# Which fraction of the observed CMBR signal is due to some foreground contaminant

1. Apr 10, 2012

### Tanelorn

One of the major concerns in any Cosmic Microwave Background (CMB) anisotropy analysis is to determine which fraction of the observed signal is due to some foreground contaminant. Two sources of foreground contamination have been firmly identified: the diffuse Galactic emission and unresolved point sources.

Have there been any further developments regarding this, and can anyone quantify the impact on the CMBR measurements? How do we know when we are looking at a foreground signal?

2. Apr 11, 2012

### Chalnoth

There's lots of work going on in this area, and lots of different ways of distinguishing between foregrounds and the CMB, or between the different foregrounds. Here are a few methods that are being either used or investigated for use today:
Internal Linear Combination (ILC)
Correlated Component Analysis (CCA)
Fast Independent Component Analysis (FastICA)
Commander (A Bayesian CMB analysis software package which includes a foreground estimate)
Spectral Matching Independent Component Analysis (SMICA)
Jade (an ICA-like algorithm)
Maximum Entropy Method (MEM)

...to name a few.

As for the types of foregrounds, well, what you've listed there are two broad categories of foregrounds. A more specific breakdown is:
1. Diffuse galactic dust (thermal emission from atoms, molecules, and small clumps of matter in our galaxy).
2. Spinning dust grains (emission from small clumps of matter that are spinning).
3. Free-free electron emission (emission from electrons colliding with one another).
4. Synchrotron emission (emission from electrons being accelerated in magnetic fields).
5. Quasars which are bright in the radio range.
6. Distant galaxy clusters (the hot cluster gas interacts with incoming CMB photons).

(note: points 1-4 are also visible in other galaxies near us, though our own galaxy is the primary culprit for these sources)

I may have forgotten one or two, but that's what I remember right now off the top of my head.

3. Apr 11, 2012

### Tanelorn

Thanks Chalnoth,

http://www.astro.ubc.ca/people/scott/faq_basic.html

"Where did the photons actually come from?

We believe that the very early Universe was very hot and dense. At an early enough time it was so hot, ie there was so much energy around, that pairs of particles and anti-particles were continually being created and annihilated again. This annihilation makes pure energy, which means particles of light - photons. As the Universe expanded and the temperature fell the particles and anti-particles (quarks and the like) annihilated each other for the last time, and the energies were low enough that they couldn't be recreated again. For some reason (that still isn't well understood) the early Universe had about one part in a billion more particles than anti-particles. So when all the anti-particles had annihilated all the particles, that left about a billion photons for every particle of matter. And that's the way the Universe is today!

So the photons that we observe in the cosmic microwave background were created in the first minute or so of the history of the Universe. Subsequently they cooled along with the expansion of the Universe, and eventually they can be observed today with a temperature of about 2.73 Kelvin."

Is the source of these CMBR photons now known with total certainty? Or is there even now still a small possibility of doubt that they could have been produced by other mechanisms early on in the BB? The reason I ask is that there does seem to be several ways that hot matter can generate these kinds of emissions.

Also I beleive that the universe didnt cool enough to become transparent until much later (~300K years). These first photons would have been absorbed and emitted again many times, so are they considered the same photons? Do they have the same energy as the orignal photons and also the same quantity?

Finally, bapowell mentioned in another thread that after subtracting the dipole for our galaxy velocity relative to the CMBR comoving sphere there remains a quadrapole and an octopole (and higher orders) representing a pattern of different CMBR temperatures seen across the sky in different directions. What could cause such a regular pattern? The last scattering comoving sphere is very large.

Last edited: Apr 11, 2012
4. Apr 11, 2012

### Chalnoth

I don't think there's any significant doubt, no.

Why would you think this? The other ways for hot matter to generate photons don't produce a thermal spectrum.

Certainly they had neither the same energy nor quantity as the earlier photons.

The pattern isn't regular. It's highly randomized, and has the expected statistical properties that the simplest models of the CMB predict.

5. Apr 11, 2012

### bapowell

Yes, as Chalnoth says, the temperature fluctuations on a given scale are random (Gaussian to within experimental error at the present time). Perhaps we mean something else by regular?

6. Apr 11, 2012

### Tanelorn

I was refering to the quadrapole octopole and multipole moments diagrams here. Unless I misunderstand their meaning, these represent a pattern of slightly different CMBR temperatures in different directions and are not caused by something local like the galactic dipole?

7. Apr 12, 2012

### bapowell

Right. These are the first few moments in the Fourier decomposition of the temperature fluctuation field. The quadrupole corresponds to fluctuations with an angular correlation of 90 degrees; the octupole, 60 degrees (in general, one has $180/\ell$ degrees.) Higher multipoles contribute smaller angular correlations to the overall temperature fluctuation. These temperature fluctuations, which exist across a range of scales, were caused by curvature perturbations which were in turn generated by inflation.

8. Apr 15, 2012

### Tanelorn

bapowell, thanks for your reply. So what you are saying is that it is believed that these multipole patterns were as a result of slight differences in the rate of inflation in different directions?
Since these are real variations in the actual CMBR itself why do we rarely see them in plots and instead just see the more common random plot with all the regular multipole patterns removed?

9. Apr 15, 2012

### bapowell

No, the rate of inflation is assumed isotropic and uniform in the simplest models. During inflation, quantum fluctuations are stretched by the exponential expansion to superhorizon scales where they become real life density perturbations. These density perturbations are imprinted in the temperature of the CMB later on. Since the CMB arrives at earth from all directions, these temperature fluctuations result in a CMB temperature field that is anisotropic. It's the temperature map -- the last scattering surface -- that is anisotropic in temperature; not the rate of expansion of inflation.
I'm confused by this statement. Which plots are you referring to? The well-known WMAP image of the CMB:

is the real temperature field: it is the sum total (appropriately weighted) of all the multipole moments!

10. Apr 15, 2012

### Tanelorn

bapowell, yes this is the WMAP of the CMBR that I know also.

However, my interpretation of what you have said is that this is not the real raw measurement data.
The real raw measurement data is this:

http://www.valdostamuseum.org/hamsmith/cmbrdipole.gif [Broken]

And when only the dipole is removed we are left with a quadrapole :

http://www.valdostamuseum.org/hamsmith/multipoleCMB.gif [Broken]

Finally when all the multipoles have been removed we end up with :

The above is my interpretation of what I have read and if it is wrong then I am probably confused with the quadrapole and multipole interpretations.

Last edited by a moderator: May 5, 2017
11. Apr 15, 2012

### bapowell

I don't understand why you see it this way. Formally, the temperature fluctuation amplitude is given by
$$\frac{\delta T}{T}(n) = \sum_{\ell, m} a_{\ell m}Y_{\ell m}(n)$$
where the $Y_{\ell m}$ are the multipole moments and $n$ is the direction vector. The full WMAP picture is the sum of each of the individual multipole moments, just as a general fluctuation can be Fourier analyzed into its consituent harmonics. Physically, this makes sense: the temperature fluctuation at a given point in the sky is the result of superposition of fluctuations existing across a range of wavelengths.

If we were to remove all the multipoles we'd have nothing left!

12. Apr 16, 2012

### Chalnoth

Erm, well, if all of the multipoles were removed, you'd have nothing. That image is what you get if you remove only the monopole and dipole signals (as well as an estimate of the foreground signal).

Edit: Whoops, I see bapowell beat me to it.

13. Apr 16, 2012

### Tanelorn

OK I think we are not understanding each other at all here.

Is this first plot with the dipole the real raw data with nothing being added or removed?
http://www.valdostamuseum.org/hamsmith/cmbrdipole.gif [Broken]

These plots show the dipole being removed and finally the galactic plane being removed at the bottom.
http://mather.gsfc.nasa.gov/cobe/phys_today_cover_small.gif [Broken]

This is where I am getting lost:
How do you get from this bottom plot to the quadrapole octupole and multipole plots?
For example, is it some kind of average over a wider angle of the sky?

Chalnoth you mentioned the monopole so I now have a new question, what are you refering to as the monopole?

Last edited by a moderator: May 5, 2017
14. Apr 16, 2012

### bapowell

I am not familiar with the details of the data aggregation process used by the satellite team, nor am I an expert on the experimental process. Physically, to obtain the dipole, you would measure the difference in temperature between spots in the sky separated by 180 degrees. This measurement will give you the dipole image you've attached. To get the quadrupole map, you would measure temperature differences at 90 degrees, and so on. This is what the differential radiometer onboard the satellite does: you measure at different angular separation and for each one you have a map showing the contribution of the associated multipole to the overall temperature fluctuation map.

As Chalnoth said, when the final map is made, the dipole contribution is not included because it contains contamination (it's not fully primordial.) So, the final WMAP image is missing the dipole contribution (but has all the others included.)

Did the mathematical expression for the overall temperature fluctuation that included in the previous message help? That's the best way that I can explain it ;)

15. Apr 16, 2012

### Tanelorn

bapowell unfortunately I prefer to understand the concept and then use this understanding to understand the math!

"Physically, to obtain the dipole, you would measure the difference in temperature between spots in the sky separated by 180 degrees. This measurement will give you the dipole image you've attached. To get the quadrupole map, you would measure temperature differences at 90 degrees, and so on. This is what the differential radiometer onboard the satellite does: you measure at different angular separation and for each one you have a map showing the contribution of the associated multipole to the overall temperature fluctuation map."

OK this helps with the understanding, they are actually different measurements and different sets of raw data.

Would you agree that a full understanding of these measurements, the method, and their interpretation are key, since much of cosmology theory rests on this.

Last edited: Apr 16, 2012
16. Apr 16, 2012

### Chalnoth

The monopole is the average level of the map, which instruments like WMAP and Planck measure very poorly. If we had only a CMB signal, this would be a very easy thing to do: simply set it to zero. But the existence of other galactic and extragalactic sources make removal of the monopole a bit of a thorny problem. Typically it involves using a simplified model of the galaxy to estimate the monopole from the data.

17. Apr 16, 2012

### bapowell

It of course depends on the level of understanding you wish to achieve. In a perfect world, yes, I'd say you should fully understand the whole process, from theory to the details of radiometer performance to orbital dynamics of the satellite. But, it ultimately comes down to what level of understanding you can live with (whether you are just curious, or whether you are doing research.) I work on inflation phenomenology (basically working out predictions of inflation models and then analyzing cosmological datasets to see if they work) and for this it's necessary to know the theory behind the cosmological perturbations, from their origin as quantum fluctuations during inflation to their eventual imprint on the CMB sky. So for me interpretation is key -- understanding how a particular inflation model makes the CMB look and why. Understanding the broad aspects of different CMB experiments (and other cosmological probes) is also important, so that you can use the optimal combination of datasets to constrain your models. However, the details of the experiment -- instrumentation, data reduction and analysis, calibration, systematics, foreground subtraction -- these are all highly technical areas that most people outside the experimental world are not experts on. Of course, there are people that know the whole gammut. I'm certainly not one of them.

18. Apr 16, 2012

### Chalnoth

Well, if you want to use CMB experiments to constrain theory, it's usually easy enough to simply make use of the power spectrum plus errors that the CMB experiments publish. You don't usually have to know the underlying formulas that generated the power spectrum, and since nearly all of the CMB information is contained in the power spectrum, you rarely need more than this.

19. Apr 16, 2012

### bapowell

Yes, I agree. On a bare minimum need-to-know basis that's right. But I think that understanding how the acoustic oscillations get set-up, or how the Sachs-Wolfe effect turns a curvature perturbation into a temperature anisotropy, are important things to know. But, yes, with the advent of Boltzmann codes like CAMB, one does not need to worry about the nuts and bolts in going from an inflationary power spectrum to the CMB.

20. Apr 16, 2012

### Chalnoth

Sorry, I was speaking about from the experiment side of things. You don't need to know how the power spectrum was measured from the experiment to get a good handle on what that power spectrum means for your chosen theoretical question.

But yes, if you are a theorist asking questions about what sorts of early universe theories are correct or not given the data, then you have to know how to go from those fundamental theories to the power spectrum.