# The meaning of z number in red shift

1. Dec 20, 2011

### kc2dws

Hello

I understand that red shift is a measurement of relative speed. What I am looking for is what the number after the z means. Is it a percent of c or, Or is it it just a scale that physics uses to note the difference between different objects.

Kevin

2. Dec 20, 2011

### Irishwake

As I understand it, it is simply as you said the relative difference between the observed and emitted frequencies.

3. Dec 22, 2011

### Staff: Mentor

4. Dec 22, 2011

### Chronos

The basic difference is the background temperature of the universe 'then' vs temperature now. For example, the background temperature at z=2 was nearly three times hotter than we now measure [a z+1 thingy].

5. Dec 22, 2011

### kc2dws

kevin

6. Dec 22, 2011

### marcus

Mostly not. Most of the redshift that is observed and that we talk about here is not Doppler redshift (depending on relative speed at some given instant of time.)

Mostly we talk about cosmological redshift. Technically different. It is a measure not of relative speed at some time but instead measureshow much distances have expanded while the light was in transit.

You will see that in the Wikipedia article that Drakkith gave link to, if you look far enough down the page. You will see a table and one of the entries will be "cosmological redshift".

that is the z we are talking about when we talk about the observed redshifts of distant galaxies. Or Type Ia supernovae with z = 1 or z = 1.5
Or quasars with z = 6. Or cosmic microwave with z = 1100. That is all cosmological redshift.

The formula does not involve speed. It involves the ratio of distance now/distance then.

z = 1 means that on average a largescale distance DOUBLED while the light was in transit.

You always add one to z to get the ratio by which distances have increased.

1+z = anow/athen you can find that in the Wikipedia Drakkith gave you

In other words if z = 2 then distances have TRIPLED while the light was in transit to us.
they are 3 times longer NOW on the day we receive the light than they were THEN when the light was emitted by the glowing gas or star and started on its way to us.

the general pattern of expansion is not like ordinary motion because nobody gets anywhere by it (everybody gets farther from everybody)
and the rate of expansion has been constantly changing all during the time the light has been traveling, so there is no one obvious rate to pick that would determine z.

7. Dec 23, 2011

### kc2dws

Thank you marcus.

I reread the article, And found the equation

8. Dec 23, 2011

### George Jones

Staff Emeritus
$z$ is related to the scale factor of the universe by
and also to the emitted and received wavelengths (and frequencies) of light (for galaxies moving with the Hubble flow).
$$z =\frac{a_{now}}{a_{then}} - 1 = \frac{a_{now} - a_{then}}{a_{then}} = \frac{\lambda_{now} - \lambda_{then}}{\lambda_{then}} = \frac{f_{then} - f_{now}}{f_{now}}.$$