arXiv subjects

Ling Zhu

Publications and source records attributed to Ling Zhu.

At least 55 records · Page 3Linked to original sources

arXiv2024

The internal dynamics and environments of Relics and compact massive ETGs with TNG50

Relic galaxies are massive, compact, quiescent objects observed in the local Universe that have not experienced any significant interaction episodes or merger events since about $z = 2$, remaining relatively unaltered since their formation. On the other hand, massive and compact Early Type Galaxies (cETGs) in the local Universe appear to show similar properties to Relic galaxies, despite having substantial accretion history. Relic galaxies, with frozen history, can provide important clues about the intrinsic processes related to the evolutionary pathways of ETGs and the role that mergers play in their evolution. Using the high-resolution cosmological simulation TNG50-1 from the Illustris Project, we investigate the assembly history of a sample of massive, compact, old, and quiescent subhalos split by satellite accretion fraction. We compare the evolutionary pathways at three cosmic epochs: $z = 2$, $z = 1.5$, and $z = 0$, using the orbital decomposition numerical method to investigate the stellar dynamics of each galactic kinematical component and their environmental correlations. Our results point to a steady pathway across time that is not strongly dependent on the environment. Relics and cETGs do not show a clear preference for high or low-density environments within the volume explored at TNG50. However, progenitors of Relic galaxies are shown to be located in high density since $z = 2$. The merger history can be recovered from the hot inner stellar halo imprints in the local Universe. In the current scenario, the mergers that drive the growth of cETGs do not give rise to a new and distinct evolutionary pathway when compared to Relics. This is despite the reported effects on the age and metallicity of the kinematic components.

astro-ph.GA↗

arXiv2023

The distribution of stellar orbits in Eagle galaxies -- the effect of mergers, gas accretion, and secular evolution

The merger history of a galaxy is thought to be one of the major factors determining its internal dynamics, with galaxies having undergone different types or mergers (e.g. dry, minor or major mergers) predicted to show different dynamical properties. We study the instantaneous orbital distribution of galaxies in the Eagle simulation, colouring the orbits of the stellar particles by their stellar age, in order to understand whether stars form in particular orbits (e.g. in a thin or thick disc). We first show that Eagle reproduces well the observed stellar mass fractions in different stellar orbital families as a function of stellar mass and spin parameter at z = 0. We find that the youngest stars reside in a thin disc component that can extend to the very inner regions of galaxies, and that older stars have warmer orbits, with the oldest ones showing orbits consistent with both hot and counter-rotating classifications, which is consistent with the trend found in the Milky-Way and other disc galaxies. We also show that counter-rotating orbits trace galaxy mergers - in particular dry mergers, and that in the absence of mergers, counter-rotating orbits can also be born from highly misaligned gas accretion that leads to star formation.

astro-ph.GA↗

arXiv2023

Unraveling the Complexity of Dwarf Galaxy Dynamics: A study of Binary Orbital Motions

We investigate the impact of binary orbital motions on the dynamical modeling of dwarf galaxies with intrinsic line-of-sight velocity dispersions ($σ_{v_r}$) of 1 to 9 km/s. Using dwarf galaxies from the Auriga level-2 and level-3 simulations, we apply the Jeans Anisotropic Multi-Gaussian Expansion modelling to tracer stars before and after including binaries to recover the dynamical masses. The recovered total masses within the half-mass radius of tracers, $M(<r_\mathrm{half})$, are always inflated due to binary motions, with greater inflations occurring for smaller $σ_{v_r}$. However, many dwarf galaxies experience central density deflated due to binary motions, with little dependences on $σ_{v_r}$. This is due to the negative radial gradients in the velocity dispersion profiles, with the fractional inflation in $σ_{v_r}$ due to binaries more significant in outskirts. An extreme binary fraction of 70% can lead to central density deflation of up to 10-20% at 3 km/s$<σ_{v_r}<$8 km/s, with $M(<r_\mathrm{half})$ inflated by 4% at 9 km/s and up to 15% at 3 km/s. A lower binary fraction of 36% leads to similar deflations, with the inflations decreasing to approximately 10% at 3 km/s and becoming statistically insignificant. The choice of binary orbit distribution models does not result in significant differences, and observational errors tend to slightly weaken the deflations in the recovered central density. Two observations separated by one year to exclude binaries lead to almost zero inflations/deflations for a binary fraction of 36% over 3 km/s$<σ_{v_r}<$9 km/s. For $σ_{v_r}\sim$1 km/s to 3 km/s, a binary fraction of 70% (36%) still results in 60% (30%) to 10% (1%) of inflations in $M(<r_\mathrm{half})$, even with two-epoch observation.

astro-ph.GA↗

arXiv2023

Experience-Based Evolutionary Algorithms for Expensive Optimization

Optimization algorithms are very different from human optimizers. A human being would gain more experiences through problem-solving, which helps her/him in solving a new unseen problem. Yet an optimization algorithm never gains any experiences by solving more problems. In recent years, efforts have been made towards endowing optimization algorithms with some abilities of experience learning, which is regarded as experience-based optimization. In this paper, we argue that hard optimization problems could be tackled efficiently by making better use of experiences gained in related problems. We demonstrate our ideas in the context of expensive optimization, where we aim to find a near-optimal solution to an expensive optimization problem with as few fitness evaluations as possible. To achieve this, we propose an experience-based surrogate-assisted evolutionary algorithm (SAEA) framework to enhance the optimization efficiency of expensive problems, where experiences are gained across related expensive tasks via a novel meta-learning method. These experiences serve as the task-independent parameters of a deep kernel learning surrogate, then the solutions sampled from the target task are used to adapt task-specific parameters for the surrogate. With the help of experience learning, competitive regression-based surrogates can be initialized using only 1$d$ solutions from the target task ($d$ is the dimension of the decision space). Our experimental results on expensive multi-objective and constrained optimization problems demonstrate that experiences gained from related tasks are beneficial for the saving of evaluation budgets on the target problem.

cs.NE↗

arXiv2023

Integrating features from lymph node stations for metastatic lymph node detection

Metastasis on lymph nodes (LNs), the most common way of spread for primary tumor cells, is a sign of increased mortality. However, metastatic LNs are time-consuming and challenging to detect even for professional radiologists due to their small sizes, high sparsity, and ambiguity in appearance. It is desired to leverage recent development in deep learning to automatically detect metastatic LNs. Besides a two-stage detection network, we here introduce an additional branch to leverage information about LN stations, an important reference for radiologists during metastatic LN diagnosis, as supplementary information for metastatic LN detection. The branch targets to solve a closely related task on the LN station level, i.e., classifying whether an LN station contains metastatic LN or not, so as to learn representations for LN stations. Considering that a metastatic LN station is expected to significantly affect the nearby ones, a GCN-based structure is adopted by the branch to model the relationship among different LN stations. At the classification stage of metastatic LN detection, the above learned LN station features, as well as the features reflecting the distance between the LN candidate and the LN stations, are integrated with the LN features. We validate our method on a dataset containing 114 intravenous contrast-enhanced Computed Tomography (CT) images of oral squamous cell carcinoma (OSCC) patients and show that it outperforms several state-of-the-art methods on the mFROC, maxF1, and AUC scores,respectively.

eess.IV↗

arXiv2022

Orbit-Superposition Dynamical Modeling of Barred Galaxies

Barred structures are important in understanding galaxy evolution, but they were not included explicitly in most dynamical models for nearby galaxies due to their complicated morphological and kinematic properties. We modify the triaxial orbit-superposition Schwarzschild implementation by Van den Bosch et al. (2008) to include barred structures explicitly. The gravitational potential is a combination of a spherical dark matter halo and stellar mass; with the 3D stellar density distribution de-projected from the observed 2D image using a two-component de-projection method, including an axisymmetric disk and a triaxial barred bulge. We consider figure rotation of the galaxy with the bar pattern speed as a free parameter. We validate the method by applying it to a mock galaxy with IFU data created from an N-body simulation with a boxy/peanut or X-shaped bar. Our model fits the observed 2D surface density and all kinematic features well. The bar pattern speed is recovered well with a relative uncertainty smaller than 10%. Based on the internal stellar orbit distribution of the model, we decompose the galaxy into an X-shaped bar, a boxy bulge, a vertically extended structure and a disk, and demonstrate that our model recovers these structures generally well, similar to the true structures in the N-body simulation. Our method provides a realistic way of modelling the bar structure explicitly for nearby barred galaxies with IFU observations.

astro-ph.GA↗

arXiv2022

Is the core-cusp problem a matter of perspective: Jeans Anisotropic Modeling against numerical simulations

Mock member stars for 28 dwarf galaxies are constructed from the cosmological Auriga simulation, which reflect the dynamical status of realistic stellar tracers. The axis-symmetric Jeans Anisotropic Multi-Gaussian Expansion (JAM) modeling is applied to 6,000 star particles for each system, to recover the underlying matter distribution. The stellar or dark matter component individually is poorly recovered, but the total profile is constrained more reasonably. The mass within the half-mass radius of tracers is recovered the tightest, and the mass between 200 and 300 pc, $M(200-300\mathrm{pc})$, is constrained ensemble unbiasedly, with a scatter of 0.167 dex. If using 2,000 particles and only line-of-sight velocities with typical errors, the scatter in $M(200-300\mathrm{pc})$ is increased by $\sim$50%. Quiescent Sagittarius dSph-like systems and star-forming systems with strong outflows show distinct features, with $M(200-300\mathrm{pc})$ mostly under-estimated for the former, and likely over-estimated for the latter. The biases correlate with the dynamical status, which is a result of contraction motions due to tidal effects in quiescent systems or galactic winds in star-forming systems, driving them out of equilibrium. After including Gaia DR3 proper motion errors, we find proper motions can be as useful as line-of-sight velocities for nearby systems at $<\sim$60 kpc. By extrapolating the actual density profiles and the dynamical constraints down to scales below the resolution, we find the mass within 150 pc can be constrained ensemble unbiasedly, with a scatter of $\sim$0.255 dex. In the end, we show that the contraction of member stars in nearby systems is detectable based on Gaia DR3 proper motion errors.

astro-ph.GA↗

arXiv2022

Constructing the Milky Way Stellar Halo in the Galactic Center by Direct Orbit Integration

The halo stars on highly radial orbits should inevitably pass the center regions of the Milky Way. Under the assumption that the stellar halo is in dynamical equilibrium and axisymmetric, we integrate the orbits of $\sim 10,000$ halo K-giants at $5\leq r \leq 50$ kpc cross-matched from LAMOST DR5 and $Gaia$ DR3. By carefully considering the selection function, we construct the stellar halo distribution at the entire regions of $r \leq 50$ kpc. We find that a double-broken power-law function well describes the stellar halo density distribution with shallower slopes in the inner regions and the two breaks at $r=10$ kpc and $r=25$ kpc, respectively. The stellar halo becomes flatter from outer to inner regions but has $q\sim 0.5$ at $r \lesssim 5$ kpc. The stellar halo becomes isotropic with a slight prograde rotation in the inner 5 kpc, and reaches velocity dispersions of $\sim 250\rm \ km\ s^{-1}$. We get a weak negative metallicity gradient of $-0.005$ dex kpc$^{-1}$ at $5\leq r \leq 50$ kpc, while there is an excess of relative metal-rich stars with [Fe/H]$>-1$ in the inner 10 kpc. The halo interlopers at $r \leq 5$ kpc from integration of our sample has a mass of $\sim1.2 \times 10^8\ M_{\odot}$ ($\sim 4.7 \times 10^7\ M_{\odot}$ at [Fe/H]$<-1.5$), which can explain 50-100% of the metal-poor stars with [Fe/H]$<-1.5$ directly observed in the Galactic central regions.

astro-ph.GA↗

arXiv2022

Milky Way Mass with K Giants and BHB Stars Using LAMOST, SDSS/SEGUE, and Gaia: 3D Spherical Jeans Equation and Tracer Mass Estimator

We measure the enclosed Milky Way mass profile to Galactocentric distances of $\sim70$ and $\sim50$ kpc using the smooth, diffuse stellar halo samples of Bird et al. The samples are LAMOST and SDSS/SEGUE K giants (KG) and SDSS/SEGUE blue horizontal branch (BHB) stars with accurate metallicities. The 3D kinematics are available through LAMOST and SDSS/SEGUE distances and radial velocities and {\it Gaia} DR2 proper motions. Two methods are used to estimate the enclosed mass: 3D spherical Jeans equation and Evans et al. tracer mass estimator (TME). We remove substructure via the Xue et al. method based on integrals of motion. We evaluate the uncertainties on our estimates due to random sampling noise, systematic distance errors, the adopted density profile, and non-virialization and non-spherical effects of the halo. The tracer density profile remains a limiting systematic in our mass estimates, although within these limits we find reasonable agreement across the different samples and the methods applied. Out to $\sim70$ and $\sim50$ kpc, the Jeans method yields total enclosed masses of $4.3\pm0.95$ (random) $\pm0.6$ (systematic) $\times10^{11}$ M$_\odot$ and $4.1\pm1.2$ (random) $\pm0.6$ (systematic) $\times10^{11}$ M$_\odot$ for the KG and BHB stars, respectively. For the KG and BHB samples we find a dark matter virial mass of $M_{200}=0.55^{+0.15}_{-0.11}$ (random) $\pm0.083$ (systematic) $\times10^{12}$ M$_\odot$ and $M_{200}=1.00^{+0.67}_{-0.33}$ (random) $\pm0.15$ (systematic) $\times10^{12}$ M$_\odot$, respectively.

astro-ph.GA↗

arXiv2022

On the robustness of triaxial Schwarzschild modelling: The effects of correcting the orbit mirroring

In the past 15 years, the triaxial Schwarzschild orbit-superposition code by van den Bosch et al. (2008) has been widely applied to study the dynamics of galaxies. Recently, Quenneville et al. (2022) reported a bug in the orbit calculation of this code, specifically in the mirroring procedure that is used to speed up the computation. We have fixed the incorrect mirroring in DYNAMITE, which is the publicly-released successor of the triaxial Schwarzschild code by van den Bosch et al. (2008). In this study, we provide a thorough quantification of how this bug has affected the results of dynamical analyses performed with this code. We compare results obtained with the original and corrected versions of DYNAMITE, and discuss the differences in the phase-space distribution of a single orbit and in the global stellar orbit distribution, in the mass estimate of the central black hole in the highly triaxial galaxy PGC 46832, and in the measurement of intrinsic shape and enclosed mass for more than 50 galaxies. Focusing on the typical scientific applications of a Schwarzschild triaxial code, in all our tests we find that differences are negligible with respect to the statistical and systematic uncertainties. We conclude that previous results with the van den Bosch et al. (2008) triaxial Schwarzschild code are not significantly affected by the incorrect mirroring.

astro-ph.GA↗

arXiv2022

The Fornax3D project: discovery of ancient massive merger events in the Fornax cluster galaxies NGC 1380 and NGC 1427

We report the discovery of ancient massive merger events in the early-type galaxies NGC 1380 and NGC 1427, members of the Fornax galaxy cluster. Both galaxies have been observed by the MUSE IFU instrument on the VLT, as part of the Fornax3D project. By fitting recently-developed population-orbital superposition models to the observed surface brightness as well as stellar kinematic, age, and metallicity maps, we obtain the stellar orbits, age and metallicity distributions of each galaxy. We then decompose each galaxy into multiple orbital-based components, including a dynamically hot inner stellar halo component which is identified as the relic of past massive mergers. By comparing to analogues from cosmological galaxy simulations, chiefly TNG50, we find that the formation of such a hot inner stellar halo requires the merger with a now-destroyed massive satellite galaxy of $3.7_{-1.5}^{+2.7} \times 10^{10}$ Msun (about $1/5$ of its current stellar mass) in the case of NGC 1380 and of $1.5_{-0.7}^{+1.6} \times10^{10}$ Msun (about $1/4$ of its current stellar mass) in the case of NGC 1427. Moreover, we infer that the last massive merger in NGC 1380 happened $\sim10$ Gyr ago based on the stellar age distribution of the re-grown dynamically cold disk, whereas the merger in NGC 1427 ended $t\lesssim 8$ Gyr ago based on the stellar populations in its hot inner stellar halo. The major merger event in NGC 1380 is the first one with both merger mass and merger time quantitatively inferred in a galaxy beyond the Local Volume. Moreover, it is the oldest and most massive merger uncovered in nearby galaxies so far.

astro-ph.GA↗

arXiv2022

The SAMI Galaxy Survey: The internal orbital structure and mass distribution of passive galaxies from triaxial orbit-superposition Schwarzschild models

Dynamical models are crucial for uncovering the internal dynamics of galaxies, however, most of the results to date assume axisymmetry, which is not representative for a significant fraction of massive galaxies. Here, we build triaxial Schwarschild orbit-superposition models of galaxies taken from the SAMI Galaxy Survey, in order to reconstruct their inner orbital structure and mass distribution. The sample consists of 161 passive galaxies with total stellar masses in the range $10^{9.5}$ to $10^{12} M_{\odot}$. We find that the changes in internal structures within 1$R_{\rm e}$ are correlated with the total stellar mass of the individual galaxies. The majority of the galaxies in the sample ($73\% \pm 3\%$) are oblate, while $19\% \pm 3\%$ are mildly triaxial and $8\% \pm 2\%$ have triaxial/prolate shape. Galaxies with $\log M_{\star}/M_{\odot} > 10.50$ are more likely to be non-oblate. We find a mean dark matter fraction of $f_{\rm{DM}} = 0.28 \pm 0.20$, within 1$R_{\rm e}$. Galaxies with higher intrinsic ellipticity (flatter) are found to have more negative velocity anisotropy $β_r$ (tangential anisotropy). $β_r$ also shows an anti-correlation with the edge-on spin parameter \lam, so that $β_r$ decreases with increasing \lam. We see evidence of an increasing fraction of hot orbits with increasing stellar mass, while warm and cold orbits show a decreasing trend. We also find that galaxies with different ($V/σ$ - $h_3$) kinematic signatures have distinct combinations of orbits. These results are in agreement with a formation scenario in which slow- and fast-rotating galaxies form through two main channels.

astro-ph.GA↗

arXiv2022

Different Formation Scenarios of Counter-rotating Stellar Disks in Nearby Galaxies

Using the integral field unit (IFU) data from Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, we select a sample of 101 galaxies with counter-rotating stellar disks and regularly-rotating ionized gas disk. We classify the 101 galaxies into four types based on the features of their stellar velocity fields. The relative fractions and stellar population age radial gradients of the four types are different in blue cloud (BC), green valley (GV) and red sequence (RS) populations. We suggest different formation scenarios for the counter-rotating stellar disks, and the key factors in the formation of counter-rotating stellar disks include: (1) the abundance of pre-existing gas in progenitor, (2) the efficiency in angular momentum consumption.

astro-ph.GA↗

arXiv2022

Mass of the dynamically hot inner stellar halo predicts the ancient accreted stellar mass

Galactic dynamical structures are fossil records of the assembly histories of galaxies. By analyzing the cosmological hydrodynamical simulation TNG50, we find that a dynamical structure that we call the "hot inner stellar halo," defined by stars on dynamically hot orbits with circularity $λ_z < 0.5$ at $3.5\,{\rm kpc}<r \lesssim 2\,R_e$, is a strong indicator of the mass of accreted satellite galaxies. We find a strong correlation between the mass of this hot inner stellar halo and the total ex situ stellar mass. There is a similarly strong correlation with the stellar mass of the most massive secondary galaxy ever merged. These TNG50 correlations are compatible with those predicted by other simulations, for example by TNG100 across the whole mass range under study (galaxy stellar masses, $M_*$, in the $10^{10.3-11.6}$\,\Msun\, range) and by EAGLE for $M_* \gtrsim 10^{10.6} $\,\Msun\, galaxies.\ This shows that our predictions are robust across different galaxy formation and feedback models and hold across a wide range of numerical resolution. The hot inner stellar halo is a product of massive and typically ancient mergers, with inner-halo stars exhibiting three main physical origins: accreted and stripped from massive satellites, dynamically heated by mergers from the bulge and/or disk in the main progenitor, and formed from star formation triggered during mergers. The mass of the hot inner stellar halo defined in this paper is a quantity that can be robustly obtained for real galaxies by applying a population-orbit superposition method to integral-field-unit spectroscopy data, out to a distance of $\sim2\,R_e$, which is possible with current observations. Hence, this paper shows that integral-field-unit observations and dynamical models of the inner regions of galaxies provide a way to quantitatively determine the mass of ancient accreted satellites.

astro-ph.GA↗

arXiv2021

Deprojection of external barred galaxies from photometry

The observations of external galaxies are projected to the 2D sky plane. Reconstructing the 3D intrinsic density distribution of a galaxy from the 2D image is challenging, especially for barred galaxies, but is a critical step for constructing galactic dynamical models. Here we present a method for deprojecting barred galaxies and we validate the method by testing against mock images created from an N-body simulation with a peanut-shaped bar. We decompose a galaxy image into a bulge (including a bar) and a disk. By subtracting the disk from the original image a barred bulge remains. We perform multi-Gaussian expansion (MGE) fit to each component, then we deproject them separately by considering the barred bulge is triaxial while the disk is axisymmetric. We restrict the barred bulge to be aligned in the disk plane and has a similar thickness to the disk in the outer regions. The 3D density distribution is thus constructed by combining the barred bulge and the disk. Our model can generally recover the 3D density distribution of disk and inner barred bulge regions, although not a perfect match to the peanut-shaped structure. By using the same initial conditions, we integrate the orbits in our model-inferred potential and the true potential by freezing the N-body simulation. We find that 85% of all these orbits have similar morphologies in these two potentials, and our model supports the orbits that generate a boxy/peanut-shaped structure and an elongated bar similar to these in the true potential.

astro-ph.GA↗

arXiv2021

Towards Interpretable-AI Policies Induction using Evolutionary Nonlinear Decision Trees for Discrete Action Systems

Black-box AI induction methods such as deep reinforcement learning (DRL) are increasingly being used to find optimal policies for a given control task. Although policies represented using a black-box AI are capable of efficiently executing the underlying control task and achieving optimal closed-loop performance, the developed control rules are often complex and neither interpretable nor explainable. In this paper, we use a recently proposed nonlinear decision-tree (NLDT) approach to find a hierarchical set of control rules in an attempt to maximize the open-loop performance for approximating and explaining the pre-trained black-box DRL (oracle) agent using the labelled state-action dataset. Recent advances in nonlinear optimization approaches using evolutionary computation facilitates finding a hierarchical set of nonlinear control rules as a function of state variables using a computationally fast bilevel optimization procedure at each node of the proposed NLDT. Additionally, we propose a re-optimization procedure for enhancing closed-loop performance of an already derived NLDT. We evaluate our proposed methodologies (open and closed-loop NLDTs) on different control problems having multiple discrete actions. In all these problems our proposed approach is able to find relatively simple and interpretable rules involving one to four non-linear terms per rule, while simultaneously achieving on par closed-loop performance when compared to a trained black-box DRL agent. A post-processing approach for simplifying the NLDT is also suggested. The obtained results are inspiring as they suggest the replacement of complicated black-box DRL policies involving thousands of parameters (making them non-interpretable) with relatively simple interpretable policies. Results are encouraging and motivating to pursue further applications of proposed approach in solving more complex control tasks.

cs.LG↗

arXiv2021

Hot and counter-rotating star-forming disk galaxies in IllustrisTNG and their real-world counterparts

A key feature of a large population of low-mass, late-type disk galaxies are star-forming disks with exponential light distributions. They are typically also associated with thin and flat morphologies, blue colors, and dynamically cold stars moving along circular orbits within co-planar thin gas disks. However, the latter features do not necessarily always imply the former, in fact, a variety of different kinematic configurations do exist. In this work, we use the cosmological hydrodynamical IllustrisTNG Simulation to study the nature and origin of dynamically hot, sometimes even counter-rotating, star-forming disk galaxies in the lower stellar mass range (between $5\times 10^9\,\mathrm{M_{\odot}}$ and $2\times 10^{10}\,\mathrm{M_{\odot}}$). We find that being dynamically hot arises in most cases as an induced transient state, for example due to galaxy interactions and merger activities, rather than as an age-dependent evolutionary phase of star-forming disk galaxies. The dynamically hot but still actively star-forming disks show a common feature of hosting kinematically misaligned gas and stellar disks, and centrally concentrated on-going star formation. The former is often accompanied by disturbed gas morphologies, while the latter is reflected in low gas and stellar spins in comparison to their dynamically cold, normal disk counterparts. Interestingly, observed galaxies from MaNGA with kinematic misalignment between gas and stars show remarkably similar general properties as the IllustrisTNG galaxies, and therefore are plausible real-world counterparts. In turn, this allows us to make predictions for the stellar orbits and gas properties of these misaligned galaxies.

astro-ph.GA↗

arXiv2021

Unravelling stellar populations in the Andromeda Galaxy

To understand the history and formation mechanisms of galaxies it is crucial to determine their current multidimensional structure. Here we focus on stellar population properties, such as metallicity and [$α$/Fe] enhancement. We devise a new technique to recover the distribution of these parameters using spatially resolved, line-of-sight averaged data. Our chemodynamical method is based on the made-to-measure (M2M) framework and results in an $N$-body model for the abundance distribution. We test our method on a mock data set and find that the radial and azimuthal profiles are well-recovered, however only the overall shape of the vertical profile matches the true profile. We apply our procedure to spatially resolved maps of mean [Z/H] and [$α$/Fe] for the Andromeda Galaxy, using an earlier barred dynamical model of M31. We find that the metallicity is enhanced along the bar, with possible maxima at the ansae. In the edge-on view the [Z/H] distribution has an X shape due to the boxy/peanut bulge; the average vertical metallicity gradient is equal to $-0.133\pm0.006$ dex/kpc. We identify a metallicity-enhanced ring around the bar, which also has relatively lower [$α$/Fe]. The highest [$α$/Fe] is found in the centre, due to the classical bulge. Away from the centre, the $α$-overabundance in the bar region increases with height, which could be an indication of a thick disc. We argue that the galaxy assembly resulted in a sharp peak of metallicity in the central few hundred parsecs and a more gentle negative gradient in the remaining disc, but no [$α$/Fe] gradient. The formation of the bar lead to the re-arrangement of the [Z/H] distribution, causing a flat gradient along the bar. Subsequent star formation close to the bar ends may have produced the metallicity enhancements at the ansae and the [Z/H] enhanced lower-$α$ ring.

astro-ph.GA↗