The Distance to Clusters: Correcting for Asphericity

Abstract

X-ray and Sunyaev-Zeldovich (SZ) effect observations can be combinedto measure the distance to clusters of galaxies. The Hubble constant,H 0 , can be inferred from the distance to low-redshift clusters.With enough clusters to measure the redshift-distance relation outto a redshift z ~ 1, it may be possible to determine the total matterdensity, Ω 0 , and the cosmological constant, Λ 0 , as well. Ifthe intracluster gas distribution is not spherical but elongatedby a factor of Z along the line of sight, the inferred distance isincreased by Z , and H 0 is decreased by the same factor. Averagingthe inferred value of H 0 over a sufficiently large sample of clusterscan reduce any systematic bias due to cluster shapes, provided theclusters are selected without any preferred orientation. Even so,elongation contributes significantly to the variance in the measureddistances and in the inferred value of H 0 . With the addition ofgravitational lensing observations, it is possible to infer the three-dimensionalshape of an individual cluster, provided the gas is in hydrostaticequilibrium. We demonstrate a specific method for finding the shapeand correcting the measured distances to individual clusters. Totest this method, we apply it to artificial observations of idealizedellipsoidal model clusters. We base the artificial X-ray observationson the Chandra X-Ray Observatory . For the SZ effect, we assume modestimprovements over current observations at the Owens Valley RadioObservatory. We recover the true distances to each of our model clusterswithout detectable bias and with statistical errors due to measurementuncertainties of 4%-6%.