Constrained Cluster Parameters from Sunyaev‐Zel’dovich Observations

Near-future SZ surveys such as ACT, SPT, APEX, and Planck will find thousandsof galaxy clusters. Multi-frequency arcminute-resolution SZ observations can,in principle, determine each cluster's gas temperature (T_e), bulk velocity(v_pec), and optical depth (tau). However, the frequency bands and detectorsensitivity employed by upcoming surveys will generally not be sufficient todisentangle the degeneracy between these three cluster parameters, even in theabsence of SZ signal contamination from point sources and imperfect primarymicrowave background subtraction. Assuming contaminants can be removed, we findthat near-future SZ surveys will be able to constrain well two cluster gasparameters that are linear combinations of tau*T_e, tau*v_z, and tau*T_e^2.Because the SZ intensity shift is nearly a linear function of tau*T_e, tau*v_z,and tau*T_e^2, a correspondence exists between the two effective gas parametersthat SZ surveys can constrain and simple line-of-sight integrals through thethree dimensional cluster. We illustrate the parameter constraints andcorrespondence to line-of-sight integrals using 3D Nbody + hydro clustersimulations and a Markov chain Monte Carlo method. We show that adding anindependent T_e measurement to upcoming SZ data breaks the parameterdegeneracy. The cluster effective velocity thus constrained is approximatelythe optical-depth-weighted velocity integrated along the cluster line of sight.A temperature prior with an error as large as 2 keV still gives bulk velocityerrors < 100 km/sec, even for a more typical cluster with an electrontemperature of 3 keV, for ACT-like SZ observations in the absence of signalcontamination. The Markov chain constraints on v_pec and tau are moreencouraging and likely more accurate than those obtained from Fisher matrices.Comment: 31 pages, 15 figures. Typo corrected; accepted by Ap