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# SMBH Mass Calculation

the post:

Astronomers Solve the Mystery of Small Galaxies with Monster Black Holes

my comment:

This post offers an interesting mystery.

'
There's a very peculiar relationship between the mass of the black hole at the center of a galaxy and the properties of the galactic host itself. For example, the bigger the galaxy, the bigger the black hole. But there are a few strange exceptions to this general trend.
'

The story claims a big SMBH can be found in a small galaxy.

What is the correct mass for this mystery?

There is only one method right now to calculate the mass of a black hole and it is not being used.

Kepler's third law of planetary motion described the relationship in an ellipse between orbit size and duration.
Newton modified this formula by including the solar mass.

Using this formula with the Keplerian orbit parameters the result is the number of solar masses at the focus.

This is being attempted with stars near the Milky Way core but unfortunately with the congestion there the observed orbit durations are always too brief for the observed orbit diameter.
This has been tried with S0-2 and S0-102.

Their observed orbits:
S0-102 axis = 260 AU, duration = 11.5 yr
S0-2 axis = 970 AU, duration 15.56 yr

With Kepler's third law and those orbit diameters:

S0-102 axis = 260 AU, calculated duration about 4000 yr
S0-2 axis = 970 AU, calculated duration about 30300 yr

Of course we do not have data for those stars spanning this number of years.

These are not valid ellipses with those parameters. The orbits are too disturbed.

I expect we do not yet have the imaging capability to observe individual stars around the cores of more distant galaxies, over such a long span of time.

When astronomers claim a specific mass for the SMBH in a galaxy the value has no basis. The current practice is simply a larger galaxy must have a larger SMBH.

Until there is actually a calculation with a valid ellipse every black hole mass must be a guess.
To claim a SMBH is more or less massive than expected has no basis. The mystery described in this story is not present; it is just confusion.

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