Mem. S.A.It. Suppl. Vol. 5, 313c© SAIt 2004

Memorie della

Supplementi

Simulating the cosmic web

L. Moscardini1, M. Roncarelli1, S. Borgani2, A. Diaferio3, K. Dolag4,

G. Murante5, V. Springel6, G. Tormen4, L. Tornatore2 and P. Tozzi7

1 Dipartimento di Astronomia, Universita di Bologna, via Ranzani 1, I-40127 Bologna,Italy e-mail: lauro.moscardini@unibo.it

2 Dipartimento di Astronomia dell’Universita di Trieste, via Tiepolo 11, I-34131 Trieste,Italy

3 Dipartimento di Fisica Generale “Amedeo Avogadro”, Universita degli Studi di Torino,Torino, Italy

4 Dipartimento di Astronomia, Universita di Padova, vicolo dell’Osservatorio 2, I-35122Padova, Italy

5 INAF, Osservatorio Astronomico di Torino, Strada Osservatorio 20, I-10025 PinoTorinese, Italy

6 Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild Strasse 1, Garching beiMunchen, Germany

7 INAF, Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131 Trieste, Italy

Abstract. We present results on the X–ray properties of clusters and groups of galax-ies, extracted from a large cosmological hydrodynamical simulation assuming the concor-dance ΛCDM cosmological model. The simulation includes radiative cooling assumingzero metallicity, star formation and supernova feedback. We compute X–ray observablesof the intra–cluster medium (ICM) for simulated groups and clusters and analyze their sta-tistical properties. Finally we discuss the contribution of the warm/hot gas located in thecosmic web to the total backgrounds, considering both the (soft and hard) X-ray and milli-metric (Sunyaev-Zel’dovich) band.

Key words. Cosmology: numerical simulations – galaxies: clusters – hydrodynamics –X–ray: galaxies

1. Introduction

To study the X-ray properties of galaxy clustersand the X-ray and millimetric emissions fromthe so-called cosmic web, we use the resultsobtained by analyzing a large-scale cosmo-logical hydrodynamical simulation of a stan-

Send offprint requests to: L. MoscardiniCorrespondence to: Dipartimento di Astronomia,via Ranzani 1, I-40127 Bologna, Italy

dard flat ΛCDM model, with matter densityΩm = 0.3, Hubble constant H0 = 70 kms−1Mpc−1, baryon density Ωbar = 0.04 and nor-malization of the power spectrum σ8 = 0.8[see Borgani et al. (2004) for more details].The run was carried out with the TreeSPHcode GADGET (Springel et al. 2001), by us-ing 4803 dark matter (DM) particles and asmany gas particles. The box size was fixed to192 h−1Mpc; the corresponding mass resolu-

314 L. Moscardini et al.: Simulating the cosmic web

tion is mDM = 4.62 × 109h−1M and mgas =

6.93×108h−1M; the Plummer-equivalent soft-ening length was 7.5h−1 comoving kpc. Thesimulation includes, besides gravity and hy-drodynamics, an accurate treatment of differ-ent physical processes acting on the intraclus-ter medium, like star formation processes (byadopting a sub-resolution multiphase modelfor the interstellar medium), feedback from su-pernovae with the effect of weak galactic out-flows, radiative gas cooling and, finally, heat-ing by a uniform, time-dependent, photoion-izing UV background. In total the simulationrequired about 40,000 CPU hours on 64 pro-cessors of the IBM-SP4 computer located atCINECA. We produced 100 snapshots (corre-sponding to 1.2 Tb of data) logarithmically eq-uispaced between z = 9 and the present time.

2. The X-ray properties of galaxyclusters and groups

Clusters and groups of galaxies have beenidentified by using a standard friends-of-friends algorithm, adopting a linking length of0.15 times the mean DM interparticle separa-tion. At z = 0 we identified 117 cluster withmass larger than 1014h−1M. The largest struc-ture we found has an emission-weighted tem-perature of T ≈ 7 keV. The simulation con-tains 72 objects with T > 2 keV, out of which23 have T > 3 keV. This very large sampleof simulated clusters and groups that are repre-sented with good enough numerical resolutionallows us to obtain reliable estimates of the X-ray observable quantities, such as luminosity,temperature and entropy. An extended analysisof the X-ray properties of our clusters at z = 0and at z ≥ 0.5 can be found in Borgani et al.(2004) and in Ettori et al. (2004), respectively.Here we summarize only the most interestingresults and refer the reader to the quoted pa-pers for a more complete discussion.

In the left panel of Fig. 1, we comparethe observed and the simulated M–T relation,computed at ρ/ρc = 500. The cluster massesare estimated by reproducing the procedurefollowed by Finoguenov et al. (2001). In par-ticular the equation of hydrostatic equilibriumis applied after fitting the gas density profile

to a β–model and assuming a polytropic equa-tion of state. The simulation results show agood agreement with the observed relation.Notice that if we compute the mass directlyfrom the simulation without following the ob-servational procedure we find a normalisationwhich is about 20 per cent higher. This resultindicates that possible biases in the observa-tional mass estimates, related to the assump-tions of β–model profile and hydrostatic equi-librium [see also the discussion by Rasia etal. (2004)], may originate differences betweensimulated and observed M–T relations.

In the right panel of Fig. 1, we comparethe observed and simulated relations betweenbolometric luminosity, LX , and emission–weighted temperature, Tew. The latter has beencomputed weighting the contribution fromeach gas particle according to its emissivity inthe [0.5-10] keV energy band. We found thatthe simulated LX–T relation provides a good fitto data at T∼> 2 keV, while it does not produceany steepening at the scale of groups (Lloyd-Davies et al. 2000). Notice that a recent anal-ysis by Osmond & Ponman (2004) actuallydemonstrates that the present quality of data isnot good enough to allow a precise determina-tion of the LX–T scaling for galaxy groups.

Not all the results from the simulation arein good agreement with the corresponding ob-servational data. For example, the tempera-ture profiles are discrepant: while their shapein the outer regions, at R∼> 0.3R180, is simi-lar to the observed one, simulation profiles aresteadily increasing towards the centers, withno evidence for an isothermal regime followedby a smooth decline at R∼< 0.3 R2500. The en-tropy properties of simulated clusters are alsoquite different from observational results. Inthe outer regions, the entropy profiles from thesimulation are remarkably self–similar, whileobservations show evidence for excess entropyat the scale of groups (Ponman et al. 2003). Inthe inner regions, we detect a significant excessentropy whose amount is almost independentof the cluster temperature. Although the result-ing S –T relation therefore deviates from theself–similar expectation, it is anyway steeperthan observed. Finally the fraction of baryonswhich cool and turn into stars within the virial

L. Moscardini et al.: Simulating the cosmic web 315

Fig. 1. Left panel: Comparison between the observed (blue filled squares) and the simulated (reddots) M–T relation, computed at ρ/ρc = 500. Right panel: Comparison between the observed(red and blue dots) and the simulated (green dots) LX − T .

regions of clusters is f∗ ' 20 per cent, with aslight tendency to be higher for colder systems.This value is substantially smaller than the onefound in simulations that do not include effi-cient feedback mechanisms, but it is still higherthan observed by about a factor of two (Lin etal. 2003).

In general, these results show that the phys-ical processes included in our simulation areable to account for the basic global prop-erties of clusters, such as the scaling rela-tions between mass, temperature and luminos-ity. At the same time, we find indications sug-gesting that a more efficient way of provid-ing non–gravitational heating from feedbackenergy compared to what is implemented inthe simulation is required: this ‘extra heating’should not only reduce the amount of gas thatcools, but also needs to ‘soften’ the gas densityprofiles of poor clusters and groups by increas-ing the entropy of the relevant gas.

3. The contributions to backgroundsfrom the cosmic web

In this Section we want to compare our numer-ical results to other datasets, particularly thoseinvolving the emission properties of the diffuse

gas. Recent results from deep Chandra obser-vations (Brandt et al. 2001; Rosati et al. 2002)have shown that the contribution to the X-raybackground from diffuse baryons in the softband [0.5-2 keV] cannot exceed (2−4)×10−13

erg s−1 cm−2 deg−2. As discussed by Voit &Bryan (2001), this upper limit can be used tofurther constrain the models aimed at describ-ing the physical processes in the gas compo-nent, like the one included in our simulation.Moreover, the intensity and the spatial distri-bution of the signal produced in the millimetricband by the SZ effect, i.e. the Compton scat-tering of the photons of the cosmic microwavebackground with the electrons associated withthe gas in the warm/hot phase (the so-calledWHIM), strongly depend on the thermal his-tory of baryons. Therefore our simulation canbe used to estimate the expected backgroundfrom diffuse, ionized baryons. Unfortunatelythe best observation to date only allow toset an upper limit to the mean comptonisa-tion parameter [y < 1.5 × 10−5, obtained bythe COBE/FIRAS experiment; Fixen et al.(1996)].

Following the work of Croft et al. (2001),we developed and implemented a softwareaimed at extracting the past-light cone, from

316 L. Moscardini et al.: Simulating the cosmic web

Fig. 2. Maps of the diffuse emission intensity in the soft band (left panel) and hard band (rightpanel).

Fig. 3. As Fig. 2, but for the emission from the WHIM.

the numerical experiment by stacking the dif-ferent outputs while avoiding spurious spa-tial alignments thanks to random recenteringsand reflections of the particle coordinates. We

started the production of an extended set of re-alistic X-ray maps, by considering the emis-sion both in the soft [0.5-2 keV] and in the hard[2-10 keV] X-ray bands. Given the large box-

L. Moscardini et al.: Simulating the cosmic web 317

Fig. 4. Maps of the thermal SZ effect. The total signal and the signal coming from the WHIMonly, are shown in the left and right panels, respectively.

size of the simulation, each map covers almost15 square degrees, thanks to the duplication ofthe original boxes at large redshifts. An exam-ple of these maps is shown in Fig. 2, where leftand right panels refer to the total emission inthe soft and hard bands, respectively.

As said, one of our main goals is to es-timate the contribution of the X-ray emissionfrom the WHIM located in the filaments to thetotal background. For this purpose, we isolatedthe emission from gas particles having a tem-perature between 105 and 107 K. The resultingmap, for the same realization shown in Fig. 2,is presented in Fig. 3. Again the results for thesoft and hard bands are shown in the left andright panels, respectively. To characterize theX-ray background in Roncarelli et al. (2004)we are computing different statistics, like themean X-ray background intensity contributedby both galaxy clusters and IGM, the redshiftdistribution of the signal and its hardness ratio,i.e. the ratio between the emission in the hardand soft bands. All the above quantities canbe directly compared to the datasets obtainedfrom deep surveys, thus providing constraintson the various processes affecting the gas com-

ponent and their relative importance. In partic-ular, for the realization shown in the previousfigures, we found that the WHIM has a contri-bution of 1.2×10−12 (1.6×10−14) erg s−1 cm−2

deg−2, in the soft (hard) bands; the total X-rayemission (i.e. including the hot gas in galaxyclusters) is approximately 3 (50) times larger.These values, if confirmed by a more robuststatistical analysis, could create a further prob-lem to the model for the gas physics includedin our simulation.

At the same time we are producing a setof maps showing the emission in the millimet-ric band produced by the thermal SZ effect.The linear relation between the SZ emissivityand gas density allows us to trace the thermalhistory of the hot gas in dark haloes and fil-aments, i.e. in a density environment that iscomplementary to that where the diffuse X-ray emission comes from. In this respect ourhydrodynamical simulation, characterized byits large computational box and sophisticatedtreatment of the gas physics, constitutes a sig-nificant improvement with respect to previoussimilar analyses (White et al. 2002; da Silva et

318 L. Moscardini et al.: Simulating the cosmic web

al. 2004). The SZ map obtained from the samerealization is shown in Fig. 4.

4. Conclusions

Our cosmological simulation shows an en-couraging agreement with some of the mostimportant observed X-ray cluster properties,like e.g. the mass-temperature and luminosity-temperature relations. However, there are alsoa number of discrepancies that remain unac-counted for (e.g. temperature and entropy pro-files). This suggests the need for yet more ef-ficient sources of energy feedback and/or theneed to consider additional physical processwhich may be able to further suppress the gasdensity at the scale of poor clusters and groups,and, at the same time, to regulate the cooling ofthe ICM in central regions.

Acknowledgements. The simulation has been real-ized using the IBM-SP4 machine at the “CentroInteruniversitario del Nord-Est per il CalcoloElettronico” (CINECA, Bologna), with CPU timeassigned thanks to an INAF–CINECA grant.

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