We present Chandra ACIS-S and ATCA radio continuum observations of the strongly lensed dusty , star-forming galaxy SPT-S J034640-5204.9 ( hereafter SPT0346-52 ) at z = 5.656 .
This galaxy has also been observed with ALMA , HST , Spitzer , Herschel , APEX , and the VLT .
Previous observations indicate that if the infrared ( IR ) emission is driven by star formation , then the inferred lensing-corrected star formation rate ( \sim 4500 M _ { \sun } yr ^ { -1 } ) and star formation rate surface density \Sigma _ { SFR } ( \sim 2000 M _ { \sun } { yr ^ { -1 } } { kpc ^ { -2 } } ) are both exceptionally high .
It remained unclear from the previous data , however , whether a central active galactic nucleus ( AGN ) contributes appreciably to the IR luminosity .
The Chandra upper limit shows that SPT0346-52 is consistent with being star-formation dominated in the X-ray , and any AGN contribution to the IR emission is negligible .
The ATCA radio continuum upper limits are also consistent with the FIR-to-radio correlation for star-forming galaxies with no indication of an additional AGN contribution .
The observed prodigious intrinsic IR luminosity of ( 3.6 \pm 0.3 ) \times 10 ^ { 13 } L _ { \sun } originates almost solely from vigorous star formation activity .
With an intrinsic source size of 0.61 \pm 0.03 kpc , SPT0346-52 is confirmed to have one of the highest \Sigma _ { SFR } of any known galaxy .
This high \Sigma _ { SFR } , which approaches the Eddington limit for a radiation pressure supported starburst , may be explained by a combination of very high star formation efficiency and gas fraction .