Major Merger Rate Research Articles

Merging History of Massive Galaxies at 3 < z < 6

The observational data of high redshift galaxies become increasingly abundant, especially since the operation of the James Webb Space Telescope, which allows us to verify and optimize the galaxy formation model at high redshifts. In this work, we investigate the merging history of massive galaxies at 3 < z < 6 using a well-developed semi-analytic galaxy formation catalog. We find that the major merger rate increases with redshift up to 3 and then flattens. The fraction of wet mergers, during which the sum of the cold gas mass is higher than the sum of the stellar mass in two merging galaxies, also increases from ∼34% at z = 0 to 96% at z = 3. Interestingly, almost all major mergers are wet at z > 3. This can be attributed to the high fraction (>50%) of cold gas at z > 3. In addition, we study some special systems of massive merging galaxies at 3 < z < 6, including the massive gas-rich major merging systems and extreme dense proto-clusters, and investigate the supermassive black hole–dark matter halo mass relation and dual active galactic nuclei. We find that the galaxy formation model reproduces the incidence of those observed massive galaxies, but fails to reproduce the relation between the supermassive black hole mass and the dark matter halo mass at z ∼ 6. The latter requires more careful estimates of the supermassive black hole masses observationally. Otherwise, it could suggest modifications of the modeling of the supermassive black hole growth at high redshifts.

A Direct Measurement of Galaxy Major and Minor Merger Rates and Stellar Mass Accretion Histories at Z < 3 Using Galaxy Pairs in the REFINE Survey

We measure the role of major and minor mergers in forming the stellar masses of galaxies over redshifts 0 < z < 3 using a combination of ∼3.25 deg2 of the deepest ground-based near-infrared imaging taken to date (Ultra Deep Survey, Ultra-VISTA, and VIDEO) as part of the collated REFINE survey. We measure the pair fraction and merger fractions for galaxy mergers of different mass ratios, and quantify the merger rate with newly measured timescales derived from the Illustris simulation as a function of redshift and merger mass ratio. For a M * > 1011 M ⊙ selection, we find that over 0 < z < 3 major mergers with mass ratios greater than 1:4 occur times on average, while minor mergers down to ratios of 1:10 occur on average times per galaxy. We also quantify the role of major and minor mergers in galaxy formation, whereby the increase in mass due to major mergers is while minor mergers account for an increase of using a M * > 1011 M ⊙ selection. We thus find that major mergers add more stellar mass to galaxies than minor mergers over this epoch. Overall, mergers will more than double the mass of massive galaxies over this epoch when selecting by stellar mass. We however find a lower increase in stellar mass when selecting by a constant number density. Finally, we compare our results to simulations, finding that minor mergers are overpredicted in Illustris and in semi-analytical models, suggesting a mismatch between observations and theory in this fundamental aspect of galaxy assembly.

Faint Quasars Live in the Same Number Density Environments as Lyman Break Galaxies at z ∼ 4

Abstract Characterizing high-z quasar environments is key to understanding the coevolution of quasars and the surrounding galaxies. To restrict their global picture, we statistically examine the g-dropout galaxy overdensity distribution around 570 faint quasar candidates at z ∼ 4, based on the Hyper Suprime-Cam Subaru Strategic Program survey. We compare the overdensity significances of g-dropout galaxies around the quasars with those around g-dropout galaxies, and find no significant difference between their distributions. A total of 4 (22) out of the 570 faint quasars, , are found to be associated with the &gt;4σ overdense regions within an angular separation of 1.8 (3.0) arcmin, which is the typical size of protoclusters at this epoch. This is similar to the fraction of g-dropout galaxies associated with the &gt;4σ overdense regions. This result is consistent with our previous work in which and of luminous quasars detected in the Sloan Digital Sky Survey exist in the &gt;4σ overdense regions within 1.′8 and 3.′0 separations, respectively. Therefore, we suggest that the galaxy number densities around quasars are independent of their luminosity, and most quasars do not preferentially appear in the richest protocluster regions at z ∼ 4. The lack of an apparent positive correlation between the quasars and the protoclusters implies that (i) the gas-rich major merger rate is relatively low in the protocluster regions, (ii) most high-z quasars may appear through secular processes, or (iii) some dust-obscured quasars exist in the protocluster regions.

A Significant Excess in Major Merger Rate for AGNs with the Highest Eddington Ratios at z &lt; 0.2

Abstract Observational studies are increasingly finding evidence against major mergers being the dominant mechanism responsible for triggering an active galactic nucleus (AGN). After studying the connection between major mergers and AGNs with the highest Eddington ratios at z = 2, we here expand our analysis to , exploring the same AGN parameter space. Using ESO VLT/FORS2 , , and color images, we examine the morphologies of 17 galaxies hosting AGNs with Eddington ratios , and 25 mass- and redshift-matched control galaxies. To match the appearance of the two samples, we add synthetic point sources to the inactive comparison galaxies. The combined sample of AGN and inactive galaxies was independently ranked by 19 experts with respect to the degree of morphological distortion. We combine the resulting individual rankings into multiple overall rankings, from which we derive the respective major merger fractions of the two samples. With a best estimate of f m,agn = 0.41 ± 0.12 for the AGN host galaxies and f m,ina = 0.08 ± 0.06 for the inactive galaxies, our results imply that our AGN host galaxies have a significantly higher merger rate, regardless of the observed wavelength or applied methodology. We conclude that although major mergers are an essential mechanism to trigger local high Eddington ratio AGNs at , the origin of of this specific AGN subpopulation still remains unclear.

Galaxy Merger Rates up to z ∼ 3 Using a Bayesian Deep Learning Model: A Major-merger Classifier Using IllustrisTNG Simulation Data

Abstract Merging is potentially the dominant process in galaxy formation, yet there is still debate about its history over cosmic time. To address this, we classify major mergers and measure galaxy merger rates up to z ∼ 3 in all five CANDELS fields (UDS, EGS, GOODS-S, GOODS-N, COSMOS) using deep learning convolutional neural networks trained with simulated galaxies from the IllustrisTNG cosmological simulation. The deep learning architecture used is objectively selected by a Bayesian optimization process over the range of possible hyperparameters. We show that our model can achieve 90% accuracy when classifying mergers from the simulation and has the additional feature of separating mergers before the infall of stellar masses from post-mergers. We compare our machine-learning classifications on CANDELS galaxies and compare with visual merger classifications from Kartaltepe et al., and show that they are broadly consistent. We finish by demonstrating that our model is capable of measuring galaxy merger rates, , that are consistent with results found for CANDELS galaxies using close pairs statistics, with . This is the first general agreement between major mergers measured using pairs and structure at z &lt; 3.

Observational Constraints on the Merger History of Galaxies since z ≈ 6: Probabilistic Galaxy Pair Counts in the CANDELS Fields

Abstract Galaxy mergers are expected to have a significant role in the mass assembly of galaxies in the early universe, but there are very few observational constraints on the merger history of galaxies at z &gt; 2. We present the first study of galaxy major mergers (mass ratios &lt;1:4) in mass-selected samples out to z ≈ 6. Using all five fields of the Hubble Space Telescope/CANDELS survey and a probabilistic pair-count methodology that incorporates the full photometric redshift posteriors and corrections for stellar mass completeness, we measure galaxy pair-counts for projected separations between 5 and 30 kpc in stellar mass selected samples at 9.7 &lt; log10(M ⋆/M ⊙) &lt; 10.3 and log10(M ⋆/M ⊙) &gt; 10.3. We find that the major merger pair fraction rises with redshift to z ≈ 6 proportional to (1 + z) m , with m = 0.8 ± 0.2 (m = 1.8 ± 0.2) for log10(M ⋆/M ⊙) &gt; 10.3 (9.7 &lt; log10(M ⋆/M ⊙) &lt; 10.3). Investigating the pair fraction as a function of mass ratio between 1:20 and 1:1, we find no evidence for a strong evolution in the relative numbers of minor to major mergers out to z &lt; 3. Using evolving merger timescales, we find that the merger rate per galaxy ( ) rises rapidly from 0.07 ± 0.01 Gyr−1 at z &lt; 1 to 7.6 ± 2.7 Gyr−1 at z = 6 for galaxies at log10(M ⋆/M ⊙) &gt; 10.3. The corresponding comoving major merger rate density remains roughly constant during this time, with rates of Γ ≈ 10−4 Gyr−1 Mpc−3. Based on the observed merger rates per galaxy, we infer specific mass accretion rates from major mergers that are comparable to the specific star formation rates for the same mass galaxies at z &gt; 3 - observational evidence that mergers are as important a mechanism for building up mass at high redshift as in situ star formation.

The frequency of dwarf galaxy multiples at low redshift in SDSS versus cosmological expectations

We quantify the frequency of companions of low redshift ($0.013 < z < 0.0252$), dwarf galaxies ($2 \times 10^8$ M$_\odot <$ M$_{*} < 5 \times 10^9$ M$_\odot$) that are isolated from more massive galaxies in SDSS and compare against cosmological expectations using mock observations of the Illustris simulation. Dwarf multiples are defined as 2 or more dwarfs that have angular separations > 55'', projected separations r$_p < 150$ kpc and relative line-of-sight velocities $\Delta V_{\rm LOS} < 150$ km/s. While the mock catalogs predict a factor of 2 more isolated dwarfs than observed in SDSS, the mean number of observed companions per dwarf is $N_c \sim 0.04$, in good agreement with Illustris when accounting for SDSS sensitivity limits. Removing these limits in the mock catalogs predicts $N_c\sim 0.06$ for future surveys (LSST, DESI), which will be complete to M$_* = 2\times 10^8$ M$_\odot$. The 3D separations of mock dwarf multiples reveal a contamination fraction of $\sim$40% in observations from projection effects. Most isolated multiples are pairs; triples are rare and it is cosmologically improbable that bound groups of dwarfs with more than 3 members exist within the parameter range probed in this study. We find that $<$1% of LMC-analogs in the field have an SMC-analog companion. The fraction of dwarf "Major Pairs'' (stellar mass ratio $>$1:4) steadily increases with decreasing Primary stellar mass, whereas the cosmological "Major Merger rate'' (per Gyr) has the opposite behaviour. We conclude that cosmological simulations can be reliably used to constrain the fraction of dwarf mergers across cosmic time.

Halo abundance and assembly history with extreme-axion wave dark matter at z ≥ 4

Abstract Wave dark matter (ψDM) composed of extremely light bosons (mψ ∼ 10 − 22 eV), with quantum pressure suppressing structures below a kpc-scale de Broglie wavelength, has become a viable dark matter candidate. Compared to the conventional free-particle ψDM (FPψDM), the extreme-axion ψDM model (EAψDM) proposed by Zhang &amp; Chiueh features a larger cut-off wavenumber and a broad spectral bump in the matter transfer function. Here, we conduct cosmological simulations to compare the halo abundances and assembly histories at z = 4–11 between three different scenarios: FPψDM, EAψDM and cold dark matter (CDM). We show that EAψDM produces significantly more abundant low-mass haloes than FPψDM with the same mψ, and therefore could alleviate the tension in mψ required by the Lyα forest data and by the kpc-scale dwarf galaxy cores. We also find that, compared to the CDM counterparts, massive EAψDM haloes are, on average, 3–4 times more massive at z = 10–11 due to their earlier formation, undergo a slower mass accretion at 7 ≲ z ≲ 11, and then show a rapidly rising major merger rate exceeding CDM by ∼ 50 per cent at 4 ≲ z ≲ 7. This fact suggests that EAψDM haloes may exhibit more prominent starbursts at z ≲ 7.

Convergence properties of halo merger trees; halo and substructure merger rates across cosmic history

We introduce gbpTrees: an algorithm for constructing merger trees from cosmological simulations, designed to identify and correct for pathological cases introduced by errors or ambiguities in the halo finding process. gbpTrees is built upon a halo matching method utilising pseudo-radial moments constructed from radially-sorted particle ID lists (no other information is required) and a scheme for classifying merger tree pathologies from networks of matches made to-and-from haloes across snapshots ranging forward-and-backward in time. Focusing on Subfind catalogs for this work, a sweep of parameters influencing our merger tree construction yields the optimal snapshot cadence and scanning range required for converged results. Pathologies proliferate when snapshots are spaced by $\lesssim{0.128}$ dynamical times; conveniently similar to that needed for convergence of semi-analytical modelling, as established by Benson etal Total merger counts are converged at the level of $\sim{5}$% for friends-of-friends (FoF) haloes of size $n_{\rm p}\gtrsim{75}$ across a factor of 512 in mass resolution, but substructure rates converge more slowly with mass resolution, reaching convergence of $\sim{10}$% for $n_{\rm p}\gtrsim{100}$ and particle mass $m_{\rm p}{\lesssim}10^{9}M_\odot$. We present analytic fits to FoF and substructure merger rates across nearly all observed galactic history ($z{\le}8.5$). While we find good agreement with the results presented by Fakhouri etal for FoF haloes, a slightly flatter dependance on merger ratio and increased major merger rates are found, reducing previously reported discrepancies with extended Press-Schechter estimates. When appropriately defined, substructure merger rates show a similar mass ratio dependance as FoF rates, but with stronger mass and redshift dependencies for their normalisation.

The Remarkable Similarity of Massive Galaxy Clusters from z ∼ 0 to z ∼ 1.9

Abstract We present the results of a Chandra X-ray survey of the eight most massive galaxy clusters at z &gt; 1.2 in the South Pole Telescope 2500 deg2 survey. We combine this sample with previously published Chandra observations of 49 massive X-ray-selected clusters at 0 &lt; z &lt; 0.1 and 90 Sunyaev–Zel’dovich–selected clusters at 0.25 &lt; z &lt; 1.2 to constrain the evolution of the intracluster medium (ICM) over the past ∼10 Gyr. We find that the bulk of the ICM has evolved self-similarly over the full redshift range probed here, with the ICM density at scaling like . In the centers of clusters ( ), we find significant deviations from self-similarity ( ), consistent with no redshift dependence. When we isolate clusters with overdense cores (i.e., cool cores), we find that the average overdensity profile has not evolved with redshift—that is, cool cores have not changed in size, density, or total mass over the past ∼9–10 Gyr. We show that the evolving “cuspiness” of clusters in the X-ray, reported by several previous studies, can be understood in the context of a cool core with fixed properties embedded in a self-similarly evolving cluster. We find no measurable evolution in the X-ray morphology of massive clusters, seemingly in tension with the rapidly rising (with redshift) rate of major mergers predicted by cosmological simulations. We show that these two results can be brought into agreement if we assume that the relaxation time after a merger is proportional to the crossing time, since the latter is proportional to .

Weighing the giants– V. Galaxy cluster scaling relations

We present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak gravitational lensing measurements. These are the first such results obtained from an analysis that simultaneously accounts for selection effects and the underlying mass function, and directly incorporates lensing data to constrain total masses. Our constraints on the scaling relations and their intrinsic scatters are in good agreement with previous studies, and reinforce a picture in which departures from self-similar scaling laws are primarily limited to cluster cores. However, the data are beginning to reveal new features that have implications for cluster astrophysics and provide new tests for hydrodynamical simulations. We find a positive correlation in the intrinsic scatters of luminosity and temperature at fixed mass, which is related to the dynamical state of the clusters. While the evolution of the nominal scaling relations over the redshift range $0.0<z<0.5$ is consistent with self similarity, we find tentative evidence that the luminosity and temperature scatters respectively decrease and increase with redshift. Physically, this likely related to the development of cool cores and the rate of major mergers. We also examine the scaling relations of redMaPPer richness and Compton $Y$ from Planck. While the richness--mass relation is in excellent agreement with recent work, the measured $Y$--mass relation departs strongly from that assumed in the Planck cluster cosmology analysis. The latter result is consistent with earlier comparisons of lensing and Planck scaling-relation-derived masses.

DRY MERGER RATE AND POST-MERGER FRACTION IN THE COMA CLUSTER CORE

ABSTRACT We evaluate the dry merger activity in the Coma cluster, using a spectroscopically complete sample of 70 red-sequence (RS) galaxies, most of which (∼75%) are located within 0.2R 200 (∼0.5 Mpc) from the cluster center, with data from the Coma Treasury Survey obtained with the Hubble Space Telescope. The fraction of close galaxy pairs in the sample is the proxy employed for the estimation of the merger activity. We identify 5 pairs and 1 triplet, enclosing a total of 13 galaxies, based on limits on projected separation and line-of-sight velocity difference. Of these systems, none show signs of ongoing interaction, and therefore we do not find any true mergers in our sample. This negative result sets a 1σ upper limit of 1.5% per Gyr for the major dry merger rate, consistent with the low rates expected in present-day clusters. Detailed examination of the images of all the RS galaxies in the sample reveals only one with low surface brightness features identifiable as the remnant of a past merger or interaction, implying a post-merger fraction below 2%.

AVOIDING PROGENITOR BIAS: THE STRUCTURAL AND MASS EVOLUTION OF BRIGHTEST GROUP AND CLUSTER GALAXIES IN HIERARCHICAL MODELS SINCEz≲ 1

The mass and structural evolution of massive galaxies is one of the hottest topics in galaxy formation. This is because it may reveal invaluable insights into the still debated evolutionary processes governing the growth and assembly of spheroids. However, direct comparison between models and observations is usually prevented by the so-called "progenitor bias", i.e., new galaxies entering the observational selection at later epochs, thus eluding a precise study of how pre-existing galaxies actually evolve in size. To limit this effect, we here gather data on high-redshift brightest group and cluster galaxies, evolve their (mean) host halo masses down to z=0 along their main progenitors, and assign as their "descendants" local SDSS central galaxies matched in host halo mass. At face value, the comparison between high redshift and local data suggests a noticeable increase in stellar mass of a factor of >2 since z~1, and of >2.5 in mean effective radius. We then compare the inferred stellar mass and size growth with those predicted by hierarchical models for central galaxies, selected at high redshifts to closely match the halo and stellar mass bins as in the data. Only hierarchical models characterized by very limited satellite stellar stripping and parabolic orbits are capable of broadly reproducing the stellar mass and size increase of a factor ~2-4 observed in cluster galaxies since z ~1. The predicted, average (major) merger rate since z~1 is in good agreement with the latest observational estimates.

Halo statistics analysis within medium volume cosmological N-body simulation

In this paper we present halo statistics analysis of a ?CDM N body cosmological simulation (from first halo formation until z = 0). We study mean major merger rate as a function of time, where for time we consider both per redshift and per Gyr dependence. For latter we find that it scales as the well known power law (1 + z)n for which we obtain n = 2.4. The halo mass function and halo growth function are derived and compared both with analytical and empirical fits. We analyse halo growth through out entire simulation, making it possible to continuously monitor evolution of halo number density within given mass ranges. The halo formation redshift is studied exploring possibility for a new simple preliminary analysis during the simulation run. Visualization of the simulation is portrayed as well. At redshifts z = 0?7 halos from simulation have good statistics for further analysis especially in mass range of 1011 ? 1014 M./h.

Ongoing growth of the brightest cluster galaxies via major dry mergers in the last ∼6 Gyr

Brightest cluster galaxies (BCGs) might have been assembled relatively late (z < 1) via mergers. By exploiting the high-resolution HST/ACS imaging, we find four BCGs (COSMOS-P 125516, 102810, 036694 and 089357) in major dry merging in 29 X-ray clusters at 0.3 ≤ z ≤ 0.6 in the Cosmological Evolutionary Survey (COSMOS). These BCGs show prominent but quiescent double nuclei with a magnitude difference of δm < 1.5 and a projected separation of rp < 10 kpc. Clear signatures of interaction such as extended plumes and/or significant asymmetries are also observed in their residual images. We infer a major merger rate of 0.55 ± 0.27 merger per Gyr at z ∼ 0.43 assuming the merger time-scale estimate of Kitzbichler & White. This inferred rate is significantly higher than the rate in the local Universe (0.12 ± 0.03 at z ∼ 0.07) presented by Liu et al. We estimate that present-day BCGs increase their luminosity (mass) by ∼35 ± 15 per cent (fmass/0.5) via major dry mergers since z = 0.6, where fmass is the mean mass fraction of companion galaxies accreted on to the central ones. Although the statistical uncertainty due to our small sample size is relatively large, our finding is consistent with both recent observational and theoretical results. Furthermore, in conjunction with our previous findings by Liu et al., the discovery of these intermediate-redshift merging BCGs is clear evidence of ongoing assembly of BCGs via major dry mergers over the last ∼6 Gyr.

Driving the growth of the earliest supermassive black holes with major mergers of host galaxies

The formation mechanism of supermassive black holes (SMBHs) in general, and of SMBHs observed as luminous quasars at redshifts in particular, remains an open fundamental question. The presence of such massive BHs at such early times, when the Universe was less than a billion years old, implies that they grew via either super-Eddington accretion, or nearly uninterrupted gas accretion near the Eddington limit; the latter, at first glance, is at odds with empirical trends at lower redshifts, where quasar episodes associated with rapid BH growth are rare and brief. In this work, I examine whether and to what extent the growth of the quasar SMBHs can be explained within the standard quasar paradigm, in which major mergers of host galaxies trigger episodes of rapid gas accretion below or near the Eddington limit. Using a suite of Monte Carlo merger tree simulations of the assembly histories of 40 likely quasar host halos, I investigate (i) their growth and major merger rates out to , and (ii) how long the feeding episodes induced by host mergers must last in order to explain the observed quasar population without super-Eddington accretion. The halo major merger rate scales roughly as , consistent with cosmological simulations at lower redshifts, with quasar hosts typically experiencing major mergers between (), compared to ∼1 for typical massive galaxies at (). The high rate of major mergers allows for nearly continuous SMBH growth if (for example) a merger triggers feeding for a duration comparable to the halo dynamical time. These findings suggest that the growth mechanisms of the earliest quasar SMBHs need not have been drastically different from their counterparts at lower redshifts.

Galaxy And Mass Assembly (GAMA): refining the local galaxy merger rate using morphological information

We use the Galaxy And Mass Assembly (GAMA) survey to measure the local Universe mass-dependent merger fraction and merger rate using galaxy pairs and the CAS (concentration, asymmetry, and smoothness) structural method, which identifies highly asymmetric merger candidate galaxies. Our goals are to determine which types of mergers produce highly asymmetrical galaxies and to provide a new measurement of the local galaxy major merger rate. We examine galaxy pairs at stellar mass limits down to M* = 108 M⊙ with mass ratios of <100:1 and line-of-sight velocity differences of ΔV < 500 km s−1. We find a significant increase in mean asymmetries for projected separations less than the sum of the individual galaxy's Petrosian 90 radii. For systems in major merger pairs with mass ratios of <4:1, both galaxies in the pair show a strong increase in asymmetry, while in minor merger systems (with mass ratios of >4:1) the lower mass companion becomes highly asymmetric, whereas the larger galaxy is much less affected. The fraction of highly asymmetric paired galaxies which have a major merger companion is highest for the most massive galaxies and drops progressively with decreasing mass. We calculate that the mass-dependent major merger fraction is fairly constant at ∼1.3–2 per cent within 109.5 < M* < 1011.5 M⊙, and increases to ∼4 per cent at lower masses. When the observability time-scales are taken into consideration, the major merger rate is found to approximately triple over the mass range we consider. The total comoving volume major merger rate over the range 108.0 < M* < 1011.5 M⊙ is (1.2 ± 0.5) × 10−3|$h^{3}_{70}$| Mpc−3 Gyr−1.

The main sequence of star-forming galaxies at z ∼ 0.6: reinstating major mergers

Abstract The relation between the star formation rate (SFR) and the stellar mass of star-forming galaxies has been used to argue that major mergers cannot be the main driver of star formation. Here, we re-examine these arguments using the representative IMAGES-CDFS sample of star-forming galaxies at z = 0.4–0.75, taking advantage of their previously established classification into pre-fusion, fusion, and relaxing galaxy mergers. Contrary to previous claims, we show there is no tension between the main-sequence scatter and the average duration of the fusion SFR peak. We confirm previous estimates of the fraction of SFR due to morphologically selected galaxies (∼23 per cent) or the SFR enhancement due to major merger during the fusion phase (∼10 per cent). However, galaxy mergers are not instantaneous processes, which implies that the total fraction of the SFR associated with galaxies undergoing major mergers must account for the three merger phases. When doing so, galaxies involved in major mergers are found to represent 53–88 per cent of the total SFR at z ∼ 0.6. The fraction of luminous infrared galaxies (LIRGs) in the fusion phase is found to be in agreement with the observed morphological fraction of LIRGs without discs and with the observed and expected major merger rates at z ≤ 1.5.

Generating merger trees for dark matter haloes: a comparison of methods

Halo merger trees describe the hierarchical mass assembly of dark matter haloes, and are the backbone for modeling galaxy formation and evolution. Merger trees constructed using Monte Carlo algorithms based on the extended Press-Schechter (EPS) formalism are complementary to those extracted from N-body simulations, and have the advantage that they are not trammeled by limited numerical resolution and uncertainties in identifying (sub)haloes and linking them between snapshots. This paper compares multiple EPS-based merger tree algorithms to simulation results using four diagnostics: progenitor mass function (PMF), mass assembly history (MAH), merger rate per descendant halo, and the unevolved subhalo mass function (USMF). In general, algorithms based on spherical collapse yield major-merger rates that are too high by a factor of two, resulting in MAHs that are systematically offset. Assuming ellipsoidal collapse solves most of these issues, but the particular algorithm investigated here that incorporates ellipsoidal collapse dramatically overpredicts the minor-merger rate for massive haloes. The only algorithm in our comparison that yields MAHs, merger rates, and USMFs in good agreement with simulations, is that by Parkinson et al. (2008). However, this is not a true EPS-based algorithm as it draws its progenitor masses from a PMF calibrated against simulations, rather than `predicted' by EPS. Finally we emphasize that the benchmarks used to test the EPS algorithms are obtained from simulations and are hampered by significant uncertainties themselves. In particular, MAHs and halo merger rates obtained from simulations by different authors reveal discrepancies that easily exceed 50 percent, even when based on the same simulation. Given this status quo, merger trees constructed using the Parkinson et al. algorithm are as accurate as those extracted from N-body simulations.

The importance of major mergers in the build up of stellar mass in brightest cluster galaxies at z = 1

Recent independent results from numerical simulations and observations have shown that brightest cluster galaxies (BCGs) have increased their stellar mass by a factor of almost two between z~0.9 and z~0.2. The numerical simulations further suggest that more than half this mass is accreted through major mergers. Using a sample of 18 distant galaxy clusters with over 600 spectroscopically confirmed cluster members between them, we search for observational evidence that major mergers do play a significant role. We find a major merger rate of 0.38 +/- 0.14 mergers per Gyr at z~1. While the uncertainties, which stem from the small size of our sample, are relatively large, our rate is consistent with the results that are derived from numerical simulations. If we assume that this rate continues to the present day and that half of the mass of the companion is accreted onto the BCG during these mergers, then we find that this rate can explain the growth in the stellar mass of the BCGs that is observed and predicted by simulations. Major mergers therefore appear to be playing an important role, perhaps even the dominant one, in the build up of stellar mass in these extraordinary galaxies.