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The evolution of satellite galaxies is shaped by their constant interaction with the circumgalactic medium surrounding central galaxies, which in turn may be affected by gas and energy ejected from the central supermassive black hole1–6. The nature of such a coupling between black holes and galaxies is, however, much debated7–9and observational evidence remains scarce10,11. Here we report an analysis of archival data on 124,163 satellite galaxies in the potential wells of 29,631 dark matter halos with masses between 1012and 1014solar masses. We find that quenched satellite galaxies are relatively less frequent along the minor axis of their central galaxies. This observation might appear counterintuitive given that black hole activity is expected to eject mass and energy preferentially in the direction of the minor axis of the host galaxy. We show, however, that the observed anisotropic signal results precisely from the ejective nature of black hole feedback in massive halos, as outflows powered by active galactic nuclei clear out the circumgalactic medium, reducing the ram pressure and thus preserving star formation in satellite galaxies. This interpretation is supported by the IllustrisTNG suite of cosmological numerical simulations, even though the model’s sub-grid implementation of black hole feedback is effectively isotropic12.

About ten per cent of ‘massive’ stars (those of more than 1.5 solar masses) have strong, large-scale surface magnetic fields1–3. It has been suggested that merging of main-sequence and pre-main-sequence stars could produce such strong fields4,5, and the predicted fraction of merged massive stars is also about ten per cent6,7. The merger hypothesis is further supported by a lack of magnetic stars in close binaries8,9, which is as expected if mergers produce magnetic stars. Here we report three-dimensional magnetohydrodynamical simulations of the coalescence of two massive stars and follow the evolution of the merged product. Strong magnetic fields are produced in the simulations, and the merged star rejuvenates such that it appears younger and bluer than other coeval stars. This can explain the properties of the magnetic ‘blue straggler’ star τSco in the Upper Scorpius association that has an observationally inferred, apparent age of less than five million years, which is less than half the age of its birth association10. Such massive blue straggler stars seem likely to be progenitors of magnetars, perhaps giving rise to some of the enigmatic fast radio bursts observed11, and their supernovae may be affected by their strong magnetic fields12.

We study the properties of Lyman-$\alpha $emitters (LAEs) and Lyman-break galaxies (LBGs) at $z$$=$3–6 using cosmological SPH simulations. We investigate two simple scenarios for explaining the observed Ly$\alpha $and rest-frame UV luminosity functions (LFs) of LAEs: (i) the “escape fraction” scenario, in which the effectiveescape fraction (including the IGM attenuation) of Ly$\alpha $photons is $f_{{\rm Ly}\alpha}$$\approx$0.1 (0.15) at $z$$=$3 (6), and (ii) the “stochastic” scenario, in which the fraction of LAEs that are turned on at $z$$=$3 (6) is ${C_{\rm stoc}}$$\approx$0.07 (0.2) after correcting for the IGM attenuation. Our comparisons with a number of different observations suggest that the stochastic scenario is preferred over the escape fraction scenario. We find that the mean values of stellar mass, metallicity and black hole mass hosted by LAEs are all smaller in the stochastic scenario than in the escape fraction scenario. In our simulations, the galaxy stellar mass function evolves rapidly, as expected in hierarchical structure formation. However, its evolution is largely compensated by a beginning decline in the specific star formation rate, resulting in little evolution of the rest-frame UV LF from $z$$=$6 to 3. The rest-frame UV LF of both LAEs and LBGs at $z$$=$3 and 6 can be described well by the stochastic scenario provided the extinction is moderate, $E$($B$$-$$V$) $\approx$0.15, for both populations, although our simulation might be overpredicting the number of bright LBGs at $z$$=$6. We also discuss the correlation function and bias of LAEs. The Ly$\alpha $LFs at $z$$=$6 in a field-of-view of 0.2 deg$^2$show a significantly larger scatter owing to cosmic variance relative to that in a $1\ $deg$^2$field, and the scatter seen in the current observational estimates of the Ly$\alpha $LF can be accounted for by cosmic variance.

We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogs generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We introduce a new method for constructing galaxy density fields and for measuring the genus statistics of its isodensity surfaces. It is based on a Delaunay tessellation field estimation (DTFE) technique that allows the definition of a piece-wise continuous density field and the exact computation of the topology of its polygonal isodensity contours, without introducing any free numerical parameter. Besides this new approach, we also employ the traditional approaches of smoothing the galaxy distribution with a Gaussian of fixed width, or by adaptively smoothing with a kernel that encloses a constant number of neighboring galaxies. Our results show that the Delaunay-based method extracts the largest amount of topological information. Unlike the traditional approach for genus statistics, it is able to discriminate between the different theoretical galaxy catalogs analyzed here, both in real space and in redshift space, even though they are based on the same underlying simulation model. In particular, the DTFE approach detects with high confidence a discrepancy of one of the semi-analytic models studied here compared with the SDSS data, while the other models are found to be consistent.

We compare the stellar masses of central and satellite galaxies predicted by three independent semi-analytical models (SAMs) with observational results obtained from a large galaxy group catalog constructed from the Sloan Digital Sky Survey. In particular, we compare the stellar mass functions of centrals and satellites, the relation between total stellar mass and halo mass, and the conditional stellar mass functions, Ph(M *|M h), which specify the average number of galaxies of stellar mass M * that reside in a halo of mass M h. The SAMs only predict the correct stellar masses of central galaxies within a limited mass range and all models fail to reproduce the sharp decline of stellar mass with decreasing halo mass observed at the low mass end. In addition, all models over-predict the number of satellite galaxies by roughly a factor of 2. The predicted stellar mass in satellite galaxies can be made to match the data by assuming that a significant fraction of satellite galaxies are tidally stripped and disrupted, giving rise to a population of intra-cluster stars (ICS) in their host halos. However, the amount of ICS thus predicted is too large compared to observation. This suggests that current galaxy formation models still have serious problems in modeling star formation in low-mass halos.

We employ numerical simulations and simple analytical estimates to argue that dark matter substructures orbiting in the inner regions of the Galaxy can be efficiently destroyed by disk shocking, a dynamical process known to affect globular star clusters. We carry out a set of fiducial high-resolution collisionless simulations in which we adiabatically grow a disk, allowing us to examine the impact of the disk on the substructure abundance. We also track the orbits of dark matter satellites in high-resolution Aquarius simulations and analytically estimate the cumulative halo and disk-shocking effect. Our calculations indicate that the presence of a disk with only 10% of the total Milky Way mass can significantly alter the mass function of substructures in the inner parts of halos. This has important implications especially for the relatively small number of satellites seen within [?]30 kpc of the Milky Way center, where disk shocking is expected to reduce the substructure abundance by a factor of 2 at 109 M and a factor of 3 at 107 M . The most massive subhalos with 1010 M survive even in the presence of the disk. This suggests that there is no inner missing satellite problem and calls into question whether these substructures can produce transient features in disks, like multi-armed spiral patterns. Also, the depletion of dark matter substructures through shocking on the baryonic structures of the disk and central bulge may aggravate the problem to fully account for the observed flux anomalies in gravitational lens systems, and significantly reduces the dark matter annihilation signal expected from nearby substructures in the inner halo.

Clusters, filaments, sheets, and voids are the building blocks of the cosmic web. Forming dark matter halos respond to these different large-scale environments, and this in turn affects the properties of galaxies hosted by the halos. It is therefore important to understand the systematic correlations of halo properties with the morphology of the cosmic web, as this informs both about galaxy formation physics and possible systematics of weak lensing studies. In this study, we present and compare two distinct algorithms for finding cosmic filaments and sheets, a task which is far less well established than the identification of dark matter halos or voids. One method is based on the smoothed dark matter density field and the other uses the halo distributions directly. We apply both techniques to one high-resolution N-body simulation and reconstruct the filamentary/sheet like network of the dark matter density field. We focus on investigating the properties of the dark matter halos inside these structures, in particular, on the directions of their spins and the orientation of their shapes with respect to the directions of the filaments and sheets. We find that both the spin and the major axes of filament halos with masses [?]1013 h -1 M are preferentially aligned with the direction of the filaments. The spins and major axes of halos in sheets tend to lie parallel to the sheets. There is an opposite mass dependence of the alignment strength for the spin (negative) and major (positive) axes, i.e. with increasing halo mass the major axis tends to be more strongly aligned with the direction of the filament, whereas the alignment between halo spin and filament becomes weaker with increasing halo mass. The alignment strength as a function of the distance to the most massive node halo indicates that there is a transit large-scale environment impact: from the two-dimensional collapse phase of the filament to the three-dimensional collapse phase of the cluster/node halo at small separation. Overall, the two algorithms for filament/sheet identification investigated here agree well with each other. The method based on halos alone can be easily adapted for use with observational data sets.

We use a suite of cosmological N-body simulations to study the properties of substructure halos (subhalos) in galaxy-sized cold dark matter halos. We extend prior work on the subject by considering the whole population of subhalos physically associated with the main system. These are defined as subhalos that have at some time in the past been within the virial radius of the halo's main progenitor and that have survived as self-bound entities to z = 0. We find that this population extends beyond three times the virial radius, and contains objects on extreme orbits, including a few with velocities approaching the nominal escape speed from the system. We trace the origin of these unorthodox orbits to the tidal dissociation of bound groups of subhalos, which results in the ejection of some subhalos along tidal streams. Ejected subhalos are primarily low-mass systems, leading to mass-dependent biases in their spatial distribution and kinematics: the lower the subhalo mass at accretion time, the less centrally concentrated and kinematically hotter their descendant population. The bias is strongest among the most massive subhalos, but disappears at the low-mass end: below a certain mass, subhalos behave just like test particles in the potential of the main halo. Overall, our findings imply that subhalos identified within the virial radius represent a rather incomplete census of the substructure physically related to a halo: only about one half of all associated subhalos are found today within the virial radius of a halo, and many relatively isolated halos may have actually been ejected in the past from more massive systems. These results may explain the age dependence of the clustering of low-mass halos reported recently by Gao et al., and has further implications for (1) the interpretation of the structural parameters and assembly histories of halos neighboring massive systems; (2) the existence of low-mass dynamical outliers, such as Leo I and And XII in the Local Group; and (3) the presence of evidence for evolutionary effects, such as tidal truncation or ram-pressure stripping, well outside the traditional virial boundary of a galaxy system.

In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use fast Fourier transforms (FFT) for calculational efficiency. However, because of the required mass assignment onto grid points in this method, the measured power spectrum [?] | df(k) |2[?] obtained with an FFT is not the true power spectrum P(k) , but instead, one that is convolved with a window function |W(k)|2 $| W(&boldsymbol;{k}) |²$ in Fourier space. In a recent paper, Jing proposed an elegant algorithm to deconvolve the sampling effects of the window function and to extract the true power spectrum, and tests using N-body simulations show that this algorithm works very well for the three most commonly used mass assignment functions, i.e., the nearest grid point, the cloud-in-cell, and the triangular-shaped cloud methods. In this paper, rather than trying to deconvolve the sampling effects of the window function, we propose to select a particular function in performing the mass assignment that can minimize these effects. An ideal window function should fulfill the following criteria: (1) compact top-hat-like support in Fourier space to minimize the sampling effects; and (2) compact support in real space to allow a fast and computationally feasible mass assignment onto grids. We find that the scale functions of Daubechies wavelet transformations are good candidates for such a purpose. Our tests using data from the Millennium Simulation show that the true power spectrum of dark matter can be accurately measured at a level better than 2% up to k = 0.7kN, without applying any deconvolution processes. The new scheme is especially valuable for measurements of higher order statistics, e.g., the bispectrum, where it can render the mass assignment effects negligible up to comparatively high k.

The detection of large quantities of dust in z [?] 6 quasars by infrared and radio surveys presents puzzles for the formation and evolution of dust in these early systems. Previously, Li et al. showed that luminous quasars at z[?] 6 can form through hierarchical mergers of gas-rich galaxies, and that these systems are expected to evolve from starburst through quasar phases. Here, we calculate the dust properties of simulated quasars and their progenitors using a three-dimensional Monte Carlo radiative transfer code, ART2 (All-wavelength Radiative Transfer with Adaptive Refinement Tree). ART2 incorporates a radiative equilibrium algorithm which treats dust emission self-consistently, an adaptive grid method which can efficiently cover a large dynamic range in both spatial and density scales, a multiphase model of the interstellar medium which accounts for the observed scaling relations of molecular clouds, and a supernova-origin model for dust which can explain the existence of dust in cosmologically young objects. By applying ART2 to the hydrodynamic simulations of Li et al., we reproduce the observed spectral energy distribution (SED) and inferred dust properties of SDSS J1148+5251, the most distant Sloan quasar. We find that the dust and infrared emission are closely associated with the formation and evolution of the quasar host. The system evolves from a cold to a warm ultraluminous infrared galaxy (ULIRG) owing to heating and feedback from stars and the active galactic nucleus (AGN). Furthermore, the AGN activity has significant implications for the interpretation of observation of the hosts. Our results suggest that vigorous star formation in merging progenitors is necessary to reproduce the observed dust properties of z [?] 6 quasars, supporting a merger-driven origin for luminous quasars at high redshifts and the starburst-to-quasar evolutionary hypothesis.

We investigate the coupled formation and evolution of galaxies and their embedded supermassive black holes using state-of-the-art hydrodynamic simulations of cosmological structure formation. For the first time, we self-consistently follow the dark matter dynamics, radiative gas cooling, and star formation, as well as BH growth and associated feedback processes, starting directly from initial conditions appropriate for the LCDM cosmology. Our modeling of the black hole physics is based on an approach that we have developed in simulations of isolated galaxy mergers. Here we examine (1) the predicted global history of BH mass assembly, (2) the evolution of the local black hole-host mass correlations, and (3) the conditions that allow rapid growth of the first quasars, and the properties of their hosts and descendants today. We find a total BH mass density in good agreement with observational estimates. The BH accretion rate density peaks at lower redshift and evolves more strongly at high redshift than the star formation rate density, but the ratio of black hole to stellar mass density shows only a moderate evolution at low redshifts. We find strong correlations between BH masses and properties of the stellar systems, agreeing well with the measured local MBH-s and MBH- M* relationships, but also suggesting (dependent on the mass range) a weak evolution with redshift in the normalization and the slope. Our simulations also produce massive black holes at high redshift, due to extended periods of exponential growth in regions that collapse early and exhibit strong gas inflows. These first supermassive BH systems, however, are not necessarily the most massive ones today, since they are often overtaken in growth by quasars that form later.

The discovery of luminous quasars at redshift z ~ 6 indicates the presence of supermassive black holes (SMBHs) of mass ~109 M when the universe was less than 1 billion years old. This finding presents several challenges for theoretical models because whether such massive objects can form so early in the LCDM cosmology, the leading theory for cosmic structure formation, is an open question. Furthermore, whether the formation process requires exotic physics such as super-Eddington accretion remains undecided. Here we present the first multiscale simulations that, together with a self-regulated model for the SMBH growth, produce a luminous quasar at z ~ 6.5 in the LCDM paradigm. We follow the hierarchical assembly history of the most massive halo in a ~3 Gpc3 volume and find that this halo of ~8 x 1012 M forming at z ~ 6.5 after several major mergers is able to reproduce a number of observed properties of SDSS J1148+5251, the most distant quasar detected at z = 6.42 (Fan et al. 2003). Moreover, the SMBHs grow through gas accretion below the Eddington limit in a self-regulated manner owing to feedback. We find that the progenitors experience vigorous star formation (up to 104 M yr-1) preceding the major quasar phase such that the stellar mass of the quasar host reaches 1012 M at z ~ 6.5, consistent with observations of significant metal enrichment in SDSS J1148+5251. The merger remnant thus obeys a similar MBH-Mbulge scaling relation observed locally as a consequence of coeval growth and evolution of the SMBH and its host galaxy. Our results provide a viable formation mechanism for z ~ 6 quasars in the standard LCDM cosmology and demonstrate a common, merger-driven origin for the rarest quasars and the fundamental MBH-Mbulge correlation in a hierarchical universe.

We present the results of a numerical study of a galactic wind model and its implications on the properties of damped Lya absorbers (DLAs) using cosmological hydrodynamic simulations. We vary both the wind strength and the internal parameters of the wind model in a series of smoothed particle hydrodynamics (SPH) simulations that include radiative cooling and heating by a UV background, star formation, and feedback from supernovae and galactic winds. To test our simulations, we examine the DLA "rate of incidence" as a function of halo mass, galaxy apparent magnitude, and impact parameter. We find that the statistical distribution of DLAs does not depend on the exact values of internal numerical parameters that control the decoupling of hydrodynamic forces when the gas is ejected from star-forming regions, although the exact spatial distribution of neutral gas may vary for individual halos. The DLA rate of incidence in our simulations at z = 3 is dominated (80%-90%) by the faint galaxies with apparent magnitude AB < 25.5. However, interestingly in a "strong wind" run, the differential distribution of DLA sight lines is peaked at Mhalo = 1012 h-1 M (AB [?] 27), and the mean DLA halo mass is [?]MDLA[?] = 1012.4 h-1 M (AB [?] 26). The DLAs in our simulations are more compact than the present-day disk galaxies, and the impact parameter distribution is very narrow unless we limit the search for the host galaxy to only bright Lyman break galaxies (LBGs). We discuss conflicts between current simulations and observations, and potential problems with hydrodynamic simulations based on the cold dark matter model.

We use numerical simulations to study the kinematic structure of remnants formed from mergers of equal-mass disk galaxies. In particular, we show that remnants of dissipational mergers, which include the radiative cooling of gas, star formation, feedback from supernovae, and the growth of supermassive black holes, are smaller, rounder, have, on average, a larger central velocity dispersion, and show significant rotation compared to remnants of dissipationless mergers. The increased rotation speed of dissipational remnants owes its origin to star formation that occurs in the central regions during the galaxy merger. We have further quantified the anisotropy, three-dimensional shape, minor-axis rotation, and isophotal shape of each merger remnant, finding that dissipational remnants are more isotropic, closer to oblate, have the majority of their rotation along their major axis, and are more disky than dissipationless remnants. Individual remnants display a wide variety of kinematic properties. A large fraction of the dissipational remnants are oblate isotropic rotators. Many dissipational remnants, and all of the dissipationless ones, are slowly rotating and anisotropic. The remnants of gas-rich major mergers can well reproduce the observed distribution of projected ellipticities, rotation parameter (V/s)*, kinematic misalignments, Ps, and isophotal shapes. The dissipationless remnants are a poor match to this data. We also investigate the properties of merger remnants as a function of initial disk gas fraction, orbital angular momentum, and the mass of the progenitor galaxies. Our results support the merger hypothesis for the origin of low-luminosity elliptical galaxies provided that the progenitor disks are sufficiently gas-rich, however our remnants are a poor match to the bright ellipticals that are slowly rotating and uniformly boxy.

The hierarchical nature of the LCDM cosmology poses serious difficulties for the formation of disk galaxies. To help resolve these issues, we describe a new, merger-driven scenario for the cosmological formation of disk galaxies at high redshifts that supplements the standard dissipational collapse model. In this picture, large gaseous disks may be produced from high angular momentum mergers of systems that are gas dominated, i.e., Mgas/(Mgas + M[?]) [?] 0.5 at the height of the merger. Pressurization from the multiphase ISM prevents the complete conversion of gas into stars during the merger, and if enough gas remains to form a disk, the remnant eventually resembles a disk galaxy. We perform numerical simulations of galaxy mergers to study how supernovae feedback strength, black hole feedback, progenitor gas fraction, merger mass ratio, and orbital geometry impact the formation of remnant disks. We find that disks can build angular momentum through mergers and the degree of rotational support of the baryons in the remnant is primarily related to feedback processes associated with star formation. Disk-dominated remnants are restricted to form in mergers that are gas dominated at the time of final coalescence. We also show that the formation of rotationally supported stellar systems in mergers is not restricted to idealized orbits, and both gas-rich major and minor mergers can produce disk-dominated stellar remnants. We suggest that the hierarchical nature of the LCDM cosmology and the physics of the ISM may act together to form spiral galaxies by building the angular momentum of disks through gas-dominated mergers at high redshifts.

We examine the evolution of the black hole mass-stellar velocity dispersion (MBH-s) relation over cosmic time, using simulations of galaxy mergers that include feedback from supermassive black hole growth. For a range in redshifts z = 0-6, we modify the virial mass, gas fraction, interstellar medium equation of state, surface mass density, and concentration of dark matter halos of the merger progenitors to match those expected at various cosmic times. We find that the slope of the MBH-s relation is insensitive to the redshift-dependent properties of merger progenitors and should be roughly constant at redshifts z = 0-6. For the same feedback efficiency that reproduces the observed amplitude of the MBH-s relation at z = 0, there is a weak redshift dependence to the normalization, corresponding to an evolution in the Faber-Jackson relation, which results from an increasing velocity dispersion for a given galactic stellar mass. We develop a formalism to connect redshift evolution in the MBH-s relation to the scatter in the local relation at z = 0. For an assumed model for the accumulation of black holes with different masses over cosmic time, we show that the scatter in the local relation places severe constraints on the redshift evolution of both the normalization and slope of the MBH-s relation. Furthermore, we demonstrate that the cosmic downsizing of the black hole population introduces a black hole mass-dependent dispersion in the MBH-s relation and that the skewness of the distribution about the locally observed MBH-s relation is sensitive to redshift evolution in the normalization and slope. In agreement with existing constraints, our simulations imply that hierarchical structure formation should produce the relation with small intrinsic scatter, as the physical origin of the MBH-s enjoys a remarkable resiliency to the redshift-dependent properties of merger progenitors.

We examine the fundamental scaling relations of elliptical galaxies formed through mergers. Using hundreds of simulations to judge the impact of progenitor galaxy properties on the properties of merger remnants, we find that gas dissipation provides an important contribution to tilt in the fundamental plane (FP) relation. Dissipationless mergers of disks produce remnants that occupy a plane similar to that delineated by the virial relation. As the gas content of progenitor disk galaxies is increased, the tilt of the resulting FP relation increases and the slope of the Re-M[?] relation steepens. For gas fractions fgas > 30%, the simulated FP scalings (Re [?] s1.55Iimg1.gif) approach those observed in the K band (Re [?] s1.53Iimg2.gif). The dissipationless merging of spheroidal galaxies and the remerging of disk galaxy remnants roughly maintain the tilt of the FP occupied by the progenitor ellipticals., Dry merging of spheroidal systems at redshifts z < 1 is then expected to maintain the stellar-mass FP relations imprinted by gas-rich merging during the epoch of rapid spheroid and supermassive black hole growth at redshifts z [?] 1-3. We estimate that [?]40%-100% of the FP tilt induced by structural properties, as opposed to stellar population effects, owes to trends in the central total-to-stellar mass ratio Mtotal/M[?] produced by dissipation. Gas cooling allows for an increase in central stellar phase-space density relative to dissipationless mergers, thereby decreasing the central Mtotal/M[?]. Lower mass systems obtain greater phase-space densities than higher mass systems, producing a galaxy mass-dependent central Mtotal/M[?] and a corresponding tilt in the FP. We account for these trends in the importance of dissipation with galaxy mass in terms of the inefficient cooling of collisionally heated gas in massive halos and dynamically varying gas consumption timescales in smaller systems.

Using a new model for quasar lifetimes and light curves derived from numerical simulations of galaxy mergers that incorporate black hole growth, we study the faint-end slope of the quasar luminosity function (QLF) and its evolution with redshift. Our model motivates a new interpretation of the QLF in which the bright end consists of quasars radiating near their peak luminosities but the faint end is mostly made up of brighter peak luminosity quasars seen in less luminous phases of evolution. The faint-end slope of the QLF is then set by the behavior of the lifetime (light curve) of quasars with peak luminosities near the observed break when they are in less luminous stages of evolution. We determine the faint-end slope of the QLF from the quasar lifetime, based on a set of simulations that encompass a wide range of host galaxy, merger, black hole, and interstellar gas properties. Brighter peak luminosity (higher black hole mass) systems undergo more violent evolution, and gas is expelled and heated more rapidly in the final stages of quasar evolution, resulting in a flatter faint-end slope (as these objects fall below the observed break in the QLF more rapidly). Therefore, as the QLF break luminosity moves to higher luminosities with increasing redshift, implying a larger typical quasar peak luminosity, the faint-end QLF slope flattens. From our model, we predict the evolution of the faint-end slope of the QLF and find good agreement with observations. Although black holes grow in an antihierarchical manner (with lower mass black holes formed primarily at lower redshifts), in our picture the observed change in slope and differential or "luminosity-dependent density evolution" in the QLF is determined by the nontrivial, luminosity-dependent quasar lifetime and physics of quasar feedback, and not by changes in the shape of the underlying peak luminosity or active black hole mass distributions.

We consider implications of our new model of quasar lifetimes and light curves for the quasar luminosity function (LF) at different frequencies and redshifts. In our picture, quasars evolve rapidly and the lifetime depends on both their instantaneous and peak luminosities. The bright end of the LF traces the peak intrinsic quasar activity, but the faint end consists of quasars that are either undergoing exponential growth to much larger masses and luminosities or are in sub-Eddington quiescent states going into or coming out of a period of peak activity. The "break" in the observed LF corresponds directly to the maximum in the intrinsic distribution of peak luminosities, which falls off at both brighter and fainter luminosities. We study this model using simulations of galaxy mergers that successfully reproduce a wide range of observed quasar phenomena, including the observed column density distribution. By combining quasar lifetimes and the distribution of maximum quasar luminosities determined from the observed hard X-ray LF with the corresponding luminosity and host system-dependent column densities, we produce the expected soft X-ray and B-band LFs. Our predictions agree exceptionally well with the observed LFs at all observed luminosities over the redshift range considered (z [?] 1) without invoking any ad hoc assumptions about an obscured population of sources. Our results also suggest that observed correlations in hard X-ray samples between the obscured fraction of quasars and luminosity can be explained in the context of our model by the expulsion of surrounding gas due to heating from accretion feedback energy as a quasar nears its peak luminosity and final black hole mass.

Based on numerical simulations of gas-rich galaxy mergers, we discuss a model in which quasar activity is tied to the self-regulated growth of supermassive black holes in galaxies. The nuclear inflow of gas attending a galaxy collision triggers a starburst and feeds black hole growth, but for most of the duration of the starburst, the black hole is "buried," being heavily obscured by surrounding gas and dust, limiting the visibility of the quasar, especially at optical and ultraviolet wavelengths. As the black hole grows, feedback energy from accretion heats the gas and eventually expels it in a powerful wind, leaving behind a "dead quasar." Between the buried and dead phases, there is a window in time during which the galaxy would be seen as a luminous quasar. Because the black hole mass, radiative output, and distribution of obscuring gas and dust all evolve strongly with time, the duration of this phase of observable quasar activity depends on both the waveband and imposed luminosity threshold. We determine the observed and intrinsic lifetimes as a function of luminosity and frequency, and calculate observable lifetimes ~10 Myr for bright quasars in the optical B band, in good agreement with empirical estimates and much smaller than our estimated black hole growth timescales ~100 Myr, naturally producing a substantial population of buried quasars. However, the observed and intrinsic energy outputs converge in the IR and hard X-ray bands as attenuation becomes weaker and chances of observation greatly increase. We also obtain the distribution of column densities along sight lines in which the quasar is seen above a given luminosity, and find that our result agrees remarkably well with observed estimates of the column density distribution from the SDSS for the appropriate luminosity thresholds. Our model reproduces a wide range of quasar phenomena, including observed quasar lifetimes, intrinsic lifetimes, column density distributions, and differences between optical and X-ray samples, having properties consistent with observations across more than 5 orders of magnitude in bolometric luminosity from 109 to 1014 L (-17 [?] MB [?] -30).

We propose a new interpretation of the quasar luminosity function (LF) derived from physically motivated models of quasar lifetimes and light curves. In our picture, quasars evolve rapidly, and their lifetime depends on both their instantaneous and peak luminosities. We study this model using simulations of galaxy mergers that successfully reproduce a wide range of observed quasar phenomena. With lifetimes inferred from the simulations, we deconvolve the observed quasar LF from the distribution of peak luminosities and show that they differ qualitatively, unlike the simple models of quasar lifetimes used previously. We find that the bright end of the LF traces the intrinsic peak quasar activity but that the faint end consists of quasars that are either undergoing exponential growth to much larger masses and higher luminosities, or are in sub-Eddington quiescent states going into or coming out of a period of peak activity. The "break" in the LF directly corresponds to the maximum in the intrinsic distribution of peak luminosities, which falls off at both brighter and fainter luminosities. Our interpretation of the quasar LF provides a physical basis for the nature and slope of the faint-end distribution, as well as the location of the break luminosity.

Recent observations have revealed a population of red massive galaxies at high redshift that are challenging to explain in terms of hierarchical galaxy formation models. We analyze this "massive galaxy problem" with two different types of hydrodynamic simulations--Eulerian total variation diminishing (TVD) and smoothed particle hydrodynamics (SPH)--of a concordance L cold dark matter (LCDM) universe. We consider two separate but connected aspects of the problem posed by these extremely red objects (EROs): (1) the mass scale of these galaxies and (2) their red colors. We perform spectrophotometric analyses of simulated galaxies in B, z, R, I, Js, Ks, and K filters and compare their near-infrared (near-IR) properties with observations at redshift z = 1-3. We find that the simulated galaxies brighter than the magnitude limit of KVega = 20 mag have stellar masses M[?] [?] 1011 h-1 M and a number density of a few times 10-4 h3 Mpc-3 at z ~ 2, in good agreement with the observed number density in the K20 survey. Therefore, our hydrodynamic simulations do not exhibit the mass-scale problem. The answer to the "redness problem" is less clear because of our poor knowledge of the amount of dust extinction in EROs and the uncertain fraction of star-forming EROs. However, our simulations can account for the observed comoving number density of ~1 x 10-4 Mpc-3 at z = 1-2 if we assume a uniform extinction of E(B - V) = 0.4 for the entire population of simulated galaxies. Upcoming observations of the thermal emission of dust in 24 mm by the Spitzer Space Telescope will help to better estimate the dust content of EROs at z = 1-3 and thus to further constrain the star formation history of the universe and theoretical models of galaxy formation.

The nature of the interaction between galaxies and the intergalactic medium (IGM) is one of the most fundamental problems in astrophysics. The accretion of gas onto galaxies provides fuel for star formation, while galactic winds transform the nearby IGM in a number of ways. One exciting technique to study this gas is through the imaging of hydrogen Lya emission. We use cosmological simulations to study the Lya signals expected from the growth of cosmic structure from z = 0-5. We show that if dust absorption is negligible, recombinations following the absorption of stellar ionizing photons dominate the total Lya photon production rate. However, galaxies are also surrounded by "Lya coronae" of diffuse IGM gas. These coronae are composed of a combination of accreting gas and material ejected from the central galaxy by winds. The Lya emission from this phase is powered by a combination of gravitational processes and the photoionizing background. While the former dominates at z ~ 0, collisional excitation following photoheating may well dominate the total emission at higher redshifts. The central regions of these systems are dense enough to shield themselves from the metagalactic ionizing background; unfortunately, in this regime our simulations are no longer reliable. We therefore consider several scenarios for the emission from the central cores, including one in which self-shielded gas does not emit at all. We show that the combination of star formation and cooling IGM gas can explain most of the observed "Lya blobs" at z ~ 3, with the important exception of the largest sources. On the other hand, except under the most optimistic assumptions, cooling IGM gas cannot explain the observations on its own.

We study the properties of galaxies at redshift z = 2 in a L cold dark matter (LCDM) universe, using two different types of hydrodynamic simulation methods--Eulerian total variation diminishing (TVD) and smoothed particle hydrodynamics (SPH)--and a spectrophotometric analysis in the Un, G, R filter set. The simulated galaxies at z = 2 satisfy the color-selection criteria proposed by Adelberger et al. and Steidel et al. when we assume Calzetti extinction with E(B - V) = 0.15. We find that the number density of simulated galaxies brighter than R < 25.5 at z = 2 is about 2 x 10-2 h3 Mpc-3 for E(B - V) = 0.15 in our most representative run, roughly 1 order of magnitude larger than that of Lyman break galaxies at z = 3. The most massive galaxies at z = 2 have stellar masses of [?]1011 M, and their observed-frame G-R colors lie in the range 0.0 < G - R < 1.0. They typically have been continuously forming stars at a rate exceeding 30 M yr-1 over a few gigayears from z = 10 to z = 2, although the TVD simulation indicates a more sporadic star formation history than the SPH simulations. On the order of half of their stellar mass was already assembled by z ~ 4. The bluest galaxies with colors -0.2 < G - R < 0.0 at z = 2 are somewhat less massive, with Mstar < 1011 h-1 M, and lack a prominent old stellar population. On the other hand, the reddest massive galaxies at z = 2 with G - R [?] 1.0 and Mstar > 1010 h-1 M completed the build-up of their stellar mass by z ~ 3. Interestingly, our study indicates that the majority of the most massive galaxies at z = 2 should be detectable at rest-frame ultraviolet wavelengths, contrary to some recent claims made on the basis of near-infrared studies of galaxies at the same epoch, provided the median extinction is less than E(B - V) < 0.3 as indicated by surveys of Lyman break galaxies at z = 3. However, our results also suggest that the fraction of stellar mass contained in galaxies that pass the color-selection criteria used by Steidel et al. (2004) could be as low as 50% of the total stellar mass in the universe at z = 2. Our simulations imply that the missing stellar mass is contained in fainter (R > 25.5) and intrinsically redder galaxies. The bright end of the rest-frame V-band luminosity function of z = 2 galaxies can be characterized by a Schechter function with parameters (Ph*, Mimg1.gif, a) = (1.8 x 10-3, - 23.4, - 1.85), while the TVD simulation suggests a flatter faint-end slope of a ~ -1.2. A comparison with z = 3 shows that the rest-frame V-band luminosity function has brightened by about 0.5 mag from z = 3 to z = 2, without a significant change in the shape. Our results do not imply that hierarchical galaxy formation fails to account for the massive galaxies at z [?] 1.

We study the evolution of the global stellar mass density in a L cold dark matter (LCDM) universe using two different types of hydrodynamic simulations (Eulerian total variation diminishing and smoothed particle hydrodynamics) and the analytical model of Hernquist & Springel. We find that the theoretical calculations all predict both a higher stellar mass density at z ~ 3 than indicated by current observations and that the peak of the cosmic star formation rate history should lie at z [?] 5. Such a star formation history implies that as much as (70%, 30%) of the total stellar mass density today must already have formed by z = (1, 3). Our results suggest that current observations at z ~ 3 are missing as much as 50% of the total stellar mass density in the universe, perhaps because of an inadequate allowance for dust obscuration in star-forming galaxies, limited sample sizes, or cosmic variance. We also compare our results with some of the updated semianalytic models of galaxy formation.

We study the gas metallicity of quasar hosts using cosmological hydrodynamic simulations of the LCDM model. Galaxy formation in the simulations is coupled with a prescription for black hole activity, enabling us to study the evolution of the metal enrichment in quasar hosts and hence explore the relationship between star/spheroid formation and black hole growth/activity. In order to assess effects of numerical resolution, we compare simulations with different particle numbers and box sizes. We find a steep radial metallicity gradient in quasar host galaxies, with gas metallicities close to solar values in the outer parts but becoming supersolar in the center. The hosts of the rare bright quasars at z ~ 5-6 have star formation rates of several hundred M yr-1 and halo masses of order ~1012 M. Already at these redshifts they have supersolar (Z/Z ~ 2-3) central metallicities, with a mild dependence of metallicity on luminosity, consistent with observed trends. The mean value of metallicity is sensitive to the assumed quasar lifetime, providing a useful new probe of this parameter. We find that lifetimes from 107 to 4 x 107 yr are favored by comparison with observational data. In both the models and observations, the rate of evolution of the mean quasar metallicity as a function of redshift is generally flat out to z ~ 4-5. Beyond the observed redshift range and out to redshift z = 6-8, we predict a slow decline of the mean central metallicity toward solar and slightly subsolar values (Z/Z ~ 0.4-1) as we approach the epoch of the first significant star formation activity.

We use a high-resolution cosmological simulation that includes hydrodynamics, multiphase star formation, and galactic winds to predict the distribution of metal line emission at z ~ 0 from the intergalactic medium (IGM). We focus on two ultraviolet doublet transitions, O VI ll1032, 1038 and C IV ll1548, 1551. Emission from filaments with moderate overdensities is orders of magnitude smaller than the background, but isolated emission from enriched dense regions with T ~ 105-105.5 K and characteristic size ~50-100 kpc can be detected above the background. We show that the emission from these regions is substantially greater when we use the metallicities predicted by the simulation (which includes enrichment through galactic winds) than when we assume a uniform IGM metallicity. Luminous regions correspond to volumes that have recently been influenced by galactic winds. We also show that the line emission is clustered on scales ~1 h-1 Mpc. We argue that although these transitions are not effective tracers of the warm-hot intergalactic medium, they do provide a route to study the chemical enrichment of the IGM and the physics of galactic winds.

We describe hydrodynamic simulations of galaxy formation in a L cold dark matter cosmology, performed using a subresolution model for star formation and feedback in a multiphase interstellar medium (ISM). In particular, we demonstrate the formation of a well-resolved disk galaxy. The surface brightness profile of the galaxy is exponential, with a B-band central surface brightness of 21.0 mag arcsec-2 and a scale length of Rd = 2.0 h-1 kpc. We find no evidence for a significant bulge component. The simulated galaxy falls within the I-band Tully-Fisher relation, with an absolute magnitude of I = -21.2 and a peak stellar rotation velocity of Vrot = 121.3 km s-1. While the total specific angular momentum of the stars in the galaxy agrees with observations, the angular momentum in the inner regions appears to be low by a factor of ~2. The star formation rate of the galaxy peaks at ~7 M yr-1 between redshifts z = 2 and 4, with the mean stellar age decreasing from ~10 Gyr in the outer regions of the disk to ~7.5 Gyr in the center, indicating that the disk did not simply form inside-out. The stars exhibit a metallicity gradient from 0.7 Z at the edge of the disk to 1.3 Z in the center. Using a suite of idealized galaxy formation simulations with different models for the ISM, we show that the effective pressure support provided by star formation and feedback in our multiphase model is instrumental in allowing the formation of large, stable disk galaxies. If ISM gas is instead modeled with an isothermal equation of state, or if star formation is suppressed entirely, growing gaseous disks quickly violate the Toomre stability criterion and undergo catastrophic fragmentation.

We study high-redshift structure formation and reionization in a LCDM universe under the assumption that the spectral power index of primordial density fluctuations is a function of length scale. We adopt a particular formulation of the "running" spectral index (RSI) model as suggested by the combined analysis of the recent Wilkinson Microwave Anisotropy Probe (WMAP) data and two other large-scale structure observations. We carry out high-resolution cosmological simulations and use them to study the formation of primordial gas clouds where the first stars are likely to form. While early structure forms hierarchically in the RSI model, quite similar to the standard power-law LCDM model, the reduced power on small scales causes a considerable delay in the formation epoch of low-mass (~106 M) "minihalos" compared with the LCDM model. The abundance of primordial star-forming gas clouds in such halos also differs by more than an order of magnitude at z > 15 between the two models. The extremely small number of gas clouds in the RSI model indicates that reionization is initiated later than z < 15, generally resulting in a smaller total Thomson optical depth than in the LCDM model. By carrying out radiative transfer calculations, we also study reionization by stellar populations formed in galaxies. We show that, in order to reionize the universe by z ~ 7, the escape fraction of ultraviolet photons from galaxies in the RSI model must be as high as 0.6 throughout the redshift range 5 < z < 18 for a stellar population similar to that of the local universe. Even with a top-heavy initial mass function representing an early population of massive stars and/or an extraordinarily high photon emission rate from galaxies, the total optical depth can only be as large as te ~ 0.1 for reasonable models of early star formation. The RSI model is thus in conflict with the large Thomson optical depth inferred by the WMAP satellite.

The observed properties of supermassive black holes suggest a fundamental link between their assembly and the formation of their host spheroids. We model the growth and activity of black holes in galaxies using L cold dark matter cosmological hydrodynamic simulations by following the evolution of the baryonic mass component in galaxy potential wells. We find that the observed steep relation between black hole mass and spheroid velocity dispersion, MBH [?] s4, is reproduced if the gas mass in bulges is linearly proportional to the black hole mass. To a good approximation, this is equivalent to assuming the conversion of a fixed fraction of gas mass into black hole mass. In this model, star formation and supernova feedback in the gas are sufficient for regulating and limiting the growth of the central black hole and of its gas supply. Black hole growth saturates because of the competition with star formation and, in particular, feedback, both of which determine the gas fraction available for accretion. Unless other processes also operate, we predict that the MBH-s relation is not set in primordial structures but is fully established at low redshifts, z [?] 2, and is shallower at earlier times. Once this relation is established, we find that central black hole masses are related to their dark matter halos simply via MBH [?][?] Mimg1.gif. We assume that galaxies undergo a quasar phase with a typical lifetime, tQ ~ 2 x 107 yr, the only free parameter of the model, and show that star formation-regulated depletion of gas in spheroids is sufficient to explain, for the most part, the decrease of the quasar population at redshift z < 3 in the optical blue band. However, with the simplest assumption of a redshift-independent quasar lifetime, the model slightly overpredicts optical quasar numbers at high redshifts, although it yields the observed evolution of number density of X-ray-faint quasars over the whole redshift range 1 < z < 6. Finally, we find that the majority of black hole mass is assembled in galaxies by z ~ 3 and that the black hole accretion rate density peaks in rough correspondence to the star formation rate density at z ~ 4-5.

Structure formation in the intergalactic medium (IGM) produces large-scale, collisionless shock waves, in which electrons can be accelerated to highly relativistic energies. Such electrons can Compton-scatter cosmic microwave background photons up to g-ray energies. We study the radiation emitted in this process using a hydrodynamic cosmological simulation of a LCDM universe. The resulting radiation, extending beyond TeV energies, has roughly constant energy flux per decade in photon energy, in agreement with the predictions of Loeb & Waxman. Assuming that a fraction xe = 0.05 of the shock thermal energy is transferred to the population of accelerated relativistic electrons, as inferred from collisionless nonrelativistic shocks in the interstellar medium, we find that the energy flux of this radiation, [?]2(dJ/d[?]) [?] 50-160 eV cm-2 s-1 sr-1, constitutes ~10% of the extragalactic g-ray background flux. The associated g-ray point sources are too faint to account for the ~60 unidentified EGRET g-ray sources, but GLAST should detect and resolve several g-ray sources associated with large-scale IGM structures for xe [?] 0.03 and many more sources for larger xe. The intergalactic origin of the shock-induced radiation can be verified through a cross-correlation with, e.g., the galaxy distribution that traces the same structure. Its shock origin may be tested by cross-correlating its properties with radio synchrotron radiation, emitted as the same accelerated electrons gyrate in postshock magnetic fields. We predict that GLAST and Cerenkov telescopes such as MAGIC, VERITAS, and HESS should resolve g-rays from nearby (redshifts z [?] 0.01) rich galaxy clusters, perhaps in the form of a ~5-10 Mpc diameter ringlike emission tracing the cluster accretion shock, with luminous peaks where the ring intersects galaxy filaments detectable even at z [?] 0.025.

We use a cosmological hydrodynamic simulation of a cold dark matter universe to investigate theoretically the relationship between high-redshift galaxies and the Lya forest at redshift z = 3. Galaxies in the simulation are surrounded by halos of hot gas, which nevertheless contain enough neutral hydrogen to cause a Lya flux decrement, its strength increasing with galaxy mass. A comparison with recent observational data by Adelberger et al. on the Lya forest around galaxies reveals that actual galaxies may have systematically less Lya absorption within 1 Mpc of them than our simulated galaxies. In order to investigate this possibility, we add several simple prescriptions for galaxy feedback on the intergalactic medium (IGM) to the evolved simulation. These include the effect of photoionizing background radiation coming from galactic sources, galactic winds whose only effect is to deposit thermal energy into the IGM, and another, kinetic model for winds, which are assumed to evacuate cavities in the IGM around galaxies. We find that only the latter is able to produce a large effect, enough to match the tentative observational data, given the energy available from star formation in the simulated galaxies. Another intriguing possibility is that a selection effect is responsible, so that galaxies with low Lya absorption are preferentially included in the sample. This is also viable but predicts galaxy properties (including clustering) that are very different from the other scenarios.

We present results on the thermal and kinetic Sunyaev-Zeldovich (SZ) effects from a sequence of high-resolution hydrodynamic simulations of structure formation, including cooling, feedback, and metal injection. These simulations represent a self-consistent thermal model that incorporates ideas from the "preheating" scenario while preserving good agreement with the low-density intergalactic medium at z ~ 3 probed by the Lya forest. Four simulations were performed, at two different resolutions with and without radiative effects and star formation. The long-wavelength modes in each simulation were the same, so we can compare the results on an object-by-object basis. We demonstrate that our simulations are converged to the subarcminute level. The effect of the additional physics is to suppress the mean Comptonization parameter by 20% and to suppress the angular power spectrum of fluctuations by just under a factor of 2 in this model, while leaving the source counts and properties relatively unchanged. We quantify how non-Gaussianity in the SZ maps increases the sample variance over the standard result for Gaussian fluctuations. We identify a large scatter in the Y-M relation that will be important in searches for clusters using the SZ effect(s).

We present some highlights of our multi-wavelength study, which involves optical broad- and narrow-band imaging, long-slit spectroscopy, high-resolution HI and CO observations, of the interacting system Arp 245. This object consists of the galaxies NGC 2992 and NGC 2993. Based on a numerical model of the collision, which was computed with a Tree-SPH code, we derive that Arp 245 is observed at an early stage of the interaction, about 100 Myr after perigalactic on, though at a time when tidal tails have already developed. At the tip of the NGC 2992 tail we find a gas reservoir of about 109Modot, or about 60% of the HI which is seen towards NGC 2992, which coincides with what appears to be a star-forming tidal dwarf galaxy, A245N. The TDGA245N exhibits properties ranging between those of dwarf irregular galaxies (structural parameters, gas content, star formation rate) and those of spiral disks (metallicity, star formation efficiency, stellar population). We speculate what the required conditions are to form a TDG, and how they can be distinguished from field dwarf irregulars.

We have performed a sequence of high-resolution hydrodynamic simulations of structure formation in a ?CDM model to study the thermal and kinetic Sunyaev-Zeldovich (SZ) effects. Including only adiabatic gas physics, we demonstrate that our simulations for the thermal effect are converged down to subarcminute scales. In this model, the angular power spectrum of cosmic microwave background (CMB) anisotropies induced by the thermal effect peaks at l104, and reaches an amplitude just below current observational upper limits. Fluctuations due to the kinetic effect are a factor of 30 lower in power and peak at slightly smaller angular scales. We identify individual SZ sources and compute their counts as a function of source strength and angular size. We present a preliminary investigation of the consequences of an early epoch of energy injection, which tends to suppress power on small angular scales, while giving rise to additional power on large scales from the reheated intergalactic matter (IGM) at high redshift.

We study the topology of the Virgo N‐body simulations and compare it with the 1.2‐Jy redshift survey of IRASgalaxies by means of the genus statistic. Four high‐resolution simulations of variants of the CDM cosmology are considered: a flat standard model (SCDM), a variant of it with higher large‐scale power (τCDM), and two low‐density universes, one open (OCDM, Ω0= 0.3) and one flat (ΛCDM, Ω0= 0.3, Λ  0.7). In all cases, the initial fluctuation amplitudes are chosen so that the simulations approximately reproduce the observed abundance of rich clusters of galaxies at the present day. The fully sampled N‐body simulations are examined down to strongly non‐linear scales, both with spatially fixed smoothing and with an adaptive smoothing technique. While the τCDM, ΛCDM and OCDM simulations have very similar genus statistics in the regime accessible to fixed smoothing, they can be separated with adaptive smoothing at small mass scales. In order to compare the N‐body models with the 1.2‐Jy survey, we extract large ensembles of mock catalogues from the simulations. These mock surveys are used to test for various systematic effects in the genus analysis and to establish the distribution of errors of the genus curve. We find that a simple multivariate analysis of the genus measurements is compromised both by non‐Gaussian distributed errors and by noise that dominates the covariance matrix. We therefore introduce a principal components analysis of the genus curve. With a likelihood ratio test we find that the 1.2‐Jy data favour the ΛCDM, τCDM and OCDM models compared with SCDM. When genus measurements for different smoothing scales are combined, the SCDM model can be excluded at a 99 per cent confidence level, while the other three models fit the 1.2‐Jy data well. These results are unlikely to be significantly modified if galaxies are biased tracers of the mass, provided that biasing preserves a monotonic relation between galaxy density and mass density.

A new method is presented to obtain a non‐parametric maximum likelihood estimate of the luminosity function and the selection function of a flux‐limited redshift survey. The method parametrizes the selection function as a series of stepwise power laws and allows possible evolution of the luminosity function. We also propose a new technique to estimate the rate of evolution of the luminosity function. This is based on a minimization of the observed large‐scale power with respect to the evolutionary model. We use an ensemble of mock surveys extracted from an N‐body simulation to verify the power of this method. We apply our estimators to the 1.2‐Jy survey of IRASgalaxies. We find a far‐infrared luminosity function in good agreement with previously published results and evidence for rather strong evolution. If the comoving number density of IRASgalaxies is assumed to scale ∝ (1 + z)P, we estimate P= 4.3 ± 1.4.