Although it is widely accepted that most galaxies have supermassive black holes at their centres(1-3), concrete proof has proved elusive. Sagittarius A* (Sgr A*)(4), an extremely compact radio source at the centre of our Galaxy, is the best candidate for proof(5-7), because it is the closest. Previous very-long-baseline interferometry observations ( at 7 mm wavelength) reported that Sgr A* is similar to 2 astronomical units (AU) in size(8), but this is still larger than the 'shadow' ( a remarkably dim inner region encircled by a bright ring) that should arise from general relativistic effects near the event horizon of the black hole(9). Moreover, the measured size is wavelength dependent(10). Here we report a radio image of Sgr A* at a wavelength of 3.5 mm, demonstrating that its size is similar to 1 AU. When combined with the lower limit on its mass(11), the lower limit on the mass density is 6.5 x 10(21) M-. pc(-3) (where M-. is the solar mass), which provides strong evidence that Sgr A* is a supermassive black hole. The power-law relationship between wavelength and intrinsic size ( size proportional to wavelength(1.09)) 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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