# Which redshift value is used in the velocity measurement of distance

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• Arman777
In summary, the conversation discusses the calculation of total velocity for a stellar object, which is defined as the sum of peculiar velocity and recession velocity. The equation for recession velocity is given, and there is a question about the value of z in the equation. The relationship between observed and cosmological redshift is also mentioned, and the paper linked attempts to challenge the accepted understanding of using only the observed redshift. The paper suggests that systematic errors in measuring redshift can lead to significant issues, but further investigation is needed to determine the actual impact of these errors.
Arman777
Gold Member
Let us say that we have a stellar object so its total velocity is defined as

$$v_{tot} = v_{pec} + V_{rec}$$

Where

$$V_{rec} = H_0r$$

and $$V(z) = \frac{cz}{1+z}[1+\frac{1}{2}(1-q_0)z - \frac{1}{6}(1-q_0-3q_0^2+j_0)z^2]$$

for small z.So my first question is what is the $z$ value here? Is it the observed redshift or the cosmological redshift?

Also, the relationship between observed and cosmological redshift is given.

$$1+z_{obs} = (1 + z_{cos})(1 + z_{earth})((1 + z_{sun})(1 + z_{source})(1 + z_{gravity})$$

If we are using the cosmological redshift then by using above equation we can write,

$$z_{cos} = \frac{1 + z_{obs}} {(1 + z_{earth})((1 + z_{sun})(1 + z_{source})(1 + z_{gravity})}-1$$

So is this what we put in (4)?

Edit: For the source you can look here https://arxiv.org/abs/1907.12639 Eqn(16) and (18)

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Generally just the observed redshift is used is my understanding. The redshift imposed by the motion of the Earth relative to the galactic medium is, in most situations, considered to be too small to be relevant. Consider, for example, an object at a redshift of ##z=1##. The maximal impact of the Earth's motion on this redshift is about 0.2%, so that if the "actual" redshift is 1, then the measured redshift might be anywhere between ##0.998## and ##1.002##.

But that's if only one object is measured. If objects across the sky are measured, the redshifts are effectively averaged, leading to much smaller effects in the final result.

This paper you posted attempts to challenge this accepted understanding, pointing out that even these small effects, if they are systematic, can cause significant issues. They point out, for instance, that large regions of the universe are moving together, so that averaging many objects in those regions will lead to a systematic offset in the redshift. They further claim that even small systematic errors can potentially cause large effects for estimated parameters.

That last claim may be a concern. I definitely know of some situations where small systematic errors can lead to large errors elsewhere. I've only skimmed the paper, so I haven't really evaluated their argument, but on the surface it appears to be incomplete. There are relatively easy ways for teams analyzing large data sets (e.g. galaxy surveys) to do cross-checks that would measure the impact of these kinds of errors. My bet is that as long as they are using spectroscopic redshifts, the systematic errors will tend to remain pretty small. But it's definitely worth further investigation to ensure this is the case.

kimbyd said:
Generally just the observed redshift is used is my understanding.
I see
kimbyd said:
They point out, for instance, that large regions of the universe are moving together, so that averaging many objects in those regions will lead to a systematic offset in the redshift.
I did not understand this part.

The changes would be small I guess. Since the current distance ladder error goal is %1 they mentioned this problem..

Arman777 said:
I see

I did not understand this part.

The changes would be small I guess. Since the current distance ladder error goal is %1 they mentioned this problem..
Right, so it's worth investigating, but the back-of-the-envelope numbers suggest that errors introduced by these systematic effects should be much less than 1%. This paper you linked argues that it might actually make a difference. My conclusion is that it's definitely worth investigating, but there's a fair chance that this is a red herring.

Arman777

## 1. What is redshift and how is it related to distance?

Redshift is a phenomenon in which light from an object appears to be shifted towards the red end of the electromagnetic spectrum. This is caused by the expansion of the universe, which stretches the wavelengths of light as it travels through space. The amount of redshift can be used to determine the distance of an object, as objects that are farther away will have a higher redshift value.

## 2. How does redshift affect the measurement of velocity?

The redshift value of an object is directly related to its velocity. The higher the redshift, the faster the object is moving away from us. This is known as the Hubble law and is used to calculate the distance and velocity of objects in the universe.

## 3. Is there a specific redshift value that is used in velocity measurements of distance?

No, there is no specific redshift value that is used in all velocity measurements of distance. The redshift value used will depend on the specific object being observed and the method of measurement being used. In general, higher redshift values indicate greater distances and velocities.

## 4. Can redshift be used to measure the distance of all objects in the universe?

No, redshift can only be used to measure the distance of objects that are moving away from us. Objects that are moving towards us will have a blueshift, and objects that are not moving relative to us will have no shift in their wavelengths. Therefore, redshift can only be used for objects that are expanding away from us due to the expansion of the universe.

## 5. Are there any limitations to using redshift in velocity measurements of distance?

Yes, there are limitations to using redshift in velocity measurements of distance. The accuracy of redshift measurements can be affected by factors such as the object's intrinsic brightness, the presence of dust or gas in the line of sight, and the effects of gravitational lensing. Additionally, redshift can only be used for objects that are relatively nearby, as the expansion of the universe causes the redshift to become too large to accurately measure for very distant objects.

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