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How Accurately Can the SZ Effect Measure Peculiar Cluster Velocities

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How Accurately Can the SZ Effect Measure Peculiar Cluster Velocities A&A 374, 1–12 (2001) Astronomy DOI: 10.1051/0004-6361:20010659 & c ESO 2001 Astrophysics How accurately can the SZ effect measure peculiar cluster velocities and bulk flows? N. Aghanim1,K.M.G´orski2,3, and J.-L. Puget1 1 IAS-CNRS, Bˆatiment 121, Universit´e Paris Sud, 91405 Orsay Cedex, France 2 ESO, Karl-Schwarzschild-Str. 2, 85748 Garching bei M¨unchen, Germany 3 Warsaw University Observatory, Poland Received 30 January 2001 / Accepted 4 May 2001 Abstract. The Sunyaev-Zel’dovich effect is a powerful tool for cosmology that can be used to measure the radial peculiar velocities of galaxy clusters, and thus to test, and constrain theories of structure formation and evolution. This requires, in principle, an accurate measurement of the effect, a good separation between the Sunyaev- Zel’dovich components, and a good understanding of the sources contributing to the signal and their effect on the measured velocity. In this study, we evaluate the error in the individual radial peculiar velocities determined with Sunyaev-Zel’dovich measurements. We estimate, for three cosmological models, the errors induced by the major contributing signals (primary Cosmic Microwave Background anisotropies, Sunyaev-Zel’dovich effect due to the background cluster population, residuals from component separation and instrumental noise). We generalise our results to estimate the error in the bulk velocity on large scales. In this context, we investigate the limitation due to the Sunyaev-Zel’dovich source (or spatial) confusion in a Planck-like instrumental configuration. Finally, we propose a strategy based on the future all-sky Sunyaev-Zel’dovich survey, that will be provided by the Planck mission, to measure accurately the bulk velocities on large scales up to redshift 1, or more. Key words. cosmology: cosmic microwave background, large-scale structure of Universe – galaxies: clusters 1. Introduction surveys, and by some established relationships which give independent distances to the objects, such as the Faber- One of the major fields of research in cosmology is the Jackson (Faber & Jackson 1976) or the Tully-Fisher (Tully study of the large scale matter distribution in the universe. & Fisher 1977) relations. Nevertheless, these methods lead On large scales, the evolution of the matter density fluctu- to uncertainties in the expansion velocity which are pro- ations is adequately described through linear physics. The portional to the distance and thus induce even larger matter distribution thus represents the imprint of the ini- uncertainties when measuring peculiar velocities on very tial density perturbations. Combined with other results, large scales. The velocity fields can be studied using galax- such as those derived from Cosmic Microwave Background ies or galaxy clusters. However, there are more advantages (CMB) observations, this kind of information can probe in studying the deviations from the Hubble flow as traced the structure formation models and the cosmological by galaxy clusters. One of these advantages comes from parameters. the fact that, on scales probed by galaxy clusters, the The luminous matter distribution can be probed underlying density fluctuations are largely in the linear through the direct observation of galaxy, or galaxy clus- regime and therefore very close to the initial conditions ter, distributions but this gives a biased view of the total from which large scale structures developed. Finally, given matter distribution. The latter can be inferred from the observed radial peculiar velocities and the potential flow velocity fields. In fact, the inhomogeneities in the mass assumption, the full three-dimensional velocity field can distribution produce deviations from the Hubble flow re- be derived using reconstruction methods (Bertschinger & ferred to as the peculiar velocities. A few methods have Dekel 1989; Zaroubi et al. 1999 and references therein). been suggested to measure the transverse velocity com- The inferred density field is, in principle, representative of ponents, e.g., Birkinshaw (1983) and Birkinshaw & Gull both the dynamical evolution of the structure and the un- (1983). However, in practice, the radial component of the derlying total matter distribution. Therefore, comparisons peculiar velocities can only be measured using redshift between the reconstructed total matter distribution from Send offprint requests to: N. Aghanim, velocity fields and CMB fluctuations and that traced by e-mail: [email protected] Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20010659 2 N. Aghanim et al.: How accurately can the SZ effect measure peculiar and bulk velocities? galaxies can test and constrain theories of structure for- In this paper, we investigate quantitatively the accuracy mation and evolution, and cosmological models. of such a measurement, within the context of Planck. Moreover, given cluster radial peculiar velocities at As described in Sects. 2 and 3, the combination of the known positions, cluster motions can be used as cosmo- so-called kinetic and thermal SZ effects allows us to mea- logical probes using various statistical quantities among sure the radial peculiar velocity. However, this measure- which are the velocity frequency distribution, the power ment is affected by errors due to astrophysical contribu- spectrum, the velocity dispersions, the pairwise velocities, tions (CMB, background cluster population), to residuals the velocity correlation function, and the bulk flows. As from the component separation and to instrumental noise. already mentioned, relative errors in the distance determi- In Sect. 5, we present the method used to evaluate the rms nation lead to the peculiar velocity uncertainty increasing error which affects the peculiar velocity measurement. We linearly with distance. As a consequence, all the statisti- give, for three cosmological models, the results obtained cal quantities derived from observed velocities suffer from for the major sources of error in terms of the rms error large errors especially at high redshifts. For example, in as a function of the cluster size for a Planck measure- the case of the bulk velocity, which is the average of the ment. These errors are evaluated using simulated maps. local velocity field smoothed over a window function of The cluster model and the map simulation are presented −1 −1 scale Rh Mpc (h = H0/(100 km s /Mpc) is the nor- in Sect. 4. In Sect. 6, we generalise the computation of malised Hubble constant), several measurements exist in the rms error to the bulk velocities at an illustrative scale − the literature (Dressler et al. 1987; Courteau et al. 1993; of 100 h 1 Mpc. We discuss our results and conclude in Willick et al. 1996; Giovanelli et al. 1998; Hudson et al. Sect. 7. 1999; Willick 1999). Whereas most of these studies agree In the following, we use the baryon density Ωb =0.06 on the reality of a significant bulk flow within 50 h−1 Mpc; (Walker et al. 1991). We discuss three cosmological mod- the situation is more controversial at larger scales where els: an open model with a density parameter Ωm =0.3, the accuracy of the determination of the bulk velocities and two flat models: one with a non-zero cosmological decreases. constant (Ωm =0.3andΩΛ =0.7), and the other with no In order to overcome the problem of large uncertainties cosmological constant (Ωm =1). in the peculiar velocities, we must find ways of measuring them with a redshift independent accuracy. In this con- 2. The SZ (thermal and kinetic) effect text, the Sunyaev-Zel’dovich (SZ) effect is a very promis- ing, and potentially sensitive, tool. As proposed initially The SZ effect comprises the so-called thermal and kinetic by Sunyaev & Zel’dovich (1980), the radial peculiar ve- effects. The thermal SZ effect is the inverse Compton in- locity of galaxy clusters can be determined using SZ mea- teraction between CMB photons and the free electrons surements, which are in addition distance independent. In of the hot intra-cluster medium. Its amplitude is charac- the forthcoming years several experiments (ground based, terised by the Compton parameter y – the integral of the balloon borne or space) will measure the SZ effect and pressure along the line of sight – which depends only on perform SZ surveys (AMIBA, ARCHEOPS, BOLOCAM, the cluster electron temperature and density (Te, ne): MAP, ...). These experiments, of which the Planck satel- Z lite1 is the best example, are designed so that the sensi- kσT y = 2 Te(l)ne(l)dl, (1) tivity, the frequency coverage and the angular resolution mec allow a very good separation of the two SZ effect compo- where k is the Boltzmann constant, σT the Thomson cross nents (thermal and kinetic, see Sect. 2), and a best possible section, me the electron mass, c the speed of light and l evaluation of the foreground (galactic and extra-galactic) is the distance along the line of sight. If the intra-cluster emissions that contribute to the measured signal. In this gas is isothermal (Te(l)=Te =const),yRis expressed as a context, we expect that the number of observed SZ clus- function of the optical depth τ (τ = σT ne(l)dl): ters will rapidly increase, thus allowing the radial peculiar velocity of clusters to be measured and providing a useful kTe · y = τ 2 (2) cosmological tool. This kind of project has already been mec undertaken on a sample of 40 known galaxy clusters with redshifts ranging between 0.1 and 0.3 by the SUZIE team The inverse Compton interaction conserves the number of (Holzapfel et al. 1997). Nevertheless, the accuracy in indi- photons and shifts their spectrum, on average, to higher vidual clusters is limited by the contamination from other frequencies. This can be observed as the induced relative components of the microwave sky. It has been suggested by monochromatic intensity difference between Compton dis- Aghanim et al.
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