View Full Version : CMBR power spectrum acoustic peaks

Staticman

2010-Jul-18, 12:47 PM

What is the meaning of the first and second acoustic peaks in cosmological terms? How are the basic parameters of the universe derived from them? I know it's not easy but try not to be too technical in the answer.

Thanks

antoniseb

2010-Jul-18, 04:50 PM

I'm sure that someone will come by with a more complete answer soon, but basically, the first and second peaks are the quadrupole and octopole variations. You can think of dipole as being an indication of our total movement against the background. Quadrupole could be something like two poles coming in and everything else pushing out (or vice versa) for the whole sky (us at the center). Octopole has twice the number of in and out directions. You could think of this as the biggest acoustic signature in the universe, but it is also (because of the whole-sky nature of this measurement) the easiest one to taint with local data. Of all the peaks, these are the ones we are relying on least right now.

StupendousMan

2010-Jul-18, 05:52 PM

One good place for a technical, but not _too_ technical, description of the CMB is Wayne Hu's page:

http://background.uchicago.edu/~whu/beginners/introduction.html

Staticman

2010-Jul-18, 06:51 PM

I'm sure that someone will come by with a more complete answer soon, but basically, the first and second peaks are the quadrupole and octopole variations. You can think of dipole as being an indication of our total movement against the background. Quadrupole could be something like two poles coming in and everything else pushing out (or vice versa) for the whole sky (us at the center). Octopole has twice the number of in and out directions. You could think of this as the biggest acoustic signature in the universe, but it is also (because of the whole-sky nature of this measurement) the easiest one to taint with local data. Of all the peaks, these are the ones we are relying on least right now.

Thanks Antoniseb, actually I',m a bit more confusd now, I just read the first peak is at l=220 multipole moment, I don't know if that is exactly a quadrupole but I suspect is not. Also I thought this two peaks were related with the Dark energy and Dark matter parameters of the LCDM model. Perhaps anyone could clarify this?

Nereid

2010-Jul-18, 07:50 PM

Thanks Antoniseb, actually I',m a bit more confusd now, I just read the first peak is at l=220 multipole moment, I don't know if that is exactly a quadrupole but I suspect is not. Also I thought this two peaks were related with the Dark energy and Dark matter parameters of the LCDM model. Perhaps anyone could clarify this?

antoniseb was answering a different question than the one you actually asked.

The location of the first peak, l ~220, is dependent on the average mass-energy density of the universe; specifically on how close it is to the critical density.

The first two peaks are, indeed, 'acoustic', in that they represent sound waves in the part of the universe we see in the CMB, at the time radiation (photons) and baryonic matter went their separate ways ('decoupled'; the 'surface of last scattering'). However, there are several physical processes which contributed to the location of the peaks, and the height of the peaks (both relative and absolute); for example, the thickness of the surface (of last scattering).

As Stupendous Man has said, Wayne Hu's site is an excellent primer on the CMB (and cosmology), and answers all your questions (I think).

Kwalish Kid

2010-Jul-19, 02:32 PM

Hu's slides are useful, but I don't think they do too much to answer the specific question.

Here's how I see the peaks: The peaks appear in a measurement of the amount of differences on a scale. So the peaks are a measurement of a sort of which size fluctuations are the most common. What fluctuations will persist in the early universe is a complicated function of its contents and its rate of expansion, so finding the peaks gives us information about this function.

Nereid

2010-Jul-19, 02:40 PM

Hu's slides are useful, but I don't think they do too much to answer the specific question.

Here's how I see the peaks: The peaks appear in a measurement of the amount of differences on a scale. So the peaks are a measurement of a sort of which size fluctuations are the most common. What fluctuations will persist in the early universe is a complicated function of its contents and its rate of expansion, so finding the peaks gives us information about this function.

Which, in turn, leads to a question back to the OP: how much more detail would you like, in answer to your question?

For example, are you looking for a 'word picture' of how a particular cosmological parameter - the thickness of the surface of last scattering, say, together with its formal uncertainty - is derived from analysis of the angular power spectrum?

Staticman

2010-Jul-19, 04:10 PM

Hu's slides are useful, but I don't think they do too much to answer the specific question.

Here's how I see the peaks: The peaks appear in a measurement of the amount of differences on a scale. So the peaks are a measurement of a sort of which size fluctuations are the most common. What fluctuations will persist in the early universe is a complicated function of its contents and its rate of expansion, so finding the peaks gives us information about this function.

Which, in turn, leads to a question back to the OP: how much more detail would you like, in answer to your question?

For example, are you looking for a 'word picture' of how a particular cosmological parameter - the thickness of the surface of last scattering, say, together with its formal uncertainty - is derived from analysis of the angular power spectrum?

Thanks Kwalid, Nereid

To be more specific: I understand the first peak to be at the angular scale (around 1 degree or l=220) where the majoritiy of the anisotropies are, and the second peak at a smaller angle scale near the limit of the beam profile. I also understand that this acoustic power spectrum comes mainly from the acoustic waves of primordial universe. What I am specifically interested in is how this information from the CMBR is translated to parameters of cosmology to constrain the LCDM model, I read somewhere that the first peak is used to set the 74% Dark energy parameter and the flatness or spatial curvature and that something like a ratio firs/second peak would give 24% Dark matter parameter,

I don't kow if I've got it right so far, and I would like to understand a bit more how is the CMBR data translated to cosmological parameters.

Perhaps this is beyond the reach of this forum but I would like to think there is people around here that knows enough about this to explain this to me, or point me to a source (not hu's page please) where this is specifically addressed.

Cougar

2010-Jul-20, 01:03 AM

I understand the first peak to be at the angular scale (around 1 degree or l=220)...

Caution: Rushed!

From what I understand, which isn't a lot, the first peak, as you say, points to an angular scale of around 1 degree. Through some other calculation, this is what is expected for the first peak. THEREFORE, space in general between the CMB and here must be roughly FLAT, or Euclidian, because if there was more or less mass in the universe, resulting in corresponding deviations from flatness, the first peak would APPEAR greater or less than 1 degree (due to the corresponding deviation from Euclidian geometry). This sets the mass of the universe at or around the "critical density." First three minutes nucleosynthesis sets the baryon density, and I guess gravitational observation sets the dark matter density. Therefore the dark energy must be what's left.

Ken G

2010-Jul-20, 01:48 AM

Yes, and one more thing to add is the physical reason why we expect the first peak to have the angular scale it has if space is flat-- which is basically the distance a sound wave can travel in the 400,000 years or so during which light and matter was tightly coupled (by the free electrons while hydrogen was still ionized). I only understand the very rough idea here, so read the Hu article for an expert's take. But what I could roughly point out is that, while hydrogen is ionized, the temperature of the radiation field and the temperature of the gas is the same, and sound waves will create temperature fluctuations on a maximum scale that is how far they can travel in that time (which we think we know because we know the temperature at recombination). Then after 400,000 years, the hydrogen recombines, and the CMB no longer tracks the sound wave propagation through the gas, leaving a cutoff in the power spectrum that we see as the first acoustic peak.

The second peak gives information about the modulation of the first peak, which as I understand it, is basically how "non-sinusoidal" the sound waves are, based on the affects of enhanced gravity in the compressed regions (not present in regular sound waves, of course). So if the energy density that goes into the sound waves is "dark energy", it won't have the same gravitational signature, so different modulation. So the second peak tells you about how the gravity is associated with the energy.

Nereid

2010-Jul-20, 01:34 PM

Thanks Kwalid, Nereid

To be more specific: I understand the first peak to be at the angular scale (around 1 degree or l=220) where the majoritiy of the anisotropies are, and the second peak at a smaller angle scale near the limit of the beam profile. I also understand that this acoustic power spectrum comes mainly from the acoustic waves of primordial universe. What I am specifically interested in is how this information from the CMBR is translated to parameters of cosmology to constrain the LCDM model, I read somewhere that the first peak is used to set the 74% Dark energy parameter and the flatness or spatial curvature and that something like a ratio firs/second peak would give 24% Dark matter parameter,

I don't kow if I've got it right so far, and I would like to understand a bit more how is the CMBR data translated to cosmological parameters.

Perhaps this is beyond the reach of this forum but I would like to think there is people around here that knows enough about this to explain this to me, or point me to a source (not hu's page please) where this is specifically addressed.

Going from the excellent, general descriptions given on Wayne Hu's website (there's an awful lot of stuff there, nearly all of it is well worth the time and effort you need to explore it carefully) to something close to what you're after will, very likely, be a rather rough journey.

Perhaps the best place to start is the heavily cited 1970 paper by Peebles and Yu: "Primeval Adiabatic Perturbation in an Expanding Universe (http://adsabs.harvard.edu/abs/1970ApJ...162..815P)" (link is to ADS abstract).

Once you've got what you need from that, the next step I'd recommend is Seljak and Zaldarriaga's even more heavily cited 1996 paper: "A Line of Sight Approach to Cosmic Microwave Background Anisotropies (http://arxiv.org/abs/astro-ph/9603033)" (link is to arXiv abstract).

After that? Probably one of the WMAP First Year papers, say Verde et al's "First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology (http://arxiv.org/abs/astro-ph/0302218)", or Spergel et al's "First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters (http://arxiv.org/abs/astro-ph/0302209)" (links to arXiv abstracts).

Others may have quite different recommendations, of course.

Staticman

2010-Jul-20, 05:36 PM

Got a lot to read, thanks Nereid, Ken and Cougar.

Kwalish Kid

2010-Jul-20, 10:26 PM

Yeah, I can't think of any better papers than the ones that Nereid provided.

Powered by vBulletin® Version 4.2.3 Copyright © 2019 vBulletin Solutions, Inc. All rights reserved.