Measuring Mass of the Cosmos: Charles Hellaby's New Paper

[marcus]

In case anyone is interested, here is a new paper just out.
Any comment?


http://arxiv.org/abs/astro-ph/0603637
The Mass of the Cosmos
Charles Hellaby
6 pages, 9 graphs in 3 figures

"We point out that the mass of the cosmos on gigaparsec scales can be measured, owing to the unique geometric role of the maximum in the areal radius. Unlike all other points on the past null cone, this maximum has an associated mass, which can be calculated with very few assumptions about the cosmological model, providing a measurable characteristic of our cosmos. In combination with luminosities and source counts, it gives the bulk mass to light ratio. The maximum is particularly sensitive to the values of the bulk cosmological parameters. In addition, it provides a key reference point in attempts to connect cosmic geometry with observations. We recommend the determination of the distance and redshift of this maximum be explicitly included in the scientific goals of the next generation of reshift surveys. The maximum in the redshift space density provides a secondary large scale characteristic of the cosmos."

It would appear that the author has thought of another way to gauge the universe's mass----or the mass of a large chunk. We already have estimates, as he points out. But apparently here is a method that has not been tried.

 

[Chronos]

I think it is wrong, marcus. I read that paper and found it . . . weak.

 

[marcus]

I think it is wrong, marcus. I read that paper and found it . . . weak.

I see

Not a big deal. I would not urge the paper on anyone---just wondered if anyone might be interested.

the kind of question it suggests to me is this: suppose you have 4 identical spiral galaxies at different distances

1. is at z = 1
2. is at z = 2
3. is at z = 3
4. is at z = 4

the question is, which galaxy looks SMALLEST in the sense of having the smallest angular size?

and if you can say that, then also which galaxy looks largest: has the biggest angular size

assume some usual cosmological parameters like-----Hubble = 71
Omega_Lambda = 0.73, Omega_matter 0.27
and that your telescope is sensitive in the infrared and can "see" the objects well enough to tell their angular sizes

 

[hellfire]

the kind of question it suggests to me is this: suppose you have 4 identical spiral galaxies at different distances

1. is at z = 1
2. is at z = 2
3. is at z = 3
4. is at z = 4

the question is, which galaxy looks SMALLEST in the sense of having the smallest angular size?

The angular size of object of size [itex]dl[/tex] located at angular distance $D_A$ is:

$$d\theta = \frac{dl}{D_A}$$

Now, go for example to my cosmological calculator and fill in the redshift:

z = 1, D_A = 5410.05 Mly
z = 2, D_A = 5701.73 Mly
z = 3, D_A = 5267.91 Mly
z = 4, D_A = 4764.96 Mly

This means that [itex]d\theta[/tex] is smallest at z ~ 2. Objects beyond z ~ 2 start increasing in angular size.

 

[Chronos]

That is an interesting artifact, hellfire.

 

[marcus]

The angular size ... is smallest at z ~ 2. Objects beyond z ~ 2 start increasing in angular size.

Right!

so to answer the question as stated, the galaxy at z = 2 looks smallest and the one at z=4 looks largest

Hellaby's idea is to process future astro data to extract an estimate of
z_max
the redshift at which galaxies look their largest.

He then proposes to derive some other information from that, like converting z_max to a distance and so forth.

IIRC Hellaby's papers go back to at least 1985. It is conceivable that he knows what he's talking about. Also possible that he doesn't----that it is not a good way to extract info about the universe from astro data.

Any other comment?

 

[Chronos]

The increase of angular size with a z cutoff just smacks me as wrong. I agree the evidence suggests this possibility, but, our universe is weird enough without introducing that complication.

 

[kmarinas86]

http://www.anzwers.org/free/universe/redshift.html
http://en.wikipedia.org/wiki/Angular_diameter_distance

It appears that the angular diameter distance is equal to the comoving distance divided by the redshift.

 

[marcus]

The increase of angular size with a z cutoff just smacks me as wrong. I agree the evidence suggests this possibility, but, our universe is weird enough without introducing that complication.

yes, in line with the droll irony of your sig.
yes, weird.
but then again maybe not so weird, maybe even intuitiveit's intuitive from what you get in the first two or three installments of ned wright's Cosmology Tutorial
remember the first time you looked at the tutorial and saw that
THE LIGHTCONES LOOK LIKE TEAR-DROPS?

when you look back you see a universe that was smaller, so an individual galaxy occupies a larger solid angle on the ball of what you see at that z

I am just trying to massage your intuition Chronos, not be rigorous, so don't argue back, just relax.

it is obvious from observations that this happens

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

there is a great way to get intuition about this fact of angular size increasing with distance after about z = 2

You can find it out for your self just by PLAYING WITH NED WRIGHT'S COSMO CALCULATOR!

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

that calculator is such a useful teaching tool!

it takes a z input
and one of the many things that it gives output is the kiloparsec diameter corresponding to ONE ARCSECOND
it outputs this in units of kpc/"

try it
you can find the exact z where the kpc/" is a max
and then check that as you increase z from there on, the kpc/" gradually slopes off
we live in a beautiful funhouse mirror vision better than any actual funhouse