High School Black hole mass and sigma (velocity dispersion)

[Singlau]

It seemed to have been asked before, but I am still a bit confused.

How is the velocity dispersion formed? Doesn't the evidence of dark matter tells us that the orbital speed is uniform in a galaxy?
Is there a direction of dispersion? (e. g velocity gets larger to the core)
And why does velocity dispersion has a positive relation with the bh mass?

It would be great if not much mathematics is needed to explain this. Thanks!

 

[resurgance2001]

I am pretty sure that orbital speed is not constant regardless of dark matter. Velocity dispersion is how much the velocities of different stars differ from one another. It shows up as Doppler shifts, blue and red, which mean invidiual spectral lines become broader.

Supermassive black holes at the centre of galaxies would cause the stars in their vicinity to have very fast orbital rates. The faster these orbital rates the greater the velocity dispersion. The bigger the black hole, the greater its pull and so one would expect the stars (and gas) in the vicinity to be orbiting faster, no? I could have got this wrong. I would like to hear what someone more experienced than myself has to say. Cheers

 

[mfb]

Doesn't the evidence of dark matter tells us that the orbital speed is uniform in a galaxy?

That is reversing the logic. We observe the orbital speeds and infer the existence of dark matter from that.

The orbital velocities very close to the central black hole are very large, but then they quickly drop within a few parsec as the central mass stays the same but the distance increases. Then they have a minimum somewhere, and then rise again slower over a few kiloparsec as the mass from stars close to the galactic center becomes relevant. Over even larger distances, dark matter gets dominant and the rotation speed stays constant or increases/decreases slowly (where we would expect a drop for regular matter alone).

At places where dark matter is relevant the central black hole is irrelevant and vice versa.

 

[Singlau]

The photo is the rotation curve of galaxies, you can see the velocity is nearly flat. Then how do people measure velocity dispersion(sigma)?

And the other question is why does larger central mass implies larger sigma. I primarily comprehend it like this: the larger the central mass, the larger the curvature of spacetime, so it allow a wider range of velocities. But I know it is wrong, as orbital velocities should follow equations.

Anyway, thanks!

 

[mfb]

Where is the issue with measuring a value that is about zero? The relative precision will be bad, the absolute precision is still fine.

the larger the central mass, the larger the curvature of spacetime, so it allow a wider range of velocities

That doesn't make sense.

The central black hole has a negligible impact on the part visible in the diagram.

 

[Adrian59]

When discussing rotation curves of galaxies, the flat looking curve that Singlau showed is often the 'go to' image. However, galaxies have a large variation in their rotation curves as on can see by looking at Vera Rubin's original paper.
(Rubin, V. (1983). ‘The Rotation of Spiral Galaxies.’ Science, New Series, vol. 220, No. 4604, pp. 1339-1344. Published by: American Association for the Advancement of Science.)
Whether this has any explanation within the various hypotheses put forward to explain the flat rotation curse, I have yet to find an answer.