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How reliable is the 66-billion-solar-mass estimate for TON 618?

I've been looking into TON 618 recently, and the part I find more interesting than the usual "biggest black hole" headline is how uncertain the actual mass estimate is.

The number you usually see is around 66 billion solar masses, but another analysis using a different emission line estimated roughly 40.7 billion.

That's still an absolutely enormous black hole, but the difference between those estimates is huge.

Since we can't observe the black hole directly, the mass has to be inferred from things like the motion of the gas around the quasar and the properties of its emission lines.

So I'm curious about the physics here:

How much uncertainty is normally expected from these virial mass estimates? And when we're dealing with an extreme quasar like TON 618, should we really be treating 66 billion as a precise measurement, or more as an approximate estimate?

I ended up going down a pretty deep rabbit hole on this and put together a longer explanation of what I found. For anyone interested, here's the video I made while researching it:

https://youtu.be/HQU93Ur0BFo

I'm especially interested in hearing from people who work with quasars or black-hole mass measurements.
#science
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