We present high resolution (0.3) Atacama Large Millimeter Array (ALMA) 870um imaging of five z~1.5-4.5 X-ray detected AGN with luminosities of L(2-8keV)>10^42 erg/s. These data provide a >~20x improvement in spatial resolution over single-dish rest-frame FIR measurements. The sub-millimetre emission is extended on scales of FWHM~0.2-0.5, corresponding to physical sizes of 1-3 kpc (median value of 1.8 kpc). These sizes are comparable to the majority of z=1-5 sub-millimetre galaxies (SMGs) with equivalent ALMA measurements. In combination with spectral energy distribution analyses, we attribute this rest-frame far-infrared (FIR) emission to dust heated by star formation. The implied star-formation rate surface densities are ~20-200 Mo/yr/kpc^2, which are consistent with SMGs of comparable FIR luminosities (i.e., L(IR)~[1-5]x10^(12)Lo). Although limited by a small sample of AGN, which all have high FIR luminosities, our study suggests that the kpc-scale spatial distribution and surface density of star formation in high-redshift star-forming galaxies is the same irrespective of the presence of X-ray detected AGN.
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