The Herschel Virgo Cluster survey, XVI : a cluster inventory

Herschel far-infrared (FIR) observations are used to construct Virgo cluster galaxy luminosity functions and to show that the cluster lacks the very bright and the numerous faint sources detected in field galaxy surveys. The FIR spectral energy distributions are fitted to obtain dust masses and temperatures and the dust mass function. The cluster is overdense in dust by about a factor of 100 compared to the field. The same emissivity (beta)-temperature relation applies for different galaxies as that found for different regions of M31. We use optical and H i data to show that Virgo is overdense in stars and atomic gas by about a factor of 100 and 20, respectively. Metallicity values are used to measure the mass of metals in the gas phase. The mean metallicity is similar to 0.7 solar, and similar to 50 per cent of the metals are in the dust. For the cluster as a whole, the mass density of stars in galaxies is eight times that of the gas and the gas mass density is 130 times that of the metals. We use our data to consider the chemical evolution of the individual galaxies, inferring that the measured variations in the effective yield are due to galaxies having different ages, being affected to varying degrees by gas loss. Four galaxy scaling relations are considered: mass-metallicity, mass-velocity, mass-star formation rate and mass-radius - we suggest that initial galaxy mass is the prime driver of a galaxy's ultimate destiny. Finally, we use X-ray observations and galaxy dynamics to assess the dark and baryonic matter content compared to the cosmological model