Halo Assembly Histories Research Articles

From Halos to Galaxies. IX. Estimate of Halo Assembly History for SDSS Galaxy Groups

The properties of the galaxies are tightly connected to their host halo mass and halo assembly history. Accurate measurement of the halo assembly history in observation is challenging but crucial to the understanding of galaxy formation and evolution. The stellar-to-halo mass ratio (M */M h) for the centrals has often been used to indicate the halo assembly time t h,50 of the group, where t h,50 is the lookback time at which a halo has assembled half of its present-day virial mass. Using mock data from the semi-analytic models, we find that M */M h shows a significant scatter with t h,50, with a strong systematic difference between the group with a star-forming central (blue group) and passive central (red group). To improve the accuracy, we develop machine learning models to estimate t h,50 for galaxy groups using only observable quantities in the mocks. Since star formation quenching will decouple the co-growth of the dark matter and baryon, we train our models separately for blue and red groups. Our models have successfully recovered t h,50, within an accuracy of ∼1.09 Gyr. With careful calibrations of individual observable quantities in the mocks with Sloan Digital Sky Survey (SDSS) observations, we apply the trained models to the SDSS Yang et al. groups and derive the t h,50 for each group for the first time. The derived SDSS t h,50 distributions are in good agreement with that in the mocks, in particular for blue groups. The derived halo assembly history, together with the halo mass, make an important step forward in studying the halo–galaxy connections in observation.

FLORAH: a generative model for halo assembly histories

ABSTRACT The mass assembly history (MAH) of dark matter haloes plays a crucial role in shaping the formation and evolution of galaxies. MAHs are used extensively in semi-analytic and empirical models of galaxy formation, yet current analytic methods to generate them are inaccurate and unable to capture their relationship with the halo internal structure and large-scale environment. This paper introduces florah (FLOw-based Recurrent model for Assembly Histories), a machine-learning framework for generating assembly histories of ensembles of dark matter haloes. We train florah on the assembly histories from the Gadget at Ultra-high Redshift with Extra Fine Time-steps and vsmdplN-body simulations and demonstrate its ability to recover key properties such as the time evolution of mass and concentration. We obtain similar results for the galaxy stellar mass versus halo mass relation and its residuals when we run the Santa Cruz semi-analytic model on florah-generated assembly histories and halo formation histories extracted from an N-body simulation. We further show that florah also reproduces the dependence of clustering on properties other than mass (assembly bias), which is not captured by other analytic methods. By combining multiple networks trained on a suite of simulations with different redshift ranges and mass resolutions, we are able to construct accurate main progenitor branches with a wide dynamic mass range from $z=0$ up to an ultra-high redshift $z \approx 20$, currently far beyond that of a single N-body simulation. florah is the first step towards a machine learning-based framework for planting full merger trees; this will enable the exploration of different galaxy formation scenarios with great computational efficiency at unprecedented accuracy.

Star-forming and Quiescent Central Galaxies Cluster Similarly: Implications for the Galaxy–Halo Connection

Abstract We measure the clustering of low-redshift SDSS galaxies as a function of stellar mass (10.0 < log (M*/M⊙) < 11.5) and specific star formation rate (sSFR) and compare the results to models of the galaxy–halo connection. We find that the auto-correlation functions of central galaxies exhibit little dependence on sSFR, with the well-known stronger clustering of quiescent galaxies mainly attributable to satellites. Because halo assembly history is known to affect distinct halo clustering, this result implies that there is little net correlation between halo assembly history and central galaxy sSFR. However, cross-correlations with satellites are stronger for quiescent centrals than star-forming centrals, consistent with quiescent centrals having more satellites in their haloes at fixed M*, as found in SDSS group catalogues. We model the galaxy–halo connection in an N-body simulation by assigning sSFRs to central galaxies in three different ways. Two of the models depend on halo assembly history (being based on halo accretion rate or concentration), while the third is independent of halo assembly history (being based on peak halo circular velocity, Vpeak, a proxy for halo mass). All three models replicate the observed auto-correlations of central galaxies, while only the Vpeak model reproduces the observed cross-correlations with satellites. This further suggests that the effects of halo assembly history may not be easily seen in auto-correlations of centrals and implies that a more complete understanding of central galaxy clustering may require more than auto-correlations of centrals alone. Additionally, the good agreement with the Vpeak model supports the idea that quiescent galaxies reside in more massive haloes than star-forming galaxies at fixed M*.

Assembly history and internal structure of cluster cold dark matter haloes

ABSTRACT We use the Phoenix simulations to study the mass assembly history and internal structures of cluster dark matter haloes ($M_{200} \gtrsim 5\times 10^{14} h^{-1}{\rm M}_\odot$). We confirm that cluster haloes grow inside-out, similar to galactic haloes. Major merger events dominate the growth of the internal region and minor mergers/diffuse accretion shape the outskirts. However, compared to galactic haloes, cluster haloes tend to have a younger and more actively evolving inner region. On average, the majority of mass ($\gtrsim 80$ per cent) in the inner region ($R\lt 0.1 r_{200}$) of Phoenix haloes is accreted after $z = 3$, while for galactic haloes, most mass in the central region has already been accreted before $z=6$. The density profiles of cluster haloes are less stable than those of galactic haloes over different radii. The enclosed mass within 50 or 150 kpc of all Phoenix haloes evolves substantially in the past ${\sim } 7$ Gyr, while galactic haloes remained stable during the same period. We suggest that the relatively younger and more active state explains the various observations of cluster haloes, especially in central regions.

A two-phase model of galaxy formation – II. The size–mass relation of dynamically hot galaxies

ABSTRACT In Paper-I, we developed a two-phase model to connect dynamically hot galaxies (such as ellipticals and bulges) with the formation of self-gravitating gas clouds (SGCs) associated with the fast assembly of dark matter haloes. Here, we explore the implications of the model for the size–stellar mass relation of dynamically hot galaxies. Star-forming sub-clouds resulting from the fragmentation of the turbulent SGC inherit its spatial structure and dynamical hotness, producing a ‘homologous’ relation, $r_{\rm f}\approx \, 100\, r_{\rm bulge}$, between the size of a dynamically hot galaxy ($r_{\rm bulge}$) and that of its host halo assembled in the fast regime ($r_{\rm f}$), independent of redshift and halo mass. This relation is preserved by the ‘dry’ expansion driven by dynamical heating when a galaxy becomes gas-poor due to inefficient cooling, and is frozen due to the stop of bulge growth during the slow assembly regime of the halo. The size–stellar mass relation is thus a simple combination of the galaxy–halo homology and the non-linear stellar mass–halo mass relation. Using a set of halo assembly histories, we reproduce all properties in the observed size–mass relation of dynamically hot galaxies, including the flattening in the low-mass end and the upturn in the massive end. The prediction matches observational data currently available to $z \approx 4$, and can be tested in the future at higher z. Our results indicate that the sizes of dynamically hot galaxies are produced by the dissipation and collapse of gas in haloes to establish SGCs in which stars form.

A two-phase model of galaxy formation: I. The growth of galaxies and supermassive black holes

ABSTRACT We develop a model for galaxy formation and the growth of supermassive black holes (SMBHs), based on the fact that cold dark matter haloes form their gravitational potential wells through a fast phase with rapid change in the potential, and that the high universal baryon fraction makes cooled gas in haloes self-gravitating and turbulent before it can form rotation-supported discs. Gas fragmentation produces subclouds so dense that cloud–cloud collision and drag on clouds are not significant, producing a dynamically hot system of subclouds that form stars and move ballistically to feed the central SMBH. Active galactic nucleus (AGN) and supernova feedback is effective only in the fast phase, and the cumulative effects are to regulate star formation and SMBH growth, as well as to reduce the amount of cold gas in haloes to allow the formation of globally stable discs. Using a set of halo assembly histories, we demonstrate that the model can reproduce a number of observations, including correlations among SMBH mass, stellar mass of galaxies and halo mass, the number densities of galaxies and SMBH, as well as their evolution over the cosmic time.

The AGORA High-resolution Galaxy Simulations Comparison Project. IV. Halo and Galaxy Mass Assembly in a Cosmological Zoom-in Simulation at z ≤ 2

In this fourth paper from the AGORA Collaboration, we study the evolution down to redshift z = 2 and below of a set of cosmological zoom-in simulations of a Milky Way mass galaxy by eight of the leading hydrodynamic simulation codes. We also compare this CosmoRun suite of simulations with dark matter-only simulations by the same eight codes. We analyze general properties of the halo and galaxy at z = 4 and 3, and before the last major merger, focusing on the formation of well-defined rotationally supported disks, the mass–metallicity relation, the specific star formation rate, the gas metallicity gradients, and the nonaxisymmetric structures in the stellar disks. Codes generally converge well to the stellar-to-halo mass ratios predicted by semianalytic models at z ∼ 2. We see that almost all the hydro codes develop rotationally supported structures at low redshifts. Most agree within 0.5 dex with the observed mass–metallicity relation at high and intermediate redshifts, and reproduce the gas metallicity gradients obtained from analytical models and low-redshift observations. We confirm that the intercode differences in the halo assembly history reported in the first paper of the collaboration also exist in CosmoRun, making the code-to-code comparison more difficult. We show that such differences are mainly due to variations in code-dependent parameters that control the time stepping strategy of the gravity solver. We find that variations in the early stellar feedback can also result in differences in the timing of the low-redshift mergers. All the simulation data down to z = 2 and the auxiliary data will be made publicly available.

The separate effect of halo mass and stellar mass on the evolution of massive disc galaxies

ABSTRACT We analyse a sample of massive disc galaxies selected from the fourth-generation Sloan Digital Sky Survey/Mapping Nearby Galaxies at Apache Point Observatory survey to investigate how the evolution of these galaxies depends on their stellar and halo masses. We applied a semi-analytic spectral fitting approach to the data from different regions in the galaxies to derive several of their key physical properties. From the best-fitting model results, together with direct observables such as morphology, colour, and the Mgb/〈Fe〉 index ratio measured within 1Re, we find that for central galaxies both their stellar and halo masses have a significant influence in their evolution. For a given halo mass, galaxies with higher stellar mass accumulate their stellar mass and become chemically enriched earlier than those with smaller stellar mass. Furthermore, at a given stellar mass, galaxies living in more massive haloes have longer star formation time-scales and are delayed in becoming chemically enriched. In contrast, the evolution of massive satellite galaxies is mostly determined by their stellar mass. The results indicate that both the assembled halo mass and the halo assembly history impact the evolution of central galaxies. Our spatially resolved analysis indicates that only the galaxy properties in the central region (0.0–0.5Re) show the dependencies described above. This fact supports a halo-driven formation scenario since the galaxies’ central regions are more likely to contain old stars formed along with the halo itself, keeping a memory of the halo formation process.

Characterizing ultra-high-redshift dark matter halo demographics and assembly histories with the gureft simulations

ABSTRACT Dark matter halo demographics and assembly histories are a manifestation of cosmological structure formation and have profound implications for the formation and evolution of galaxies. In particular, merger trees provide fundamental input for several modelling techniques, such as semi-analytic models (SAMs), sub-halo abundance matching (SHAM), and decorated halo occupation distribution models. Motivated by the new ultra-high-redshift (z ≳ 10) frontier enabled by JWST, we present a new suite of Gadget at Ultrahigh Redshift with Extra-Fine Timesteps (gureft) dark matter-only cosmological simulations that are carefully designed to capture halo merger histories and structural properties in the ultra-z universe. The simulation suite consists of four 10243-particle simulations with box sizes of 5, 15, 35, and 90 Mpc h−1, each with 170 snapshots stored between 40 ≥ z ≥ 6. With the unprecedented number of available snapshots and strategically chosen dynamic range covered by these boxes, gureft uncovers the emerging dark matter halo populations and their assembly histories in the earliest epochs of cosmic history. In this work, we present the halo mass functions (HMF) between z ∼ 20 and 6 down to log (Mvir/M⊙) ∼ 5, and show that at high redshift, these robust HMFs can differ substantially from commonly used analytic approximations or older fitting functions in the literature. We also present key physical properties of the ultra-high z halo population, such as concentration and spin, as well as their mass growth and merger rates, and again provide updated fitting functions.

Accurate halo mass functions from the simplest excursion set theory

ABSTRACT Excursion set theory is a powerful and widely used tool for describing the distribution of dark matter haloes, but it is normally applied with simplifying approximations. We use numerical sampling methods to study the mass functions predicted by the theory without approximations. With a spherical top-hat window and a constant δ = 1.5 threshold, the theory accurately predicts mass functions with the M200 mass definition, both unconditional and conditional, in simulations of a range of matter-dominated cosmologies. For Λ cold dark matter at the present epoch, predictions lie between the M200m and M200c mass functions. In contrast, with the same window function, a non-constant threshold based on ellipsoidal collapse predicts uniformly too few haloes. This work indicates a new way to simply and accurately evaluate halo mass functions, clustering bias, and assembly histories for a range of cosmologies. We provide a fitting function that accurately represents the predictions of the theory for a wide range of parameters.

On bursty star formation during cosmological reionisation – how does it influence the baryon mass content of dark matter halos?

Abstract The baryon mass content (i.e. stellar and gas mass) of dark matter halos in the early Universe depends on both global factors – for example, ionising ultraviolet (UV) radiation background – and local factors – for example, star formation efficiency and assembly history. We use a lightweight semi-analytical model to investigate how both local and global factors impact the halo baryon mass content at redshifts of $z\geq 5$ . Our model incorporates a time delay between when stars form and when they produce feedback of $0\leq t^d/\mathrm{Myr} \leq 30$ , which can drive bursts of star formation, and a mass and redshift-dependent UV background, which captures the influence of cosmological reionisation on gas accretion onto halos. We use statistically representative halo assembly histories and assume that the cosmological gas accretion rate is proportional to the halo mass accretion rate. Delayed ( $t^d$ >0) feedback leads to oscillations in gas mass with cosmic time, behaviour that cannot be captured with instantaneous feedback ( $t^d$ =0). Highly efficient star formation drives stronger oscillations, while strong feedback impacts when oscillations occur; in contrast, inefficient star formation and weak feedback produce similar long-term behaviour to that observed in instantaneous feedback models. If the delayed feedback timescale is too long, a halo retains its gas reservoir but the feedback suppresses star formation. Our model predicts that lower mass systems (halo masses $m_\mathrm{h} \leq 10^7 \mathrm{M}_\odot$ ) at $z \leq 10$ should be strongly gas deficient ( $m_\mathrm{g}\rightarrow 0$ ), whereas higher mass systems retain their gas reservoirs because they are sufficiently massive to continue accreting gas through cosmological reionisation. Interestingly, in higher mass halos, the median $m_\star/(m_\star+m_\mathrm{g}) \simeq 0.01-0.05$ , but is a factor of 3–5 smaller when feedback is delayed. Our model does not include seed supermassive black hole feedback, which is necessary to explain massive quenched galaxies in the early Universe.

From Halos to Galaxies. VII. The Connections between Stellar Mass Growth History, Quenching History, and Halo Assembly History for Central Galaxies

The assembly of galaxies over cosmic time is tightly connected to the assembly of their host dark matter halos. We investigate the stellar mass growth history and the chemical enrichment history of central galaxies in the Sloan Digital Sky Survey Mapping Nearby Galaxies at Apache Point Observatory. We find that the derived stellar metallicity of passive central galaxies is always higher than that of the star-forming ones. This stellar metallicity enhancement becomes progressively larger toward low-mass galaxies (at a given epoch) and earlier epochs (at a given stellar mass), which suggests strangulation as the primary mechanism for star formation quenching in central galaxies not only in the local Universe but also very likely at higher redshifts up to z ∼ 3. We show that at the same present-day stellar mass, passive central galaxies assembled half of their final stellar mass ∼2 Gyr earlier than star-forming central galaxies, which agrees well with the semi-analytic model. Exploring the semi-analytic model, we find that this is because passive central galaxies reside in, on average, more massive halos with a higher halo mass increase rate across cosmic time. As a consequence, passive central galaxies are assembled faster and also quenched earlier than their star-forming counterparts. While at the same present-day halo mass, different halo assembly history also produces a very different final stellar mass of the central galaxy within, and halos assembled earlier host more massive centrals with a higher quenched fraction, in particular around the “golden halo mass” at 1012 M ⊙. Our results call attention back to the dark matter halo as a key driver of galaxy evolution.

A differentiable model of the evolution of dark matter halo concentration

ABSTRACT We introduce a new model of the evolution of the concentration of dark matter haloes, c(t). For individual haloes, our model approximates c(t) as a power law with a time-dependent index, such that at early times, concentration has a nearly constant value of c ≈ 3–4, and as cosmic time progresses, c(t) smoothly increases. Using large samples of halo merger trees taken from the Bolshoi–Planck and MultiDark Planck 2 cosmological simulations, we demonstrate that our three-parameter model can approximate the evolution of the concentration of individual haloes with a typical accuracy of 0.1 dex for $t\gtrsim 2\, {\rm Gyr}$ for all Bolshoi–Planck and MultiDark Planck 2 haloes of present-day peak mass $M_{0}\gtrsim 10^{11.5}\, {\rm M}_{\odot }$. We additionally present a new model of the evolution of the concentration of halo populations, which we show faithfully reproduces both average concentration growth and the diversity of smooth trajectories of c(t), including capturing correlations with halo mass and halo assembly history. Our publicly available source code, diffprof, can be used to generate Monte Carlo realizations of the concentration histories of cosmologically representative halo populations. diffprof is differentiable due to its implementation in the jax autodiff library, which facilitates the incorporation of our model into existing analytical halo model frameworks.

Constraining interacting dark energy models with the halo concentration–mass relation

ABSTRACT The interacting dark energy (IDE) model is a promising alternative cosmological model that has the potential to solve the fine-tuning and coincidence problems by considering the interaction between dark matter and dark energy. Previous studies have shown that the energy exchange between the dark sector components in this model can significantly affect the dark matter halo properties. In this study, by utilizing a large set of cosmological N-body simulations, we analyse the redshift evolution of the halo concentration–mass (c–M) relation in the IDE model, and show that the c–M relation is a sensitive proxy of the interaction strength parameter ξ2, especially at lower redshifts. Furthermore, we construct parametrized formulae to quantify the dependence of the c–M relation on ξ2 at redshifts ranging from z = 0 to z = 0.6. Our parametrized formulae provide a useful theoretical tool in constraining ξ2 with the observational c–M relation. As a first attempt, we use the data from X-ray, gravitational lensing, and galaxy rotational curve observations and obtain a tight constraint on ξ2, i.e. ξ2 = 0.071 ± 0.034. Our work demonstrates that the halo c–M relation, which reflects the halo assembly history, is a powerful probe to constrain the IDE model.

On the edge: the relation between stellar and dark matter haloes of Milky Way-mass galaxies

ABSTRACTWe investigate the build-up of the accreted stellar and dark matter haloes of Milky Way-like galaxies in APOSTLE suite of cosmological hydrodynamics simulations. We show that the stellar halo is made up primarily of stars stripped from a small number of massive dwarfs, most of which are disrupted by the present day. The dark matter halo, on the other hand, is made up primarily of small unresolved subhaloes (≲106 M⊙) and a ‘smooth’ component consisting of particles which were never bound to a subhalo. Despite these differences, the massive dwarfs that make up the majority of the stellar halo also contribute a significant fraction of the dark matter. The stars and dark matter stripped from these dwarfs are related through their kinematics and this leaves imprints in the phase-space structure of the haloes. We examine the relation between the location of features, such as caustics, in the phase space of the stars and dark halo properties. We show that the ‘edge’ of the stellar halo is a probe of dark matter halo mass and assembly history. The edges of Milky Way-mass galaxies should be visible at a surface brightness of 31–36 mag arcsec−2.

On the choice of the most suitable indicator for the assembly state of dark matter haloes through cosmic time

ABSTRACT The dynamical state and morphological features of galaxies and galaxy clusters, and their high-redshift precursors, are tightly connected with their assembly history, encoding crucial information about the formation and evolution of such cosmic structures. As a first step towards finding an optimal indicator of the assembly state of observed structures, we use a cosmological simulation of a moderate volume to critically examine the best definition of an indicator that is able to discriminate dark matter haloes undergoing mergers and/or strong accretion from haloes experimenting a relaxed evolution. Using a combination of centre offset, virial ratio, mean radial velocity, sparsity, and ellipticity of the dark matter halo, we study how the thresholds on these parameters, as well as their relative weights, should evolve with redshift to provide the best classification possible. This allows us to split a sample of haloes in a totally relaxed, a marginally relaxed and an unrelaxed subsamples. The resulting classification strongly correlates with the merging activity obtained from the analysis of complete merger trees extracted from whole simulation data. The results on how the different indicators depend on redshift and halo mass, and their optimal combination to better match the true assembly history of haloes, could constitute relevant hints to find a suitable set of indicators applicable to observational data.

Diffstar: a fully parametric physical model for galaxy assembly history

ABSTRACT We present Diffstar , a smooth parametric model for the in situ star formation history (SFH) of galaxies. The Diffstar model is distinct from traditional SFH models because it is parametrized directly in terms of basic features of galaxy formation physics. Diffstar includes ingredients for: the halo mass assembly history; the accretion of gas into the dark matter halo; the fraction of gas that is eventually transformed into stars, ϵms; the time-scale over which this transformation occurs, τcons; and the possibility that some galaxies will experience a quenching event at time tq, and may subsequently experience rejuvenated star formation. We show that our model is sufficiently flexible to describe the average stellar mass histories of galaxies in both the IllustrisTNG (TNG) and UniverseMachine (UM) simulations with an accuracy of ∼0.1 dex across most of cosmic time. We use Diffstar to compare TNG to UM in common physical terms, finding that: (i) star formation in UM is less efficient and burstier relative to TNG; (ii) UM galaxies have longer gas consumption time-scales, relative to TNG; (iii) rejuvenated star formation is ubiquitous in UM, whereas quenched TNG galaxies rarely experience sustained rejuvenation; and (iv) in both simulations, the distributions of ϵms, τcons, and tq share a common characteristic dependence upon halo mass, and present significant correlations with halo assembly history. We conclude with a discussion of how Diffstar can be used in future applications to fit the SEDs of individual observed galaxies, as well as in forward-modelling applications that populate cosmological simulations with synthetic galaxies.

Modelling the galaxy–halo connection with machine learning

ABSTRACT To extract information from the clustering of galaxies on non-linear scales, we need to model the connection between galaxies and haloes accurately and in a flexible manner. Standard halo occupation distribution (HOD) models make the assumption that the galaxy occupation in a halo is a function of only its mass, however, in reality; the occupation can depend on various other parameters including halo concentration, assembly history, environment, and spin. Using the IllustrisTNG hydrodynamical simulation as our target, we show that machine learning tools can be used to capture this high-dimensional dependence and provide more accurate galaxy occupation models. Specifically, we use a random forest regressor to identify which secondary halo parameters best model the galaxy–halo connection and symbolic regression to augment the standard HOD model with simple equations capturing the dependence on those parameters, namely the local environmental overdensity and shear, at the location of a halo. This not only provides insights into the galaxy formation relationship but also, more importantly, improves the clustering statistics of the modelled galaxies significantly. Our approach demonstrates that machine learning tools can help us better understand and model the galaxy–halo connection, and are therefore useful for galaxy formation and cosmology studies from upcoming galaxy surveys.

Insights into the origin of halo mass profiles from machine learning

ABSTRACT The mass distribution of dark matter haloes is the result of the hierarchical growth of initial density perturbations through mass accretion and mergers. We use an interpretable machine-learning framework to provide physical insights into the origin of the spherically-averaged mass profile of dark matter haloes. We train a gradient-boosted-trees algorithm to predict the final mass profiles of cluster-sized haloes, and measure the importance of the different inputs provided to the algorithm. We find two primary scales in the initial conditions (ICs) that impact the final mass profile: the density at approximately the scale of the haloes’ Lagrangian patch RL ($R\sim 0.7\, R_L$) and that in the large-scale environment (R ∼ 1.7 RL). The model also identifies three primary time-scales in the halo assembly history that affect the final profile: (i) the formation time of the virialized, collapsed material inside the halo, (ii) the dynamical time, which captures the dynamically unrelaxed, infalling component of the halo over its first orbit, (iii) a third, most recent time-scale, which captures the impact on the outer profile of recent massive merger events. While the inner profile retains memory of the ICs, this information alone is insufficient to yield accurate predictions for the outer profile. As we add information about the haloes’ mass accretion history, we find a significant improvement in the predicted profiles at all radii. Our machine-learning framework provides novel insights into the role of the ICs and the mass assembly history in determining the final mass profile of cluster-sized haloes.

A deep learning approach to halo merger tree construction

ABSTRACT A key ingredient for semi-analytic models of galaxy formation is the mass assembly history of haloes, encoded in a tree structure. The most commonly used method to construct halo merger histories is based on the outcomes of high-resolution, computationally intensive N-body simulations. We show that machine learning (ML) techniques, in particular Generative Adversarial Networks (GANs), are a promising new tool to tackle this problem with a modest computational cost and retaining the best features of merger trees from simulations. We train our GAN model with a limited sample of merger trees from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulation suite, constructed using two halo finders–tree builder algorithms: SUBFIND – D-TREES and ROCKSTAR – ConsistentTrees. Our GAN model successfully learns to generate well-constructed merger tree structures with high temporal resolution, and to reproduce the statistical features of the sample of merger trees used for training, when considering up to three variables in the training process. These inputs, whose representations are also learned by our GAN model, are mass of the halo progenitors and the final descendant, progenitor type (main halo or satellite), and distance of a progenitor to that in the main branch. The inclusion of the latter two inputs greatly improves the final learned representation of the halo mass growth history, especially for SUBFIND-like ML trees. When comparing equally sized samples of ML merger trees with those of the EAGLE simulation, we find better agreement for SUBFIND-like ML trees. Finally, our GAN-based framework can be utilized to construct merger histories of low- and intermediate-mass haloes, the most abundant in cosmological simulations.