Abstract
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 sub-mm images from Herschel-SPIRE
with mm-wave Bolocam maps. Our analysis simultaneously models the SZ effect
signal, the population of cosmic infrared background (CIB) galaxies, and
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 HST observations. Utilizing a set of realistic mock
observations, we employ a forward modelling approach that accounts for the
non-Gaussian covariances between 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 intra-cluster medium (ICM) within R$_2500$ to
be $y \rangle_2500 = 1.56 10^-4$, with corresponding 68~per
cent credible interval $1.42,1.63 10^-4$, and a MAP ICM electron
temperature of $T_sz \rangle_2500 = 22.4$~keV
with 68~per cent credible interval spanning $10.4,33.0$~keV. This is in good
agreement with the pressure-weighted temperature obtained from Chandra
X-ray observations, $T_x,pw\rangle_2500 = 17.4
2.3$~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 $T_sz \rangle_2500$ at the $1$~keV
level, sufficiently precise to probe ICM physics and to inform X-ray
temperature calibration.
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