{'fraction_non_alphanumeric': 0.03174510034033564, 'fraction_numerical': 0.024938387513202674, 'mean_word_length': 4.396770107663078, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Is WMAP3 normalization compatible with the X-Ray cluster abundance?

We present the mass and X-ray temperature functions derived from a sample of more than 15,000 galaxy clusters of the MareNostrum Universe cosmological SPH simulations. In these simulations, we follow structure formation in a cubic volume of 500/h Mpc on a side assuming cosmological parameters consistent with either the first or third year WMAP data and gaussian initial conditions. We compare our numerical predictions with the most recent observational estimates of the cluster X-ray temperature functions and find that the low normalization cosmological model inferred from the 3 year WMAP data results is barely compatible with the present epoch X-ray cluster abundances. We can only reconcile the simulations with the observational data if we assume a normalization of the Mass-Temperature relation which is a factor of 2.5--3 smaller than our non-radiative simulations predict. This deviation seems to be too large to be accounted by the effects of star formation or cooling in the ICM, not taken into account in these simulations.


INTRODUCTION
Clusters of galaxies are strong X-ray emitters that can be observed at large distances using the XMM-Newton and Chandra X-ray telescopes. They are excellent cosmological probes that can be used to put strong constraints on the matter density of the universe, (Ω M ), the normalization of primordial density fluctuations (σ 8 ) and the associated spectral index (n). The number of massive clusters in cold dark matter-dominated cosmologies is known to be exponentially dependent on σ 8 (Seth & Tormen 2002), as has been extensively confirmed by simulations. Therefore, the determination of the abundance of massive clusters gives one of the best constraints on the normalization of the initial power spectrum of density fluctuations, provided we adopt gaussian initial conditions. An independent measurement of the cosmological parameters comes from the study of CMB anisotropies. The most recent data from 3 year WMAP satellite (Spergel et al. 2007) (WMAP3) gives a value for σ 8 ∼ 0.76 ± 0.05 to within 1σ error. This is smaller than the previous value of σ 8 = 0.84 ± 0.04 estimated from the first year WMAP data (Spergel et al. 2003) (WMAP1). This difference in the normalization and the matter content (Ω M = 0.24 vs. Ω M = 0.3), translates into large differences, up to an order of magnitude as we will show in this letter, in the number density of the most massive objects formed at present in the Universe. Other recent papers independently also argue against the low values of σ 8 obtained from WMAP3 (Evrard et. al. 2007;Rozo et. al. 2007).
In order to compare the theoretical cluster mass function for a particular cosmological model with the observed abundance of X-ray clusters as a function of the ICM gas temperature, one has to assume that the Mass-Temperature relation is sufficiently well known. The main obstacle is the accuracy in the determination of this relation. Small differences can lead to large changes in the determination of cluster mass (see e.g Henry (2004)) from the X-ray temperature. Estimations of the M-T relation from gas dynamical simulations show large discrepancies, mainly due to numerical resolution effects as well as to the physics involved (see Ascasibar et al. (2006) for a review). Most previous numerical studies on the comparison of cluster mass functions and X-ray temperature and/or luminosity functions have either high numerical resolution and a low number of objects or larger statistics but with very low resolution.
The aim of this letter is to study the X-ray cluster Temperature Function (XTF) obtained from a set of largescale non-radiative gas dynamical simulations with sufficient numerical resolution and statistics to cover the range of temperatures for which observational estimates of the cluster abundance are known. Our main goal is to test whether the observed number of X-ray emitting galaxy clusters can be obtained in a cosmological model with parameters consistent with WMAP3 or WMAP1 data at the present time. For this purpose, we compute the XTF directly from simulations and compare them with the most recent observational estimates. At the same time, we derive the values for the normalization of the M-T relation that best fit the simulation mass functions to the observed XTF and compare them with the M-T resulting from the simulations.

SIMULATIONS
To study the X-ray cluster abundance, we have performed a series of non-radiative SPH simulations with the gadget2 code (Springel 2005) at the Barcelona Supercomputer Center. Starting at redshift z = 40, we followed the non-linear evolution of structures in gas and dark matter (DM) to the present epoch (z = 0) within a comoving cube of 500h −1 Mpc on a side. The so-called MareNostrum universe is the SPH simulation with 2 × 1024 3 particles (muc ). We assumed a concordance cosmological model with the following parameters: total matter density Ω m = 0.3, the baryon density Ω b = 0.045, cosmological constant Ω Λ = 0.7, Hubble parameter h = 0.7, slope of the power spectrum n = 1 and normalization σ 8 = 0.9. We also ran the same simulation with exactly the same initial data but lower mass resolution (2 × 512 3 , mucl ) as described in Gottlöber & Yepes (2007).
After the release of the 3-year WMAP data, we complemented our numerical data set with new simulations of the same computational box but using WMAP3 cosmological parameters: Ω m = 0.24, Ω b = 0.0418, Ω Λ = 0.76, h = 0.73, n = 0.95 and σ 8 = 0.75. We have changed both Ω M and σ 8 (rather than only σ 8 ) so as to remain on the WMAP degeneracy line for these two parameters. As in the concordance model, the power spectrum was kindly provided by Wayne Hu, who computed it by direct numerical integration of the Boltzmann code. We generated the initial conditions for the WMAP3-compatible simulations with 2 × 512 3 (muw ) particles in exactly the same way as for the MareNostrum Universe. In order to study the effects of cosmic variance, we have completed a second simulation with a different random realization (mu2w ). Furthermore, and driven by the results obtained for the XTF from these simulations, we have also repeated the MareNostrum Universe realization of the WMAP3 cosmology, but with a higher normalization of the initial power spectrum (σ 8 = 0.8), consistent within 1σ with the WMAP3 best fit (muwhs ). In Table 1, we summarize the main characteristics of the simulations and the corresponding acronyms for reference in what follows. The best fit values of the Mass-Temperature relations from clusters obtained in each simulation are also shown in the last two columns (see § 4). The clusters have been identified in the simulations by means of a hierarchical Friends-of-Friends (FOF) halo finder as described in Gottlöber & Yepes (2007). For comparison with observational data, we have estimated total masses (dark + gas) of clusters at different spherical overdensities (200, 500, 2500) with respect to the critical density. To this end, we started at the position of the most massive substructure of the clusters iden-  Table 1 tified with FOF and used the Bound Density Maxima algorithm (Klypin et al. 1999) to find the spherical overdensities.

CLUSTER MASS FUNCTIONS
In Fig. 1 we plot the resulting cumulative mass functions for all the simulations described in Table 1. In this figure, the total mass of objects corresponds to the region enclosing an overdensity of 200 around the center of mass found as described in the previous section. As can be deduced from this figure, there are no significant resolution effects on the number of objects as a function of mass. The mass functions for simulations muc and mucl nicely overlap each other despite the fact that they differ by a factor of 8 in mass resolution and a factor of ∼ 3 in spatial resolution. On the other hand, there is a significant difference in the number of cluster-size objects depending on the cosmological model. The number density of clusters with masses M 200 ≥ 5 × 10 14 h −1 M ⊙ in both simulations with the low normalization, best-fit WMAP3 cosmological parameters, muw and mu2w , is ∼ 10 times smaller than for the simulations of the concordance ΛCDM model. The muwhs simulation with σ 8 = 0.8 has a number density ∼ 2 higher than the simulations with σ 8 = 0.75, but still is a factor of ∼ 5 smaller than in the concordance cosmology. Finally, Fig  1 also shows that the effects of cosmic variance is not important in determining the abundance of clusters at these scales. The agreement of the mass functions for the two different realizations of the WMAP3 cosmologi-cal model clearly confirms this. On the other hand, we have also checked for the possible effects of small volume sampling in the determination of the mass function for the most massive objects. To this end, we have compared our mass function for the muwhs simulation with the mass function obtained from a dark matter only simulation of the same cosmological model as muwhs and number of particles but larger computational volume (1.5 Gpc). This simulation has been done also at MareNostrum with the gadget2 code by P. Fosalba for the Dark Energy Survey project. The agreement between the two mass functions is remarkable for halos with masses Therefore, we conclude that the estimation of the cluster mass function from our simulations is robust and not likely to be affected by numerical effects. Now, our purpose is to compare them with data coming from X-ray observations of clusters. As our simulations include gas dynamics, we can directly measure the X-ray temperature from the gas content of our halos. In DM-only simulations, one has to rely on the Mass-X-ray Temperature relation to transform mass into temperature or vice versa. Here we will do the same exercise and compare the calculated XTFs.

X-RAY TEMPERATURE FUNCTION
The most recent published data for the XTF of nearby clusters uses temperatures derived from X-ray observations mainly by the ASCA satellite (Ikebe et al. 2002;Henry 2004) as a measure of the mean temperature of the ICM. The differences shown in the temperatures of clusters from these two datasets reflect the systematic errors in the observed XTF. For our simulated clusters, we computed several temperature estimations: the emissionweighted temperature, T e w by weighting the temperature of each SPH particle within the cluster by their X-Ray luminosity. We also computed the spectroscopic temperature, T X , following the procedure described in Vikhlinin (2006), which is suppose to give a more accurate value of the observed temperature of an X-ray emmitting plasma. Therefore, in what follows we will use T X for the simulated clusters.
In Fig. 2 we show the cumulative XTF as a function of the spectroscopic T X for the clusters found in simulations described in Table 1. We also represent the observational data as points with error bars as described in Henry (2004). The observational data were rescaled to units of h = 1.
The predicted number density of X-ray clusters above a given temperature for the muc and mucl simulations with σ 8 = 0.9 is in good agreement with the data. Again, as in the case of mass, the WMAP3 most favored cosmological model underpredicts the density of X-ray clusters with respect to the observations by a factor of ∼ 10 for clusters with T x > 4 keV. The situation is slightly better for the higher normalization muwhs simulation. But still, it predicts a factor of ∼ 6 fewer density of clusters hotter than T x > 4 keV than in reality.
We showed in Fig 1 that effects of resolution are negligible in the estimate of the cumulative mass function for massive clusters. This could not be the case for the temperature estimates from the gas particles. In order to check whether the XTF could be affected by resolution, we also show in Fig 2 a comparison of the XTF Fig. 2.-Cumulative X-Ray Temperature function for two different cosmologies. Same notation as in Fig. 1. Solid triangles and squares represent Ikebe et al. (2002) and Henry (2004) data, respectively. Errors were computed as explained in Henry (2004). between muc and mucl simulations. As can be seen, the spectroscopic temperature estimate of clusters is biased high when low mass resolution is used in a SPH simulation. Thus, we expect that the difference in XTF shown between muc concordance model simulation with 1024 3 particles and the WMAP3 lower resolution simulations (512 3 ) is in fact a lower limit. If we increased the mass resolution of the latter, we would obtain a larger difference with respect to the muc and data.

DISCUSSION
We have shown in the previous sections that the low normalized WMAP3 cosmological simulations underpredict the abundance of X-ray clusters by a factor that ranges between 6 − 10 with respect to estimates from ASCA observations. Now, our estimates are based on the results from non-radiative gas dynamical simulations of the ICM. There is still no clear answer to what extent cooling and star formation are important in the thermodynamics of the ICM. The extreme complexity of the processes involved presents a serious challenge for simulating them accurately in a cosmological setting. Results from simulations which incorporate some modeling of these processes have shown that the M-T relation is not strongly affected by non-gravitational heating (Borgani et al. 2004;Nagai, Vikhlinin & Kravtsov 2007). A rather more important ingredient in the determination of the XTF from mass functions is the intrinsic scatter of the M-T relation. If the scatter is big, then a rather low normalization power spectrum can in principle give high enough XTF to be compatible with observations. Given the very good statistical sample of objects in our simulations, we can reliably estimate not only the M-T relation but also the intrinsic scatter due to the cluster dynamics. In Table 1, we report the least-square fit values of the M 200 /M ⊙ h −1 = (M 0 /M ⊙ h −1 )(T X /3 keV) α for the different simulations where errors in both the slope α and normalization M 0 correspond to 1σ in the fit. We can also make a reliable estimate of the intrinsic scatter in the M 200 − T X relation. The linear fit of the log M 200 versus log T X has a Pearson's correlation coefficient better than 0.99 for all simulations. The maximum intrinsic scatter, ∆ log M 0 , is also shown in Table 1 we fix the slope, α, to the best fit value obtained from each simulation (see Table 1) we find a value for normal-ization parameter log M 0 = 14.10 − 14.13 for WMAP3 σ 8 = 0.75 simulations and log M 0 = 14.19 − 14.22 for the σ 8 = 0.8 WMAP3 simulation. Finally, if we assume the self-similar behavior of the M-T scaling relation, α = 3/2, then, the best fit values for M 0 are quite similar: log M 0 = 14.20 − 14.26 for the muwhs simulation and log M 0 = 14.12 − 14.17 for the muw + mu2w simulations. Therefore, the normalization of the M 200 − T x relation needed to fit the observational XTF for the σ 8 = 0.75 muw and mu2w simulations is a factor of 0.40 − 0.45 dex (∼ 2.5 − 2.8 times ) smaller than the best fit values shown in Table 1. For the σ 8 = 0.8 WMAP3 muwhs simulation this factor is 0.36 − 0.39 dex (∼ 2.3 − 2.4 factor). As we have seen, the maximum scatter derived from our WMAP3 non-radiative gas dynamical simulations is ∼ ±0.28−0.31 dex (i.e. a factor of ∼ 2 ). It is not clear that non-gravitational heating could affect the thermodynamics of the ICM in such a way that this could account for a factor of ∼ 2.5−2.8 lower normalization with respect to the predictions of the simulations reported here. For instance, the normalization for the emission-weighted M 500 − T ew from SPH simulations including cooling and star formation Borgani et al. (2004) is a factor of 1.46 smaller than the value we obtained for our muwhs simulation. If we compare the normalization of the spectroscopic M 500 − T x from the radiative cluster simulations of Nagai, Vikhlinin & Kravtsov (2007) with ours, the difference is within a factor of 1.5 − 1.6.
In conclusion, it seems unlikely that we can reproduce the observational estimates of abundance of Xray clusters with a normalization of the power spectrum as low as the best fit value given by WMAP3. A slightly higher normalization of σ 8 = 0.8 alleviates the problem, although the cluster abundance still lies below the observational estimates. Considerably steeper slopes and lower normalization of the M-T relation are needed to reconcile the predicted mass functions of clusters with the observed XTF in this case. Alternative explanations which retain a low normalisation of σ 8 appeal to the effects of primordial non-gaussianity (Sadeh, Rephaeli & Silk 2006) or to dynamical dark energy (Bartelmann, Doran, Wetterich 2006). However for the standard cosmological model, X-ray clusters of galaxies seem to prefer a higher σ 8 than predicted by the CMB anisotropies, in agreement with the abundance of optical clusters from SDSS (Rozo et. al. 2007).