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Metal-mass-to-light ratios of the Perseus cluster out to the virial radius

We analyzed XMM-Newton data of the Perseus cluster out to $\sim$1 Mpc, or approximately half the virial radius. Using the flux ratios of Lyalpha lines of H-like Si and S to Kalpha line of He-like Fe, the abundance ratios of Si/Fe and S/Fe of the intracluster medium (ICM) were derived using the APEC plasma code v2.0.1. The temperature dependence of the line ratio limits the systematic uncertainty in the derived abundance ratio. The Si/Fe and S/Fe in the ICM of the Perseus cluster show no radial gradient. The emission-weighted averages of the Si/Fe and S/Fe ratios outside the cool core are 0.91 +- 0.08 and 0.93 +- 0.10, respectively, in solar units according to the solar abundance table of Lodders (2003). These ratios indicate that most Fe was synthesized by supernovae Ia. We collected K-band luminosities of galaxies and calculated the ratio of Fe and Si mass in the ICM to K-band luminosity, iron-mass-to-light ratio (IMLR) and silicon-mass-to-light ratio (SMLR). Within $\sim$1 Mpc, the cumulative IMLR and SMLR increase with radius. Using Suzaku data for the northwest and east directions, we also calculated the IMLR out to $\sim$ 1.8 Mpc, or about the virial radius. We constrained the SMLR out to this radius and discussed the slope of the initial mass function of stars in the cluster. Using the cumulative IMLR profile, we discuss the past supernova Ia rate.