Abstract We present high-resolution (0.3 arcsec) Atacama Large Millimeter Array (ALMA) 870 μm imaging of five z ≈ 1.5–4.5 X-ray detected AGN (with luminosities of L2–8keV > 1042 erg s−1). These data provide a ≳20 times improvement in spatial resolution over single-dish rest-frame far-infrared (FIR) measurements. The sub-millimetre emission is extended on scales of FWHM ≈ 0.2 arcsec–0.5 arcsec, 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 FIR emission to dust heated by star formation. The implied star-formation rate surface densities are ≈20–200 M⊙ yr−1 kpc−2, which are consistent with SMGs of comparable FIR luminosities (i.e. LIR ≈ [1–5] × 1012 L⊙). 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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