PDA

View Full Version : Comparing maximum available stellar light within ranges of redshift

mkline55
2012-Nov-09, 08:54 PM
Viewing the universe around us as a series of shells, what is the relationship between the light from shells of equal thickness? Assume first, the scale is large enough that the contents are nearly isotropic, and second there is no extinction. Also assume that the shells are not spaced so far as that their contents are much different due to age differences.

Successively larger shells should be observed with successively larger redshift values according to Hubble's law. So, if I were to define shell A by its redshift range of z=0.10 to z=0.15 and shell B with a range of z=0.15 to 0.20, while the light sources in shell B are more numerous than those in shell A, they are also more distant. I believe the total light which could potentially reach a receiver at the center is equal for each shell of equal thickness, regardless of thickness or shell size.

This seems to be logical, but if faulty logic paid better, I'd be retired by now. Can someone please confirm the math?

And, just to be clear, I do not view the universe as a sphere with us at the center. I am merely using this viewpoint to quantify amounts of light we could potentially receive at various levels of redshift.

Cougar
2012-Nov-09, 10:43 PM
Assume first, the scale is large enough that the contents are nearly isotropic....

If you are just working with a fictional, infinite universe, then I guess you could assume this, but our Universe is not isotropic with respect to time. Obviously, if you go back far enough, there is a point where there are no galaxies and no stars, and the problem fizzles.

Another complication (or maybe the same one) is that redshift z is not linear with time.

I think you're just being a little too ambitious by putting this in the realm of the universe. You can work the problem simply by using concentric shells, and the volume of the shells is going to be proportional (or essentially equivalent) to the light from that shell (to be divided by the distance squared). You can confirm the math on this yourself! The volume of a sphere is V={4 \over 3} \pi r^3. To get the volume of a particular shell, just subtract off the volume of the sphere interior to that shell. You can do it!

mkline55
2012-Nov-13, 02:21 PM
Not really an answer, Cougar, but I appreciate the effort. It's not really a question of volume, which, as you say, is easily calculated. It's a matter of calculus. Each successively larger shell of equal thickness has more light sources, but each source is farther away. In addition, each shell could be carved into an inner and outer shell, of 1/2 the thickness, and the outer of hose two shell would have more sources, but again, they would all be farther away than those in the inner shell.

If it helps to eliminate any issues about time, isotropy, or anything else, change the model to an observer adjacent to a solid crystal. Carve out successively larger scoops (half shells) of the crystal. Each shell is 1 mm thick. What is the relationship of the gravitational pull of a shell with an inner radius of 10 cm to on with an inner radius of 17 cm as seen by the observer?

tusenfem
2012-Nov-13, 02:26 PM
Not really an answer, Cougar, but I appreciate the effort. It's not really a question of volume, which, as you say, is easily calculated. It's a matter of calculus. Each successively larger shell of equal thickness has more light sources, but each source is farther away. In addition, each shell could be carved into an inner and outer shell, of 1/2 the thickness, and the outer of hose two shell would have more sources, but again, they would all be farther away than those in the inner shell.

Well, that's why infinitesimal calculus was invented ...

mkline55
2012-Nov-13, 06:41 PM
I worked out the result as a converging series. Each shell has the same total luminousity from the observer's standpoint. It works out to be 4 pi times the density times the shell thickness times the individual luminousity of each object. Radius is eliminated from the equation. So, as long as the shells are of the same thickness, say 50 Mpc, what an observer at the center would see is that one shell with an inner radius of 200 Mpc has the same potential luminousity as one with an inner radius of 2000 Mpc. Local stars aside, extinction and age differences would be factors that affect the observation.

antoniseb
2012-Nov-13, 07:35 PM
... Local stars aside, extinction and age differences would be factors that affect the observation.
OK, so this is a variation on the Olbers Paradox thread that's been going on in the Astronomy section... but with some modern sense of the universe. What you didn't mention (above) is that there are factors that increase the dimming with distance once you get to cosmological scale.

mkline55
2012-Nov-13, 08:06 PM
OK, so this is a variation on the Olbers Paradox thread that's been going on in the Astronomy section... but with some modern sense of the universe. What you didn't mention (above) is that there are factors that increase the dimming with distance once you get to cosmological scale.

If by factors that increase the dimming, you mean extinction and age differences, I thought I covered that in the original question: "Assume first, the scale is large enough that the contents are nearly isotropic, and second there is no extinction. Also assume that the shells are not spaced so far as that their contents are much different due to age differences."

I'll check out that other thread. Thanks.

mkline55
2012-Nov-13, 08:28 PM

antoniseb
2012-Nov-13, 08:39 PM
If by factors that increase the dimming, you mean extinction and age differences, I thought I covered that ...
No, I meant (using the mainstream model) that things are moving away from us at an increasing pace as they increase in z, and so the increased separation between photons has a dimming effect to our detectors. Once you get to z=1, this is already a big effect. At z=10, it is a huge effect.

mkline55
2012-Nov-13, 09:17 PM
No, I meant (using the mainstream model) ...

Thanks. I had left out that aspect. My math works only in an idealized universe with specific limitations. I have the right numbers, just the wrong universe.

George
2012-Nov-14, 01:19 AM
Thanks. I had left out that aspect. My math works only in an idealized universe with specific limitations. I have the right numbers, just the wrong universe. Using most people's favorite universe -- it's the best one I've found ;) -- the redshifting will also produce a lower light energy result with distance.

mkline55
2012-Nov-14, 01:55 PM
the redshifting will also produce a lower light energy result with distance.

I believe I understand what you are saying. So, the photons now reaching us that started their journey billions of years in the past now have less energy than when they started, adding yet another variable to my already improbable math. Where did that energy go?

Hornblower
2012-Nov-14, 04:02 PM
I believe I understand what you are saying. So, the photons now reaching us that started their journey billions of years in the past now have less energy than when they started, adding yet another variable to my already improbable math. Where did that energy go?

Let me take a stab at answering. The energy in the photons did not go anywhere. Our basis for describing the amount of energy in a photon changed as a result of the fundamental expansion. I will leave it to others to elaborate on it rigorously. I am too rusty to go any further after being away from practicing modern physics for over 40 years.

ngc3314
2012-Nov-14, 04:19 PM
Another way to look at "were did the photon energy go" is that, using Emmy Noether's connection between conservation laws and symmetries, conservation of energy is conjugate to space having the same properties at all times (http://en.wikipedia.org/wiki/Noether's_theorem#Example_1:_Conservation_of_energ y). Expanding spacetime violates that symmetry, so the basis of energy conservation is broken across cosmological scales.

mkline55
2012-Nov-14, 04:35 PM
the basis of energy conservation is broken across cosmological scales.

I think my original question has been answered. In order to avoid drifting too far, I'll pursue this additional concept on my own, at least until I find something I need help with. Thanks again.