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Cedric G. Lacey

Publications and source records attributed to Cedric G. Lacey.

At least 37 records · Page 2Linked to original sources

The FLAMINGO project: cosmological hydrodynamical simulations for large-scale structure and galaxy cluster surveys

We introduce the Virgo Consortium's FLAMINGO suite of hydrodynamical simulations for cosmology and galaxy cluster physics. To ensure the simulations are sufficiently realistic for studies of large-scale structure, the subgrid prescriptions for stellar and AGN feedback are calibrated to the observed low-redshift galaxy stellar mass function and cluster gas fractions. The calibration is performed using machine learning, separately for three resolutions. This approach enables specification of the model by the observables to which they are calibrated. The calibration accounts for a number of potential observational biases and for random errors in the observed stellar masses. The two most demanding simulations have box sizes of 1.0 and 2.8 Gpc and baryonic particle masses of $1\times10^8$ and $1\times10^9 \text{M}_\odot$, respectively. For the latter resolution the suite includes 12 model variations in a 1 Gpc box. There are 8 variations at fixed cosmology, including shifts in the stellar mass function and/or the cluster gas fractions to which we calibrate, and two alternative implementations of AGN feedback (thermal or jets). The remaining 4 variations use the unmodified calibration data but different cosmologies, including different neutrino masses. The 2.8 Gpc simulation follows $3\times10^{11}$ particles, making it the largest ever hydrodynamical simulation run to $z=0$. Lightcone output is produced on-the-fly for up to 8 different observers. We investigate numerical convergence, show that the simulations reproduce the calibration data, and compare with a number of galaxy, cluster, and large-scale structure observations, finding very good agreement with the data for converged predictions. Finally, by comparing hydrodynamical and `dark-matter-only' simulations, we confirm that baryonic effects can suppress the halo mass function and the matter power spectrum by up to $\approx20$ per cent.

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The complex interplay of AGN jet-inflated bubbles and the intracluster medium

We use SWIFT, a smoothed particle hydrodynamics code, to simulate the evolution of bubbles inflated by active galactic nuclei (AGN) jets, as well as their interactions with the ambient intracluster medium (ICM). These jets inflate lobes that turn into bubbles after the jets are turned off (at $t=50$ Myr). Almost all of the energy injected into the jets is transferred to the ICM very quickly after they are turned off, with roughly $70$ per cent of it in thermal form and the rest in kinetic. At late times ($t>500$ Myr) we find the following: 1) the bubbles draw out trailing filaments of low-entropy gas, similar to those recently observed, 2) the action of buoyancy and the uplift of the filaments dominates the energetics of both the bubbles and the ICM and 3) almost all of the originally injected energy is in the form of gravitational potential energy, with the bubbles containing $15$ per cent of it, and the rest contained in the ICM. These findings indicate that feedback proceeds mainly through the displacement of gas to larger radii. We find that the uplift of these filaments permanently changes the thermodynamic properties of the ICM by reducing the central density and increasing the central temperature (within $30$ kpc). We propose that jet feedback proceeds not only through the heating of the ICM (which can delay cooling), but also through the uplift-related reduction of the central gas density. The latter also delays cooling, on top of reducing the amount of gas available to cool.

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Active galactic nuclei jets simulated with smoothed particle hydrodynamics

Simulations of active galactic nuclei (AGN) jets have thus far been performed almost exclusively using grid-based codes. We present the first results from hydrodynamical tests of AGN jets, and their interaction with the intracluster medium (ICM), using smoothed particle hydrodynamics (SPH) as implemented in the SWIFT code. We launch these jets into a constant-density ICM, as well as ones with a power-law density profile. We also vary the jet power, velocity, opening angle and numerical resolution. In all cases we find broad agreement between our jets and theoretical predictions for the lengths of the jets and the lobes they inflate, as well as the radii of the lobes. The jets first evolve ballistically, and then transition to a self-similar phase, during which the lobes expand in a self-similar fashion (keeping a constant shape). In this phase the kinetic and thermal energies in the lobes and in the shocked ICM are constant fractions of the total injected energy. In our standard simulation, two thirds of the initially injected energy is transferred to the ICM by the time the jets are turned off, mainly through a bow shock. Of that, $70\%$ is in kinetic form, indicating that the bow shock does not fully and efficiently thermalise while the jet is active. At resolutions typical of large cosmological simulations ($m_\mathrm{gas}\approx10^7$ $\mathrm{M}_\odot$), the shape of the lobes is close to self-similar predictions to an accuracy of $15\%$. This indicates that the basic physics of jet-inflated lobes can be correctly simulated even at such resolutions ($\approx500$ particles per jet).

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The buildup of galaxies and their spheroids: the contributions of mergers, disc instabilities and star formation

We use the GALFORM semi-analytical model of galaxy formation and the Planck-Millennium simulation to investigate the origins of stellar mass in galaxies and their spheroids. We compare the importance of mergers and disc instabilities, as well as the starbursts that they trigger. We find that the fraction of galaxy stellar mass formed \textit{ex situ} ($f_\mathrm{ex}$) increases sharply from $M_*=10^{11}$ M$_\odot$ upwards, reaching $80\%$ at $M_*=10^{11.3}$ M$_\odot$. For low-mass galaxies we find larger \textit{\textit{ex situ}} contributions at $z=0$ than in other models ($7$-$12\%$), with a decrease towards higher redshifts. The global \textit{ex situ} fraction of all stellar mass falls sharply with redshift, from $40\%$ at $z=0$ to $3\%$ at $z=10$. Major mergers contribute roughly half of the \textit{ex situ} mass, with minor mergers and smooth accretion of satellites both accounting for $\approx25\%$, almost independent of stellar mass and redshift. Mergers dominate in building up high-mass ($M_\mathrm{*,sph}>10^{11}$ M$_\odot$) and low-mass ($M_\mathrm{*,sph}<10^{8.5}$ M$_\odot$) spheroids. Disc instabilities and their associated starbursts dominate for intermediate-mass spheroids ($10^{8.5}<M_\mathrm{*,sph}<10^{11}$ M$_\odot$) at $z=0$. The mass regime where pseudobulges dominate is in agreement with observed pseudobulge fractions, but the peak value in the pseudobulge fraction predicted by GALFORM is likely too high. The total contributions of disc instabilities and their starbursts are roughly equal at $z=0$, with the former dominating for lower-mass spheroids (peak at $M_\mathrm{*,sph}=10^{9.5}$ M$_\odot$) and the latter for higher-mass ones (peak at $M_\mathrm{*,sph}=10^{10.5}$ M$_\odot$).

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Spin-driven jet feedback in idealised simulations of galaxy groups and clusters

We implement a black hole spin evolution and jet feedback model into SWIFT, a smoothed particle hydrodynamics code. The jet power is determined self-consistently assuming Bondi accretion, using a realistic, spin-dependant efficiency. The jets are launched along the spin axis of the black hole, resulting in natural reorientation and precession. We apply the model to idealised simulations of galaxy groups and clusters, finding that jet feedback successfully quenches gas cooling and star formation in all systems. Our group-size halo ($M_\mathrm{200}=10^{13}$ $\mathrm{M}_\odot$) is quenched by a strong jet episode triggered by a cooling flow, and it is kept quenched by a low-power jet fed from hot halo accretion. In more massive systems ($M_\mathrm{200}\geq 10^{14}$ $\mathrm{M}_\odot$), hot halo accretion is insufficient to quench the galaxies, or to keep them quenched after the first cooling episode. These galaxies experience multiple episodes of gas cooling, star formation and jet feedback. In the most massive galaxy cluster that we simulate ($M_\mathrm{200}=10^{15}$ $\mathrm{M}_\odot$), we find peak cold gas masses of $10^{10}$ $\mathrm{M}_\odot$ and peak star formation rates of a few times $100$ $\mathrm{M}_\odot\mathrm{yr}^{-1}$. These values are achieved during strong cooling flows, which also trigger the strongest jets with peak powers of $10^{47}$ $\mathrm{erg}\hspace{0.3mm}\mathrm{s}^{-1}$. These jets subsequently shut off the cooling flows and any associated star formation. Jet-inflated bubbles draw out low-entropy gas that subsequently forms dense cooling filaments in their wakes, as seen in observations.

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Statistics of galaxy mergers: bridging the gap between theory and observation

We present a study of galaxy mergers up to $z=10$ using the Planck Millennium cosmological dark matter simulation and the {\tt GALFORM} semi-analytical model of galaxy formation. Utilising the full ($800$ Mpc)$^3$ volume of the simulation, we studied the statistics of galaxy mergers in terms of merger rates and close pair fractions. We predict that merger rates begin to drop rapidly for high-mass galaxies ($M_*>10^{11.3}-10^{10.5}$ $M_\odot$ for $z=0-4$), as a result of the exponential decline in the galaxy stellar mass function. The predicted merger rates increase and then turn over with increasing redshift, by $z=3.5$, in disagreement with hydrodynamical simulations and semi-empirical models. In agreement with most other models and observations, we find that close pair fractions flatten or turn over at some redshift (dependent on the mass selection). We conduct an extensive comparison of close pair fractions, and highlight inconsistencies among models, but also between different observations. We provide a fitting formula for the major merger timescale for close galaxy pairs, in which the slope of the stellar mass dependence is redshift dependent. This is in disagreement with previous theoretical results that implied a constant slope. Instead we find a weak redshift dependence only for massive galaxies ($M_*>10^{10}$ M$_\odot$): in this case the merger timescale varies approximately as $M_*^{-0.55}$. We find that close pair fractions and merger timescales depend on the maximum projected separation as $r_\mathrm{max}^{1.32}$. This is in agreement with observations of small-scale clustering of galaxies, but is at odds with the linear dependence on projected separation that is often assumed.

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Qwind3: UV line-driven accretion disc wind models for AGN feedback

The ultraviolet (UV) bright accretion disc in active galactic nuclei (AGN) should give rise to line driving, producing a powerful wind which may play an important role in AGN feedback as well as in producing structures like the broad line region. However, coupled radiation-hydrodynamics codes are complex and expensive, so we calculate the winds instead using a non-hydrodynamical approach (the Qwind framework). The original Qwind model assumed the initial conditions in the wind, and had only simple radiation transport. Here, we present an improved version which derives the wind initial conditions and has significantly improved ray-tracing to calculate the wind absorption self consistently given the extended nature of the UV emission. We also correct the radiation flux for relativistic effects, and assess the impact of this on the wind velocity. These changes mean the model is more physical, so its predictions are more robust. We find that, even when accounting for relativistic effects, winds can regularly achieve velocities $\simeq$ (0.1-0.5) $c$, and carry mass loss rates which can be up to 30% of the accreted mass for black hole masses of $10^{7-9}$ $\mathrm{M}_\odot$, and mass accretion rates of 50% of the Eddington rate. Overall, the wind power scales as a power law with the black hole mass accretion rate, unlike the weaker scaling generally assumed in current cosmological simulations that include AGN feedback. The updated code, Qwind3, is publicly available in GitHub

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How well is angular momentum accretion modelled in semi-analytic galaxy formation models?

Gas cooling and accretion in haloes delivers mass and angular momentum onto galaxies. In this work, we investigate the accuracy of the modelling of this important process in several different semi-analytic (SA) galaxy formation models (GALFORM, L-GALAXIES and MORGANA) through comparisons with a hydrodynamical simulation performed with the moving-mesh code AREPO. Both SA models and the simulation were run without any feedback or metal enrichment, in order to focus on the cooling and accretion process. All of the SA models considered here assume that gas cools from a spherical halo. We found that the assumption that the gas conserves its angular momentum when moving from the virial radius, $r_{\rm vir}$, to the central region of the halo, $r\sim 0.1 r_{\rm vir}$, is approximately consistent with the results from our simulation, in which gas typically retains $70-80\%$ of its angular momentum during this process. We also found that, compared to the simulation, the MORGANA model tends to overestimate the mean specific angular momentum of cooled-down gas, the L-GALAXIES model also tends to overestimate this in low-redshift massive haloes, while the two older GALFORM models tend to underestimate the angular momentum. In general, the predictions of the new GALFORM cooling model developed by Hou et al. agree the best with the simulation.

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Halo Merger Tree Comparison: Impact on Galaxy Formation Models

We examine the effect of using different halo finders and merger tree building algorithms on galaxy properties predicted using the GALFORM semi-analytical model run on a high resolution, large volume dark matter simulation. The halo finders/tree builders HBT, ROCKSTAR, SUBFIND and VELOCIRAPTOR differ in their definitions of halo mass, on whether only spatial or phase-space information is used, and in how they distinguish satellite and main haloes; all of these features have some impact on the model galaxies, even after the trees are post-processed and homogenised by GALFORM. The stellar mass function is insensitive to the halo and merger tree finder adopted. However, we find that the number of central and satellite galaxies in GALFORM does depend slightly on the halo finder/tree builder. The number of galaxies without resolved subhaloes depends strongly on the tree builder, with VELOCIRAPTOR, a phase-space finder, showing the largest population of such galaxies. The distributions of stellar masses, cold and hot gas masses, and star formation rates agree well between different halo finders/tree builders. However, because VELOCIRAPTOR has more early progenitor haloes, with these trees GALFORM produces slightly higher star formation rate densities at high redshift, smaller galaxy sizes, and larger stellar masses for the spheroid component. Since in all cases these differences are small we conclude that, when all of the trees are processed so that the main progenitor mass increases monotonically, the predicted GALFORM galaxy populations are stable and consistent for these four halo finders/tree builders.

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Efficient exploration and calibration of a semi-analytical model of galaxy formation with deep learning

We implement a sample-efficient method for rapid and accurate emulation of semi-analytical galaxy formation models over a wide range of model outputs. We use ensembled deep learning algorithms to produce a fast emulator of an updated version of the GALFORM model from a small number of training examples. We use the emulator to explore the model's parameter space, and apply sensitivity analysis techniques to better understand the relative importance of the model parameters. We uncover key tensions between observational datasets by applying a heuristic weighting scheme in a Markov chain Monte Carlo framework and exploring the effects of requiring improved fits to certain datasets relative to others. Furthermore, we demonstrate that this method can be used to successfully calibrate the model parameters to a comprehensive list of observational constraints. In doing so, we re-discover previous GALFORM fits in an automatic and transparent way, and discover an improved fit by applying a heavier weighting to the fit to the metallicities of early-type galaxies. The deep learning emulator requires a fraction of the model evaluations needed in similar emulation approaches, achieving an out-of-sample mean absolute error at the knee of the K-band luminosity function of 0.06 dex with less than 1000 model evaluations. We demonstrate that this is an extremely efficient, inexpensive and transparent way to explore multi-dimensional parameter spaces, and can be applied more widely beyond semi-analytical galaxy formation models.

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Determining the systemic redshift of Lyman-alpha emitters with neural networks and improving the measured large-scale clustering

We explore how to mitigate the clustering distortions in Lyman-$α$ emitters (LAEs) samples caused by the miss-identification of the Lyman-$α$ (Ly$α$) wavelength in their Ly$α$ line profiles. We use the Ly$α$ line profiles from our previous LAE theoretical model that includes radiative transfer in the interstellar and intergalactic mediums. We introduce a novel approach to measure the systemic redshift of LAEs from their Ly$α$ line using neural networks. In detail, we assume that, for a fraction of the whole LAE population their systemic redshift is determined precisely through other spectral features. We then use this subset to train a neural network that predicts the Ly$α$ wavelength given a Ly$α$ line profile. We test two different training sets: i) the LAEs are selected homogeneously and ii) only the brightest LAEs are selected. In comparison with previous approaches in the literature, our methodology improves significantly both accuracy and precision in determining the Ly$α$ wavelength. In fact, after applying our algorithm in ideal Ly$α$ line profiles, we recover the clustering unperturbed down to 1cMpc/h. Then, we test the performance of our methodology in realistic Ly$α$ line profiles by downgrading their quality. The machine learning techniques work well even if the Ly$α$ line profile quality is decreased considerably. We conclude that LAE surveys such as HETDEX would benefit from determining with high accuracy the systemic redshift of a subpopulation and applying our methodology to estimate the systemic redshift of the rest of the galaxy sample.

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Lyman-alpha emitters in a cosmological volume II: the impact of the intergalactic medium

In the near future galaxy surveys will target Lyman alpha emitting galaxies (LAEs) to unveil the nature of the dark energy. It has been suggested that the observability of LAEs is coupled to the large scale properties of the intergalactic medium. Such coupling could introduce distortions into the observed clustering of LAEs, adding a new potential difficulty to the interpretation of upcoming surveys. We present a model of LAEs that incorporates Lyman-alpha radiative transfer processes in the interstellar and intergalactic medium. The model is implemented in the GALFORM semi-analytic model of galaxy of formation and evolution. We find that the radiative transfer inside galaxies produces selection effects over galaxy properties. In particular, observed LAEs tend to have low metallicities and intermediate star formation rates. At low redshift we find no evidence of a correlation between the spatial distribution of LAEs and the intergalactic medium properties. However, at high redshift the LAEs are linked to the line of sight velocity and density gradient of the intergalactic medium. The strength of the coupling depends on the outflow properties of the galaxies and redshift. This effect modifies the clustering of LAEs on large scales, adding non linear features. In particular, our model predicts modifications to the shape and position of the baryon acoustic oscillation peak. This work highlights the importance of including radiative transfer physics in the cosmological analysis of LAEs.

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The evolution of radio jets across cosmic time

We present predictions for the evolution of radio emission from Active Galactic Nuclei (AGNs). We use a model that follows the evolution of Supermassive Black Hole (SMBH) masses and spins, within the latest version of the GALFORM semi-analytic model of galaxy formation. We use a Blandford-Znajek type model to calculate the power of the relativistic jets produced by black hole accretion discs, and a scaling model to calculate radio luminosities. First, we present the predicted evolution of the jet power distribution, finding that this is dominated by objects fuelled by hot halo accretion and an ADAF accretion state for jet powers above $10^{32}\mathrm{W}$ at $z=0$, with the contribution from objects fuelled by starbursts and in a thin disc accretion state being more important for lower jet powers at $z=0$ and at all jet powers at high redshifts ($z\geq3$). We then present the evolution of the jet power density from the model. The model is consistent with current observational estimates of jet powers from radio luminosities, once we allow for the significant uncertainties in these observational estimates. Next, we calibrate the model for radio emission to a range of observational estimates of the $z=0$ radio luminosity function. We compare the evolution of the model radio luminosity function to observational estimates for $0<z<6$, finding that the predicted evolution is similar to that observed. Finally, we explore recalibrating the model to reproduce luminosity functions of core radio emission, finding that the model is in approximate agreement with the observations.

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AGNs at the cosmic dawn: predictions for future surveys from a $Λ$CDM cosmological model

Telescopes to be launched over the next decade-and-a-half, such as JWST, EUCLID, ATHENA and Lynx, promise to revolutionise the study of the high redshift Universe and greatly advance our understanding of the early stages of galaxy formation. We use a model that follows the evolution of the masses and spins of supermassive black holes (SMBHs) within a semi-analytic model of galaxy formation to make predictions for the Active Galactic Nucleus (AGN) luminosity function at $z\geq7$ in the broadband filters of JWST and EUCLID at near-infrared wavelengths, and ATHENA and Lynx at X-ray energies. The predictions of our model are relatively insensitive to the choice of seed black hole mass, except at the lowest luminosities ($L_{\mathrm{bol}}<10^{43}\mathrm{ergs^{-1}}$) and the highest redshifts ($z>10$). We predict that surveys with these different telescopes will select somewhat different samples of SMBHs, with EUCLID unveiling the most massive, highest accretion rate SMBHs, Lynx the least massive, lowest accretion rate SMBHs, and JWST and ATHENA covering objects inbetween. At $z=7$, we predict that typical detectable SMBHs will have masses, $M_{\mathrm{BH}}\sim10^{5-8}M_{\odot}$, and Eddington normalised mass accretion rates, $\dot{M}/\dot{M}_{\mathrm{Edd}}\sim0.6-2$. The SMBHs will be hosted by galaxies of stellar mass $M_{\star}\sim10^{8-10}M_{\odot}$, and dark matter haloes of mass $M_{\mathrm{halo}}\sim10^{11-12}M_{\odot}$. We predict that the detectable SMBHs at $z=10$ will have slightly smaller black holes, accreting at slightly higher Eddington normalised mass accretion rates, in slightly lower mass host galaxies compared to those at $z=7$, and reside in haloes of mass $M_{\mathrm{halo}}\sim10^{10-11}M_{\odot}$.

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Galaxy formation in the Planck Millennium: the atomic hydrogen content of dark matter halos

We present recalibrations of the GALFORM semi-analytical model of galaxy formation in a new N-body simulation with the Planck cosmology. The Planck Millennium simulation uses more than 128 billion particles to resolve the matter distribution in a cube of $800$ Mpc on a side, which contains more than 77 million dark matter haloes with mass greater than $2.12 \times 10^{9} h^{-1} {\rm M_{\odot}}$ at the present day. Only minor changes to a very small number of model parameters are required in the recalibration. We present predictions for the atomic hydrogen content (HI) of dark matter halos, which is a key input into the calculation of the HI intensity mapping signal expected from the large-scale structure of the Universe. We find that the HI mass $-$ halo mass relation displays a clear break at the halo mass above which AGN heating suppresses gas cooling, $\approx 3 \times 10^{11} h^{-1} M_{\rm \odot}$. Below this halo mass, the HI content of haloes is dominated by the central galaxy; above this mass it is the combined HI content of satellites that prevails. We find that the HI mass - halo mass relation changes little with redshift up to $z=3$. The bias of HI sources shows a scale dependence that gets more pronounced with increasing redshift.

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The evolution of the UV-to-mm extragalactic background light: evidence for a top-heavy initial mass function?

We present predictions for the UV-to-mm extragalactic background light (EBL) from a recent version of the GALFORM semi-analytical model of galaxy formation which invokes a top-heavy stellar initial mass function (IMF) for galaxies undergoing dynamically-triggered bursts of star formation. We combine GALFORM with the GRASIL radiative transfer code for computing fully self-consistent UV-to-mm spectral energy distributions for each simulated galaxy, accounting for the absorption and re-emission of stellar radiation by interstellar dust. The predicted EBL is in near-perfect agreement with recent observations over the whole UV-to-mm spectrum, as is the evolution of the cosmic spectral energy distribution over the redshift range for which observations are available ($z\lesssim1$). We show that approximately 90~per~cent of the EBL is produced at $z<2$ although this shifts to higher redshifts for sub-mm wavelengths. We assess whether the top-heavy IMF in starbursts is necessary in order to reproduce the EBL at the same time as other key observables, and find that variant models with a universal solar-neighborhood IMF display poorer agreement with EBL observations over the whole UV-to-mm spectrum and fail to match the counts of galaxies in the sub-mm.

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The evolution of SMBH spin and AGN luminosities for $z<6$ within a semi-analytic model of galaxy formation

Understanding how Active Galactic Nuclei (AGN) evolve through cosmic time allows us to probe the physical processes that control their evolution. We use an updated model for the evolution of masses and spins of supermassive black holes (SMBHs), coupled to the latest version of the semi-analytical model of galaxy formation GALFORM using the Planck cosmology and a high resolution Millennium style dark matter simulation to make predictions for AGN and SMBH properties for $0 < z < 6$. We compare the model to the observed black hole mass function and the SMBH versus galaxy bulge mass relation at $z=0$, and compare the predicted bolometric, hard X-ray, soft X-ray and optical AGN luminosity functions to observations at $z < 6$, and find that the model is in good agreement with the observations. The model predicts that at $z<2$ and $L_{\mathrm{bol}} < 10^{43} \mathrm{ergs^{-1}}$, the AGN luminosity function is dominated by objects accreting in an Advection Dominated Accretion Flow (ADAF) disc state, while at higher redshifts and higher luminosities the dominant contribution is from objects accreting via a thin disc or at super-Eddington rates. The model also predicts that the AGN luminosity function at $z<3$ and $L_{\mathrm{bol}} < 10^{44} \mathrm{ergs^{-1}}$ is dominated by the contribution from AGN fuelled by quiescent hot halo accretion, while at higher luminosities and higher redshifts, the AGN luminosity function is dominated by the contribution from AGN fuelled by starbursts triggered by disc instabilities. We employ this model to predict the evolution of SMBH masses, Eddington ratios, and spins, finding that the median SMBH spin evolves very little for $0<z<6$.

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A comparison between semi-analytical gas cooling models and cosmological hydrodynamical simulations

We compare the mass cooling rates and cumulative cooled-down masses predicted by several semi-analytical (SA) cooling models with cosmological hydrodynamical simulations performed using the AREPO code (ignoring processes such as feedback and chemical enrichment). The SA cooling models are the new GALFORM cooling model introduced in Hou et al. (2017), along with two earlier GALFORM cooling models and the L-GALAXIES and MORGANA cooling models. We find that the predictions of the new GALFORM cooling model are generally in best agreement with the simulations. For halos with $M_{\rm halo}\lesssim 3\times 10^{11}\,{\rm M}_{\odot}$, the SA models predict that the timescale for radiative cooling is shorter than or comparable to the gravitational infall timescale. Even though SA models assume that gas falls onto galaxies from a spherical gas halo, while the simulations show that the cold gas is accreted through filaments, both methods predict similar mass cooling rates, because in both cases the gas accretion occurs on similar timescales. For halos with $M_{\rm halo}\gtrsim 10^{12}\,{\rm M}_{\odot}$, gas in the simulations typically cools from a roughly spherical hot gas halo, as assumed in the SA models, but the halo gas gradually contracts during cooling, leading to compressional heating. SA models ignore this heating, and so overestimate mass cooling rates by factors of a few. At low redshifts halo major mergers or a sequence of successive smaller mergers are seen in the simulations to strongly heat the halo gas and suppress cooling, while mergers at high redshifts do not suppress cooling, because the gas filaments are difficult to heat up. The new SA cooling model best captures these effects.

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