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efanton
2016-Jan-24, 06:37 AM
From what I am reading there always seems to be a discrepancy between the calculated galaxy rotation curve and the observed rotation curve.
This is one of the reasons, but not the only reason, for the 'need' of dark matter.

If I understand it correctly the calculations they use are based on estimated mass of a star for its distance from the centre. They then use red-shift to guestimate the actual speed of the star. It strikes me that there an awful of of 'guestimation' going on here to calculate galaxy rotation speed.

It then occurred to me that we have clearly defined formula's to produce spirals, and virtually all spirals found in nature are logarithmic spirals.

I've done some googling and come up with a blank. Why hasnt some one not tried to correlate the spirals that we can see when viewing a galaxies and the variables which we can accurately measure.

As the formula for a logarithmic spiral is relatively simple
r=ae ^theta

It could well be that the a e or theta are a global constant in all galaxies and this would then allow a graph to be developed that gave fairly accurate star speeds, masses etc similar to the graphs created by Henrietta Leavitt for Cepheid variables

PS. can anyone tell me how to get formulas right in posts. Tried umpteen times but failed miserably.

Shaula
2016-Jan-24, 09:01 AM
When you are doing rotation curve calculations for near edge on distant galaxies you don't look at bulk redshift, you look at the differential redshift across the disk. I don't know why you think this is guesstimation? You are looking at changes in a single object, and thus any intervening or model dependent errors will cancel out leaving the driver for the changes you see intrinsic relative velocity. Which is just the Doppler shift. What part of that makes you uncomfortable?

slang
2016-Jan-24, 09:50 AM
"They" in one particular case was Vera Rubin, who measured the velocity of gas clouds in M31. Here's a readable article (http://scitation.aip.org/content/aip/magazine/physicstoday/article/59/12/10.1063/1.2435662) with some references.

(As for formulas: try "Reply with quote" on some posts that have them to see how its done, using TeX.)

John Mendenhall
2016-Jan-24, 11:32 AM
IIRC, spiral arms propagate through the disk of the galaxy. The spiral arms are a density wave, not a collection of stars moving as a group. But I could be wrong.

Cougar
2016-Jan-24, 01:28 PM
If I understand it correctly the calculations they use are based on estimated mass of a star for its distance from the centre.

No, the mass of the orbiting star is irrelevant. It's the estimated visible mass interior to the star's orbit that should yield that star's orbital velocity. Since all these velocities are well below a significant fraction of the speed of light, Newton's equation for the effect of gravity should give a close prediction. But it doesn't. It's like there must be 6-8 times more mass than we detect that is interior to the orbit in order to account for the star's velocity.

Cougar
2016-Jan-24, 01:59 PM
Note also that all the mass exterior to a star's orbit essentially "cancels out" and has little effect on the star's orbit. Remarkably, Newton proved this geometrically in his Principia, but for a uniform spherical configuration. Galaxies are like flattened spheres, and their mass density is only roughly uniform within successive shells of a certain thickness at successive distances from the center. So Newton's proof is close but not exactly right for this configuration, but as I understand it, the expected orbital velocity is better estimated using elliptic integrals, as exemplified in this 2011 paper (http://www.raa-journal.org/raa/index.php/raa/article/viewFile/858/629).

John Mendenhall
2016-Jan-24, 03:10 PM
IIRC, spiral arms propagate through the disk of the galaxy. The spiral arms are a density wave, not a collection of stars moving as a group. But I could be wrong.

Hm, yes, the Wiki articla is here:

https://en.wikipedia.org/wiki/Spiral_galaxy

I heard Frank Shu lecture once about 1977. His lecture was great.

efanton
2016-Jan-24, 04:27 PM
When you are doing rotation curve calculations for near edge on distant galaxies you don't look at bulk redshift, you look at the differential redshift across the disk.

Thanks Shaula, that clear up a question I had about exactly how they approached these measurements

No, the mass of the orbiting star is irrelevant. It's the estimated visible mass interior to the star's orbit that should yield that star's orbital velocity.

thanks Cougar, for the correction.

Although I misunderstood the process of how physicists get the rotation curve it strikes me there has to be a correlation between the spiral shape and the interior mass to a star's orbit. If stars are orbiting faster you would expect to see tighter curves and conversely if they were orbiting slower you would expect to see more gentle curves

So isnt it logical that the interior mass to the star's orbit might correlate to the shape of the spiral? If there was a direct correlation then surely this would lead to better estimates

Cougar
2016-Jan-24, 05:07 PM
So isnt it logical that the interior mass to the star's orbit might correlate to the shape of the spiral?

Well, the shape, thickness, etc. of the spiral arms can be quite varied. Some have two arms, some have more. But perhaps more importantly, there is typically a lot of mass in between the spiral arms, in the form of stars, dust, and gas. It's not just the spiral part.

For a long time, the longevity of the spiral arms was a mystery, since they should "wind up" and become tighter over time. As John has pointed out, they are currently thought to be density waves, not a collection of stars moving as a group (solving the "winding problem"). A particular star may be orbiting outside a spiral arm, but as the density wave moves through the disk, that star may find itself inside the arm, without significant change to that star's orbit or velocity.

mapguy
2016-Jul-26, 04:28 PM
...there is typically a lot of mass in between the spiral arms, in the form of stars, dust, and gas... a particular star may be orbiting outside a spiral arm, but as the density wave moves through the disk, that star may find itself inside the arm...
So -- even though images of spiral galaxies might visually suggest that their arms are full of stars, and the areas in-between arms appear to be pretty empty -- is it the current thinking that the density of stars inside an arm is actually no different than the density of stars in-between arms?

kzb
2016-Jul-26, 05:54 PM
So -- even though images of spiral galaxies might visually suggest that their arms are full of stars, and the areas in-between arms appear to be pretty empty -- is it the current thinking that the density of stars inside an arm is actually no different that the density of stars in-between arms?

No, I think the density in the spiral arms is higher. But by how much I don't know -it might not be much. They are brighter because of more recent star formation (more bright stars) but also because of higher stellar density generally.

Cougar
2016-Jul-27, 02:16 AM
So -- even though images of spiral galaxies might visually suggest that their arms are full of stars, and the areas in-between arms appear to be pretty empty -- is it the current thinking that the density of stars inside an arm is actually no different than the density of stars in-between arms?

I was going to agree with kzb and disclaim what I'd said before, but now I'm thinking if the arm is a density wave that moves through the conglomeration of otherwise orbiting stars, etc., this means the arm rotates into a whole new set of stars and gas over time, which must have been there all along. At any one time, the arm would have higher density (as kzb said) because that's what defines it.

As to the actual measured ratio of densities, note that I'm a simple amateur theoretician, and I haven't really researched this area. :D

George
2016-Jul-27, 01:50 PM
I recall that the density wave (ie spiral arms) is analogous to traffic jams on the highways. The gas and dust is in the disk to begin with, like cars on the road, but it piles-up as it propagates, then un-piles behind it.

mapguy
2016-Jul-27, 01:59 PM
So galactic arms are the regions in the disk where there is an increase in the density of... what, exactly? Matter?

Hornblower
2016-Jul-27, 02:34 PM
So galactic arms are the regions in the disk where there is an increase in the density of... what, exactly? Matter?
The aggregate of stars, gas and dust. The overall density is only modestly greater than that between the arms, but in a galaxy with bright arms it includes a sprinkling of heavyweight young stars that are disproportionately luminous for their mass. A main sequence star of 10 solar masses has several thousand times the Sun's luminosity.

Noclevername
2016-Jul-27, 03:57 PM
So the gravity of all that mass holds onto more stars?

01101001
2016-Jul-27, 04:49 PM
So the gravity of all that mass holds onto more stars?

Delays them on their trip through.

kzb
2016-Jul-27, 05:16 PM
I think there has to be some kind of perturbation to start off the density waves. The Whirlpool galaxy has enhanced spiral structure and star formation rate several times our own galaxy's rate. Even though it is not as big. This is because of strong perturbations induced by its satellite galaxy.

I've been unable to find anything which says by how much the stellar density is enhanced in a spiral arm, so that is an interesting question. I do recall some publications which argued we currently inhabit a region which is under-dense compared to the average for our galactic radius, and that will be because we aren't in a major spiral arm.

Grey
2016-Jul-27, 07:53 PM
So the gravity of all that mass holds onto more stars?Remember that the big stars are short-lived. The thought is that the density waves trigger new star formation, and that among those new stars are some of the big, bright ones. As it passes by, those bright stars die, leaving only the fainter ones (and there are new bright stars further along). So there's not that much difference in density or even really in the number of stars (there is some difference, it's just not a huge one), but the arm has a higher proportion of young, hot stars. That's also why the arms are bluer than the rest of the disk.

SRH
2016-Jul-29, 12:15 AM
IF the stars are fairly stationary, and the spiral moves around because the density wave moves around,
then isn't the "problem" that "the outer stars are moving too fast given the interior mass" misstated?

The question should be "why does the outer edge of the density wave move so fast?", not the stars' movement.
Is this correct?

ngc3314
2016-Jul-29, 12:27 AM
No, the stars move at the velocities we measure, and that is what doesn't match the mass profile of directly detected matter. The pattern speed is different from this in density-wave theory - it is tricky to measure but has been done in some cases, using either small-scale changes in Doppler shift caused by the ripples in speed as stars fall into or club out of the extra gravity in a wave peak, or the pattern of velocity dispersion (line width) crossing a spiral feature. That is, both the stars (gas) and density peaks have significant (but different) orbital velocities. Interesting things happen when they match (corotation resonance) or differ by amounts related to the period of small perturbations about a circular orbit (Lindblad resonances). The dust lanes are expected to switch from inside to outside the arms at corotation, and the arms may change character (amplitude, width) on crossing a Lindblad resonance.