  The aim of this study is to quantify the infrared luminosity of clusters as a
function of redshift and compare this with the X-ray luminosity. This can
potentially constrain the origin of the infrared emission to be intracluster
dust and/or dust heated by star formation in the cluster galaxies. We perform a
statistical analysis of a large sample of galaxy clusters selected from
existing databases and catalogues.We coadd the infrared IRAS and X-ray RASS
images in the direction of the selected clusters within successive redshift
intervals up to z = 1. We find that the total infrared luminosity is very high
and on average 20 times higher than the X-ray luminosity. If all the infrared
luminosity is to be attributed to emission from diffuse intracluster dust, then
the IR to X-ray ratio implies a dust-to-gas mass abundance of 5e-4. However,
the infrared luminosity shows a strong enhancement for 0.1 < z < 1, which
cannot be attributed to cluster selection effects. We show that this
enhancement is compatible with a star formation rate in the member galaxies
that is typical of the central Mpc of the Coma cluster at z = 0 and evolves
with the redshift as (1+z)^5. It is likely that most of the infrared luminosity
that we measure is generated by the ongoing star formation in the member
galaxies. From theoretical predictions calibrated on extinction measurements
(dust mass abundance equal to 1e-5), we expect only a minor contribution, of a
few percent, from intracluster dust.
