Should luminosity distance be 0 at z=0?

  • Context: Graduate 
  • Thread starter Thread starter johnio09
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the concept of luminosity distance in cosmology, particularly at redshift z=0. Participants are examining the implications of equations from a specific paper regarding the relationship between luminosity distance and comoving distance, as well as the potential for mathematical errors arising from these definitions.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes a divide by zero error in a formula from a paper when applying the luminosity distance at z=0, questioning the treatment of comoving distance in this context.
  • Another participant asserts that at z=0, the comoving distance is not zero but equal to the luminosity distance, relating it to the inverse square law.
  • A similar viewpoint is reiterated, emphasizing that the only scenario where comoving distance is zero is when one is at the source.
  • Concerns are raised about the paper's assertion that luminosity distance is purely a function of redshift, prompting questions about how to relate it to Hogg's equations, which involve luminosity and flux.
  • One participant expresses difficulty in following the paper and suggests that the relation d_L=(1+z)d_c is what the authors intended.
  • Another participant notes the lack of discussion regarding the influence of matter/radiation density evolution at different redshifts, referencing Hogg's work on cosmological distance measures.

Areas of Agreement / Disagreement

Participants express differing interpretations of the equations and concepts related to luminosity and comoving distances, indicating that multiple competing views remain without a consensus on the correct interpretation.

Contextual Notes

There are unresolved assumptions regarding the definitions of luminosity and comoving distances, as well as the implications of redshift on these measures. The discussion also highlights potential gaps in the paper's treatment of density evolution.

johnio09
Messages
4
Reaction score
0
I am working on coding up the luminosity function for blazars but I have ran into a problem. In equations 1-3 of this paper https://arxiv.org/pdf/1912.01622 they state that the flux can be broken down into two components: one where z=0 and one part that is the evolutionary factor. The problem I have noticed is that in their equation for z=0 (eq. 3), there is 𝐿_𝛾 in the denominator, which is a function of the luminosity distance (eq. 2) https://ned.ipac.caltech.edu/level5/Hogg/Hogg4.html, the comoving distance would be 0 when z=0, resulting in luminosity distance being 0 when z=0 (according to 𝑑_𝐿=(1+𝑧)d_c). Hence this results in a divide by 0 error when trying to use their formula. Could somebody please help me understand what's going on? Thank you.
 
Astronomy news on Phys.org
At z=0 the comoving distance is not zero, but equal to the luminosity distance. I.e. it's just the same then as the distance one would infer from the inverse square law when looking at a source of known intrinsic luminosity in a non-expanding space (eq. 19 in Hogg).
With growing z the two distances diverge (by the 1+z factor).

The only case when the comoving distance is zero, is when you're at the source (as with any other distance).
 
Bandersnatch said:
At z=0 the comoving distance is not zero, but equal to the luminosity distance. I.e. it's just the same then as the distance one would infer from the inverse square law when looking at a source of known intrinsic luminosity in a non-expanding space (eq. 19 in Hogg).
With growing z the two distances diverge (by the 1+z factor).

The only case when the comoving distance is zero, is when you're at the source (as with any other distance).
eq 19 in Hogg, however, is a function of luminosity and flux. In eq 2 of the other paper they state that luminosity distance is purely a function of redshift, if I am not mistaken. How would I be able to relate Hogg's equation to make it so that it is only a function of redshift?
 
I find the paper a bit too hard to follow, but I'd wager they just mean the d_L=(1+z)d_c relation.
 
Looking over it I came to similar conclusion. What I find interesting is that they aren't showing the influence of the matter/radiation density evolution at different redshifts.
Hoggs if I recall addresses this in his comologicsl distance measures article.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 14 ·
Replies
14
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
646
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 16 ·
Replies
16
Views
9K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 10 ·
Replies
10
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K