Why Does Angular Diameter Distance Decrease After Redshift z=1.5?

In summary, the angular diameter distance starts to decrease after a certain redshift (around z = 1.5) because our universe was much smaller back then. This is because the angular-size distance is based on the angular diameter of some standard ruler at the time the light was emitted, and since pure expansion does not change angles, the distance of the object when the light was emitted is smaller than its present-day distance by a factor of z+1. This can be seen in the example of the CMB, where the matter that emitted the light was only 41 million light years away from us at the time of emission, but is now about 45 billion light years away due to the expansion of the universe.
  • #1
semiserious
2
0
Hi,
Can anyone explain (physically) why the angular diameter distance starts to decrease after a certain redshift (around z = 1.5)? Thanks
 
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  • #2
semiserious said:
Hi,
Can anyone explain (physically) why the angular diameter distance starts to decrease after a certain redshift (around z = 1.5)? Thanks
Simply put: our universe was much smaller back then.
 
  • #3
semiserious said:
Hi,
Can anyone explain (physically) why the angular diameter distance starts to decrease after a certain redshift (around z = 1.5)? Thanks

Chalnoth said:
Simply put: our universe was much smaller back then.

Semi, you got your answer! Chalnoth put it concisely.

One thing you could concentrate on understanding is this: the angular diameter of something is the angular diameter it had when the light was emitted and started on its way to us.

Because pure expansion does not change angles. If you think diagrammatically, the lightrays are not spread apart or squinched together by expansion. They are just stretched out longer.

But the angular-size distance is just based on the angular diameter of some standard ruler (like a 100 thousand lightyear galaxy), and since the angle spread of the incoming light does not change
the angular size distance equals the distance of the object when the light was emitted.

And that is smaller than the presentday distance by a factor of z+1.
 
  • #4
semiserious said:
Hi,
Can anyone explain (physically) why the angular diameter distance starts to decrease after a certain redshift (around z = 1.5)? Thanks

Chalnoth said:
Simply put: our universe was much smaller back then.

Semi, you got your answer! Chalnoth put it concisely.

One thing you could concentrate on understanding is this: the angular diameter of something is the angular diameter it had when the light was emitted and started on its way to us.

Because pure expansion does not change angles. If you think diagrammatically, the lightrays are not spread apart or squinched together by expansion. They are just stretched out longer.

But the angular-size distance is just based on the angular diameter of some standard ruler (like a 100 thousand lightyear galaxy), and since the angle spread of the incoming light does not change
the angular size distance equals the instantaneous proper distance to the object measured on the day when the light was emitted.

And that is smaller than the presentday distance by a factor of z+1.

So think about this example: the matter that emitted the CMB which we are now detecting is now about 45 billion LY from us. But the redshift of that ancient light is z = 1090. So the distances have increased by a factor of z+1 = 1091. Not to be too fussy, distances have increased by a factor of 1100.

So when the light was emitted, that matter was only about 41 million LY from our matter! When the ancient light was emitted, the matter was much much closer
 
  • #5


The angular diameter distance is a measure of the physical size of an object in the sky, taking into account the effect of its distance from us. As the redshift increases, it means that the object is moving away from us at a faster rate, which causes its light to stretch and appear more red. This also means that the object is getting farther away from us, and as a result, its angular diameter distance starts to decrease.

This decrease in angular diameter distance can be explained by the expansion of the universe. At higher redshifts, the universe was smaller and more compact, so the same amount of expansion will result in a smaller increase in distance compared to objects at lower redshifts. This means that the apparent size of an object at a certain redshift will be smaller compared to the same object at a lower redshift.

Additionally, the decrease in angular diameter distance can also be attributed to the curvature of space-time. As the universe expands, the curvature of space-time changes, causing the path of light to bend and the apparent size of distant objects to decrease.

In summary, the reason why the angular diameter distance starts to decrease after a certain redshift is due to the combination of the expansion of the universe and the changing curvature of space-time. This phenomenon is a result of the nature of our expanding universe and can be observed and measured through the redshift of objects in the sky.
 
1.

What is Angular Diameter Distance?

Angular Diameter Distance is a measure of the physical size of an object relative to its angular size as seen from a particular point of observation. In other words, it is the distance between two points on an object divided by the angle between them, and it is often used in astronomy to describe the size of celestial objects.

2.

How is Angular Diameter Distance calculated?

The formula for calculating Angular Diameter Distance is DA = do/θ, where DA is the angular diameter distance, do is the physical diameter of the object, and θ is the angular size of the object as seen from the observer's perspective. This calculation is based on the principles of trigonometry.

3.

What units are used to measure Angular Diameter Distance?

Angular Diameter Distance is typically measured in units of distance, such as kilometers or parsecs. However, it can also be expressed in terms of an angle, such as degrees or radians. The units used may vary depending on the context and the specific calculations being performed.

4.

How does Angular Diameter Distance differ from other distance measures?

Angular Diameter Distance differs from other distance measures, such as luminosity distance or comoving distance, in that it takes into account the angular size of an object as seen from a specific point of observation. This makes it a more accurate measure of an object's physical size, rather than just its distance from the observer.

5.

Why is Angular Diameter Distance important in astronomy?

Angular Diameter Distance is important in astronomy because it allows us to accurately measure the physical sizes of celestial objects, such as stars, galaxies, and clusters of galaxies. It also helps us understand the spatial distribution of these objects in the universe and how they are affected by the expanding universe.

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