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Prospects for the Planck Satellite: limiting the Hubble Parameter by SZE/X-ray Distance Technique R. Holanda & J. A. S. Lima (IAG-USP) I Workshop “Challenges of New Physics in Space” (2009)

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Summary The Recent measurements of H 0 Sunyaev-Zeldovich effect (SZE) and X-ray surface brightness technique for measuring distance from galaxy clusters H 0 estimates from SZE/X-ray technique by using some cosmological sceneries Prospects for the Planck Satellite Conclusions Summary

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The Hubble Parameter An accurate value for the Hubble parameter has proved extremely challenging. An approach has been to measure distances of nearby objects and use this knowledge to calibrate the brightness of more distant objects compared to the nearby ones. The Hubble Space Telescope Key Project (Freedman et al 2001) calibrated five secondary distance indicators by using a fiducial Cepheid Period-Luminosity (PL) relation based on variables located in the Large Magellanic Cloud (LMC). Distance modulus to LMC adopted = 18.5 ±0.1 mag

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The Hubble Parameter measurements Two significant sources of systematic error: The distance to LMC: independent estimates disagree by as much as 0.5 mag. “We note that if the distance modulus to the LMC is 18.3 mag, there will be a resulting 10% increase in the value of H 0 to 79 km/s/Mpc.” (Freedmann et al 2001) * The effect of the metallicity on the Cepheid P-L relation is also controversial. Riess et aI. (2005) and Sandage et al. (2006) analyzed independently the same data (four SNe Ia) and obtained values which are discrepant by twice the systematic erros. Sandage et al. used a metallicity-dependent P-L relation. R05 H 0 = 73 ± 4 Km/s/Mpc ; S06 H 0 = 62 ± 6 Km/s/Mpc

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The Hubble Parameter measurements Spergel et al. (WMAP3) obtained H 0 =73 ± 3 km/s/Mpc from CMB (assuming flat spatial geometry, time independent vacuum energy and cold dark matter) More recently, Russel (2009, Journal of astrophysics and astrophysics accepted) by using the morphologically type dependent K-band Tully-Fischer relation obtained H 0 = 83.4 ± 5 km/s/Mpc (218 ScI galaxies) Therefore, it is still very important to improve and compare the estimates of H 0 among independent methods.

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Sunyaev-Zeldovich Effect and X-ray + The Sunyaev-Zel'dovich effect is a small distortion of the CMB spectrum provoked by the scattering of the CMB photons by hot electrons in galaxy clusters. When combined with other observations of galaxies clusters such as X-ray emission from the intracluster gas is possible to calculate the angular diameter distance (ADD) from the cluster.

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Measurements of the h parameter from ADD (SZE/X-ray) It should be stressed, however, that in the above quoted determinations of the Hubble constant, a specific cosmology was fixed from the very beginning (flat ΛCDM; Ω M =0.3). An interesting possibility to break the degeneracy is a joint analysis involving the ADD, baryon acoustic oscillations (BAO) signature and a CMB signature known as Shift Parameter. In a joint analysis is possible to use a maximum likelihood that can be determined by a χ 2 statistics. We estimate H 0 by using 25 ADD from ellipsoidal geometry clusters obtained from SZE and X-ray surface brightness (De Filippis et al. 2005). But here, we relaxed the flat geometry of the ΛCDM model and tested the dependence of the method with the equation of state parameter.

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*(in preparation) ΛCDM Model (Ω k ≠0)Flat ωCDM (p=ωρ)

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Prospects for the Planck Mission The Planck satellite is a mission of the European Space Agency (launch Date - 05-14-2009). It has been estimated that Planck will see about 30.000 galaxy clusters over the whole sky via the tSZ e ﬀ ect. So, It will produce a large all-sky sample of clusters with easily computable selection criteria. 0 ≤ z ≤ 0.5 180 clusters 10 bins (Δz = 0.05) 18/bin 8% 0.5 ≤ z ≤ 0.8 96 clusters 6 bins 16/bin 10% 0.8 ≤ z ≤ 1 64 clusters 4 bins 16/bin 12% ADD error 2. Fiducial Model = ωCDM (h = 0.71; Ω X = 0.7; Ω M = 0.30, ω = - 0.76 ) 1. Fiducial Model = ΛCDM (h = 0.73; Ω k = -0.01; Ω Λ = 0.735; Ω M = 0.276 ) We simulate this sample of ADD by using two fiducial models with best fits from De Filippis et al. (2005) sample. Currently we have 307 SNe Ia (Union08). Let us now assume that in the near future we will have 340 Galaxy Clusters

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Fiducial Model = ΛCDM (h = 0.73; Ω k = -0.01; Ω Λ = 0.736; Ω M = 0.27 )Fiducial Model = ωCDM (h = 0.71; Ωx = 0.7; Ω M = 0.30, ω = - 0.76 ) A larger and better ADD sample supply constraints significantly restrictive on the parameters space. This simple analysis illustrates the interest for obtaining a larger galaxy cluster sample with simultaneous measurements of SZE and X-ray surface brightness.

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25 ADD from clusters by using the spherical β-Model to describe the clusters (Bonamente et al sample (2006)) + BAO + SP 25 ADD from clusters by using the elliptical β- model to describe the clusters (De Filippis et al. Sample (2005)) + BAO + SP ΛCDM Local Physics and Cosmology: Effects from Cluster Geometry We cannot see a significant influence of the geometries assumed to describe the cluster on the H 0 measurement.

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A better understanding on the intrinsic cluster shape is necessary. Any discrepancy with independent determinations of h must be associated with a possible triaxiality of the clusters. Local Physics and Cosmology: Effects from Cluster Geometry Can the cosmology decides on the geometry of the galaxy clusters?* WMAP3 * In preparation

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Conclusions The combination of independent phenomena (SZE/X-ray, BAO and shift parameter) provides an interesting method to constrain the Hubble parameter. The geometry of the ΛCDM universe has an insignificant influence on the h measurements, which also remains statistically the same even applying a flat ωCDM model instead. The central h (≈ 0.73) value derived here is in agreement with others recent estimates coming from WMAP and Hubble Space telescope Key Project, where h=0.73. We assess the ability of the Planck satellite mission, which aims at collecting a large number of galaxy clusters, to obtain more restrictive limits in parameters space (h x Ω M, h x Ω k etc )

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