1. Discussion of the ATM theory/thread has no place in Q&A. Please stop. Now.

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Originally Posted by kzb
Probably the spiral arms themselves do, there is fine structure in the curve. The up and down wiggles in the curve are because the distribution of mass with radius is not a completely smooth decrease. The spiral arms are probably major contributors to this lack of smoothness.

But if you mean stars going at different speeds at the same radius, i.e because they are or are not in a spiral arm, I think they will have been averaged out in the generation of the curve.
So, lost information?
Consider a disc galaxy where radial velocity can be measured, but proper motion cannot, for being too small (Is it still the case with Gaia data releases?).
If the galaxy is face on then radial velocity will be measured as zero everywhere. Rotation is pure proper motion, which is assumed immeasurable.
If the galaxy is edge on, then you still cannot measure the rotation curve!
Because a line of sight, say, 8 kpc besides the centre will not be only stars 8 kpc from centre and rotating straight towards or away from us. Same line of sight will also include stars 10 kpc from centre but 6 kpc in front of of centre and with proper motion towards centre, and stars 10 kpc from centre and 6 kpc behind the centre and with proper motion away from centre - all of them indistinguishable from each other.
Whereas in case of tilted disc, you can measure the actual distance from centre of each star, and also measure radial speed. And using the somehow known tilt angle compute the full rotation speed.
Do spiral galaxies typically possess mirror symmetry and even number of arms (2 or 4)? Or do spiral galaxies commonly possess axial symmetry with odd number of arms?

3. Originally Posted by chornedsnorkack
If the galaxy is edge on, then you still cannot measure the rotation curve!
Because a line of sight, say, 8 kpc besides the centre will not be only stars 8 kpc from centre and rotating straight towards or away from us. Same line of sight will also include stars 10 kpc from centre but 6 kpc in front of of centre and with proper motion towards centre, and stars 10 kpc from centre and 6 kpc behind the centre and with proper motion away from centre - all of them indistinguishable from each other.
Your statement would surprise hundreds of astronomers who have measured and published the rotation curves of edge-on spiral galaxies.

How do they do it? Well, consider the following simplified method. Suppose you look at an edge-on spiral galaxy, at a position which is, say, 1 arcminute to the left of the center, corresponding to a tangential distance of, say, 5 kpc from the center. You are correct that at that position, we will see the combined light of

a) stars which circle the center at a distance of 5 kpc. These stars will be moving purely radially -- let's say, toward us -- and so we'll see a large negative radial velocity -- say, -100 km/s. That corresponds to their actual circular velocity in orbit around the center.

b) stars which circle the center at a larger distance of, say, 10 kpc, but which are on the far side of the galaxy. These stars will be moving toward us and also to the left, and so the radial velocity we measure will be only a fraction of the actual circular velocity. Suppose that the radial velocity turns out to be only -60 km/s.

c) stars which circle the center at a larger distance of, say, 10 kpc, but which are on the NEAR side of the galaxy. These stars will be moving toward us and to the right, so, again, the radial velocity we measure will be just a fraction of their actual circular velocity. Suppose it's -60 km/s.

So, what our instruments will measure is a broad range of radial velocities, ranging from -100 km/s down to, say, -60 or -50 km/s. What we can do is concentrate on the high-velocity edge of this range. Under reasonable assumptions (again, this is a simplified version of the story), the highest velocities should correspond to the stars which are coming straight toward us; for those stars, the angular separation of 1 arcminute from the center of the galaxy corresponds to the radius of their orbit.

We can then conclude that, at a radius of 1 arcminute = 5 kpc, the circular velocity of stars is -100 km/s.

Repeat for other angular distances from the center of the galaxy, and we can build up a rotation curve.

4. A couple of quick int in this uscussion:

- Spiral galaxy disks are pretty thin, known from when they are seen edge-on. When best situated for rotation-curve studies we see them at maybe 20 degrees from edge-on, to strongly limit the contamination of stars from elsewhere at each point, reduce issues from dust extinction hiding some of the stars, and still have circular motions well represented instead of random (especially radial and "vertical" ones).

- we don't just have rotation curves. For both stars and gas, there are fully sampled 2-dimensional velocity fields now measured for thousands of galaxies (from such surveys as MANGA, SAMI, CALIFA). Noncircular motions appear in such data as angular offsets between the kinematic orientation and that seen from the starlight, globally or locally (so isovelocity contours "wiggle" - they often do this crossing spiral arms, when the arm has enough excess density to perturb orbits of things crossing it). We know from this where there are strong motions departing from ~circular orbits (notably along bars where the gravitational potential is not even approximately circularly symmetric).

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Does the short axis of the ellipse (where rotation is pure proper motion) give the radial profile of average radial velocity?

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Some inputs which might be helpful; basically following on from ngc3314's MaNGA hint.

MaNGA (Mapping Nearby Galaxies at APO) official site (link). One can download the data to one's heart's content (from here).

Modeling disk galaxy rotation curves with MaNGA and Stan is a Discussion thread in the old Galaxy Zoo Talk; it shows what an amateur can do, and how to produce rotation curves from MaNGA data (as well get estimates of out-of-plane motions).
Last edited by Jean Tate; 2018-Jul-01 at 09:20 PM. Reason: MaNGA data site added

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Originally Posted by kzb
I do not know why other spiral galaxies should be much different to our own galaxy in this respect. Look at the data for the Milky Way. In our locality the relative motions are a few km/s in all directions.
Thanks kzb:

Papers have now been found which show a radial velocity dispersion for the Milky way.

The ATM thread has been started by the way, for anyone interested.

https://arxiv.org/abs/1805.00275 Fig 10 shows radial velocity dispersion of 140km/s
https://arxiv.org/abs/0803.1826 table 5 and 6 has radial velocity dispersion 113km/s

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Originally Posted by john hunter
Thanks kzb:

Papers have now been found which show a radial velocity dispersion for the Milky way.

The ATM thread has been started by the way, for anyone interested.

https://arxiv.org/abs/1805.00275 Fig 10 shows radial velocity dispersion of 140km/s
https://arxiv.org/abs/0803.1826 table 5 and 6 has radial velocity dispersion 113km/s
Both of those references pertain to the very central region of the galaxy, and within the bulge.

This is a special area and not representative of the galaxy disk. There is a massive black hole nearby and the the MW is a barred spiral, so the orbits in this area are not at all circular.

Also the radial velocity dispersion means just what it says, it is not a measure of the net motion towards (or away from) the centre.

Your second reference even says this:

<<The radial velocities of the cool, late-type stars have approximately a symmetrical distribution with its center at ~-7.8(+/-10.3) km/s and a standard deviation ~113.7(+/-10.3) km/s.>>

This means the net velocity towards the centre is a paltry 7.8km/s, with an uncertainty large enough that this could be due to chance. The 113.7km/s is the dispersion, not the average speed.
Last edited by kzb; 2018-Jul-03 at 11:34 AM.

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Do bars of barred spirals rotate?

10. kzb
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Originally Posted by chornedsnorkack
Do bars of barred spirals rotate?
You would think so because the ends connect to spiral arms, which do "rotate". If the bar didn't co-rotate the arms would be disconnected.

The star orbits in the bar region are a long way from circular, but they are orbiting.

I don't think my last message was definitive enough about the conclusion.

Which is, the second reference actually comprehensively disproves the hypothesis.

The hypothesis requires an average inward radial velocity of the order 100 km/s. The second reference finds this velocity to be more than an order of magnitude lower than what is required. So this alone makes the hypothesis untenable.

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