How do I measure the distance of a galaxy using conventional terms?

[Skolon]

Expressing the cosmological distances with conventional terms is very confusing. For instance, if we say that "a galaxy is a 1 billion light years away" what this is really mean?
1. If all moves stopped (moves in space and expansion) the light will travel from that galaxy (center of it) and us for 1 billion years.
2. The light traveled 1 billion years before we observed it.
3. When light was emitted from galaxy, the distance was "1 billion light years", but because expansion the light traveled a different distance/time.
4. None of above.

So, I understand why cosmologist are using z for a distant object. But the value of z doesn't say anything about topology of Universe and his dynamics. What are cosmologist using to describe that aspects of Universe?

 

[Chronos]

2. is called the observable universe. That is our starting point. The rest is still model dependent.

 

[Skolon]

Wow, this is a little strange because that mean that when we say "a galaxy that is a billion light years away" we are not talking about a distance but about a period.

 

[marcus]

Expressing the cosmological distances with conventional terms is very confusing. For instance, if we say that "a galaxy is a 1 billion light years away" what this is really mean?
1. If all moves stopped (moves in space and expansion) the light will travel from that galaxy (center of it) and us for 1 billion years.
2. The light traveled 1 billion years before we observed it.
3. When light was emitted from galaxy, the distance was "1 billion light years", but because expansion the light traveled a different distance/time.
4. None of above.

So, I understand why cosmologist are using z for a distant object. But the value of z doesn't say anything about topology of Universe and his dynamics. What are cosmologist using to describe that aspects of Universe?

In your #1 you hit on one of the most often used definitions of distance in cosmology. It is known as "proper distance". I think of it as "freeze-frame" distance because to define it you imagine freezing the expansion process at a certain moment in time. Then you have time to send a light signal or a radar pulse---the distance does not change while you are trying to measure it.

To define proper distance, you have to say what you mean by the present moment---the moment in time when you freeze expansion. The distance will then be the distance at that moment in time. So you need an idea of "universe time". There is a standard way cosmologists have of defining universal time. (Something which observers at rest throughout the universe could in principle all agree on.) That sounds like it might be complicated to define but turns out to be surprisingly simple.

2. is called the observable universe. That is our starting point. The rest is still model dependent.

Wow, this is a little strange because that mean that when we say "a galaxy that is a billion light years away" we are not talking about a distance but about a period.

I think you are right, Skolon. The "lookback time" or "light travel time" is a measure of time, not distance. It is not very useful as a gauge of distance. It is not something we directly observe. We calculate how many years the light has traveled using a model.
I also found Chronos post confusing.

 

[marcus]

Skolon, I like your definitions #1 and #3. Both come under the general heading of "proper distance".

#3 is the proper distance the galaxy was at the moment the light was emitted.

The Cosmos Calculator (link in my signature) will calculate it for you if you type in a redshift. In that calculator it is called the "then" proper distance. The proper distance at the moment we receive the light is what it labels "now".

Both "then" and "now" distances are useful in cosmology. The standard calculators will give them to you if you plug in an observed redshift. They are your distances #1 and #3.

The light travel time is not a distance (as you point out it is a time interval) but it is useful information too---and cosmology calculators will give you that as well.

The quickest calculator to use is the one at Ned Wright's website. He is a UCLA cosmologist. You google "cosmo calculator" or you google "wright calculator".

Then all you have to do is type in the observed redshift and you get all this stuff. The redshift (the fractional lengthening of the wavelengths) is what we actually SEE. Everything else, namely the distances then and now and light travel time, are things that have to be calculated using a math model based on all the observational data that has accumulated over the years.

If you have questions about how to use these calculators---what the outputs mean, etc.---please ask. It's good to get acquainted with them.

I like one called "cosmos calculator" because the output is clear and simple. But with it you have to first type in three numbers which are supplied for you in the other calculator. So there is that extra bother: at the start of every session you have to type in .27, .73, and 71 . There is a pedagogical reason for this---it gets students familiar with the basic model parameters (matter fraction, lambda fraction, current Hubble rate.) So it's part of a teaching strategy, but it is a nuisance.

 

[Skolon]

Marcus, can you explain me more about The Cosmos Calculator?

When I look to this http://en.wikipedia.org/wiki/Lambda-CDM_model#Parameters", I don't know what to put on Omega and Lambda.
I use 73.8 Km/sec/Mpc for H and I try to find z for that galaxy that have a "speed away from us now" equal with the speed of light.

 

[marcus]

Marcus, can you explain me more about The Cosmos Calculator?

Cosmos Calculator is a calculator for beginners. You may be more comfortable with a more advanced "professional" level calculator where the terminology is not so simplified.

The professor who posted this calculator is a woman Siobhan Morgan. I like her way of simplifying the language. It is for her beginning astronomy students.
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

For MATTER DENSITY put in .27
For COSMOLOGICAL CONSTANT put in .73
For HUBBLE put in 71

Then put in anything you want for the redshift Z, you can keep trying different values.

The reason matter density is .27 is that baryonic matter is .04 and dark matter is .23 and so total matter is .04+.23

All these numbers have ranges of uncertainty, they are approximate. I just happen to say Hubble parameter is 71. You can put in something else like 70.4 which is what Wikipedia says http://en.wikipedia.org/wiki/Lambda-CDM_model#Parameters

Basically the reason I habitually use .27, .73 and 71 is because I also use Ned Wright's calculator and those are the default values he uses in his. Eventually when the errorbars narrow down he will probably change his parameters a little and I will change with him.
It is less trouble for me if I keep together with Ned Wright.

If you are using .27, .73, 71, then try Z = 1.4

or to get a teensy bit closer, try Z = 1.41

If you want something a bit more advanced, google "wright calculator".
Ned Wright gives more decimal places of accuracy and uses more professional terminology.
I like Miss Morgan's because I think she is slightly more "user friendly" or at least "beginner friendly".

 

[marcus]

Using Ned Wright's calculator and his customary choice of parameters .27-.73-71 I get that the redshift you want is closer to 1.407.

That would mean that if you observe a galaxy and measure the redshift to be 1.407 then you can infer that the distance to the galaxy is increasing at rate c.

(except for some small amount of random motion which the galaxy might have, relative to background----IOW if it is sitting still , and we have corrected for our own motion as observers, then the distance to it is increasing at rate c.)

But that level of precision is kind of bogus because it depends on the arbitrary choice of H to be 71---and other choices like that. There is an errorbar. And also you could take H to be 70.4 as Wikipedia does. Then the answer for z would not be 1.407.
It would be something else around about 1.4.

 

[Skolon]

If you are using .27, .73, 71, then try Z = 1.4

or to get a teensy bit closer, try Z = 1.41

I found something amusing.
If I use on Cosmos Calculator H=70.4, Omega=0.2726 and Lambda=0.7274 on Mozilla (version 3.6.22) I must put z=1.13 to obtain "Speed away from us now" = speed of light.

Instead, on IE (v. 6.0) with same parameters I must use z=1.42 for the same result.
I think this is the right answer because on Mozilla I have other obvious faults, like "Age of the Universe now = 20.17 billion years" (13.74 billions on IE 6).

About "Distance Modulus": I don't understand how the absolute magnitude can be known when for a given object we have just apparent magnitude (which I guess can be measured)?

LE: About http://www.astro.ucla.edu/~wright/CosmoCalc.html" ... I need more time to comprehend all from there.
But from both calculators I got my answers for my first post:
1) 13.94 Gly (proper distance now)
2) 9.176 Gy (light travel time)
3) 5.76 GLY (proper distance then)