ap-6-11.dvi Acta Polytechnica Vol. 51 No. 6/2011 Observing Galaxy Clusters with eROSITA: Simulations J. Hölzl, J. Wilms, I. Kreykenbohm, Ch. Schmid, Ch. Grossberger, M. Wille, W. Eikmann, T. Brand Abstract The eROSITA instrument on board theRussian Spectrum Roentgen Gamma spacecraft, which will be launched in 2013, will conduct an all sky survey inX-rays. Amain objective of the survey is to observe galaxy clusters in order to constrain cosmological parameters and to obtain further knowledge about dark matter and dark energy. For the simulation of the eROSITA survey we present a Monte-Carlo code generating a mock catalogue of galaxy clusters distributed according to the mass function of [1]. The simulation generates the celestial coordinates as well as the cluster mass and redshift. From these parameters, the observed intensity and angular diameter are derived. These are used to scaleChandra cluster images as input for the survey-simulation. Keywords: Galaxy clusters, cosmology, eROSITA, simulation. 1 Introduction In recent years, our knowledge about the cosmolog- ical parameters has increased significantly through, e.g., precision measurements of the cosmic mi- crowave background [2] and the Supernova Cosmol- ogy Project [3]. Measurements of the expansion his- tory of our universe have provided evidence for the existence of a dark energy component which domi- nates all other contents of the universe and drives expansion [4]. A complementary method for mea- suring the cosmological parameters is to perform ob- servations of large-scale structures. Galaxy clusters form inareasoverdensewith respect to themeanden- sity of the universe and therefore trace the large-scale structure, such that a statistically complete sample of clusters provides us with information about the cosmological parameters [4]. By combining differ- entmeasurements, degeneracies of parameters canbe broken [4]. The mass function of clusters depends on the density parameter Ωm and the amplitude of the primordial power spectrum σ8. The evolution of the mass function and also the amplitude and the shape of the power spectrum of the spatial cluster distribu- tion P(k) [5] are strongly influenced by dark matter and dark energy [4]. The baryonic acoustic oscilla- tions, which enable the curvature of space to bemea- sured, are also imprinted on the large-scale structure. In the followingwe present a simulation generating a catalogue of galaxy clusters, which is used as an in- put for the complete simulation of the eROSITA all sky survey [6]. Galaxy clusters are the largest virialized struc- tures in the universe. The space between the galax- ies is filled with an intracluster medium with tem- peratures of several tens of millions of degrees, which causes X-ray emission in the energy band of ∼ 2–15keV. The gas traces the gravitational poten- tial of the cluster, therefore the totalmassof the clus- ter can be calculated by measuring the temperature and density profile [7]. 2 eROSITA eROSITA (extended ROentgen Survey with an Imaging Telescope Array) is one of two instru- ments on the Russian Spectrum Roentgen Gamma mission [8]. It consists of seven co-aligned identi- cal Wolter-I X-ray telescopes with 54 nested mirrors each. Each of the Wolter telescopes is equipped with an identical pnCCD camera developed by the MPI Halbleiterlabor. The pnCCDs, which are backside- illuminated Charge Coupled Devices (CCDs), are advanced versions of the pnCCDs flying on XMM- Newton [9]. The main science drivers of eROSITA are High Precision Cosmology, i.e., determination of the cosmological parameters independent of Cos- micMicrowaveBackground and Supernovameasure- ments, and the study of dark matter and dark en- ergy. eROSITA will perform a deep all sky survey for four years, followed by pointed observations of selected fields. The flux limit will be at least one order of magnitude lower than the flux limit of the ROSAT All Sky Survey [10]. With an effective area of ∼ 1500cm2 at 1.5keV, eROSITAwill detect about 50000–100000 galaxy clusters [4]. 3 Mass function As a cluster mass function, the function from [1] was used (Fig. 1): dn dM = f(σ) ρm M dlnσ−1 dM (1) 17 Acta Polytechnica Vol. 51 No. 6/2011 Fig. 1: Halo mass function from [1] for redshifts of 0, 1 and 2.5 for halos with an overdensity of 500 relative to the critical density at redshift z. The y-axis is plotted with a factor M2/ρ0. The function shows a strong redshift evolution, the number density of clusters decreases with increasing redshift where n = dN dV is the number density of halos, ρm is the mean matter density of the universe, and σ is the root mean square of the linear matter power spectrum at redshift z. The function f(σ) has been calibrated by N-body simulations for redshifts up to z =2.5 [1]. Clusters are identified as isolated density peaks and the halo mass is calculated in a spherical area around the peak enclosing a specified overden- sity. [1] describes the redshift evolution of the mass function through interpolation formulae or, alterna- tively, splines for the fitting parameters f(σ). The redshift also enters through σ(z). 4 Simulation As a lower limit for the cluster mass we chose 1013 M�. Up to a redshift of z = 2.5, the mass function gives about 23 million clusters with a mass larger than the limit. In the first step, the celestial coordinates, redshift, and mass were generated via the rejection sampling method [12]. The LX − M relation by [11] was used to obtain the luminosity as a function of the mass. After sampling the cat- alogue, it was converted into a FITS file to be used as an input for the simulation of the survey, which is performed with the Simulation of X-ray Telescopes (SIXT) software [6]. Each entry of the catalogue links to an Chandra image of a galaxy cluster pro- vided by Reiprich (private communication), which is scaled in size and luminosity according to the corre- sponding mass and redshift generated in the simula- tion, and to a spectrum. 5 Summary and conclusions We generated a mock catalogue of galaxy clusters using a Monte-Carlo code. The final source cat- alogue contains Chandra-images of galaxy clusters, which are scaled in luminosity and diameter accord- ing to the mass and redshift sampled by the sim- ulation. The next step is to take the correlation- function, which is the Fourier-transformof the power spectrum [5], into account when sampling the clus- ter positions such that the celestial coordinates are not longer independent of redshift and mass (the mass enters because of the redshift evolution of the mass function). This will allow us to perform a realistic simulation of eROSITA’s observing pro- gram. 18 Acta Polytechnica Vol. 51 No. 6/2011 This research was funded by the Bundesmin- isterium für Wirtschaft und Technologie under Deutsches Zentrum für Luft- und Raumfahrt grant numbers 50 QR 0903 and 50 OR 0801. References [1] Tinker, J., Kravtsov, A. V., Klypin, A., et al.: Astrophys. J. 688, 709, 2008. [2] Komatsu, E., Smith, K. M., Dunkley, J., et al.: Astrophys. J. Suppl. Ser. 192, 18, 2011. [3] Perlmutter, S., Schmidt, B. P.: In K. Weiler (ed.) Supernovae and Gamma-Ray Bursters. Lecture Notes in Physics, Berlin Springer Ver- lag, 598, 195, 2003. 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Johannes Hölzl Jörn Wilms Ingo Kreykenbohm Christian Schmid Christoph Grossberger Michael Wille Wiebke Eikmann Thorsten Brand Dr. Karl Remeis-Sternwarte/ECAP Universität Erlangen-Nürnberg,Germany 19