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Phys.org's Hiding black hole found says:

A research team led by Shunya Takekawa at the National Astronomical Observatory of Japan noticed HCN-0.009-0.044, a gas cloud moving strangely near the center of the galaxy 25,000 light-years away from Earth in the constellation Sagittarius. They used ALMA (Atacama Large Millimeter/submillimeter Array) to perform high-resolution observations of the cloud and found that it is swirling around a massive invisible object.

Takekawa says, "Detailed kinematic analyses revealed that an enormous mass, 30,000 times that of the sun, was concentrated in a region much smaller than our solar system. This and the lack of any observed object at that location strongly suggests an intermediate-mass black hole. By analyzing other anomalous clouds, we hope to expose other quiet black holes."

The paper is Indication of Another Intermediate-mass Black Hole in the Galactic Center and is open access.

The quote in the second paragraph is all over the internet. I have found that sciencedaily and iflscience both link back to the same quote on an official NAO page here.

Takekawa explains, “Detailed kinematic analyses revealed that an enormous mass, 30,000 times that of the Sun, was concentrated in a region much smaller than our Solar System.”

Questions: How do they know that the central mass is "concentrated in a region much smaller than our Solar System"?

This answer about the paper and subsequent discussions below it don't seem to shed any light on this particular question. The NAO page does not indicate the origin of the quote, I'm wondering if it is a translation of a corresponding Japanese language page on the same site that explains further.

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The authors were able to successfully model the motion of the gas streams as Keplerian orbits around an object of $\sim30000M_{\odot}$. In doing so, they derived some key quantities, such as the pericentric distances of these two gas components (the "Balloon" and the "Stream"). One has its closest approach at $\sim0.21$ pc; the other has its closest approach at $\sim0.07$ pc ($14000\text{ AU}$). This places the pericenter well inside the Oort Cloud, and therefore inside the Solar System.

Therefore, given that it's highly unlikely that the Balloon skims the surface of the central object, we can say that the object's radius is certainly less than that of the Oort Cloud, and by extension, the Solar System. This is a key part of the argument that the object is, in fact, an intermediate mass black hole, as they note on Page 5. It's basically the same logic used to constrain the size of Sagittarius A* based on those infrared flares observed last year.

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    $\begingroup$ Ah, thanks! I was thinking circa 100 AU, but that's not the right number. I guess by the time the quote made it to popular media it should have had an explainer attached. I think that the general public still thinks that Pluto is the edge of the solar system. $\endgroup$ – uhoh Mar 4 at 16:02
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    $\begingroup$ @uhoh I agree; it's definitely misleading, and I'd say a bad move on the part of the journalist. $\endgroup$ – HDE 226868 Mar 8 at 0:30
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I just asked Shunya Takekawa, the first author of the paper, if they actually constrained the size to be "smaller than the Solar System", or if it's just the media's take on "$<0.07\,\mathrm{pc}$".

He answered:

Indeed, the latter is true. It might be an exaggerated expression.
Sorry for the confusion.

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    $\begingroup$ +1 extra credit for the personal research $\endgroup$ – uhoh Mar 5 at 12:28

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