Conflict between reionization and the most distant object

[thenewmans]

Using time to measure distance (I hope that’s OK), the big bang is 13.7b light years away. The farthest we can see is 12.7b light years. That’s because the universe was opaque for a billion years before reionization. Yet the most distant object (GRB 090429B) is 13.1b light years away. That’s too far to see. I must have something wring here.

 

[marcus]

Using time to measure distance ...The farthest we can see is 12.7b light years. That’s because the universe was opaque for a billion years before reionization...

It is all right to use light travel time as a way of expressing distance IF you know how to convert to proper distance measure.

Because the U has a varying expansion history, the conversion is not straightforward. It takes a couple of minutes on the calculator. So I never use travel time to express distance---its too much of a nuisance.

I would suggest you get into the habit of using and thinking in proper distance. That is the distance that is used in stating Hubble law and that goes with the standard cosmo model.
The proper distance to a galaxy at some moment is what you would measure if you freeze expansion at that moment and then use any conventional means like radar or light pulse. The point is by freezing expansion, you have time to measure without the distance constantly changing.

What we actually measure is typically a redshift. So there are online calculators to convert redshift to distance. They'll tell you the proper distance the thing is NOW, at the time we receive its light, and also the distance it WAS BACK THEN when it emitted the light.
(that may be labeled the thing's "angular size distance" just a technical term for it).

Google "wright calculator" and put in 1100 for z. That is the redshift of the farthest stuff we can see---when it constituted the hot gas emitting what is now our microwave background.

You will find that the distance now to the farthest visible stuff is 45 billion light years.

You will also find the distance to the farthest visible material THEN, when it emitted the light was about 1/1100 of that, namely 41 million lightyears.

So the distance to the material whose glow we now see as background WAS 41 million when the light was emitted and now it is 1100 times farther, namely 45 billion.

The calculator will also give you the light travel time for z = 1100. It is approximately 13.7 billion years. (a few hundred thousand years does not show up on a scale of billions, so if you subtract 400,000 from 13.7 billion you still have 13.7 billion ).

 

[Chronos]

Reionization occurred about 380,000 years after the big bang, not a billion years.

 

[marcus]

Newmans,
You say the farthest we can see is 12.7 billion light years. I never heard that or read of anybody saying that.

Maybe you would like to explain? Give some detail?

Also I never heard of the universe being "opaque" for a billion years.

The opaqueness I'm familiar with ended about 380,000 years after the start of expansion.
That is roughly a third of a MILLION. Very different from a billion.

So clue us in. How does the U get to be opaque for a billion years?

During the "Dark Age" the U was not actually opaque. Neutral hydrogen is transparent to most wavelengths---it interacts only to certain selected ones. The Dark Age was dark because it lacked sources of light---stars took a while to form.

Reionization refers to something that happened around the formation of the first stars. Sort of in the range redshift z = 6 to 20. We can SEE back to z = 1100. So space cannot have been opaque during the Dark Age. (or only in a very selective sense, to certain wavelengths that neutral hydrogen gas can scatter)

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

Chronos, I think you meant to say RECOMBINATION, not reionization:

Reionization occurred about 380,000 years after the big bang, not a billion years.

Recombination occurred some 380,000 years after the start of expansion according to standard model.
=================================
http://en.wikipedia.org/wiki/Reionization

==quote==
The first phase change of hydrogen in the universe was recombination, which occurred at a redshift z = 1100 (400,000 years after the Big Bang), due to the cooling of the universe to the point where the rate of combination of an electron and proton to form neutral hydrogen was higher than the ionization rate of hydrogen. The universe was opaque before recombination because photons scatter off free electrons (and, to a significantly lesser extent, free protons), but it became transparent as more and more electrons and protons combined to form hydrogen atoms. While electrons in neutral hydrogen (or other atoms or molecules) can absorb photons of some wavelengths by going to an excited state, a universe full of neutral hydrogen will be relatively opaque only at those wavelengths, and transparent over most of the spectrum. The Dark Ages start at that point, because there are no light sources yet other than the gradually darkening cosmic background radiation.
The second phase change occurred once objects started to form in the early universe energetic enough to ionize neutral hydrogen. As these objects formed and radiated energy, the universe went from being neutral back to being an ionized plasma, between 150 million and one billion years after the Big Bang (at a redshift 6 < z < 20). By now, however, matter has been diluted by the expansion of the universe, and scattering interactions are much less frequent than before recombination..
==endquote==
Fortunately Wikipedia is OK on this.
However there are some bad information sources that google turns up, which confuse recombination with reionization and say Dark Age was opaque. Beware! The web has its pitfalls.

 

[Chronos]

Oops, I did mean recombination. I usually refer to this as the 'surface of last scattering' to avoid confusion. And you correctly note the universe was not opaque to EM during the reionization era, whereas it was opaque prior to recombination.

 

[thenewmans]

Newmans,
You say the farthest we can see is 12.7 billion light years. I never heard that or read of anybody saying that. Maybe you would like to explain? Give some detail? …

Fortunately Wikipedia is OK on this.
However there are some bad information sources that google turns up, which confuse recombination with reionization and say Dark Age was opaque. Beware! The web has its pitfalls.

You nailed it. Somewhere, Wikipedia said that reionization is opaque. But all I can find now is this diagram that says it’s 10% opaque. I guess that means it’s 90% transparent.
http://en.wikipedia.org/wiki/File:Reion_diagram.jpg

I would suggest you get into the habit of using and thinking in proper distance. That is the distance that is used in stating Hubble law and that goes with the standard cosmo model. The proper distance to a galaxy at some moment is what you would measure if you freeze expansion at that moment …

You will find that the distance now to the farthest visible stuff is 45 billion light years.

You will also find the distance to the farthest visible material THEN, when it emitted the light was about 1/1100 of that, namely 41 million lightyears.

To get the proper distance, do I freeze it now or freeze in “THEN?” In other words, is the proper distance to the farthest visible stuff 45bly or 41mly?

I’m surprised physicists would prefer this over light travel time or redshift Z since these are the most common methods I see in articles and papers.

 

[marcus]

To get the proper distance, do I freeze it now or freeze in “THEN?” In other words, is the proper distance to the farthest visible stuff 45bly or 41mly?

I’m surprised physicists would prefer this over light travel time or redshift Z since these are the most common methods I see in articles and papers.

The proper distance is always associated with a particular moment in time. The proper distance NOW is also called "radial comoving".
If you google "wright calculator" and use what is probably the most used online cosmo calculator to get the distance related to a redshift, what you see labeled "comoving radial distance" is actually the NOW proper.
Ned Wright points out that this distance is the one that works in Hubble law.

Proper distance at various times is what you get in the standard Friedman equation model.

It is also what you MEASURE using a standard candle observed at a given redshift.

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

So proper distance is ubiquitous. I don't imply that everybody LIKES it better than the several other ways of writing distance. It just comes up all the time in discussions/applications.

1. basic to formulation of very common law (v = Hd)
2. formulation of the universally used standard cosmic model (Friedman, LambdaCDM)
3. direct consequence of measuring the modulus ("mu") and the redshift ("z")

The point about 3. is that stuff dims according to inverse square of the proper distance. And also dims according to the lengthening of wavelength---which is by the factor 1+z.

So if you measure the z (of say a standard candle supernova) and also the logarithmic dimming modulus then you have, in effect, measured the NOW proper distance.

Because of the quaint traditional way the modulus is defined (based on the age-old magnitude scale) the now proper distance is

[10^(mu/5 + 1)]/(1+z) parsecs

You can multiply that by 3.26 to get freeze-frame lightyears. The first factor is what the distance would be if all the dimming were inverse square. It looks funny because the traditional way mu is defined is funny. It overestimates the distance by a factor of 1+z because NOT all the dimming is due to inverse square spreading out of the energy.
Dividing by 1+z adjusts for that overestimate by accounting for the light being weakened by having its wavelength increased by that factor.