How did they estimate the mass of Sgr A*'s companion G2 without knowing what it was?

Question

Gizmodo.com's Astronomers Spot Unprecedented Flashes From Our Galaxy's Black Hole mentions Sgr A*'s companion gas cloud G2.

That Wikipedia article says:

First noticed as something unusual in images of the center of the Milky Way in 2002, the gas cloud G2, which has a mass about three times that of Earth, was confirmed to be likely on a course taking it into the accretion zone of Sgr A* in a paper published in Nature in 2012.

but later in the same section says:

Nothing was observed during and after the closest approach of the cloud to the black hole, which was described as a lack of "fireworks" and a "flop".[57] Astronomers from the UCLA Galactic Center Group published observations obtained on March 19 and 20, 2014, concluding that G2 was still intact (in contrast to predictions for a simple gas cloud hypothesis) and that the cloud was likely to have a central star.

and

Professor Andrea Ghez et al. suggested in 2014 that G2 is not a gas cloud but rather a pair of binary stars that had been orbiting the black hole in tandem and merged into an extremely large star.

Question: Without knowing what this object is, how could its mass be determined to be only 3 times Earth's mass, way too small to measurably perturb the other stars in close orbits around Sgr A*?

Relevant and interesting reading: The Story of a Boring Encounter with a Black Hole

Answer 1

To put it simply, you can't.

Both cases are explained in these two papers:

Binary: https://arxiv.org/pdf/1410.1884.pdf
Just a Cloud: https://arxiv.org/pdf/1112.3264.pdf

In both cases you have to assume some kind of model to account for the detected fluxes in different near-infrared bands.

• In the "Just-a-cloud" case you would need a cloud with 3 solar masses and a temperature of about 550 K.
• In the "binary-merger" case you would need a 2 solar mass main sequence star covered in gas and dust (possibly generated by a recent merger with a companion, which, however, would somewhat distort the 2 solar mass estimate).