arXiv subjects

J. Stuart B. Wyithe

Publications and source records attributed to J. Stuart B. Wyithe.

At least 55 records · Page 3Linked to original sources

arXiv2018

The impact of feedback and the hot halo on the rates of gas accretion onto galaxies

We investigate the physics that drives the gas accretion rates onto galaxies at the centers of dark matter haloes using the EAGLE suite of hydrodynamical cosmological simulations. We find that at redshifts $z{\le}2$ the accretion rate onto the galaxy increases with halo mass in the halo mass range $10^{10}-10^{11.7}M_{\odot}$, flattens between the halo masses $10^{11.7}-10^{12.7}M_{\odot}$, and increases again for higher-mass haloes. However, the galaxy gas accretion does not flatten at intermediate halo masses when AGN feedback is switched off. To better understand these trends, we develop a physically motivated semi-analytic model of galaxy gas accretion. We show that the flattening is produced by the rate of gas cooling from the hot halo. The ratio of the cooling radius and the virial radius does not decrease continuously with increasing halo mass as generally thought. While it decreases up to ${\sim}10^{13}M_{\odot}$ haloes, it increases for higher halo masses, causing an upturn in the galaxy gas accretion rate. This may indicate that in high-mass haloes AGN feedback is not sufficiently efficient. When there is no AGN feedback, the density of the hot halo is higher, the ratio of the cooling and virial radii does not decrease as much and the cooling rate is higher. Changes in the efficiency of stellar feedback can also increase or decrease the accretion rates onto galaxies. The trends can plausibly be explained by the re-accretion of gas ejected by progenitor galaxies and by the suppression of black hole growth, and hence AGN feedback, by stellar feedback.

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arXiv2018

On the observability of individual Population III stars and their stellar-mass black hole accretion disks through cluster caustic transits

We summarize panchromatic Extragalactic Background Light data to place upper limits on the integrated near-infrared surface brightness (SB) that may come from Population III stars and possible accretion disks around their stellar-mass black holes (BHs) in the epoch of First Light, broadly taken from z$\simeq$7-17. Theoretical predictions and recent near-infrared power-spectra provide tighter constraints on their sky-signal. We outline the physical properties of zero metallicity Population III stars from MESA stellar evolution models through helium-depletion and of BH accretion disks at z$\gtrsim$7. We assume that second-generation non-zero metallicity stars can form at higher multiplicity, so that BH accretion disks may be fed by Roche-lobe overflow from lower-mass companions. We use these near-infrared SB constraints to calculate the number of caustic transits behind lensing clusters that the James Webb Space Telescope and the next generation ground-based telescopes may observe for both Population III stars and their BH accretion disks. Typical caustic magnifications can be $μ$$\simeq$10$^4$-10$^5$, with rise times of hours and decline times of $\lesssim$1 year for cluster transverse velocities of $v_{T}$$\lesssim$1000 km s$^{-1}$. Microlensing by intracluster medium objects can modify transit magnifications, but lengthen visibility times. Depending on BH masses, accretion-disk radii and feeding efficiencies, stellar-mass BH accretion-disk caustic transits could outnumber those from Population III stars. To observe Population III caustic transits directly may require to monitor 3-30 lensing clusters to AB$\lesssim$29 mag over a decade.

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arXiv2018

MUSE spectroscopy and deep observations of a unique compact JWST target, lensing cluster CLIO

We present the results of a VLT MUSE/FORS2 and Spitzer survey of a unique compact lensing cluster CLIO at z = 0.42, discovered through the GAMA survey using spectroscopic redshifts. Compact and massive clusters such as this are understudied, but provide a unique prospective on dark matter distributions and for finding background lensed high-z galaxies. The CLIO cluster was identified for follow up observations due to its almost unique combination of high mass and dark matter halo concentration, as well as having observed lensing arcs from ground based images. Using dual band optical and infra-red imaging from FORS2 and Spitzer, in combination with MUSE optical spectroscopy we identify 89 cluster members and find background sources out to z = 6.49. We describe the physical state of this cluster, finding a strong correlation between environment and galaxy spectral type. Under the assumption of a NFW profile, we measure the total mass of CLIO to be M$_{200} = (4.49 \pm 0.25) \times 10^{14}$ M$_\odot$. We build and present an initial strong-lensing model for this cluster, and measure a relatively low intracluster light (ICL) fraction of 7.21 $\pm$ 1.53% through galaxy profile fitting. Due to its strong potential for lensing background galaxies and its low ICL, the CLIO cluster will be a target for our 110 hour JWST 'Webb Medium-Deep Field' (WMDF) GTO program.

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arXiv2017

Dark-ages Reionization and Galaxy Formation Simulation - X. The small contribution of quasars to reionization

Motivated by recent measurements of the number density of faint AGN at high redshift, we investigate the contribution of quasars to reionization by tracking the growth of central supermassive black holes in an update of the Meraxes semi-analytic model. The model is calibrated against the observed stellar mass function at $z\sim0.6-7$, the black hole mass function at $z\lesssim0.5$, the global ionizing emissivity at $z\sim2-5$ and the Thomson scattering optical depth. The model reproduces a Magorrian relation in agreement with observations at $z<0.5$ and predicts a decreasing black hole mass towards higher redshifts at fixed total stellar mass. With the implementation of an opening angle of 80 deg for quasar radiation, corresponding to an observable fraction of ${\sim}23.4$ per cent due to obscuration by dust, the model is able to reproduce the observed quasar luminosity function at $z\sim0.6-6$. The stellar light from galaxies hosting faint AGN contributes a significant or dominant fraction of the UV flux. At high redshift, the model is consistent with the bright end quasar luminosity function and suggests that the recent faint $z\sim4$ AGN sample compiled by Giallongo et al. (2015) includes a significant fraction of stellar light. Direct application of this luminosity function to the calculation of AGN ionizing emissivity consequently overestimates the number of ionizing photons produced by quasars by a factor of 3 at $z\sim6$. We conclude that quasars are unlikely to make a significant contribution to reionization.

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arXiv2017

Dark-ages reionization and galaxy formation simulation XI: Clustering and halo masses of high redshift galaxies

We investigate the clustering properties of Lyman-break galaxies (LBGs) at $z\sim6$ - $8$. Using the semi-analytical model {\scshape Meraxes} constructed as part of the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation (DRAGONS) project, we predict the angular correlation function (ACF) of LBGs at $z\sim6$ - $8$. Overall, we find that the predicted ACFs are in good agreement with recent measurements at $z\sim 6$ and $z\sim 7.2$ from observations consisting of the Hubble eXtreme Deep Field (XDF), the Hubble Ultra-Deep Field (HUDF) and Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) field. We confirm the dependence of clustering on luminosity, with more massive dark matter haloes hosting brighter galaxies, remains valid at high redshift. The predicted galaxy bias at fixed luminosity is found to increase with redshift, in agreement with observations. We find that LBGs of magnitude $M_{\rm AB(1600)} < -19.4$ at $6\lesssim z \lesssim 8$ reside in dark matter haloes of mean mass $\sim 10^{11.0}$- $10^{11.5} M_{\rm \odot}$, and this dark matter halo mass does not evolve significantly during reionisation.

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arXiv2017

The formation of hot gaseous haloes around galaxies

We use a suite of hydrodynamical cosmological simulations from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project to investigate the formation of hot hydrostatic haloes and their dependence on feedback mechanisms. We find that the appearance of a strong bimodality in the probability density function (PDF) of the ratio of the radiative cooling and dynamical times for halo gas provides a clear signature of the formation of a hot corona. Haloes of total mass $10^{11.5}-10^{12}{\rm{M}}_{\odot}$ develop a hot corona independent of redshift, at least in the interval $z=0-4$ where the simulation has sufficiently good statistics. We analyse the build up of the hot gas mass in the halo, $M_{\rm{hot}}$, as a function of halo mass and redshift and find that while more energetic galactic winds powered by SNe increases $M_{\rm{hot}}$, AGN feedback reduces it by ejecting gas from the halo. We also study the thermal properties of gas accreting onto haloes and measure the fraction of shock-heated gas as a function of redshift and halo mass. We develop analytic and semianalytic approaches to estimate a `critical halo mass', $M_{\rm{crit}}$, for hot halo formation. We find that the mass for which the heating rate produced by accretion shocks equals the radiative cooling rate, reproduces the mass above which haloes develop a significant hot atmosphere. This yields a mass estimate of $M_{\rm{crit}} \approx 10^{11.7}{\rm{M}}_{\odot}$ at $z=0$, which agrees with the simulation results. The value of $M_{\rm{crit}}$ depends more strongly on the cooling rate than on any of the feedback parameters.

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arXiv2017

Dark-ages Reionization and Galaxy Formation Simulation - XIII. AGN quenching of high-redshift star formation in ZF-COSMOS-20115

Massive quiescent galaxies (MQGs) are thought to have formed stars rapidly at early times followed by a long period of quiescence. The recent discovery of a MQG, ZF-COSMOS-20115 at $z\sim4$, only 1.5 Gyr after the big bang, places new constraints on galaxy growth and the role of feedback in early star formation. Spectroscopic follow-up confirmed ZF-COSMOS-20115 as a MQG at $z=3.717$ with an estimated stellar mass of ${\sim}10^{11}\mathrm{M}_\odot$, showing no evidence of recent star formation. We use the Meraxes semi-analytic model to investigate how ZF-COSMOS-20115 analogues build stellar mass, and why they become quiescent. We identify three analogue galaxies with similar properties to ZF-COSMOS-20115. We find that ZF-COSMOS-20115 is likely hosted by a massive halo with virial mass of ${\sim}10^{13}\mathrm{M}_\odot$, having been through significant mergers at early times. These merger events drove intense growth of the nucleus, which later prevented cooling and quenched star formation. ZF-COSMOS-20115 likely remained quiescent at $z<3.7$. We find that the analogues host the most massive black holes in our simulation and were luminous quasars at $z\sim5$, indicating that ZF-COSMOS-20115 and other MQGs may be the descendants of high-redshift quasars. In addition, the model suggests that ZF-COSMOS-20115 formed in a region of intergalactic medium that was reionized early.

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arXiv2017

Dark ages reionization & galaxy formation simulation XII: Bubbles at dawn

Direct detection of regions of ionized hydrogen (HII) has been suggested as a promising probe of cosmic reionization. Observing the redshifted 21-cm signal of hydrogen from the epoch of reionization (EoR) is a key scientific driver behind new-generation, low-frequency radio interferometers. We investigate the feasibility of combining low-frequency observations with the Square Kilometre Array and near infra-red survey data of the Wide-Field Infrared Survey Telescope to detect cosmic reionization by imaging HII bubbles surrounding massive galaxies during the cosmic dawn. While individual bubbles will be too small to be detected, we find that by stacking redshifted 21-cm spectra centred on known galaxies, it will be possible to directly detect the EoR at $z \sim 9-12$, and to place qualitative constraints on the evolution of the spin temperature of the intergalactic medium (IGM) at $z \geq 9$. In particular, given a detection of ionized bubbles using this technique, it is possible to determine if the IGM surrounding them is typically in absorption or emission. Determining the globally-averaged neutral fraction of the IGM using this method will prove more difficult due to degeneracy with the average size of HII regions.

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arXiv2017

Dark-ages reionization and galaxy formation simulation - IX. Economics of reionizing galaxies

Using a series of high-resolution hydrodynamical simulations we show that during the rapid growth of high-redshift (z > 5) galaxies, reserves of molecular gas are consumed over a time-scale of 300Myr, almost independent of feedback scheme. We find that there exists no such simple relation for the total gas fractions of these galaxies, with little correlation between gas fractions and specific star formation rates. The bottleneck or limiting factor in the growth of early galaxies is in converting infalling gas to cold star-forming gas. Thus, we find that the majority of high redshift dwarf galaxies are effectively in recession, with demand (of star formation) never rising to meet supply (of gas), irrespective of the baryonic feedback physics modelled. We conclude that the basic assumption of self-regulation in galaxies - that they can adjust total gas consumption within a Hubble time - does not apply for the dwarf galaxies thought to be responsible for providing most UV photons to reionize the high redshift Universe. We demonstrate how this rapid molecular time-scale improves agreement between semi-analytic model predictions of the early Universe and observed stellar mass functions.

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arXiv2017

Dark-ages Reionization & Galaxy Formation Simulation VIII. Suppressed growth of dark matter halos during the Epoch of Reionization

We investigate how the hydrostatic suppression of baryonic accretion affects the growth rate of dark matter halos during the Epoch of Reionization. By comparing halo properties in a simplistic hydrodynamic simulation in which gas only cools adiabatically, with its collisionless equivalent, we find that halo growth is slowed as hydrostatic forces prevent gas from collapsing. In our simulations, at the high redshifts relevant for reionization (between ${\sim}6$ and ${\sim}11$), halos that host dwarf galaxies ($\lesssim 10^{9} \mathrm{M_\odot}$) can be reduced by up to a factor of 2 in mass due to the hydrostatic pressure of baryons. Consequently, the inclusion of baryonic effects reduces the amplitude of the low mass tail of the halo mass function by factors of 2 to 4. In addition, we find that the fraction of baryons in dark matter halos hosting dwarf galaxies at high redshift never exceeds ${\sim}90\%$ of the cosmic baryon fraction. When implementing baryonic processes, including cooling, star formation, supernova feedback and reionization, the suppression effects become more significant with further reductions of ${\sim}30\%$ to 60\%. Although convergence tests suggest that the suppression may become weaker in higher resolution simulations, this suppressed growth will be important for semi-analytic models of galaxy formation, in which the halo mass inherited from an underlying N-body simulation directly determines galaxy properties. Based on the adiabatic simulation, we provide tables to account for these effects in N-body simulations, and present a modification of the halo mass function along with explanatory analytic calculations.

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arXiv2017

Dark-ages reionization and galaxy-formation simulation - VI. The origins and fate of the highest known redshift galaxy

Using Hubble data, including new grism spectra, Oesch et al. recently identified GN-z11, an $M_\textrm{UV}$=-21.1 galaxy at $z$=11.1 (just 400Myr after the big bang). With an estimated stellar mass of $\sim$10$^9$M$_{\odot}$, this galaxy is surprisingly bright and massive, raising questions as to how such an extreme object could form so early in the Universe. Using \Meraxes{}, a semi-analytic galaxy-formation model developed as part of the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) programme, we investigate the potential formation mechanisms and eventual fate of GN-z11. The volume of our simulation is comparable to that of the discovery observations and possesses two analogue galaxies of similar luminosity to this remarkably bright system. Existing in the two most massive subhaloes at $z$=11.1 ($M_\textrm{vir}$=1.4$\times 10^{11}$M$_{\odot}$ and 6.7$\times 10^{10}$M$_{\odot}$), our model analogues show excellent agreement with all available observationally derived properties of GN-z11. Although they are relatively rare outliers from the full galaxy population at high-$z$, they are no longer the most massive or brightest systems by $z$=5. Furthermore, we find that both objects possess relatively smooth, but extremely rapid mass growth histories with consistently high star formation rates and UV luminosities at $z{>}11$, indicating that their brightness is not a transient, merger-driven feature. Our model results suggest that future wide-field surveys with the \textit{James Webb Space Telescope} may be able to detect the progenitors of GN-z11 analogues out to $z{\sim}$13--14, pushing the frontiers of galaxy-formation observations to the early phases of cosmic reionization and providing a valuable glimpse of the first galaxies to reionize the Universe on large scales.

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arXiv2016

The growth of disks and bulges during hierarchical galaxy formation. II: metallicity, stellar populations and dynamical evolution

We investigate the properties of the stellar populations of model galaxies as a function of galaxy evolutionary history and angular momentum content. We use the new semi-analytic model presented in Tonini et al. (2016). This new model follows the angular momentum evolution of gas and stars, providing the base for a new star formation recipe, and treatment of the effects of mergers that depends on the central galaxy dynamical structure. We find that the new recipes have the effect of boosting the efficiency of the baryonic cycle in producing and recycling metals, as well as preventing minor mergers from diluting the metallicity of bulges and ellipticals. The model reproduces the stellar mass - stellar metallicity relation for galaxies above 1e10 solar masses, including Brightest Cluster Galaxies. Model disks, galaxies dominated by instability-driven components, and merger-driven objects each stem from different evolutionary channels. These model galaxies therefore occupy different loci in the galaxy mass-size relation, which we find to be in accord with the Atlas 3D classification of disk galaxies, fast rotators and slow rotators. We find that the stellar populations' properties depend on the galaxy evolutionary type, with more evolved stellar populations being part of systems that have lost or dissipated more angular momentum during their assembly history.

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arXiv2016

The spatial distribution of neutral hydrogen as traced by low HI mass galaxies

The formation and evolution of galaxies with low neutral atomic hydrogen (HI) masses, M$_{\rm HI}$$<$10$^{8}h^{-2}$M$_{\odot}$, are affected by host dark matter halo mass and photoionisation feedback from the UV background after the end of reionization. We study how the physical processes governing the formation of galaxies with low HI mass are imprinted on the distribution of neutral hydrogen in the Universe using the hierarchical galaxy formation model, GALFORM. We calculate the effect on the correlation function of changing the HI mass detection threshold at redshifts $0 \le z \le 0.5$. We parameterize the clustering as $ξ(r)=(r/r_{0})^{-γ}$ and we find that including galaxies with M$_{\rm HI}$$<$10$^{8}h^{-2}$M$_{\odot}$ increases the clustering amplitude $r_{0}$ and slope $γ$ compared to samples of higher HI masses. This is due to these galaxies with low HI masses typically being hosted by haloes with masses greater than 10$^{12}{h}^{-1}$M$_{\odot}$, and is in contrast to optically selected surveys for which the inclusion of faint, blue galaxies lowers the clustering amplitude. We show the HI mass function for different host dark matter halo masses and galaxy types (central or satellite) to interpret the values of $r_{0}$ and $γ$ of the clustering of HI-selected galaxies. We also predict the contribution of low HI mass galaxies to the 21cm intensity mapping signal. We calculate that a dark matter halo mass resolution better than $\sim$10$^{10}{h}^{-1}$M$_{\odot}$ at redshifts higher than 0.5 is required in order to predict converged 21cm brightness temperature fluctuations.

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arXiv2016

Dark-ages reionization and galaxy formation simulation--VII. The sizes of high-redshift galaxies

We investigate high-redshift galaxy sizes using a semi-analytic model constructed for the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation project. Our fiducial model, including strong feedback from supernovae and photoionization background, accurately reproduces the evolution of the stellar mass function and UV luminosity function. Using this model, we study the size--luminosity relation of galaxies and find that the effective radius scales with UV luminosity as $R_\mathrm{e}\propto L^{0.25}$ at $z{\sim}5$--$9$. We show that recently discovered very luminous galaxies at $z{\sim}7$ (Bowler et al. 2016) and $z{\sim}11$ (Oesch et al. 2016) lie on our predicted size--luminosity relations. We find that a significant fraction of galaxies at $z>8$ will not be resolved by JWST, but GMT will have the ability to resolve all galaxies in haloes above the atomic cooling limit. We show that our fiducial model successfully reproduces the redshift evolution of average galaxy sizes at $z>5$. We also explore galaxy sizes in models without supernova feedback. The no-supernova feedback models produce galaxy sizes that are smaller than observations. We therefore confirm that supernova feedback plays an important role in determining the size--luminosity relation of galaxies and its redshift evolution during reionization.

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arXiv2016

Dark-ages reionization and galaxy formation simulation - III. Modelling galaxy formation and the epoch of reionization

We introduce Meraxes, a new, purpose-built semi-analytic galaxy formation model designed for studying galaxy growth during reionization. Meraxes is the first model of its type to include a temporally and spatially coupled treatment of reionization and is built upon a custom (100 Mpc)$^3$ N-body simulation with high temporal and mass resolution, allowing us to resolve the galaxy and star formation physics relevant to early galaxy formation. Our fiducial model with supernova feedback reproduces the observed optical depth to electron scattering and evolution of the galaxy stellar mass function between $z$=5 and 7, predicting that a broad range of halo masses contribute to reionization. Using a constant escape fraction and global recombination rate, our model is unable to simultaneously match the observed ionizing emissivity at $z{\lesssim}6$. However, the use of an evolving escape fraction of 0.05-0.1 at $z{\sim}6$, increasing towards higher redshift, is able to satisfy these three constraints. We also demonstrate that photoionization suppression of low mass galaxy formation during reionization has only a small effect on the ionization history of the inter-galactic medium. This lack of `self-regulation' arises due to the already efficient quenching of star formation by supernova feedback. It is only in models with gas supply-limited star formation that reionization feedback is effective at regulating galaxy growth. We similarly find that reionization has only a small effect on the stellar mass function, with no observationally detectable imprint at $M_{\rm *}{>}10^{7.5}\,{\rm M_{\odot}}$. However, patchy reionization has significant effects on individual galaxy masses, with variations of factors of 2-3 at $z$=5 that correlate with environment.

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arXiv2016

Dark-ages reionization & galaxy formation simulation V: morphology and statistical signatures of reionization

We use the Dark-ages, Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) framework to investigate the effect of galaxy-formation physics on the morphology and statistics of ionized hydrogen (HII) regions during the Epoch of Reioinization (EoR). DRAGONS self-consistently couples a semi-analytic galaxy-formation model with the inhomogeneous ionizing UV background, and can therefore be used to study the dependence of morphology and statistics of reionization on feedback phenomena of the ionizing source galaxy population. Changes in galaxy-formation physics modify the sizes of HII regions and the amplitude and shape of 21-cm power spectra. Of the galaxy physics investigated, we find that supernova feedback plays the most important role in reionization, with HII regions up to $\approx 20$ per cent smaller and a fractional difference in the amplitude of power spectra of up to $\approx 17$ per cent at fixed ionized fraction in the absence of this feedback. We compare our galaxy-formation-based reionization models with past calculations that assume constant stellar-to-halo mass ratios and find that with the correct choice of minimum halo mass, such models can mimic the predicted reionization morphology. Reionization morphology at fixed neutral fraction is therefore not uniquely determined by the details of galaxy formation, but is sensitive to the mass of the haloes hosting the bulk of the ionizing sources. Simple EoR parametrizations are therefore accurate predictors of reionization statistics. However, a complete understanding of reionization using future 21-cm observations will require interpretation with realistic galaxy-formation models, in combination with other observations.

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arXiv2016

The clustering and halo occupation distribution of Lyman-break galaxies at $z\sim4$

We investigate the clustering of Lyman-break galaxies (LBGs) at $z\sim4$. Using the hierarchical galaxy formation model GALFORM, we predict, for the first time using a semi-analytical model with feedback from active galactic nuclei (AGN), the angular correlation function (ACF) of LBGs and find agreement within $3\,σ$ with new measurements of the ACF from surveys including the Hubble eXtreme Deep Field (XDF) and CANDELS field. Our simulations confirm the conclusion reached using independent models that although the predicted ACFs reproduce the trend of increased clustering with luminosity, the dependence is less strong than observed. We find that for the detection limits of the XDF field central LBGs at $z\sim 4$ predominantly reside in haloes of mass $\sim 10^{11}-10^{12}h^{-1}M_{\rm \odot}$ and that satellites reside in larger haloes of mass $\sim 10^{12}-10^{13}h^{-1}M_{\rm \odot}$. The model predicts fewer bright satellite LBGs at $z\sim4$ than is inferred from measurements of the ACF at small scales. By analysing the halo occupation distribution (HOD) predicted by the model, we find evidence that AGN feedback affects the HOD of central LBGs in massive haloes. This is a new high-redshift test of this important feedback mechanism. We investigate the effect of photometric errors in the observations on the ACF predictions. We find that the observational uncertainty in the galaxy luminosity reduces the clustering amplitude and that this effect increases towards faint galaxies, particularly on small scales. To compare properties of model with observed LBGs this uncertainty must be considered.

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arXiv2016

Dark-ages reionization & galaxy formation simulation IV: UV luminosity functions of high-redshift galaxies

In this paper we present calculations of the UV luminosity function from the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) project, which combines N-body, semi-analytic and semi-numerical modelling designed to study galaxy formation during the Epoch of Reionization. Using galaxy formation physics including supernova feedback, the model naturally reproduces the UV LFs for high-redshift star-forming galaxies from $z{\sim}5$ through to $z{\sim}10$. We investigate the luminosity--star formation rate (SFR) relation, finding that variable SFR histories of galaxies result in a scatter around the median relation of $0.1$--$0.3$ dex depending on UV luminosity. We find close agreement between the model and observationally derived SFR functions. We use our calculated luminosities to investigate the luminosity function below current detection limits, and the ionizing photon budget for reionization. We predict that the slope of the UV LF remains steep below current detection limits and becomes flat at $M_\mathrm{UV}{\gtrsim}{-14}$. We find that $48$ ($17$) per cent of the total UV flux at $z{\sim}6$ ($10$) has been detected above an observational limit of $M_\mathrm{UV}{\sim}{-17}$, and that galaxies fainter than $M_\mathrm{UV}{\sim}{-17}$ are the main source of ionizing photons for reionization. We investigate the luminosity--stellar mass relation, and find a correlation for galaxies with $M_\mathrm{UV}{<}{-14}$ that has the form $M_*{\propto}10^{-0.47M_\mathrm{UV}}$, in good agreement with observations, but which flattens for fainter galaxies. We determine the luminosity--halo mass relation to be $M_\mathrm{vir}{\propto}10^{-0.35M_\mathrm{UV}}$, finding that galaxies with $M_\mathrm{UV}{=}{-20}$ reside in host dark matter haloes of $10^{11.0\pm 0.1}\mathrm{M_\odot}$ at $z{\sim}6$, and that this mass decreases towards high redshift.

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