COBE- and Cluster-Normalized CDM Simulations

a r X i v :a s t r o -p h /0007060v 1 5 J u l 2000COBE -AND CLUSTER-NORMALIZED CDM SIMULATIONS

T.PIRAN ?,H.EL-AD ??,H.MARTEL §and M.LECAR ??Racah Institute for Physics,The Hebrew University,Jerusalem,91904Israel ?Harvard-Smithsonian Center for Astrophysics,60Garden Street,Cambridge,MA 02138,USA §Department of Astronomy,University of Texas,Austin,TX 78712,USA We introduce a set of four new publicly available N -body simulations,the most recent addi-tions to the Texas P 3M Database .Our models probe the less studied parameter space region of moderate volume (100h ?1Mpc box)combined with ?ne mass resolution (∝1012M ⊙,roughly comparable to a L ?galaxy),making these simulations especially suitable for study of major large-scale structure (LSS)features such as voids,and for comparison with the largest three-dimensional redshift surveys currently available.Our cosmological models (LCDM,TOCDM,OCDM,TCDM)are all COBE -normalized,and when possible (LCDM and TOCDM)also cluster-normalized,based on the X-ray cluster M –T relation.The COBE -and cluster-

normalized LCDM model reiterates the attractiveness of this currently favored model which

does not require the introduction of tilt in order to ?t the constraints imposed by observations

of other cosmological parameters.

1Introduction

N -body simulations are an essential tool for probing LSS and galaxy formation.As large,high-resolution simulations are computationally costly,one has to carefully consider the added e?ort resulting from increasing the simulations’volume or from improving their resolution.In this context,most simulations gravitate towards a design stressing either of these two con?icting goals.The largest three-dimensional redshift surveys currently available are situated somewhere in between these two extremes:a M ?galaxy in the CfA2survey is visible out to 100h ?1Mpc.A simulation designed to match these surveys must have both the required resolution to identify the dark matter (DM)halos associated with such galaxies,and this moderately large volume.

The other essential consideration of simulation design is the choice of cosmological models probed.Ideally,one would want to examine a certain range of the relevant cosmological param-eters (H 0,?0,λ0,?B0,n ,σ8),but this is often not an attainable goal.In this work we focus on cosmological models with currently favored values of H 0,?0(and λ0),and require that all

Table1:Simulation Parameters

L box L cell M particle [h?1Mpc][h?1kpc][?0h?1M⊙] 25631403

25631203

Table2:Model Parameters

Model?0nσcont

8

(2)(4)(6)(8)

0.6500.91±0.09yes

OCDM0.310.46

0.650.71.00±0.09yes

TCDM10.70.72

0.500.53±0.05no

COBE- and Cluster-Normalized CDM Simulations

COBE- and Cluster-Normalized CDM Simulations

COBE- and Cluster-Normalized CDM Simulations

Figure1:CMB Angular Power Spectra:Observations vs.Models

aged to achieve cluster normalization.The two other models are not cluster-normalized.The OCDM model was designed as a direct companion to the LCDM model,where all the cosmolog-ical parameters in both these models—except the value ofλ0—are the same.The TCDM model is our best attempt with an?0=1model,where we used the lowest possibleσ8value which does not require h<0.55or n<0.7.For comparison,we have also included in Table2(and in Fig.1)the familiar SCDM model,although it is not one of the cosmological models simulated.

3Results

In Fig.1we compare the theoretical CMB angular power spectra of the models simulated here with the recent BOOMERanG3anisotropy measurements.In Fig.2we present cumulative halo mass functions for the two sets of models simulated.Our two cluster-normalized models,LCDM and TOCDM,reproduce similar mass functions.The observational point in the?gure1n(T> 4.0keV)=1.5±0.4×10?6h3Mpc?3is in good agreement with the LCDM cluster abundance.The TOCDM curve follows closely the LCDM curve,but for the former cosmology the observational point would be shifted along the horizontal axis by a factor0.31/3.However,it should be noted that there are still signi?cant uncertainties associated with both the observational measurements of cluster abundance and the theoretical modeling of the M–T relation.9

There are two curves for each cosmological model in Fig.2—one representing the mass function as measured in the100h?1Mpc box,the other measured in the40h?1Mpc box.As illustrated in the?gure,for each model there is excellent agreement between the two curves.

COBE- and Cluster-Normalized CDM Simulations

Figure2:Halo Mass Functions

4Summary

In this paper we introduce two matching sets of four cosmological models.We derive halo mass functions for all models and use the small box,high resolution simulations in order to verify the validity of the mass function in the large box for halos as small as≈1012?0h?1M⊙.The simulations presented here are unique as they both cover a volume comparable to current large three-dimensional redshift surveys and at the same time resolve cluster masses down to M?. While the simulations were designed mostly in order to achieve COBE—and,when possible (LCDM and TOCDM),also cluster—normalization,they also serve to demonstrate the attrac-tiveness of the LCDM model.Requests for the simulations presented in this paper,or for other data from the Texas P3M Database,should be sent to database@http://m.wendangku.net/doc/4d2bb08171fe910ef12df842.html. Acknowledgments

We are indebted to Mike Gross for his stimulating help and friendship.We thank Ue-Li Pen for helpful discussions and comments.HE was supported by a Smithsonian Predoctoral Fellow-ship.This work was supported by NASA grants NAG5-7363and NAG5-7812;NSF grant ASC 9504046;and the Texas Advance Research Program grant3658-0624-1999.

References

1.A.Blanchard et al,A&A,submitted,astro-ph/9908037(1999).

2.C.J.Copi,D.N.Schramm and M.S.Turner,ApJ455,95(1995).

3.P.de Bernardis et al,Nature404,955(2000).

4.M.A.K.Gross,R.S.Somerville,J.R.Primack,J.Holtzman and A.Klypin,MNRAS301,

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8.A.G.Riess et al,AJ116,1009(1998).

9.P.T.P.Viana and A.R.Liddle,MNRAS303,535(1999).

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