Thread: Dark matter and doppler effect

Hi everybody,

The calculations of the normal rotation period of the galaxies we observe depends on their observed mass, but it also depends on the doppler effect from their recession. The more they speed away from us, the more their period is stretched. When we calculate this period, thus when we calculate their rotational speed, we have to include doppler effect in the calculations, which increases that speed. Has anybody thought of not including the doppler effect in the calculations? If not, can somebody do these calculations for a couple of galaxies and tell me if their rotational speed is still too fast to account for their observable mass?

We don't measure the period of galaxy rotation to get the rotation speed (That would be a bit difficult, since galaxy rotation periods are hundreds of millions of years long.)

Instead, we measure the Doppler shifts of the different regions of the Galaxy directly.

Here's how it works: We look at a galaxy that we see somewhat edge on. Because of its rotation, the stars on one side are moving towards us with respect to the galaxy's center and the star on the other side are moving away. The galaxy as a whole has a velocity, so the actual Doppler shift we get is a combination of both the star's motion with respect to the galaxy and the galaxy's motion with respect to us. So let's say we look at the stars halfway out from the center of the galaxy on one side, and compare them to stars the same distance from the center on the other side. If U is the speed of the galaxy itself, v1 the stars on one side and v2 the stars on the other. We will measure a speed of U+v1 for one side and U-v2 for the other.

If we take the difference between these measurements we get (U+v1)-(U-v2)= v1+v2. The motion of the galaxy drops out of the equation and has no bearing. Since the stars we measured where equal distances from the center of the galaxy (just on opposite sides), we know that v1=v2 and can simplify to 2(v1) or 2(v2). In other words both v1 and v2 are equal to 1/2 the difference between them. This gives us the speed of stars at this distance from the center of the galaxy and thus the rotation rate at this distance. (we do have to adjust for the fact that we are seeing the galaxy at an angle so these stars aren't moving straight at or away from us, but it just takes a little trigonometry to do that.)

If we do that same thing for stars a different distances from the center of the galaxy, we get the rotation rates at all those different distances. If we plot this out, we get the galaxy's "rotation curve"

When we do this, not only do we find that the galaxies rotate faster than they should, but the rotation curves are wrong also. If you look at a typical spiral galaxy, most of its stars are in the central bulge and then it thins out as you move outward to the disk. With this distribution, the central bulge should dominate when determining how the stars in the disk orbit and the further away these stars are from the center, the slower they should orbit. What we see is that the orbital speed stay's almost the same as you move outward. What this seems to indicate is that not only is there more mass than what we see, but most of it is spread out differently from the stuff we see.

Thus dark matter. Not only does its non interaction via electromagnetism make it so that we don't see it, it also explains why it is not distributed in the same way as the matter we do see is.

Thanks Janus,

I just had a discussion on this question on another forum, and I had the same answer about the predicted and observed curves not being the same, which is a very good argument against my idea. I am still wondering about the effect that the calculation I was proposing would have on the observed curve though. It would slow down the speeds a bit, but would the mean speed from the predicted curve be close to the mean speed from the observed one?



A: predicted rotation curve
B: observed rotation curve

Originally Posted by Le Repteux

Thanks Janus,

I just had a discussion on this question on another forum, and I had the same answer about the predicted and observed curves not being the same, which is a very good argument against my idea. I am still wondering about the effect that the calculation I was proposing would have on the observed curve though. It would slow down the speeds a bit, but would the mean speed from the predicted curve be close to the mean speed from the observed one?



A: predicted rotation curve
B: observed rotation curve

No.
1. Even if the recession of the galaxy had such an effect, astronomers would know to correct for it when plotting the rotation curve. This would be quite obvious as the Doppler effect is more pronounced with the distance of the galaxy and the effect would be more pronounced when viewing further galaxies. In addition, with the case of the Andromeda galaxy, which is approaching, the effect would be reversed.
2. Any such effect would only change the scale of the curve, not its shape.
3. The Doppler effect for receding galaxies, if not accounted for, would tend to reduce the observed orbital speeds. The observed speeds are higher than the predicted ones. Thus once you corrected for it, the real orbital speeds would be even faster, The Doppler shift wouldn't cause the difference between predicted and observed velocities, just make it look smaller than it is.

The upshot is that the professionals in this field know what they are doing and know what effects they need to account for which they can ignore when they make their observation. Something as simple as correcting for the Doppler effect, if need be, is not going to escape their attention.

Originally Posted by Janus

3. The Doppler effect for receding galaxies, if not accounted for, would tend to reduce the observed orbital speeds. The observed speeds are higher than the predicted ones. Thus once you corrected for it, the real orbital speeds would be even faster, The Doppler shift wouldn't cause the difference between predicted and observed velocities, just make it look smaller than it is.

Isn't that the inverse? Since the red shift would slow down the speeds, if you take it away from the data, the speeds should thus increase, no?

Originally Posted by Janus

Thus dark matter. Not only does its non interaction via electromagnetism make it so that we don't see it, it also explains why it is not distributed in the same way as the matter we do see is.

How does the lack of electromagnetic interaction explain the distribution? Because it doesn't lose kinetic energy by emitting EM? Is loss of kinetic energy by emitting EM the explanation for why most of the bright matter is located nearer the center?