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Copernicus
2019-Jan-27, 07:35 AM
I was wondering if there were certain ways to combine red shift. Like transverse, radial, and gravitational.

grant hutchison
2019-Jan-27, 11:58 AM
There sure are.

Grant Hutchison

George
2019-Jan-27, 04:57 PM
What about separating those three vectors? Is accuracy tied to distance accuracy only?

Ken G
2019-Jan-27, 08:51 PM
Think in terms of the shifts being due to multiplicative factors, like a redshift is a factor by which you multiply the wavelength. Then if you have more than one going on, simply multiply the factors.

ngc3314
2019-Jan-28, 03:09 AM
That is, if there are contributions to redshift z1, z2, z3, the total we observe after they all operate is (1+z1) x (1+z2) x (1+z3) and so on. This also applies to subsections of the usual cosmological redshift, for calculation of how far apart the lines of sight of two images are when they pass through a galaxy halo or other gas cloud at some intermediate redshift, or the predicted temperature of the microwave background as it affects a galaxy observed at some redshift. An actual Doppler contribution, the way galaxy rotation is usually treated, acts like one of the factors as well, albeit so small compared to unity that it's quite common just to use the additive approximation for it.

George
2019-Jan-28, 04:14 PM
That is, if there are contributions to redshift z1, z2, z3, the total we observe after they all operate is (1+z1) x (1+z2) x (1+z3) and so on. This also applies to subsections of the usual cosmological redshift, for calculation of how far apart the lines of sight of two images are when they pass through a galaxy halo or other gas cloud at some intermediate redshift, or the predicted temperature of the microwave background as it affects a galaxy observed at some redshift. An actual Doppler contribution, the way galaxy rotation is usually treated, acts like one of the factors as well, albeit so small compared to unity that it's quite common just to use the additive approximation for it. That all makes sense. So the peculiar motion (ie Doppler) is negligible and gets tossed for the more distant galaxies. But you didn't toss the transverse redshift component for these distant objects, but I assume it should be tossed, since it's hard to imagine any "sideways" expansion, right?

My question is for the closer galaxies where Doppler motions aren't trivial, though still small. I assume distance must be known to separate the components, or is there some spectral feature that reveals the differences?

Ken G
2019-Jan-28, 05:59 PM
But you didn't toss the transverse redshift component for these distant objects, but I assume it should be tossed, since it's hard to imagine any "sideways" expansion, right?Right. Though Vera Rubin apparently did once quip it is oddly convenient that we attribute the redshift to motion in the only direction we can easily measure (because it shows up to lower order in that direction). But she may have said that when observations were still limited to low effective v/c, and that's no longer true, so if there were transverse effects we'd probably have discovered some kind of problem by now.

My question is for the closer galaxies where Doppler motions aren't trivial, though still small. I assume distance must be known to separate the components, or is there some spectral feature that reveals the differences?
Frequency shift is always just multiplication by a factor, so there is never any way to separate its causes. What's more, the causes themselves can be coordinate dependent! It is possible to choose coordinates where the redshift of some quasar is a normal Doppler shift, so when people say "quasars show cosmological redshift not Doppler shifts" they are making a somewhat imprecise statement. What they mean is that to get a given quasar to show its shift as a Doppler shift, you would have to use coordinates that rather force the issue and are probably not the most natural or simplest choice to make (as per our other discussion!).

Copernicus
2019-Jan-28, 05:59 PM
Think in terms of the shifts being due to multiplicative factors, like a redshift is a factor by which you multiply the wavelength. Then if you have more than one going on, simply multiply the factors.

If one was combining the red-shifts, could it be the gravitational redshift * multiplied by the radial redshift divided by the transvers redshift?

b(1-b^2)^{.5} ((1+b)/(1-b))^{.5}

for a total of

z+1=b(b+1)

Ken G
2019-Jan-28, 09:42 PM
Actually the radial and transverse relativistic Doppler shifts cannot be broken into independent factors, they are just one combined factor, the Doppler shift factor. If you want to break up the Doppler shift factor into two factors, one is due to time dilation and looks like dividing the frequency by the Lorentz factor, and the other is due to the time-of-flight effect that results from the finite speed of light but is not a relativistic effect and is there for any wave. You can further break those down into two factors for the motion of the source, and two factors for the motion of the receiver, but the velocities don't add in a simple way.

Copernicus
2019-Jan-30, 12:38 AM
Actually the radial and transverse relativistic Doppler shifts cannot be broken into independent factors, they are just one combined factor, the Doppler shift factor. If you want to break up the Doppler shift factor into two factors, one is due to time dilation and looks like dividing the frequency by the Lorentz factor, and the other is due to the time-of-flight effect that results from the finite speed of light but is not a relativistic effect and is there for any wave. You can further break those down into two factors for the motion of the source, and two factors for the motion of the receiver, but the velocities don't add in a simple way.

Ken,

Are there any circumstances where that equation could be close to appropriate?

Ken G
2019-Jan-30, 02:28 AM
I can't think of one, it would be unusual to have the same beta appear in three different factors.

LaurieAG
2019-Jan-30, 08:31 AM
Are there any circumstances where that equation could be close to appropriate?

In face on galaxies the Doppler shift factor would be at a minimum and in side on galaxies the factor would be at its maximum.

Copernicus
2019-Jan-30, 12:58 PM
I can't think of one, it would be unusual to have the same beta appear in three different factors.

Right. I thought of that too. But I also thought there might be some points at which they could have dimensional factors that were, for example 50 percent of the other or some such thing. I was just wondering if the equation it self could be valid. When I set z=0 the number beta would be equal to the inverse golden ratio, but I can't think of that meaning anything.