# Black hole mass and sigma (velocity dispersion)

• B
• Singlau
In summary, the conversation discusses the formation of velocity dispersion and its relationship with dark matter and black holes in galaxies. It is observed that the orbital speeds in galaxies vary, with evidence of dark matter suggesting a uniform speed. The conversation also touches on the measurement of velocity dispersion and the impact of central mass on its magnitude. There is a debate on whether the central black hole or dark matter has a greater influence on the rotation curve of galaxies.
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!

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.

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.

## 1. What is a black hole?

A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. It is created when a massive star collapses and its core becomes infinitely dense, creating a singularity.

## 2. How is the mass of a black hole determined?

The mass of a black hole is determined by measuring the gravitational effects it has on its surroundings. This can be done by observing the orbits of nearby stars or gas clouds, as well as the distortion of light around the black hole.

## 3. What is sigma (velocity dispersion) and how does it relate to black hole mass?

Sigma, also known as velocity dispersion, is a measure of the random motions of stars in a galaxy. It is related to the mass of a black hole through the M-sigma relation, which states that the mass of a black hole is proportional to the velocity dispersion of stars in its host galaxy.

## 4. Is there a limit to the mass of a black hole?

It is currently believed that there is no upper limit to the mass of a black hole. Supermassive black holes, which can have masses billions of times that of our sun, have been observed in the centers of galaxies. However, there is a theoretical limit known as the Eddington limit, which is the maximum mass that a black hole can have before the radiation emitted from the accretion disk around it becomes too strong and prevents further growth.

## 5. Can the mass of a black hole change?

Yes, the mass of a black hole can change over time. Black holes can grow by accreting matter from their surroundings, such as gas and stars. They can also merge with other black holes, resulting in a larger mass. On the other hand, black holes can also lose mass through the process of Hawking radiation, although this is extremely slow for large black holes.

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