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Early assembly of the most massive galaxies

The current consensus is that galaxies begin as small density fluctuations in the early Universe and grow by in situ star formation and hierarchical merging. Stars begin to form relatively quickly in sub-galactic sized building blocks called haloes which are subsequently assembled into galaxies. However, exactly when this assembly takes place is a matter of some debate. Here we report that the stellar masses of brightest cluster galaxies, which are the most luminous objects emitting stellar light, some 9 billion years ago are not significantly different from their stellar masses today. Brightest cluster galaxies are almost fully assembled 4-5 Gyrs after the Big Bang, having grown to more than 90% of their final stellar mass by this time. Our data conflict with the most recent galaxy formation models based on the largest simulations of dark matter halo development. These models predict protracted formation of brightest cluster galaxies over a Hubble time, with only 22% of the stellar mass assembled at the epoch probed by our sample. Our findings suggest a new picture in which brightest cluster galaxies experience an early period of rapid growth rather than prolonged hierarchical assembly.

The stellar mass of a BCG depends upon the hierarchical build up of its host dark matter halo and its stellar evolution history, along with the baryonic physics of the galaxy.
We base our study of BCGs on photometry in the infrared wavebands J (1.26 µm) and K s (2.14 µm). Infrared imaging is essential at these large redshifts to compensate for the redshifting of the early-type galaxy spectra. Also, these wavebands are less sensitive than optical light to the presence of young stars and are a more accurate tracer of the underlying old stellar population and, hence, of the stellar mass of the systems. Fig. 1 shows an infrared image of the cluster J2235 from our sample (see also Supplementary Fig. 1).
We start by examining the ages of the stars themselves in these galaxies using the run of J − K s colour evolution with redshift as shown in Fig. 2. For BCGs at the redshift of our sample the J − K s colour predictions for the models separate clearly. For the comparison sample at lower redshift we use X-ray selected clusters 19 which are well matched in mass to our own cluster sample. There is a remarkable agreement between the data and the hybrid model (see Fig. 2  To compare with theory we use the haloes from the Millennium Simulation 1 (http://www.mpa-garching.mpg.de/millennium) matched to the total mass of our clusters, estimated from their X-ray luminosity (see Supplementary Information). The mass range of our five clusters (Table 1) has excellent overlap with the combined z = 1.08 and z = 1.5 halo samples 4 (Supplementary Fig. 3). The predicted hierarchical mass build up of BCGs in these 250 haloes is also shown in Fig. 3. The corresponding mass of the simulated BCGs has grown to an average of only 1.92 (±0.38) × 10 11 M ⊙ (s.d.) by this time, some 22% of the observed value. The data are inconsistent with the prediction at the level of 4σ (one-tailed P = 0.008, degrees of freedom d.f. = 4; based on a Student's t distribution appropriate for small samples).
To check the stability of the BCG assembly predictions we selected massive haloes 5 from the independent Durham semi-analytic model 5 which also uses the Millennium Simulation 1 but incorporates a different treatment of the baryon physics close to active galactic nuclei, partly in order to better reproduce the abundance of massive elliptical galaxies at high redshift. Using the same selection limits we find that the BCG mass fractions compared to the present day are 0.22 +0. 18 −0.09 at z = 1 and 0.17 +0.12 −0.07 at z = 1.5, indicating good agreement between the two semi-analytical models.
It is well known that the estimates of stellar mass from photometry even for earlytype galaxies such as BCGs depend on the underlying stellar evolution model used. To investigate this sensitivity we have applied three independent stellar population synthesis codes to early-type galaxies at the mean redshift of our sample (z = 1.3) using a range of model parameters (see Supplementary Table 1). These results show that the K s band stellar mass estimates remain significantly discrepant from the semi-analytic predictions (one-tailed P ≤ 0.02, d.f. = 4) for the vast majority of parameters considered across the three models, reaching a value for one-tailed P of ≥ 0.05 in one of the three only if the stellar formation epoch z f is less than 2.5 together with a stellar metallicity less than the solar value. This situation is incompatible with observations of BCGs and massive earlytype galaxies in general (see Supplementary Information). We conclude that there remains a significant discrepancy between the recent semi-analytic models of galaxy formation coupled to the largest N-body simulations and the stellar masses of BCGs at the centres of 6 the most massive clusters.
In comparison to recent studies 20 , this work significantly extends the redshift baseline over which BCG evolution has been investigated to z = 1.5, equivalent to a look-back time ≃ 65% the age of the Universe. Although the first glimpse of the z > 1 BCG population reveals galaxies with a range of stellar masses, there is on average considerably less stellar mass evolution than expected, with the bulk (≥ 90%) of the stellar mass already in place by z ≃ 1.5, corresponding to only about 4-5 Gyrs after the Big Bang; the current models predict a considerably longer timescale of about 11 Gyr for the same growth, Despite this there is evidence that merging is still underway in our high redshift sample. The BCG in J0849 at z = 1.26 has a nearby companion (projected separation of about 6 kpc) with which it is likely to undergo dissipationless merging in the future 21 . Of the other clusters in our sample, the BCG and its neighbour (projected separation of about 15 kpc) in J1252 are also possible merger candidates. Assuming that mergers take place in both these cases, the fraction of BCG stellar mass already assembled (based on the K s fluxes of the main components) is ≃ 84% and ≃ 60% for J0849 and J1252 respectively, supporting the contention that most of the growth has actually already taken place in these two BCGs.

7
The timescale for the mass assemblage is similar to the age of the component stars (2 − 3 Gyrs), a situation that appears to resembles classical monolithic collapse 22, 23 rather than hierarchical formation. To form a galaxy of stellar mass 10 12 M ⊙ over 4 Gyrs requires a mass deposition rate of about 250 M ⊙ yr −1 and an efficient mechanism to feed the gas into the inner regions of the halo where it can form stars. Unfortunately the merging process becomes inefficient for massive galaxies because merger induced shocks lead to heating as opposed to radiative cooling of the gas 24 . One recent suggestion 25 is that the early assembly of massive galaxies at z ≥ 2 is driven by narrow streams of dense cold gas which penetrate the shock-heated region greatly increasing the efficiency of the gas deposition and associated star formation. Thus, the fraction of time that young BCGs spend undergoing a major merger event could be ≤ 10%, with the stellar mass assembly dominated by this 'stream-fed' process 25 . Alternatively, a deficiency may lie in the semi-analytic treatment of the physical processes in the densest environments during early hierarchical assembly; this contention is supported by the fact that current predictions are moderately consistent with observations of the evolution of luminous red galaxies 26,27 , whereas our results, which focus on the most massive subset of this population, the BCGs, differ much more from the model predictions.
In a wider context the hierarchical simulations and their semi-analytic prescriptions have arguably provided an excellent way of generating mock catalogues of galaxies to 8 compare with real data, but our results show that they do not account for the assemblage history of all galaxies. Larger simulations may provide a better statistical probe of both the merging history of the largest haloes and cluster-mass trends. If BCGs collapsed and formed at high redshift in a single burst of intense star formation then they may well be dusty and in sufficient numbers to be detectable with the coming generation of submillimetre surveys, which will cover areas large enough to detect objects as rare as BCGs.
The ongoing XCS survey will find many more high redshift clusters and we anticipate that our results will stimulate independent studies of BCGs as new clusters are found in the redshift 'desert' beyond z = 1.5 from infrared and X-ray based surveys such as eRosita.     The cluster X-ray The photometry for J1252 and J0849 were sourced from the literature 14,21 and for these galaxies the total K s magnitudes and J − K s colours were measured in similar aperture sizes. All data have been analysed in an identical manner for direct comparison (see Supplementary Information).
The errors on the stellar masses include all photometric errors and the uncertainty in the calibration with the semi-analytic model 4 . All errors are 1σ (s.d.). For each cluster we identified the brightest galaxy from the K s -band magnitudes of all galaxies within 500 kpc of the cluster X-ray centroid because for approximately 95% of clusters the BCG lies within this radius 30 . All identified BCGs have optical spectra confirming their cluster membership 11,[13][14][15]18 .
Early assembly of the most massive galaxies

Supplementary Information
We provide further details of the observations and data reduction; carry out a comparison of the cluster masses used in the Millennium Simulation with those of our high redshift sample; and we also discuss the BCG mass determinations in greater detail and how these are affected by uncertainties in the stellar formation history of the galaxies.

Observations and Data Reduction
The MOIRCS instrument on the Subaru Telescope provides imaging and low-resolution spectroscopy over a total field-of-view of 4 ′ ×7 ′ with a pixel scale of 0.117 ′′ per pixel. This In order to compare our data with simulations we use the bolometric X-ray luminosity of each system (L X ) 11,12,34,35 as this can be used to determine cluster mass from power-law scaling relations 36,37 . For J2235 we use the published X-ray luminosity 15 Total X-ray luminosities for our clusters were measured using apertures of at least 50 arcsec radius, corresponding to about 500 kpc at z = 1, which is close to R 500 for massive clusters. From the Millennium Gas simulation 40 the ratio of L X at R 200 and R 500 is only 1.03, which adds weight to the assumption that L X measured at R 500 captures nearly all the X-ray emission. Finally, we calculate the M 200 values using the conversion from M 500 (ref. 41). In the absence of cool core clusters at high redshifts 38 there is no need to exclude the core emission from these estimates. The L X values and final M 200 mass estimates for our clusters are shown in Table 1 of the main text.
To demonstrate stability we note that using cluster temperature, where available, as a proxy for mass 38  there are still 32 clusters at z = 1.08 and a further 6 at z = 1.5 with a mass larger than our most massive cluster J2235.

Stability of BCG Mass Estimates
Most studies of the K band Hubble diagram for BCGs have assumed that the near-IR light is a direct proxy for stellar mass 9, 20, 45-47 , sometimes using colours to confirm the presence of an old stellar population. However, estimates of the stellar masses of galaxies are known to depend on the underlying stellar evolution model used, leading to degeneracy and systematic uncertainties. In particular some stellar evolution models 48,49 are known to produce younger ages and smaller stellar masses compared to others. In order to investigate these systematic effects in our BCG mass estimates, to provide plausible errors and to identify the major assumptions on which our results depend, we study the effect of using a representative set of different stellar models covering an appropriate range of values for the important parameters.
We concentrate on three simple-stellar population (SSP) synthesis models: Bruzual and Charlot 28   while a study of the CMR in the Lynx cluster 57 (J0849) at z = 1.26 implies a mean stellar age of 3.2 Gyr, corresponding to z f > 3.7, with the stellar content of the bright elliptical galaxies in place and formed by z ∼ 3. Similar conclusions are reached for the early-type galaxies in J1252 from two studies of the colour-magnitude relation, which both suggest z f = 2.7 − 3.6 with subsequent passive evolution 14,58,59 . We conclude that since observations suggest Z ≥ 1.0 Z ⊙ and z f ≥ 3.0, our central result of negligible stellar mass evolution is not seriously compromised by the age and metallicity caveats and remains significant for the most plausible stellar evolution histories of these galaxies.
In order to further investigate systematic effects, some authors 53,54 have attempted to calibrate stellar mass from the SSP models with independent estimates of gravitational mass from velocity dispersion measurements. This has uncovered potentially serious systematic offsets (0.3 − 0.4 dex) between the two mass estimators for galaxies at z ∼ 1.
Such offsets are currently difficult to interpret as there is evidence that they may equally well be produced by biases in dynamical mass measurements or evolution in the dynamical structure of galaxies, as by biases in the photometric stellar mass determinations 54 .
However, we note that the hybrid model shown in Fig