Q and U parameters for polarization

[Anne-Sylvie]

Hello everyone :)

The CMB is polarized. I read in Dodelson's book "Modern Cosmology" that we can expect a signal of polarization weaker than the signal of temperature.
Is it only because the Stokes parameters obey $$I^2 = Q^2 + U^2 $$ (I drop V because Thomson scatering can't create V polarization) ? Or is there any other (more physical) reason ?

And I heard too that $$\langle Q \rangle = \langle U \rangle = 0$$ but I can't figure out why it is the case.

Thanks for your answers. :)

 

[Chalnoth]

Hello everyone :)

The CMB is polarized. I read in Dodelson's book "Modern Cosmology" that we can expect a signal of polarization weaker than the signal of temperature.
Is it only because the Stokes parameters obey $$I^2 = Q^2 + U^2 $$ (I drop V because Thomson scatering can't create V polarization) ? Or is there any other (more physical) reason ?

And I heard too that $$\langle Q \rangle = \langle U \rangle = 0$$ but I can't figure out why it is the case.

Thanks for your answers. :)

It's because only a small fraction of the CMB photons are polarized.

 

[Anne-Sylvie]

It's because only a small fraction of the CMB photons are polarized.

Maybe I wasn't clear enough with my question.
I am wondering why are they so few polarized photons. :)

 

[Chalnoth]

Maybe I wasn't clear enough with my question.
I am wondering why are they so few polarized photons. :)

Right, it's because of the physics of how they were emitted. Most of the photons are randomized by the random scatter that occurred before the photons left the CMB. But those random motions were correlated, giving rise to some small amount of polarization.

 

[sardar]

Hello there,

The Q and U parameters for polarization are important quantities in studying the Cosmic Microwave Background (CMB). The CMB is a relic radiation from the early universe and it has been found to have a small amount of polarization, which is a measure of the direction in which the electric field of the radiation oscillates. This polarization is important because it can provide information about the early universe and its evolution.

The signal of polarization is weaker than the signal of temperature because of the way the Stokes parameters (I, Q, U, V) are defined. As you mentioned, the relationship between them is given by $$I^2 = Q^2 + U^2$$, which means that the polarization signal is always smaller than the temperature signal. This is a mathematical consequence of how the polarization is measured and does not have a physical reason behind it.

As for the question of why $$\langle Q \rangle = \langle U \rangle = 0$$, this is due to the statistical properties of the CMB. Since the CMB is a random field, the average value of Q and U over the entire sky is expected to be zero. This is similar to the average value of the temperature over the entire sky being zero. However, this does not mean that there is no polarization present in the CMB. It just means that on average, the polarization is evenly distributed in all directions.

I hope this helps to clarify your questions about the Q and U parameters for polarization. Keep exploring and learning about the CMB, it is a fascinating field of study!