Cosmic acoustics -- why no intermediate waves on CMB map

[jordankonisky]

I fully understand the representation of the set of waves that are either at full compression or full rarefaction at recombination, thus, yielding a CMB map. But at this time are there no waves that are intermediate, e.g. 50% of the way to full compression or full rarefaction. Why don't these show up in the CMB map.

Jo

 

[bapowell]

Why do you suspect they aren't there?

 

[jordankonisky]

That's my question. I would think they they are there, but want to understand how they are taken into account in contributing to the power spectrum which emphasizes the fundamental tone and its overtones. Am I thinking about this correctly or am I missing something basic in the acoustic analysis?

 

[Chalnoth]

I fully understand the representation of the set of waves that are either at full compression or full rarefaction at recombination, thus, yielding a CMB map. But at this time are there no waves that are intermediate, e.g. 50% of the way to full compression or full rarefaction. Why don't these show up in the CMB map.

Jo

The CMB has power at all wavelengths. Some wavelengths just have more signal than others.

 

[jordankonisky]

Much appreciate your help and patience. So waves that have not attained full compression and rarefaction at the time of recombination would have a lower photon energy (ie, deltaT) compared to a waves that are exactly at full compression or rarefaction. That is, these intermediate waves would have a temp differential that would be much lower then those of fully compressed and and rarefied, resulting in lower signals. Thus, they would be a part of the power spectrum, but dwarfed by the fundamental and overtone peaks. Am I thinking about this right?

 

[Chalnoth]

Much appreciate your help and patience. So waves that have not attained full compression and rarefaction at the time of recombination would have a lower photon energy (ie, deltaT) compared to a waves that are exactly at full compression or rarefaction. That is, these intermediate waves would have a temp differential that would be much lower then those of fully compressed and and rarefied, resulting in lower signals. Thus, they would be a part of the power spectrum, but dwarfed by the fundamental and overtone peaks. Am I thinking about this right?

No, they don't have a lower energy. They have a lower variance. That means that typically if you look at any two points separated by 1 degree on the sky (the first peak), then the typical difference in temperature will be a lot greater than at 2 degrees or 0.5 degrees (I believe the second peak is at close to 0.33 degrees).

Here's a plot of the data (WMAP in black, SPT in blue, ACT in orange):
http://lambda.gsfc.nasa.gov/product...s/nineyear/cosmology/images/med/gh9_f01_M.png
Source:
http://lambda.gsfc.nasa.gov/product...eyear/cosmology/wmap_9yr_cosmology_images.cfm

 

[jordankonisky]

Thanks, getting there. Is each CMB patch comprised of overlapping acoustic waves? If yes, wouldn't there be a need to resolve the individual waves through something like a Fourier analysis in order to construct the power spectrum?

 

[bapowell]

Yes, each multipole moment receives contributions from perturbations across all wavelengths.

 

[Chalnoth]

Thanks, getting there. Is each CMB patch comprised of overlapping acoustic waves? If yes, wouldn't there be a need to resolve the individual waves through something like a Fourier analysis in order to construct the power spectrum?

Yes. The spherical harmonic transform that is used is the analog of the Fourier transform.

The way it works is you ask, "What are the possible waves that can exist on a spherical surface, noting that if you go around the circle completely in any direction, the wave has to have the same value?" The answer is the spherical harmonics, which are pretty complicated, but behave very much like sinusoidal waves. The parameter ##\ell## is analogous to the ##k## that is used in Fourier transforms, with ##\ell## representing an approximate wavelength of ##180/\ell## degrees. There is a second parameter, ##m##, which sets the direction of the wave on the sphere. Both parameters are integers. When we take the power spectrum, we are taking the variance of the amplitudes of the waves with different ##m## values but the same ##\ell##.

 

[jordankonisky]

I know that the total amount of matter (dark plus atomic) can be determined from the character of the fundamental wave of the CMB. In contrast, the overtone waves provide information on the amount of atomic matter only. Why is this? I know that we can calculate these parameters from the NASA Lambda CMB power spectrum calculator, but was wondering if there is an independent way to determine these parameters from the CMB that does not rely on the calculator program. Thanks for any help.

 

[Chalnoth]

I know that the total amount of matter (dark plus atomic) can be determined from the character of the fundamental wave of the CMB. In contrast, the overtone waves provide information on the amount of atomic matter only. Why is this? I know that we can calculate these parameters from the NASA Lambda CMB power spectrum calculator, but was wondering if there is an independent way to determine these parameters from the CMB that does not rely on the calculator program. Thanks for any help.

It is impossible to estimate the parameters from the CMB without the use of some pretty complicated numerical computations. You can get a rough idea of what some of the parameters do, but that's about it.

For example, the first peak on the power spectrum represents matter that has just had enough time to fall into overdense regions. The second peak is matter that has had enough time to fall in then bounce back out. Dark matter doesn't bounce (as it feels no pressure), so it doesn't contribute to the height of the second peak. The ratio between those two peaks, then, gives an estimate of the baryon/dark matter ratio.

If you want a more comprehensive concept of what the various cosmological parameters do, you can check out the animations here:
http://space.mit.edu/home/tegmark/movies.html
(Click on different parameters on the right to see how changing those parameters changes the power spectrum)

 

[jordankonisky]

Thanks so much answering my questions about acoustic waves, the CMB and the power spectrum. I especially appreciated the level of your responses.

 

[marcus]

...
For example, the first peak on the power spectrum represents matter that has just had enough time to fall into overdense regions. The second peak is matter that has had enough time to fall in then bounce back out. Dark matter doesn't bounce (as it feels no pressure), so it doesn't contribute to the height of the second peak. The ratio between those two peaks, then, gives an estimate of the baryon/dark matter ratio.

If you want a more comprehensive concept of what the various cosmological parameters do, you can check out the animations here:
http://space.mit.edu/home/tegmark/movies.html
...

Nice animations! Thanks for posting them. I tried slow motion, suggested in the directions---you click to the left of the box containing the variable.
So you can see what happens when you increase the baryonic fraction of matter, slowly.

I'm not happy with this: "Dark matter doesn't bounce (as it feels no pressure), so it doesn't contribute to the height of the second peak." It is pointing in the right direction, but I can't get it to make sense. If DM did bounce by what mechanism would it therefore contribute?

Here's a Caltech tutorial quote: http://ned.ipac.caltech.edu/level5/Sept02/Reid/Reid5_2.html
"The relative heights of the peaks are an indication of [PLAIN]http://ned.ipac.caltech.edu/level5/New_Gifs/big_omega.gifb in that an increase in baryon density results in an enhancement of the odd peaks".

Here's what Wayne Hu says in his tutorial: http://background.uchicago.edu/~whu/araa/node10.html
"The baryons enhance only the compressional phase, i.e. every other peak. For the working cosmological model these are the first, third, fifth... Physically, the extra gravity provided by the baryons enhance compression into potential wells."