Final answer:
The total luminosity of Sgr A*, a supermassive black hole in the center of the Milky Way Galaxy, is not readily quantified as Sgr A* itself is not luminous, but its environment can emit radiation influenced by the black hole's presence.
Step-by-step explanation:
The total luminosity of the source Sgr A*, located at the center of our Milky Way Galaxy, can be inferred based on its mass and the properties of the stars and luminous matter within the galaxy. Sgr A* is not a traditional star but a supermassive black hole with a mass of about 4 million solar masses. The luminosity of Sgr A* across all wavelengths is relatively low compared to its mass due to the nature of black holes, which do not emit light in the same way as stars. However, the area surrounding Sgr A* can emit radiation due to the acceleration of matter as it approaches the event horizon. The comparison of luminosities among astronomical objects generally uses the mass-luminosity relationship, which suggests that luminosity varies approximately as the fourth power of the mass. Considering the immense mass of Sgr A*, it would be expected to have a high luminosity if it behaved like a star; however, its actual observed luminosity is much lower because it is not a luminous object in the standard sense.
Therefore, while exact figures are not provided, the significance of Sgr A*'s luminosity lies less in its own emission and more in the activity and emissions from its surrounding environment.