What is the basis of Rotation Curve?

[Lino]

I have been reading about rotation curves, and the I understand the basics, but I am trying to understand the basis / meaning of the curves?

Are the findings based on redshifts of individual stars / "bins of light" at set distances from the centre of the galaxy? And given that the predominance of the stars / bins are at the outer "edge" of the galaxy, are there corrections to the data for this?

I appreciate that these are likely "big picture" questions, and am happy to get pointers to articles / papers that can help my understanding.

Thanking you in advance,

Noel.

 

[mfb]

And given that the predominance of the stars / bins are at the outer "edge" of the galaxy

Are they?

You can take galaxies that can be resolved in telescopes, where it is easy to measure the red/blueshift for each part of the galaxy separately.

 

[Lino]

Are they?

You can take galaxies that can be resolved in telescopes, where it is easy to measure the red/blueshift for each part of the galaxy separately.

Thanks mfb, and understood, but I understand that the rotation curve is best considered for an edge-on galaxy, & if I resolve any star in an edge-on galaxy, how do I know how far from the centre it is (using a dart board example, when looked at edge-on, is the dart outside the scoring areas, in the outer double score ring, or the inner triple score ring, or one of the single score sections)?

Even if I do know where the star is (& I appreciate that this is a simplistic view), I assume that I need to make a correction to the reading - for example to recognise that the light had to climb a distance of the gravity well of the galaxy.

 

[mfb]

If you see it edge-on, you always see the summed effects of many stars, and need unfolding (or a fit model) to get the rotation curves.

Even if I do know where the star is (& I appreciate that this is a simplistic view), I assume that I need to make a correction to the reading - for example to recognise that the light had to climb a distance of the gravity well of the galaxy.

That should be a negligible effect, as it scales with $v^2/c^2$, while redshift is $v/c$.

 

[Lino]

If you see it edge-on, you always see the summed effects of many stars, and need unfolding (or a fit model) to get the rotation curves.

That should be a negligible effect, as it scales with $v^2/c^2$, while redshift is $v/c$.

Thanks mfb. I hadn't come across unfolding previously, so that will give me some reading avenues.

 

[Lino]

Sorry mfb, I've been thinking about this for a while, but it is still not clear to me.

... it scales with $v^2/c^2$... .

What is the 'it' that you are referring to?

Thanks,

Noel.

 

[mfb]

Gravitational redshift of light ("to recognise that the light had to climb a distance of the gravity well of the galaxy."). v is the escape velocity at the point the light starts.

 

[Lino]

Gravitational redshift of light ("to recognise that the light had to climb a distance of the gravity well of the galaxy."). v is the escape velocity at the point the light starts.

Thanks mfb.

 

[Lino]

[Gravitational redshift ] scales with $v^2/c^2$, while redshift is $v/c$.

mfb, Can I follow up on this again please? I have two questions.
1. In the above quote, the $v$ in the first part represent escape velocity (as you have said), is the $v$ in the second part the same escape velocity?
2. The real purpose of my OP was to try to gain an understanding of the mechanics behind the calculation of a galactic rotation curve, and in particular the nature / reason for any corrections that need to be made to the readings (in order to get a correct result). Are there any corrections that are generally made to redshift readings in order to calculate the rotation curve of a galaxy?

As always, thanks in advance,

Noel.

 

[mfb]

mfb, Can I follow up on this again please? I have two questions.
1. In the above quote, the $v$ in the first part represent escape velocity (as you have said), is the $v$ in the second part the same escape velocity?

The second v is the motion of the object approximated by the escape velocity. They are not the same (otherwise the objects would escape...), but I ignored small prefactors. For a circular orbit around a central mass, those velocities differ by a factor of $\sqrt{2}$.

2. The real purpose of my OP was to try to gain an understanding of the mechanics behind the calculation of a galactic rotation curve, and in particular the nature / reason for any corrections that need to be made to the readings (in order to get a correct result). Are there any corrections that are generally made to redshift readings in order to calculate the rotation curve of a galaxy?

I'm sure they are, but I think they are all small. Check papers about those measurements, it should be explained there.

 

[Lino]

Thanks mfb.