Measurement of the Relativistic Sunyaev-Zeldovich Correction in RX J1347.5-1145

We present a measurement of the relativistic corrections to the thermal Sunyaev-Zel'dovich (SZ) effect spectrum, the rSZ effect, toward the massive galaxy cluster RX J1347.5-1145 by combining submillimeter images from Herschel-SPIRE with millimeter wavelength Bolocam maps. Our analysis simultaneously models the SZ effect signal, the population of cosmic infrared background galaxies, and the galactic cirrus dust emission in a manner that fully accounts for their spatial and frequency-dependent correlations. Gravitational lensing of background galaxies by RX J1347.5-1145 is included in our methodology based on a mass model derived from the Hubble Space Telescope observations. Utilizing a set of realistic mock observations, we employ a forward modeling approach that accounts for the non-Gaussian covariances between the observed astrophysical components to determine the posterior distribution of SZ effect brightness values consistent with the observed data. We determine a maximum a posteriori (MAP) value of the average Comptonization parameter of the intracluster medium (ICM) within R (2500) to be y(2500) = 1.56 x 10(-4), with corresponding 68% credible interval [1.42, 1.63] x 10(-4), and a MAP ICM electron temperature of T (sz)(2500) = 22.4 keV with 68% credible interval spanning [10.4, 33.0] keV. This is in good agreement with the pressure-weighted temperature obtained from Chandra X-ray observations, T (x,pw)(2500) = 17.4 +/- 2.3 keV. We aim to apply this methodology to comparable existing data for a sample of 39 galaxy clusters, with an estimated uncertainty on the ensemble mean T (sz)(2500) at the similar or equal to 1 keV level, sufficiently precise to probe ICM physics and to inform X-ray temperature calibration.