# Meaning of phrase "at redshift"

1. Sep 17, 2014

### center o bass

I have heard cosmologists use the phrase "at redshift", presumably indicating the location of something. Are redsifts used to specify locations in cosmology, and if so, how is that done?

2. Sep 17, 2014

### Staff: Mentor

The redshift basically indicates location, yes, if you interpret that as "location in spacetime". The reason cosmologists give the redshift instead of a distance (e.g., "1 billion light-years away") or a time (e.g., "1 billion years ago") is that the redshift is what we actually observe, and how it translates into a distance or a time depends on other cosmological parameters whose values we haven't necessarily pinned down. So rather than have to specify which particular values of all those parameters are being assumed when a distance or a time is given based on an observed redshift, cosmologists just give the observed redshift directly.

3. Sep 18, 2014

### center o bass

Is this idea based on Hubbles law? I.e. that $v = H d$ where v is the velocity of a galaxy and d is it's distance from us? Using that
$$v/c :=z = (\lambda - \lambda_0)/\lambda_0 = d/H$$
we see that given the redshift $z$, we can determine $d$. Is this the basic idea?

4. Sep 18, 2014

### Chalnoth

Essentially, yes.

It's worth noting that the local motions of galaxies can cause their redshifts to vary by as much as about $\pm$0.003 from this value. For far-away galaxies, this is inconsequential. But for nearby galaxies, the redshift can't reasonably be used as a distance measure due to this uncertainty.

5. Sep 18, 2014

### Staff: Mentor

Yes, but the expansion rate of the universe (which is what $H$ refers to) changes with time, and we don't know how, exactly, it changes with time.

6. Sep 18, 2014

### center o bass

Indeed, but it does not change as fast that $d = H z$ will be significantly tomorrow (or next year) from what it was today?

7. Sep 19, 2014

### Jorrie

Note that the equation that you have used is approximate and only holds for low z (z << 1). Using H0 = 67.9 km s-1 Mpc-1, z=1 represents a recession speed of 0.77c (231,000 km/s) and a proper distance of 11 billion light years (3.8 Mpc), which you can see do not quite fit the equation.

8. Sep 19, 2014

### Staff: Mentor

It's not a question of how fast $H$ is changing right now. It's a question of how much $H$ changed during all the time that the light we are seeing now from an object with a given redshift $z$ was traveling. The larger the redshift $z$, the more $H$ will have changed during the light's travel, so the worse an approximation the formula $d = H z$, which assumes that $H$ is constant, will be. (Alternatively, instead of using the value of $H$ right now in the formula, you could use some sort of average value of $H$ over the travel time of the light, but then the value of $H$ you used in the formula would depend on $z$.)