Although it is widely accepted that most galaxies have supermassive black holes (SMBHs) at their centers1-3, concrete proof has proved elusive. Sagittarius A* (Sgr A*)4, an extremely compact radio source at the center of our Galaxy, is the best candidate for proof5-7, because it is the closest. Previous Very Long Baseline Interferometry (VLBI) observations (at 7mm) have detected that Sgr A* is 2 astronomical unit (AU) in size8, but this is still larger than the "shadow" (a remarkably dim inner region encircled by a bright ring) arising from general relativistic effects near the event horizon9. Moreover, the measured size is wavelength dependent10. Here we report a radio image of Sgr A* at a wavelength of 3.5mm, demonstrating that its size is 1 AU. When combined with the lower limit on its mass11, the lower limit on the mass density is 6.5*1021 Msun pc-3, which provides the most stringent evidence to date that Sgr A* is an SMBH. The power-law relationship between wavelength and intrinsic size (size \propto wavelength1.09), explicitly rules out explanations other than those emission models with stratified structure, which predict a smaller emitting region observed at a shorter radio wavelength.
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