My question is how to find the luminousity distance from the above two equations by relating them.kimbyd said:Wikipedia has a good page:
https://en.wikipedia.org/wiki/Distance_measures_(cosmology)
I don't think you need to do anything special in the above case. The relative scale factor between the emission and observation is sufficient (this gives you the redshift).
Or the other way if ne be the no. density of photons at te then flux will beApashanka said:If photons are emmitted from a galaxy A at te to galaxy B (receives at present time a=1,t0) ,x being the comoving distance ,and current distance be dL
L(t0)=a(te)2L(te)
Flux(Φ0)=a(te)2L(te)/4πdL2
In comoving frame ∅=L(te)/4πx2
Is there any way to relate Φ and ∅ to find the luminousity distance dL??
Actually what I mean to say is that is the formula relating Φ(to) and ∅ valid so that dL comes out to be x/a(te) ??PeterDonis said:@Apashanka you have already been given a good answer and a reference by @kimbyd. You need to read the article linked to and then ask further questions if you are having trouble with something in that article, or you need to address questions specifically to what @kimbyd said in post #2 (pay particular attention to the last paragraph).
What's the scale factor at emission?Apashanka said:Actually what I mean to say is that is the formula relating Φ(to) and ∅ valid so that dL comes out to be x/a(te) ??
As in the Wikipedia page @kimbyd has provided dL vs dA is given ,dL alone is not given as function of z
Yes.kimbyd said:What's the scale factor at emission?
What's the scale factor at observation?
That's all you need. That and the definition of redshift: ##z + 1 = 1/a##.
It's hard for me to say because I'm a little unsure of your notation. But I think you're getting closer at least.Apashanka said:Yes.
Is relation between Φ(to) and ∅ correct.??
Is so then dL will be x(1+z)
The arguments are this which I gavekimbyd said:It's hard for me to say because I'm a little unsure of your notation. But I think you're getting closer at least.
Apashanka said:Or the other way if ne be the no. density of photons at te then flux will be
Φ(te)=necE(te),
Φ(to)=noca(te)E(te)
where no is the no. density of photons at the observed time.=nea(te)3/a(t0)3
c is the speed of light.(constt. throughout the expansion)
Φ(te) is the same as in the comoving coordinate =∅ .
If a(to)=1(present time)
then Φ(to)=a(te)4necE(te)
,Φ(to)=a(te)4∅Is this the way that they are related ??,if so then from the quoted part above dL can be calculated which is dL=x/a(te)??
I'm still not sure what you mean by ∅. Usually this character refers to the empty set.Apashanka said:The arguments are this which I gave
No ∅ is the flux received by the observer in the co-moving frame.kimbyd said:I'm still not sure what you mean by ∅. Usually this character refers to the empty set.
Is this supposed to refer to the comoving distance from us to the galaxy where the signal is observed?
Okay. I read your statement as this was the co-moving coordinate.Apashanka said:No ∅ is the flux received by the observer in the co-moving frame.
If Φ(te) be the emmited flux at te by the emmiter ,observer in the comoving frame will receive the same , that's why Φ(te)=∅
I have mentioned this in post #10
Okay thankskimbyd said:Okay. I read your statement as this was the co-moving coordinate.
Generally the emitted flux and observed flux are wildly different, but I think it's okay if you're talking about a uniform photon gas. In which case yes, the flux falls off as ##1/a^4## as time increases.
But it sounds like you're not referring to a uniform photon gas here (as in the CMB), but rather one galaxy's emitted light. In which case you have to take into account how much space the light spreads out into. This is why when computing the luminosity distance, an integral over the expansion is required.
Will you give some suggestion regarding thiskimbyd said:In which case you have to take into account how much space the light spreads out into. This is why when computing the luminosity distance, an integral over the expansion is required.
Luminosity distance is a measure of the distance between two objects in space, taking into account the amount of light that is emitted by each object. It is used to calculate the distance to galaxies and other celestial objects.
Luminosity distance is calculated using the inverse square law, which states that the intensity of light decreases in proportion to the square of the distance from the source. This means that the farther away an object is, the less bright it appears.
Luminosity distance is important in astronomy because it allows us to accurately measure the distance to objects that are very far away, such as galaxies and quasars. This helps us understand the structure and evolution of the universe.
Luminosity distance and angular diameter distance are both measures of distance in astronomy, but they are calculated using different methods. Luminosity distance takes into account the brightness of an object, while angular diameter distance is based on the apparent size of an object in the sky.
Luminosity distance is affected by the expansion of the universe, as the light from distant objects is stretched and becomes less bright as it travels through expanding space. This is known as cosmological redshift and is an important factor in calculating luminosity distance.