Problem with Surface Brightness & cosmological parameters

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Discussion Overview

The discussion revolves around the relationship between surface brightness and cosmological parameters, particularly in the context of redshift and the implications for determining cosmological models. Participants explore the mathematical dependence of surface brightness on redshift and its potential to inform cosmological parameters.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the relationship of surface brightness \(\Sigma \propto (1+z)^{-4}\) and questions whether this can be used to determine cosmological parameters through redshift and scale factor evolution.
  • Another participant references a paper that discusses the relationship but notes it does not provide a clear answer regarding the implications for cosmological parameters.
  • A participant expresses confusion about the independence of the surface brightness relationship from distances, suggesting that this independence complicates the determination of cosmological parameters like \(\Omega\).
  • There is a mention of different measures used for standard candles and rulers, specifically luminosity distance and angular diameter distance, which may relate to the discussion of surface brightness.

Areas of Agreement / Disagreement

Participants express uncertainty and confusion regarding the implications of the surface brightness relationship for cosmological parameters. There is no consensus on whether this relationship can effectively inform the values of \(\Omega\) or the redshift \(z\).

Contextual Notes

Participants highlight limitations in the existing literature, particularly regarding the independence of surface brightness from distance measures and the implications for cosmological models.

ChrisVer
Science Advisor
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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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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 :/
 
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?
 

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