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Benjamin P. Moster

Publications and source records attributed to Benjamin P. Moster.

At least 19 recordsLinked to original sources

The Connection between Mergers and AGN Activity in Simulated and Observed Massive Galaxies

We analyze a suite of $30$ high resolution zoom-in cosmological hydrodynamic simulations of massive galaxies with stellar masses $M_{\ast} > 10^{10.9} M_\odot$, with the goal of better understanding merger activity in AGN, AGN activity in merging systems, SMBH growth during mergers, and the role of gas content. Using the radiative transfer code \textsc{Powderday}, we generate HST-WFC3 F160W synthetic observations of redshift $0.5 < z < 3$ central galaxies, add noise properties similar to the CANDELS survey, and measure morphological properties from the synthetic images using commonly adopted non-parametric statistics. We compare the distributions of morphological properties measured from the synthetic images with a sample of inactive galaxies and X-ray selected AGN hosts from CANDELS. We study the connection between mergers and AGN activity in the simulations, the synthetic images, and the observed CANDELS sample. We find that, in both the simulations and CANDELS, even the most luminous $(L_{\rm bol} > 10^{45}$ erg s$^{-1})$ AGN in our sample are no more likely than inactive galaxies $(L_{\rm bol} < 10^{43}$ erg s$^{-1})$ to be found in merging systems. We also find that AGN activity is not overall enhanced by mergers, nor enhanced at any specific time in the $1$ Gyr preceding and following a merger. Even gas rich major mergers (stellar mass ratio $>$1:4) do not necessarily enhance AGN activity or significantly grow the central SMBH. We conclude that in the simulated massive galaxies studied here, mergers are not the primary drivers of AGN.

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Predictions on the stellar-to-halo mass relation in the dwarf regime using the empirical model for galaxy formation EMERGE

One of the primary goals when studying galaxy formation is to understand how the luminous component of the Universe, galaxies, relates to the growth of structure which is dominated by the gravitational collapse of dark matter haloes. The stellar-to-halo mass relation probes how galaxies occupy dark matter haloes and what that entails for their star formation history. We deliver the first self-consistent empirical model that can place constraints on the stellar-to-halo mass relation down to log stellar mass $\log_{10}(m^*/\mathrm{M}_{\odot}) \leq 5.0$ by fitting our model directly to Local Group dwarf data. This is accomplished by penalising galaxy growth in late-forming, low-mass haloes by mimicking the effects of reionization. This process serves to regulate the number density of galaxies by altering the scatter in halo peak mass $M^{\mathrm{peak}}_{h}$ at fixed stellar mass, creating a tighter scatter than would otherwise exist without a high-$z$ quenching mechanism. Our results indicate that the previously established double-power law stellar-to-halo mass relation can be extended to include galaxies with $\log_{10}(M^{\mathrm{peak}}_{\mathrm{h}}/\mathrm{M}_{\odot})\gtrsim 10.0$. Furthermore, we show that haloes with $\log_{10}(M^{\mathrm{peak}}_{\mathrm{h}}/\mathrm{M}_{\odot})\lesssim 9.3$ by $z=4$ are unlikely to host a galaxy with $\log_{10}(m^*/\mathrm{M}_{\odot}) > 5.0$.

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Observational Measures of Halo Properties Beyond Mass

Different properties of dark matter haloes, including growth rate, concentration, interaction history, and spin, correlate with environment in unique, scale-dependent ways. While these halo properties are not directly observable, galaxies will inherit their host haloes' correlations with environment. In this paper, we show how these characteristic environmental signatures allow using measurements of galaxy environment to constrain which dark matter halo properties are most tightly connected to observable galaxy properties. We show that different halo properties beyond mass imprint distinct scale-dependent signatures in both the galaxy two-point correlation function and the distribution of distances to galaxies' $k$th nearest neighbours, with features strong enough to be accessible even with low-resolution (e.g., grism) spectroscopy at higher redshifts. As an application, we compute observed two-point correlation functions for galaxies binned by half-mass radius at $z=0$ from the Sloan Digital Sky Survey, showing that classic galaxy size models (i.e., galaxy size being proportional to halo spin) as well as other recent proposals show significant tensions with observational data. We show that the agreement with observed clustering can be improved with a simple empirical model in which galaxy size correlates with halo growth.

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EMERGE: Constraining merging probabilities and timescales of close galaxy pairs

Theoretical models are vital for exploring the galaxy merger process, which plays a crucial role in the evolution of galaxies. Recent advances in modelling have placed tight constraints on the buildup of stellar material in galaxies across cosmic time. Despite these successes, extracting the merger rates from observable data remains a challenge. Differences in modelling techniques, combined with limited observational data, drive conflicting conclusions on the merging timescales of close pairs. We employ an empirical model for galaxy formation that links galaxy properties to the growth of simulated dark matter halos, along with mock lightcone galaxy catalogues, to probe the dependencies of pair merging probabilities and merging timescales. In this work, we demonstrate that the pair merging probabilities are best described by a logistic function and that mean merging timescales can be well approximated by a linear relation in the projected separation and line of sight velocity difference in observed pairs. Together, our fitting formulae can accurately predict merger rates from galaxy pairs to at least $z\sim4$ under a wide variety of pair selection criteria. Additionally, we show that some commonly used pair selection criteria may not represent a suitable sample of galaxies to reproduce underlying merger rates. Finally, we conclude from our analysis that observation timescales are primarily driven by dynamics and are not strongly impacted by the star formation properties of the component galaxies.

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Globular cluster numbers in dark matter haloes in a dual formation scenario: an empirical model within EMERGE

We present an empirical model for the number of globular clusters (GCs) in galaxies based on recent data showing a tight relationship between dark matter halo virial masses and GC numbers. While a simple base model forming GCs in low-mass haloes reproduces this relation, we show that a second formation pathway for GCs is needed to account for observed younger GC populations. We confirm previous works that reported the observed linear correlation as being a consequence of hierarchical merging and its insensitivity to the exact GC formation processes at higher virial masses, even for a dual formation scenario. We find that the scatter of the linear relation is strongly correlated with the relative amount of smooth accretion: the more dark matter is smoothly accreted, the fewer GCs a halo has compared to other haloes of the same mass. This scatter is smaller than that introduced by halo mass measurements, indicating that the number of GCs in a galaxy is a good tracer for its dark matter mass. Smooth accretion is also the reason for a lower average dark matter mass per GC in low-mass haloes. Finally, we successfully reproduce the observed general trend of GCs being old and the tendency of more massive haloes hosting older GC systems. Including the second GC formation mechanism through gas-rich mergers leads to a more realistic variety of GC age distributions and also introduces an age inversion in the halo virial mass range $\log M_\mathrm{vir}/\mathrm{M}_\odot = 11{-}13$.

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Exoplanet Detection using Machine Learning

We introduce a new machine learning based technique to detect exoplanets using the transit method. Machine learning and deep learning techniques have proven to be broadly applicable in various scientific research areas. We aim to exploit some of these methods to improve the conventional algorithm based approaches presently used in astrophysics to detect exoplanets. Using the time-series analysis library TSFresh to analyse light curves, we extracted 789 features from each curve, which capture the information about the characteristics of a light curve. We then used these features to train a gradient boosting classifier using the machine learning tool lightgbm. This approach was tested on simulated data, which showed that is more effective than the conventional box least squares fitting (BLS) method. We further found that our method produced comparable results to existing state-of-the-art deep learning models, while being much more computationally efficient and without needing folded and secondary views of the light curves. For Kepler data, the method is able to predict a planet with an AUC of 0.948, so that 94.8 per cent of the true planet signals are ranked higher than non-planet signals. The resulting recall is 0.96, so that 96 per cent of real planets are classified as planets. For the Transiting Exoplanet Survey Satellite (TESS) data, we found our method can classify light curves with an accuracy of 0.98, and is able to identify planets with a recall of 0.82 at a precision of 0.63.

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EMERGE: Empirical predictions of galaxy merger rates since $z\sim6$

We explore the galaxy-galaxy merger rate with the empirical model for galaxy formation, Emerge. On average, we find that between $2$ per cent and $20$ per cent of massive galaxies ($\log_{10}(m_{*}/M_{\odot}) \geq 10.3$) will experience a major merger per Gyr. Our model predicts galaxy merger rates that do not scale as a power-law with redshift when selected by descendant stellar mass, and exhibit a clear stellar mass and mass-ratio dependence. Specifically, major mergers are more frequent at high masses and at low redshift. We show mergers are significant for the stellar mass growth of galaxies $\log_{10}(m_{*}/M_{\odot}) \gtrsim 11.0$. For the most massive galaxies major mergers dominate the accreted mass fraction, contributing as much as $90$ per cent of the total accreted stellar mass. We reinforce that these phenomena are a direct result of the stellar-to-halo mass relation, which results in massive galaxies having a higher likelihood of experiencing major mergers than low mass galaxies. Our model produces a galaxy pair fraction consistent with recent observations, exhibiting a form best described by a power-law exponential function. Translating these pair fractions into merger rates results in an inaccurate prediction compared to the model intrinsic values when using published observation timescales. We find the pair fraction can be well mapped to the intrinsic merger rate by adopting an observation timescale that decreases linearly with redshift as $T_{\mathrm{obs}} = -0.36(1+z)+2.39$ [Gyr], assuming all observed pairs merge by $z=0$.

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The Universe at z>10: Predictions for JWST from the UniverseMachine DR1

The James Webb Space Telescope (JWST) is expected to observe galaxies at $z>10$ that are presently inaccessible. Here, we use a self-consistent empirical model, the UniverseMachine, to generate mock galaxy catalogues and lightcones over the redshift range $z=0-15$. These data include realistic galaxy properties (stellar masses, star formation rates, and UV luminosities), galaxy-halo relationships, and galaxy-galaxy clustering. Mock observables are also provided for different model parameters spanning observational uncertainties at $z<10$. We predict that Cycle 1 JWST surveys will very likely detect galaxies with $M_*>10^7 M_\odot$ and/or $M_{1500}<-17$ out to at least $z\sim 13.5$. Number density uncertainties at $z>12$ expand dramatically, so efforts to detect $z>12$ galaxies will provide the most valuable constraints on galaxy formation models. The faint-end slopes of the stellar mass/luminosity functions at a given mass/luminosity threshold steepen as redshift increases. This is because observable galaxies are hosted by haloes in the exponentially falling regime of the halo mass function at high redshifts. Hence, these faint-end slopes are robustly predicted to become shallower below current observable limits ($M_\ast < 10^7M_\odot$ or $M_\mathrm{1500}>-17$). For reionization models, extrapolating luminosity functions with a constant faint-end slope from $M_{1500}=-17$ down to $M_{1500}=-12$ gives the most reasonable upper limit for the total UV luminosity and cosmic star formation rate up to $z\sim 12$. We compare to three other empirical models and one semi-analytic model, showing that the range of predicted observables from our approach encompasses predictions from other techniques. Public catalogues and lightcones for common fields are available online.

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GalaxyNet: Connecting galaxies and dark matter haloes with deep neural networks and reinforcement learning in large volumes

We present the novel wide & deep neural network GalaxyNet, which connects the properties of galaxies and dark matter haloes, and is directly trained on observed galaxy statistics using reinforcement learning. The most important halo properties to predict stellar mass and star formation rate (SFR) are halo mass, growth rate, and scale factor at the time the mass peaks, which results from a feature importance analysis with random forests. We train different models with supervised learning to find the optimal network architecture. GalaxyNet is then trained with a reinforcement learning approach: for a fixed set of weights and biases, we compute the galaxy properties for all haloes and then derive mock statistics (stellar mass functions, cosmic and specific SFRs, quenched fractions, and clustering). Comparing these statistics to observations we get the model loss, which is minimised with particle swarm optimisation. GalaxyNet reproduces the observed data very accurately ($χ_\mathrm{red}=1.05$), and predicts a stellar-to-halo mass relation with a lower normalisation and shallower low-mass slope at high redshift than empirical models. We find that at low mass, the galaxies with the highest SFRs are satellites, although most satellites are quenched. The normalisation of the instantaneous conversion efficiency increases with redshift, but stays constant above $z\gtrsim0.7$. Finally, we use GalaxyNet to populate a cosmic volume of $(5.9~\mathrm{Gpc})^3$ with galaxies and predict the BAO signal, the bias, and the clustering of active and passive galaxies up to $z=4$, which can be tested with next-generation surveys, such as LSST and Euclid.

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Hot phase generation by supernovae: resolution, chemistry and thermal conduction

Supernovae (SN) generate hot gas in the interstellar medium (ISM), help setting the ISM structure and support the driving of outflows. It is important to resolve the hot gas generation for galaxy formation simulations at solar mass and sub-parsec resolution which realise individual supernova (SN) explosions with ambient densities varying by several orders of magnitude in a realistic multi-phase ISM. We test resolution requirements by simulating SN blast waves at three metallicities ($Z = 0.01, 0.1$ and $1 Z_{\odot}$), six densities and their respective equilibrium chemical compositions ($n=0.001$ cm$^{-3}$ - $100$ cm$^{-3}$), and four mass resolutions ($0.1$ - $100$ M$_{\odot}$), in three dimensions. We include non-equilibrium cooling and chemistry, a homogenous interstellar radiation field, and shielding with a modern pressure-energy smoothed particle hydrodynamics (SPH) method including isotropic thermal conduction and a meshless-finite-mass (MFM) solver. We find stronger resolution requirements for chemistry and hot phase generation than for momentum generation. While at $10$ M$_{\odot}$ the radial momenta at the end of the Sedov phase start converging, the hot phase generation and chemistry require higher resolutions to represent the neutral to ionised hydrogen fraction at the end of the Sedov phase correctly. Thermal conduction typically reduces the hot phase by $0.2$ dex and has little impact on the chemical composition. In general, our $1$, and $0.1$ M$_{\odot}$ results agree well with previous numerical and analytic estimates. We conclude that for the thermal energy injection SN model presented here resolutions higher than $10$ M$_{\odot}$ are required to model the chemistry, momentum and hot phase generation in a multi-phase ISM.

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The GRIFFIN project -- Formation of star clusters with individual massive stars in a simulated dwarf galaxy starburst

We describe a population of young star clusters (SCs) formed in a hydrodynamical simulation of a gas-rich dwarf galaxy merger resolved with individual massive stars at sub-parsec spatial resolution. The simulation is part of the GRIFFIN (Galaxy Realizations Including Feedback From INdividual massive stars) project. The star formation environment during the simulation spans seven orders of magnitude in gas surface density and thermal pressure, and the global star formation rate surface density ($Σ_\mathrm{SFR}$) varies by more than three orders of magnitude during the simulation. Young SCs more massive than $M_{\mathrm{*,cl}}\sim 10^{2.5}\,M_{\odot}$ form along a mass function with a power-law index $α\sim-1.7$ ($α\sim-2$ for $M_{\mathrm{*,cl}}\gtrsim10^{3}\,M_{\odot}$) at all merger phases, while the normalization and the highest SC masses (up to $\sim 10^6 M_{\odot}$) correlate with $Σ_\mathrm{SFR}$. The cluster formation efficiency varies from $Γ\sim20\%$ in early merger phases to $Γ\sim80\%$ at the peak of the starburst and is compared to observations and model predictions. The massive SCs ($\gtrsim10^4\,M_{\odot}$) have sizes and mean surface densities similar to observed young massive SCs. Simulated lower mass clusters appear slightly more concentrated than observed. All SCs form on timescales of a few Myr and lose their gas rapidly resulting in typical stellar age spreads between $σ\sim0.1-2$ Myr ($1σ$), consistent with observations. The age spreads increase with cluster mass, with the most massive cluster ($\sim10^6\, M_{\odot}$) reaching a spread of $5\, \mathrm{Myr}$ once its hierarchical formation finishes. Our study shows that it is now feasible to investigate the SC population of entire galaxies with novel high-resolution numerical simulations.

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Empirical constraints on the formation of early-type galaxies

We present constraints on the formation and evolution of early-type galaxies (ETGs) with the empirical model EMERGE. The parameters of this model are adjusted so that it reproduces the evolution of stellar mass functions, specific star formation rates, and cosmic star formation rates since $z\approx10$ as well as 'quenched' galaxy fractions and correlation functions. We find that at fixed halo mass present-day ETGs are more massive than late-type galaxies, whereas at fixed stellar mass ETGs populate more massive halos in agreement with lensing results. This effect naturally results from the shape and scatter of the stellar-to-halo mass relation and the galaxy formation histories. The ETG stellar mass assembly is dominated by 'in-situ' star formation below a stellar mass of $3\times10^{11}\mathrm{M}_\odot$ and by merging and accretion of 'ex-situ' formed stars at higher mass. The mass dependence is in tension with current cosmological simulations. Lower mass ETGs show extended star formation towards low redshift in agreement with recent estimates from IFU surveys. All ETGs have main progenitors on the 'main sequence of star formation' with the 'red sequence' appearing at $z \approx 2$. Above this redshift, over 95 per cent of the ETG progenitors are star-forming. More than 90 per cent of $z \approx 2$ 'main sequence' galaxies with $m_* > 10^{10}\mathrm{M}_\odot$ evolve into present-day ETGs. Above redshift 6, more than 80 per cent of the observed stellar mass functions above $10^{9}\mathrm{M}_\odot$ can be accounted for by ETG progenitors with $m_* > 10^{10}\mathrm{M}_\odot$. This implies that current and future high redshift observations mainly probe the birth of present-day ETGs. The source code and documentation of EMERGE are available at github.com/bmoster/emerge.

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On the origin of magnetic driven winds and the structure of the galactic dynamo in isolated galaxies

We investigate the build-up of the galactic dynamo and subsequently the origin of a magnetic driven outflow. We use a setup of an isolated disc galaxy with a realistic circum-galactic medium (CGM). We find good agreement of the galactic dynamo with theoretical and observational predictions from the radial and toroidal components of the magnetic field as function of radius and disc scale height. We find several field reversals indicating dipole structure at early times and quadrupole structure at late times. Together with the magnetic pitch angle and the dynamo control parameters $R_α$, $R_ω$ and $D$ we present strong evidence for an $α^2$-$Ω$ dynamo. The formation of a bar in the centre leads to further amplification of the magnetic field via adiabatic compression which subsequently drives an outflow. Due to the Parker-Instability the magnetic field lines rise to the edge of the disc, break out and expand freely in the CGM driven by the magnetic pressure. Finally, we investigate the correlation between magnetic field and star formation rate. Globally, we find that the magnetic field is increasing as function of the star formation rate surface density with a slope between $0.3$ and $0.45$ in good agreement with predictions from theory and observations. Locally, we find that the magnetic field can decrease while star formation increases. We find that this effect is correlated with the diffusion of magnetic field from the spiral arms to the inter-arm regions which we explicitly include by solving the induction equation and accounting for non-linear terms.

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The Outer Stellar Halos of Galaxies: how Radial Merger Mass Deposition, Shells and Streams depend on Infall-Orbit Configurations

Galaxy mergers are a fundamental part of galaxy evolution. To study the resulting mass distributions of different kinds of galaxy mergers, we present a simulation suite of 36 high-resolution isolated merger simulations, exploring a wide range of parameter space in terms of mass ratios (mu = 1:5, 1:10, 1:50, 1:100) and orbital parameters. We find that mini mergers deposit a higher fraction of their mass in the outer halo compared to minor mergers, while their contribution to the central mass distribution is highly dependent on the orbital impact parameter: for larger pericentric distances we find that the centre of the host galaxy is almost not contaminated by merger particles. We also find that the median of the resulting radial mass distribution for mini mergers differs significantly from the predictions of simple theoretical tidal-force models. Furthermore, we find that mini mergers can increase the size of the host disc significantly without changing the global shape of the galaxy, if the impact occurs in the disc plane, thus providing a possible explanation for extended low-surface brightness disks reported in observations. Finally, we find clear evidence that streams are a strong indication of nearly circular infall of a satellite (with large angular momentum), whereas the appearance of shells clearly points to (nearly) radial satellite infall.

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Astro2020: Empirically Constraining Galaxy Evolution

Over the past decade, empirical constraints on the galaxy-dark matter halo connection have significantly advanced our understanding of galaxy evolution. Past techniques have focused on connections between halo properties and galaxy stellar mass and/or star formation rates. Empirical techniques in the next decade will link halo assembly histories with galaxies' circumgalactic media, supermassive black holes, morphologies, kinematics, sizes, colors, metallicities, and transient rates. Uncovering these links will resolve many critical uncertainties in galaxy formation and will enable much higher-fidelity mock catalogs essential for interpreting observations. Achieving these results will require broader and deeper spectroscopic coverage of galaxies and their circumgalactic media; survey teams will also need to meet several criteria (cross-comparisons, public access, and covariance matrices) to facilitate combining data across different surveys. Acting on these recommendations will continue enabling dramatic progress in both empirical modeling and galaxy evolution for the next decade.

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Magnetic buoyancy in simulated galactic discs with a realistic circum galactic medium

We present simulations of isolated disc galaxies in a realistic environment performed with the Tree-SPMHD-Code Gadget-3. Our simulations include a spherical circum-galactic medium (CGM) surrounding the galactic disc, motivated by observations and the results of cosmological simulations. We present three galactic models with different halo masses between 10e10 Msol and 10e12 Msol, and for each we use two different approaches to seed the magnetic field, as well as a control simulation without a magnetic field. We find that the amplification of the magnetic field in the centre of the disc leads to a biconical magnetic outflow of gas that magnetizes the CGM. This biconical magnetic outflow reduces the star formation rate (SFR) of the galaxy by roughly 40 percent compared to the simulations without magnetic fields. As the key aspect of our simulations, we find that small scale turbulent motion of the gas in the disc leads to the amplification of the magnetic field up to tens of 10e-6 G, as long as the magnetic field strength is low. For stronger magnetic fields turbulent motion does not lead to significant amplification but is replaced by an alpha-omega dynamo. The occurance of a small scale turbulent dynamo becomes apparent through the magnetic power spectrum and analysis of the field lines' curvature. In accordance with recent observations we find an anti-correlation between the spiral structure in the gas density and in the magnetic field due to a diffusion term added to the induction equation.

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EMERGE - An empirical model for the formation of galaxies since $z\sim10$

We present EMERGE, an Empirical ModEl for the foRmation of GalaxiEs, describing the evolution of individual galaxies in large volumes from $z\sim10$ to the present day. We assign a star formation rate to each dark matter halo based on its growth rate, which specifies how much baryonic material becomes available, and the instantaneous baryon conversion efficiency, which determines how efficiently this material is converted to stars, thereby capturing the baryonic physics. Satellites are quenched following the delayed-then-rapid model, and they are tidally disrupted once their subhalo has lost a significant fraction of its mass. The model is constrained with observed data extending out to high redshift. The empirical relations are very flexible, and the model complexity is increased only if required by the data, assessed by several model selection statistics. We find that for the same final halo mass galaxies can have very different star formation histories. Nevertheless, the average star formation and accretion rates are in good agreement with models following an abundance matching strategy. Galaxies that are quenched at $z=0$ typically have a higher peak star formation rate compared to their star-forming counterparts. The accretion of stars can dominate the total mass of massive galaxies, but is insignificant for low-mass systems, independent of star-formation activity. EMERGE predicts stellar-to-halo mass ratios for individual galaxies and introduces scatter self-consistently. We find that at fixed halo mass, passive galaxies have a higher stellar mass on average. The intra-cluster-mass in massive haloes can be up to 8 times larger than the mass of the central galaxy. Clustering for star-forming and quenched galaxies is in good agreement with observational constraints, indicating a realistic assignment of galaxies to haloes.

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The Origin and Evolution of Fast and Slow Rotators in the Illustris Simulation

Using the Illustris simulation, we follow thousands of elliptical galaxies back in time to identify how the dichotomy between fast and slow rotating ellipticals (FRs and SRs) develops. Comparing to the $\textrm{ATLAS}^\textrm{3D}$ survey, we show that Illustris reproduces similar elliptical galaxy rotation properties, quantified by the degree of ordered rotation, $λ_\textrm{R}$. There is a clear segregation between low-mass ($M_{\rm *} < 10^{11} M_{\rm \odot}$) ellipticals, which form a smooth distribution of FRs, and high-mass galaxies ($M_{\rm *} > 10^{11.5} M_{\rm \odot}$), which are mostly SRs, in agreement with observations. We find that SRs are very gas poor, metal rich and red in colour, while FRs are generally more gas rich and still star forming. We suggest that ellipticals begin naturally as FRs and, as they grow in mass, lose their spin and become SRs. While at $z = 1$, the progenitors of SRs and FRs are nearly indistinguishable, their merger and star formation histories differ thereafter. We find that major mergers tend to disrupt galaxy spin, though in rare cases can lead to a spin-up. No major difference is found between the effects of gas-rich and gas-poor mergers and the amount of minor mergers seem to have little correlation with galaxy spin. In between major mergers, lower-mass ellipticals, which are mostly gas-rich, tend to recover their spin by accreting gas and stars. For galaxies with $M_{\rm *}$ above $\sim 10^{11} M_{\rm \odot}$, this trend reverses; galaxies only retain or steadily lose their spin. More frequent mergers, accompanied by an inability to regain spin, lead massive ellipticals to lose most of ordered rotation and transition from FRs to SRs.

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