙古大学天文与物理学院）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
We characterize the 3-D spatial variations of [Fe/H], [Mg/H], and [Mg/Fe] in stars at the time of their formation, across 11 simulated Milky Way (MW)- and M31-mass galaxies in the FIRE-2 simulations, to inform initial conditions for chemical tagging. The overall scatter in [Fe/H] within a galaxy decreased with time until $\approx 7$ Gyr ago, after which it increased to today: this arises from a competition between a reduction of azimuthal scatter and a steepening of the radial gradient in abundance over time. The radial gradient is generally negative, and it steepened over time from an initial…
We study the two main constituent galaxies of a constrained simulation of the Local Group as candidates for the Milky Way (MW) and Andromeda (M31). We focus on the formation of the stellar discs and its relation to the formation of the group as a rich system with two massive galaxies, and investigate the effects of mergers and accretion as drivers of morphological transformations. We use a state-of-the-art hydrodynamical code which includes star formation, feedback and chemical enrichment to carry out our study. We run two simulations, where we include or neglect the effects of radiation press…
This review discusses the structure and evolution of the Milky Way, in the context of opportunities provided by asteroseismology of red giants. The review is structured according to the main Galactic components: the thin disk, thick disk, stellar halo, and the Galactic bar/bulge. The review concludes with an overview of Galactic archaeology and chemical tagging, and a brief account of the upcoming HERMES survey with the AAT.
Using kinematics from Gaia and the large elemental abundance space of the second data release of the GALAH survey, we identify two new members of the Fimbulthul stellar stream, and chemically tag them to massive, multi-metallic globular cluster $ω$ Centauri. Recent analysis of the second data release of Gaia had revealed the Fimbulthul stellar stream in the halo of the Milky Way. It had been proposed that the stream is associated with the $ω$ Centauri, but this proposition relied exclusively upon the kinematics and metallicities of the stars to make the association. In this work, we find our t…
Collisionless simulations of the CDM cosmology predict a plethora of dark matter substructures in the halos of Milky Way sized galaxies, yet the number of known luminous satellites galaxies is very much smaller, a discrepancy that has become known as the `missing satellite problem'. The most massive substructures have been shown to be plausibly the hosts of the brightest satellites, but it remains unclear which processes prevent star formation in the many other, purely dark substructures. We use high-resolution hydrodynamic simulations of the formation of Milky Way sized galaxies in order to t…
We use hydrodynamical simulations to construct a new coherent picture for the gas flow in the Central Molecular Zone (CMZ), the region of our Galaxy within $R\leq 500\, \mathrm{pc}$. We relate connected structures observed in $(l,b,v)$ data cubes of molecular tracers to nuclear spiral arms. These arise naturally in hydrodynamical simulations of barred galaxies, and are similar to those that can be seen in external galaxies such as NGC4303 or NGC1097. We discuss a face-on view of the CMZ including the position of several prominent molecular clouds, such as Sgr B2, the $20\,{\rm km\, s^{-1}}$ an…
In the standard paradigm of galaxy formation and evolution, the baryonic component of galaxies forms from the collapse and condensation of gas within dark matter haloes, and later grows from continuous accretion of gaseous mass, both in diffuse form and in mergers with other systems. After a first period of rapid and violent halo growth, the gas settles into a rotationally-supported structure, eventually giving rise to the formation of a stellar disc. Stars evolve and return chemically-processed gas and energy to the interstellar medium, mainly through Type II supernova explosions. In the disc…
We present an analytic model of the stellar mass distribution of the Milky Way bar. The model is obtained by fitting a multi-component parametric density distribution to a made-to-measure N-body model of Portail et al., constructed to match a variety of density and kinematics observational data. The analytic model reproduces in detail the 3D density distribution of the N-body bar including the X-shape. The model and the gravitational potential it generates are available as part of the software package AGAMA for galactic dynamics, and can be readily used for orbit integrations, hydrodynamical s…
Stars born from the same molecular cloud should be nearly homogeneous in their element abundances. The concept of chemical tagging is to identify members of disrupted clusters by their clustering in element abundance space. Chemical tagging requires large samples of stars with precise abundances for many individual elements. With uncertainties of $σ_{[X/{\rm Fe}]}$ and $σ_{\rm [Fe/H]} \simeq 0.05$ for 10 elements measured for $>10^4$ stars, the APOGEE DR12 spectra may be the first well-suited data set to put this idea into practice. We find that even APOGEE data offer only $\sim 500$ independe…
We identify a simulated Milky Way analog in the EAGLE suite of cosmological hydrodynamical simulations. This galaxy not only shares similar global properties as the Milky Way, but was specifically selected because its merger history resembles that currently known for the Milky Way. In particular we find that this Milky Way analog has experienced its last significant merger (with a stellar mass ratio $\sim 0.2$) at $z\sim 1.2$. We show that this merger affected both the dynamical properties of the stars present at the time, contributing to the formation of a thick disk, and also leading to a si…
We use dark matter only and full hydrodynamical Constrained Local UniversE Simulations (CLUES) of the formation of the Local Group to study the density profile of subhaloes of the simulated Milky Way and Andromeda galaxies. We show that the Einasto model provides the best description of the subhaloes' density profile, as opposed to the more commonly used NFW profile or any generalisation of it. We further find that the Einasto shape parameter \nEin\ is strongly correlated with the total subhalo mass, pointing towards the notion of a non-universality of the subhaloes' density profile. We observ…
We introduce project NIHAO (Numerical Investigation of a Hundred Astrophysical Objects), a set of 100 cosmological zoom-in hydrodynamical simulations performed using the gasoline code, with an improved implementation of the SPH algorithm. The haloes in our study range from dwarf to Milky Way masses, and represent an unbiased sampling of merger histories, concentrations and spin parameters. The particle masses and force softenings are chosen to resolve the mass profile to below 1% of the virial radius at all masses, ensuring that galaxy half-light radii are well resolved. Using the same treatme…
We model the gas dynamics of barred galaxies using a three-dimensional, high-resolution, $N$-body+hydrodynamical simulation and apply it to the Milky Way in an attempt to reproduce both the large-scale structure and the clumpy morphology observed in Galactic H\emissiontype{I} and CO $l-v$ diagrams. Owing to including the multi-phase interstellar medium, self-gravity, star-formation and supernovae feedback, the clumpy morphology, as well as the large-scale features, in observed $l-v$ diagrams are naturally reproduced. We identify in our $l-v$ diagrams with a number of not only large-scale pecul…
Observational evidence shows that low-redshift galaxies are surrounded by extended haloes of multiphase gas, the so-called 'circumgalactic medium' (CGM). To study the survival of relatively cool gas (T < 10^5 K) in the CGM, we performed a set of hydrodynamical simulations of cold (T = 10^4 K) neutral gas clouds travelling through a hot (T = 2x10^6 K) and low-density (n = 10^-4 cm^-3) coronal medium, typical of Milky Way-like galaxies at large galactocentric distances (~ 50-150 kpc). We explored the effects of different initial values of relative velocity and radius of the clouds. Our simulatio…
Stellar cluster formation in a Milky Way-sized galaxy at z>4 -- II. A hybrid formation scenario for the nuclear star cluster and its connection to the nuclear stellar ring
We present gas flow models for the Milky Way based on high-resolution grid-based hydrodynamical simulations. The basic galactic potential we use is from a N-body model constrained by the density of red clump giants in the Galactic bulge. We augment this potential with a nuclear bulge, two pairs of spiral arms and additional mass at the bar end to represent the long bar component. With this combined model we can reproduce many features in the observed ($l,v$) diagram with a bar pattern speed of $33\; {\rm km}\;{\rm s}^{-1}\;{\rm kpc}^{-1}$ and a spiral pattern speed of $23\; {\rm km}\;{\rm s}^{…
In the first paper we presented 27 hydrodynamical cosmological simulations of galaxies with total masses between $5 \times 10^8$ and $10^{10}\,\mathrm{M}_\odot$. In this second paper we use a subset of these cosmological simulations as initial conditions (ICs) for more than forty hydrodynamical simulations of satellite and host galaxy interaction. Our cosmological ICs seem to suggest that galaxies on these mass scales have very little rotational support and are velocity dispersion ($σ$) dominated. Accretion and environmental effects increase the scatter in the galaxy scaling relations (e.g. si…
In the standard disk galaxy formation model, the sizes of galactic disks are tightly related to the spin parameters $λ$ of their dark matter haloes. The model has been wildly adopted by various semi-analytic galaxy formation models which have been extremely successful to interpret a large body of observational data. However, the size-$λ$ correlation was rarely seen in most modern hydrodynamical simulations of galaxy formation. In this short paper, we make use of 4 sets of large hydrodynamical simulations to explore the size-spin parameter relation with a large sample of simulated disk galaxies…
We show for the first time, that a fully cosmological hydrodynamical simulation can reproduce key properties of the innermost region of the Milky Way. Our high resolution simulation matches the profile and kinematics of the Milky Way's boxy/peanut-shaped bulge, and hence we can use it to reconstruct and understand the bulge assembly. In particular, the age dependence of the X-shape morphology of the simulated bulge parallels the observed metallicity dependent split in the red clump stars of the inner Galaxy. We use this feature to derive an observational metric that allows us to quantify when …
We study the orbital phase-space of dark matter (DM) halos in the AURIGA suite of cosmological hydrodynamics simulations of Milky Way analogues. We characterise halos by their spherical action distribution, a function of the specific angular momentum, and the radial action, of the DM particles. By comparing DM-only and hydrodynamical simulations of the same halos, we investigate the contraction of DM halos caused by the accumulation of baryons at the centre. We find a small systematic suppression of the radial action in the DM halos of the hydrodynamical simulations, suggesting that the common…
Recovering extra-tidal open cluster members via multi-elemental chemical tagging
Instituto Interdisciplinario de Ciencias Básicas (ICB), CONICET-UNCuyo（基础科学跨研究所 (ICB)，CONICET-门多萨大学）；Consejo Nacional de Investigaciones Científicas y Técnicas（国家科学研究委员会）
We model dust evolution in Milky Way-like galaxies by post-processing the IllustrisTNG cosmological hydrodynamical simulations in order to predict dust-to-gas ratios and grain size distributions. We treat grain-size-dependent dust growth and destruction processes using a 64-bin discrete grain size evolution model without spatially resolving each galaxy. Our model broadly reproduces the observed dust--metallicity scaling relation in nearby galaxies. The grain size distribution is dominated by large grains at $z\gtrsim 3$ and the small-grain abundance rapidly increases by shattering and accretio…
A recent observational study of haloes of nearby Milky Way-like galaxies shows that only half (four out of eight) of the current sample exhibits strong negative metallicity ([Fe/H]) gradients. This is at odds with predictions from hydrodynamical simulations where such gradients are ubiquitous. In this Letter, we use high resolution cosmological hydrodynamical simulations to study the [Fe/H] distribution of galactic haloes. We find that kinematically selected stellar haloes, including both in-situ and accreted particles, have an oblate [Fe/H] distribution. Spherical [Fe/H] radial profiles show …
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 have examined the resolved stellar populations at large galactocentric distances along the minor axis (from 10 kpc up to between 40 and 75 kpc), with limited major axis coverage, of six nearby highly-inclined Milky Way-mass disc galaxies using HST data from the GHOSTS survey. We select red giant branch stars to derive stellar halo density profiles. The projected minor axis density profiles can be approximated by power laws with projected slopes of between $-2$ and $-3.7$ and a diversity of stellar halo masses of $1-6\times 10^{9}M_{\odot}$, or $2-14\%$ of the total galaxy stellar masses. Th…
We present the analysis of a suite of simulations run with different particle-and grid-based cosmological hydrodynamical codes and compare them with observational data of the Milky Way. This is the first study to make comparisons of properties of galaxies simulated with particle and grid-based codes. Our analysis indicates that there is broad agreement between these different modelling techniques. We study the velocity dispersion - age relation for disc stars at z=0 and find that four of the simulations are more consistent with observations by Holmberg et al. (2008) in which the stellar disc a…
We present results from the "Mint" resolution DC Justice League suite of Milky Way-like zoom-in cosmological simulations, which extend our study of nearby galaxies down into the ultra-faint dwarf (UFD) regime for the first time. The mass resolution of these simulations is the highest ever published for cosmological Milky Way zoom-in simulations run to $z=0$, with initial star (dark matter) particle masses of 994 (17900) M$_\odot$, and a force resolution of 87 pc. We study the surrounding dwarfs and UFDs, and find the simulations match the observed dynamical properties of galaxies with $-3 < M_…
We compare galaxy morphology predicted by the Illustris hydrodynamical simulation and a semi-analytic model (SAM) grafted in the halo merger trees from the Illustris-Dark matter simulation. Morphology is classified according to the luminous profile and the kinematic bulge-to-total ratio for Illustris galaxy, and the bulge-to-total stellar mass ratio for SAM galaxy. For late-type galaxies in the Illustris catalogue, most of their counterparts in the SAM model have the same type, and the consistency between two models is higher for lower mass galaxies. For early-type (ET) galaxies in Illustris, …
Stars of a common origin are thought to have similar, if not nearly identical, chemistry. Chemical tagging seeks to exploit this fact to identify Milky Way subpopulations through their unique chemical fingerprints. In this work, we compare the chemical abundances of dwarf stars in wide binaries to test the abundance consistency of stars of a common origin. Our sample of 31 wide binaries is identified from a catalog produced by cross-matching APOGEE stars with UCAC5 astrometry, and we confirm the fidelity of this sample with precision parallaxes from Gaia DR2. For as many as 14 separate element…
Vertically extended, high velocity dispersion stellar distributions appear to be a ubiquitous feature of disc galaxies, and both internal and external mechanisms have been proposed to be the major driver of their formation. However, it is unclear to what extent each mechanism can generate such a distribution, which is likely to depend on the assembly history of the galaxy. To this end, we perform 16 high resolution cosmological-zoom simulations of Milky Way-sized galaxies using the state-of-the-art cosmological magneto-hydrodynamical code \textlcsc{AREPO}, and analyse the evolution of the vert…
We discuss a novel approach to "weighing" the Milky Way dark matter halo, one that combines the latest samples of halo stars selected from the Sloan Digital Sky Survey (SDSS) with state-of-the-art numerical simulations of Milky Way analogs. The fully cosmological runs employed in the present study include "Eris", one of the highest-resolution hydrodynamical simulations of the formation of a M_vir=8e11 M_sun late-type spiral, and the dark-matter only M_vir=1.7e12 M_sun "Via Lactea II" simulation. Eris provides an excellent laboratory for creating mock SDSS samples of tracer halo stars, and we s…
Disc galaxies like the Milky Way are expected to be surrounded by massive coronae of hot plasma that may contain a significant fraction of the so-called missing baryons. We investigate whether the local (|vLSR|<400 km/s) warm-hot absorption features observed towards extra-Galactic sources or halo stars are consistent with being produced by the cooling of the Milky Way's corona. In our scheme, cooling occurs at the interface between the disc and the corona and it is triggered by positive supernova feedback. We combine hydrodynamical simulations with a dynamical 3D model of the galactic fountain…
Ongoing surveys are in the process of measuring the chemical abundances in large numbers of stars, with the ultimate goal of reconstructing the formation history of the Milky Way using abundances as tracers. However, interpretation of these data requires that we understand the relationship between stellar distributions in chemical and physical space, i.e., how similar in chemical abundance do we expect a pair of stars to be as a function of the distance between their formation sites. We investigate this question by simulating the gravitational collapse of a turbulent molecular cloud extracted …
Our 'home galaxy' - the Milky Way - is a fairly large spiral galaxy, prototype of the most common morphological class in the local Universe. Although being only a galaxy, it is the only one that can be studied in unique detail: for the MilkyWay and for a number of members of the Local Group, a wealth of observational data is available about the ages and chemical abundances of their stars. Much more information is expected to come in the next few years, from ongoing and planned spectroscopic and astrometric surveys, providing a unique benchmark for modern theories of galaxy formation. In this r…
We use 30 high-resolution dark matter halos of the $Caterpillar$ simulation suite to probe the first stars and galaxies of Milky Way-mass systems. We quantify the environment of the high-$z$ progenitors of the Milky Way and connect them to the properties of the host and satellites today. We identify the formation sites of the first generation of Population III (Pop III) stars ($z$ ~ 25) and first galaxies ($z$ ~ 22) with several different models based on a minimum halo mass including a simple model for Lyman-Werner feedback. Through this method we find approximately 23,000 $\pm$ 5,000 Pop III …
We introduce the ARTEMIS simulations, a new set of 42 zoomed-in, high-resolution (baryon particle mass of ~ 2x10^4 Msun/h), hydrodynamical simulations of galaxies residing in haloes of Milky Way mass, simulated with the EAGLE galaxy formation code with re-calibrated stellar feedback. In this study, we analyse the structure of stellar haloes, specifically the mass density, surface brightness, metallicity, colour and age radial profiles, finding generally very good agreement with recent observations of local galaxies. The stellar density profiles are well fitted by broken power laws, with inner …
We present a study using the second data release of the GALAH survey of stellar parameters and elemental abundances of 15 pairs of stars identified by Oh et al 2017. They identified these pairs as potentially co-moving pairs using proper motions and parallaxes from Gaia DR1. We find that 11 very wide (>1.7 pc) pairs of stars do in fact have similar Galactic orbits, while a further four claimed co-moving pairs are not truly co-orbiting. Eight of the 11 co-orbiting pairs have reliable stellar parameters and abundances, and we find that three of those are quite similar in their abundance patterns…
