Black hole mass and sigma (velocity dispersion)

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Discussion Overview

The discussion revolves around the relationship between black hole mass and velocity dispersion in galaxies, exploring concepts of orbital speed, dark matter, and the dynamics of stars near supermassive black holes. Participants seek to understand the formation of velocity dispersion, its implications for black hole mass, and the measurement of these phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about how velocity dispersion is formed and its relation to dark matter, questioning whether orbital speed is uniform in galaxies.
  • One participant clarifies that velocity dispersion reflects the differences in velocities of stars, which can be observed through Doppler shifts in spectral lines.
  • There is a suggestion that supermassive black holes cause faster orbital rates for nearby stars, leading to greater velocity dispersion, although this is noted as a point needing further validation.
  • Another participant argues that the relationship between dark matter and orbital speed is complex, noting that orbital velocities near a black hole are high but drop at greater distances, where dark matter becomes more influential.
  • Concerns are raised about how velocity dispersion is measured, particularly in the context of rotation curves that appear flat, and the implications of central mass on velocity dispersion.
  • One participant challenges the reasoning that larger central mass leads to a wider range of velocities due to spacetime curvature, indicating that this perspective may be flawed.
  • A reference to Vera Rubin's work highlights the variability in galaxy rotation curves, suggesting that the flat rotation curve may not fully explain the dynamics at play.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between dark matter, orbital speed, and velocity dispersion, indicating that multiple competing perspectives remain unresolved. There is no consensus on the implications of central black hole mass on velocity dispersion or the interpretation of rotation curves.

Contextual Notes

Limitations include the complexity of measuring velocity dispersion in the presence of dark matter and the assumptions underlying the interpretation of rotation curves. The discussion reflects a range of hypotheses without definitive conclusions.

Singlau
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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!
 
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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
 
Singlau said:
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.
 
1485575892576.png

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

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