Measuring Distances Across Billions of Light Years

[superpaul3000]

I hear a lot about astronomers using type IA supernovae to accurately measure large scale distances over billions of light years to do things like measure the rate of expansion of the universe. I doubt that the calculation of this distance is simply based on the inverse square law. So my question is what other factors are used in calculating that distance? One I can think of off the top of my head is from SR we know that objects traveling quickly away from us have their emitted light red shifted and luminosity reduced. We can see the red shift in these distant galaxies but do the astronomers account for the proper amount of reduction in light intensity when calculating these distances?

 

[Tanelorn]

I think they are measuring light frequency not light intensity or amplitude.

 

[superpaul3000]

I think they are measuring light frequency not light intensity or amplitude.

I think you can only measure the relative velocity of an object by measuring frequency. Thats how we know that the further away a galaxy is from us the faster it is moving and thus the universe is expanding. However, in order to measure distance you need light intensity, the inverse square law, and some other factors. I guess you would use the frequency to determine velocity and then velocity to determine the expected reduction in brightness. That is what I am trying to confirm. I also want to know if there are additional factors.

 

[BillSaltLake]

Brightness is proportional to the inverse of the product D²(1+z)². However, the "D" here is special: it's the integral from the time the light was emitted to now of (c/a)dt, where "a" is the expansion parameter (a = 1 now, and was <1 at earlier times).

 

[Chalnoth]

I hear a lot about astronomers using type IA supernovae to accurately measure large scale distances over billions of light years to do things like measure the rate of expansion of the universe. I doubt that the calculation of this distance is simply based on the inverse square law.

Well, yes, it is a bit more complicated than that. Basically, the analysis takes three stages:
1. A redshift is measured. This is relatively easy by looking at specific emission lines, and usually redshifts are very robust.
2. Regularize the supernova. Basically, not all supernovas are the same: some are brighter than others at the source. But fortunately for us, the intrinsic brightness of supernovae appears to be strongly related to other parameters, such as how long they last (brighter supernovae tend to last longer). So empirically we correlate the intrinsic brightness of the supernovae with other estimates.
3. Use General Relativity combined with a model for the expansion to compute how much the supernova will have dimmed based upon its redshift. This calculation is known as the "luminosity distance", and is compared against the measured brightness of the supernova. The comparison between the calculated luminosity distance and the measured brightness is then used to determine the parameters of the model used to calculate the luminosity distance.