Problem with Surface Brightness & cosmological parameters

In summary, the paper does not give a clear answer about whether knowing its value for known candles or yardsticks, is a good way to determine the cosmological parameters.
  • #1
ChrisVer
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I have a problem with some question I had to answer for the Surface Brightness [itex]\Sigma \propto \frac{Flux}{Angular~area}= \frac{F}{\Omega}[/itex].
I was able to show that [itex] \Sigma \propto (1+z)^{-4} [/itex]
Then the question asks whether knowing its value for known candles or yardsticks, is a good way to determine the cosmological parameters...

I think that determining it will allow us to determine the redshift [itex]z[/itex] and thus the scale factor [itex]a[/itex] and its evolution. So we can know how [itex]a[/itex] evolves and thus obtain the cosmological parameters from the Friedmann equations. Is that wrong?
However, somewhere I read that the dependence of [itex](1+z)^{-4}[/itex] is independent on the cosmological model ,something that made me think I was wrong... :(

Any idea?
 
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  • #3
I have read this paper, unfortunately it doesn't give a clear answer (except for the ~(1+z)^-4 relationship I extracted) and the plots with different cosmological parameters models are done for the astrophysical distances and not surface brightness (independent of those distances)...

The last independence is making me confused...if it's independent on distances (and distances give Omegas) it shouldn't give any answer for Omegas... But then my question about the redshift $z$ is still annoying me :/
 
  • #4
ChrisVer said:
I have read this paper, unfortunately it doesn't give a clear answer (except for the ~(1+z)^-4 relationship I extracted) and the plots with different cosmological parameters models are done for the astrophysical distances and not surface brightness (independent of those distances)...

The last independence is making me confused...if it's independent on distances (and distances give Omegas) it shouldn't give any answer for Omegas... But then my question about the redshift $z$ is still annoying me :/
Luminosity distance is the measure that is used for standard candles, angular diameter distance the measure for standard rulers.

Does that help any?
 
  • #5


First of all, I would like to clarify that the equation \Sigma \propto (1+z)^{-4} is a valid relationship between surface brightness and redshift, assuming a homogeneous and isotropic universe. This is known as the luminosity distance-redshift relation and is derived from the Friedmann equations, which describe the evolution of the universe.

In terms of using surface brightness as a tool for determining cosmological parameters, it can be a useful method, but it is not the only one. Other methods, such as the cosmic microwave background radiation or the Hubble constant, can also provide valuable information about the cosmological parameters.

In terms of the statement that the dependence of (1+z)^{-4} is independent of the cosmological model, this is partially true. The relationship is independent of the exact details of the cosmological model, such as the matter content or the expansion rate. However, it does depend on the overall geometry of the universe, as described by the curvature parameter. So while the relationship is not specific to a particular cosmological model, it is still affected by the overall structure of the universe.

In conclusion, using surface brightness as a tool for determining cosmological parameters can be a valuable approach, but it should not be relied upon as the only method. It is important to consider multiple measurements and techniques in order to obtain a more robust understanding of the universe and its parameters.
 

1. What is the problem with surface brightness in cosmology?

The problem with surface brightness in cosmology is that it can vary depending on the distance and redshift of the observed object. This makes it difficult to accurately measure the intrinsic brightness of an object and therefore to determine its distance and other cosmological parameters.

2. How does surface brightness relate to cosmological parameters?

Surface brightness is an important factor in determining the distance and other cosmological parameters of an object. It is used in conjunction with other measurements, such as redshift and luminosity, to calculate the object's distance and therefore its position in the universe.

3. What causes variations in surface brightness?

There are several factors that can cause variations in surface brightness, including the distance of the object, its redshift, and the amount of dust and gas present between the object and the observer. These variations can make it difficult to accurately measure the intrinsic brightness of an object.

4. How do scientists account for the problem of surface brightness in their measurements?

Scientists use various techniques, such as statistical methods and corrections for dust and gas, to account for the problem of surface brightness in their measurements. They also compare their results with other measurements and observations to ensure their accuracy.

5. What impact does the problem of surface brightness have on our understanding of the universe?

The problem of surface brightness has a significant impact on our understanding of the universe, as it affects our ability to accurately measure distances and other cosmological parameters. It is an ongoing challenge for scientists to account for this problem and improve our understanding of the universe.

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