Observations by the Atacama Large Millimetre/sub-millimetre Array of the 358 GHz continuum emission of the gravitationally lensed quasar host RX J0911.4+0551 have been analysed. They complement earlier Plateau de Bure Interferometer observations of the CO(7-6) emission. The good knowledge of the lensing potential obtained from Hubble Space Telescope observations of the quasar makes a joint analysis of the three emissions possible. It gives evidence for the quasar source to be concentric with the continuum source within 0.31 kpc and with the CO(7-6) source within 1.10 kpc. It also provides a measurement of the size of the continuum source, 0.76 $pm$ 0.04 kpc FWHM, making RX J0911.4+0551 one of the few high redshift galaxies for which the dust and gas components are resolved with dimensions being measured. Both are found to be very compact, the former being smaller than the latter by a factor of $sim$3.4$pm$0.4. Moreover, new measurements of the CO ladder $-$ CO(10-9) and CO(11-10) $-$ are presented that confirm the extreme narrowness of the CO line width (107$pm$20 km s$^{-1}$ on average). Their mere detection implies higher temperature and/or density than for typical quasar hosts at this redshift and suggests a possible contribution of the central AGN to gas and dust heating. The results are interpreted in terms of current understanding of galaxy evolution at the peak of star formation. They suggest that RX J0911.4+0551 is a young galaxy in an early stage of its evolution, having experienced no recent major mergers, star formation being concentrated in its centre.
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