Schwarzschild radius

[scalbers]

I'd have to research this exactly, though I think the main differences relate to the history of the slowing of the expansion (at first), then having the expansion more recently speed up. This may shift the observable horizon somewhat from the Hubble constant implied value. One thing I can say is that the accelerating expansion will make the number of galaxies viewable within our horizon decrease with time. The sky may be rather lonely in the distant future.

 

The "flatness" of the universe would also be a factor if it differed significantly from 1.

[Martin]

This may shift the observable horizon somewhat from the Hubble constant implied value...

 

What do you mean by the "Hubble implied value"? Do you mean c/H the Hubble radius. It is important to distinguish this from the radius of the observable universe.

 

one idea of observable universe radius

is HOW FAR AWAY NOW is stuff that could have sent us a photon which we are now receiving

 

i.e. what the the PRESENT DISTANCE OF THE FARTHEST STUFF WE COULD IN PRINCIPLE SEE

 

that is called the particle horizon and IIRC it is estimated at about 47 billion ly

 

 

 

another idea of horizon is THE PRESENT DISTANCE OF SOMETHING THAT TODAY COULD SEND A SIGNAL THAT WOULD EVENTUALLY GET HERE.

 

IIRC that horizon is estimated at around 16 or 17 billion ly

 

Neither of these two horizon radii (47 or 16) are the same as the Hubble Radius.

 

the Hubble radius is only 13-14 billion ly. That is not the radius of the observable universe!

 

It is only present distance of stuff that is currently receding at the speed of light. We see stuff way past that.

[scalbers]

Yes, I was thinking of the Hubble radius. I'm wondering what that would correspond to if the universe had a history of expanding at a uniform rate. This would be different from the actual situation with variable expansion rates.

 

So the Hubble radius should roughly correspond to the age of the most distant objects we can see. And would it be the distance those objects were when their light was emitted (and thus their present "apparent" distance)? Well according to this Wikipedia article, this distance was actually much less - on the order of 40 million light years:

 

http://en.wikipedia.org/wiki/Observable_universe

 

Martin's distance, "THE PRESENT DISTANCE OF SOMETHING THAT TODAY COULD SEND A SIGNAL THAT WOULD EVENTUALLY GET HERE" of 16-17 billion light years makes sense, however this isn't really addressed in the Wikipedia article. This value might be closer to the Hubble radius if it weren't for the variable expansion rate?

 

On another note I like the notion that objects do exist beyond the observable horizon and they are actually receding from us faster than the speed of light.

[Martin]

...

 

So the Hubble radius should roughly correspond to the age of the most distant objects we can see. And would it be the distance those objects were when their light was emitted (and thus their present "apparent" distance)?

...

 

That sounds confused. I don't understand exactly. The most distant sources of radiation---the most distant object we can see---are 40-some billion LY away.

That is because the light from them has been traveling almost the entire age of the universe, some 13 billion years!

 

The Hubble radius has nothing to do with it. It is not the distance these sources are at present. It is not the distance that these sources were when they emitted the light.

 

IIRC the distance that the CMB sources were when they emitted the CMB light that we are now getting as microwave was about 40 MILLION LY.

 

You should play around with Ned Wright calculator, put in z = 1100 for the CMB.

 

Well according to this Wikipedia article, this distance was actually much less - on the order of 40 million light years:

 

http://en.wikipedia.org/wiki/Observable_universe

 

I can't take the time to check up on Wikipedia. Some of their articles are excellent, some contain mistakes, or are poorly written and thus confusing.

 

If you want to get straightened out, spend some time with Ned Wright's cosmology tutorial, and play around with his cosmology calculator. he is a professional cosmologist----Wiki authors are a mixed bag.

 

40 million LY sounds right for a type of distance called ANGULAR SIZE DISTANCE.

 

there are a handful of different distance measures, brightness, angular size, present-day distance, light travel-time or lookback time....

they do not coincide.

 

the distance used for most purposes is the present-day distance-----the distance to the object at the present moment in time calculated according to the standard metric (the FRW distance measure). This is the distance that works in the Hubble law

v = H d

recession speed is proportional to distance, by the present value of the Hubble parameter

=================================

http://www.astro.ucla.edu/~wright/CosmoCalc.html

when you put in z = 1100 (actually a better figure would be 1070, but not to put too fine a point on it)

 

you get that the present distance of the source is 45.6 BILLION ly

and the angular size distance, the distance it was when it emitted the light, is 41.5 MILLION ly

and the light travel time is 13.665 billion years

out of a total age of universe of 13.666 billion years

which means the universe was roughly a million years old, or some substantial fraction thereof like 480,000 years, when the light was emitted.

 

hope this helps and that you can get your head around these figures

 

the hubble radius has nothing to do with the size of the observable universe, we can observe stuff that is WAY beyond that, WAY outside the hubble sphere. the hubble radius is merely the presentday distance of stuff that is right now receding from us at the speed of light

(most stuff in the observable universe is receding faster than c)

[scalbers]

Thanks for the references - I'll see if I can get the calculator to load. I do like Wikipedia as a quick look though. I appreciate your clarification on what the Hubble distance does actually correspond to, though I wonder if your explanation might need to be corrected for the changing H over time.

 

I think it's interesting to sort out some of the various distances according to what is affecting them. In other words, how would Ned's calculator be impacted if:

 

a) the universe were static, but has an age of 13.7 billion years (somehow being magically created)

 

b) the universe is expanding according to the current Hubble constant, and this value was a constant over history (instead of the actual decleration followed by acceleration).

 

I wonder what the "apparent" distance of the oldest objects (at least galaxies) would be if you consider their angular diameter that we see and their actual linear diameter at the time the light was emitted.

 

Also, what would that distance you referred to in post #27 (16-17 billion LY - "THE PRESENT DISTANCE OF SOMETHING THAT TODAY COULD SEND A SIGNAL THAT WOULD EVENTUALLY GET HERE") be if we had a universe that was expanding at a constant rate?

 

Hope that's a little bit clearer, though I think I had actually answered part of my own unclear "apparent distance" question in the subsequent sentence that was omitted from your quotation

[Martin]

I wonder what the distance of the oldest objects (at least galaxies) would be if you consider their angular diameter that we see and their actual linear diameter at the time the light was emitted.

...

 

that is the definition of the angular size distance.

it is the distance based on how big a fixed ruler looks

 

IIRC out past z = 1.6, a fixed ruler looks bigger the farther away it is

this is a good thing to understand if you want to learn some basic cosmology

 

===============

 

you said something that suggests you think that the Hubble parameter is equivalent to the rate the universe is expanding, so if expansion is accelerating you would expect the H to be increasing

 

but this is not true. the Hubble parameter is decreasing and is expected to continue decreasing indefinitely far into the future (according to the prevailing LCDM model)

 

however the rate of expansion has been increasing for several billion years already

 

the quantity you want to understand is a(t) the scale factor in the FRW metric. if you write the timederivative as a'(t) then acceleration means that a'(t) is increasing, or that a" is positive

 

however H(t) is defined to be a'/a

it can decrease as long as a(t) is increasing faster than a'(t)

============

 

we probably should have a cosmology tutorial

the main question is would people work at it.

one of the big things would be to spend time experimenting with Wright's calculator and also Morgan's (which gives recession speeds)

============

 

cosmology is essentially about solutions to the Einstein field equation in a simplified form called the Friedmann equations.

I don't know how to answer some of your WHAT-IF questions because I don't immediately see how they could correspond to solutions of the Friedmann model. for example what if a(t) was not changing? I don't know because in all the solutions a(t) is dynamically changing in response to the energy density. It is too much of a fantasy to think about unphysical things---it would take a smarter person than me to make physics out of some of these what-if situations.

I tend to stay in the General Relativity (i.e. Friedmann equation) rut and just vary the physical parameters in that context.

 

In Wright's calculator you can vary the parameters all over the place and create totally weird universes with different growth histories and different H etc----but they all obey Einstein and none of them that I know of would have constant a(t) or contant a'(t). I could be wrong, havent thought about it much. But that's my hunch. why don't you try the calculators out and vary the parameters and see what you can make happen, if you are curious?

[scalbers]

I had tried the calculator using Firefox in Windows XP and it failed to load, at least in this universe. Should I try Internet Explorer?

 

Yes, I had heard about objects looking larger beyond a certain distance. To clarify though, would a given object have a larger angular diameter, rather than simply a larger inferred linear diameter as it is viewed from farther away?

[Martin]

I had tried the calculator using Firefox in Windows XP and it failed to load, at least in this universe. Should I try Internet Explorer?

 

Yes, I had heard about objects looking larger beyond a certain distance. To clarify though, would a given object have a larger angular diameter, rather than simply a larger inferred linear diameter as it is viewed from farther away?

 

You tried this

http://www.astro.ucla.edu/~wright/CosmoCalc.html

and it wouldn't load?

 

that is very unusual. maybe the trouble is temporary. I get it with Firefox.

 

Angular diameter. YES! you get the idea.

the same size object has a larger angular diameter if it is farther away, after about z = 1.6

 

from here out to 1.6, it shrinks with distance and has a smaller angle the larger the redshift

around 1.6 it has its minimum angular size

then if youn continue on past 1.6 the angular diameter gets larger with increasing redshift i.e. distance

 

it is because the early universe was small, so things appear big in it, when it is projected on the full 360 degree sky. kind of weird when you first hear the idea----funhouse mirrors etc.----but a real effect

[scalbers]

I've tried various Ned Wright UCLA links on three different browsers today to no avail so far.

 

Following up on the angular diameter phenomenon, is there any qualitative way this can be discerned in looking at images such as the Hubble Deep Field?

[Martin]

I've tried various Ned Wright UCLA links on three different browsers today to no avail so far.

that is strange

there are other online calculators which people tell me use the same algorithms. I will get some links.

Morgan's is actually nicer than Wright's in a certain way. The only thing is you have to type in the three parameters (0.27, 0.73, 71), whereas Wright gives them to you as the default. So Morgan's takes longer to use, but just a few seconds.

 

Then there is one at "geocities" that I never tried but am told is excellent*.

http://www.geocities.com/alschairn/cc_e.htm

this is Hellfire's calculator (he is a poster on some other board)

 

 

I know of yet another but will just get links for the first two.

many of the links I'm using including Morgan's calculator are gathered here

http://www.scienceforums.net/forum/showthread.php?p=384716#post384716

Morgan's calculator is here

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

 

 

 

Following up on the angular diameter phenomenon, is there any qualitative way this can be discerned in looking at images such as the Hubble Deep Field?

That is an interesting question! In 2006 a technical paper was written about this question. The author was Hellaby at Uni Capetown SA.

It requres improved instruments (Hellaby said the next generation----expected within the next 10 years) to measure the angular sizes of many objects with high resolution. Or maybe COUNT the number of objects at different redshifts. Not sure how he plans to do it. Some statistical method will have to be used because one has no precise standard diameter of galaxy. It is a hard thing to do observationally. But Hellaby thought that it would be possible and could be piggybacked onto the regular gathering of data for other continuing studies. He had a particular reason he wanted to know the exact redshift (I think it is z = 1.6 or thereabouts) where there is the turnaround and past that point samesize things start looking larger (angular).

 

I guess you asked about a QUALITATIVE way. One way is to look at those oval maps of the CMB sky. Those mottled red and blue temperature maps. Those bump in the variation of temperature are random ripples in a small sphere that was only radius 41 million ly at the time

so if you see like 120 or 130 little fluctuation ripple bumps going around the circumference, each one of those is only a million ly wide.

because the circumference is less than 130 million ly.

I am simplifying, the fluctuation bumps are all sizes. They are basically acoustic noise. their power spectrum is called the acoustic power spectrum. But anyway a bump that used to be only a million ly diameter has been expanded to have a huge diameter.

That is not really satisfactory because it involves trusting what the experts tell us. It would be nice to have a photograph of some galaxies that would make it obvious. But they would have to be well beyond z = 1.6 and resolved to a point where you can measure the outline, not just a fuzzy dot.

 

So I think the right answer is NOT YET. In case you are curious I can get a link to Hellaby's article, but it is technical so only the introduction and conclusions parts at beginning and end are accessible. Still, as a reality check, just in case you want:

http://arxiv.org/abs/astro-ph/0603637

he talks about the "maximum of the areal radius". that comes at roughly around 1.6

he wants to use a lot of observations to determine it with higher accuracy, not calculated from model, but observed. he wants to pin down that 1.6 number, because he says he can use it to derive the mass density of the universe (mass per unit volume)

which is another number (Omega) that they are very interested in knowing.

 

exciting times in cosmology

 

*another person who programmed their own cosmo calculator is Jorrie, but Jorrie says (quoting from another board where he hangs out) that he likes Hellfire's. I don't know either. I just continue using Ned Wright's

Hi Hellfire' date=' thanks.

I've looked at your calculator code today and noticed that you have put in the latest WMAP value (8.24E-5) for Omega_r. This is now my favorite cosmo-calculator! *biggrin*

[scalbers]

Yes, this is worth exploring a bit, as is done here in the context of radio sources...

 

http://arxiv.org/PS_cache/astro-ph/pdf/0309/0309390v2.pdf

[Martin]

Let's see what the title and abstract look like

 

http://arxiv.org/abs/astro-ph/0309390

 

I was interested to see there is more about this than I realized. I checked the list of papers which had cited the one you mentioned.

Thanks for the reference.

 

I hope you succeeded in finding a calculator that loads.