## Wednesday, December 12, 2012

### peculiar motion and the CMB

the CMB-dipole is usually interpreted as motion dipole, i.e. generated by the earth's movement relative to the CMB and would in this interpretation not contain any cosmological information. are there other imprints in the CMB due to peculiar motion of the observer?

bonus question: how large would seasonal variations of the CMB motion dipole be?

bonus question 2: can you estimate the order of magnitude of $(10^{10}!)$?

1. other imprints: a proper motion in viewing directions other than the direction of motion (unmeasurably small, alas). is proportional to the sine of the angle between viewing direction and the motion.

seasonal variations: (30 km/s) / (300 000 km/s)

bonus 2: go to the logarithm; then it is very easy!

Uli Bastian

2. bonus question: completely correct, there would be seasonal variations of the CMB temperature of the order of $\upsilon/c\simeq10^{-4}$.

3. bonus question 2: a very coarse application of the Stirling-formula $\log(n!)\simeq n\log(n)$ yields $\log(10^{10}!) \simeq 10^{10}\log(10^{10})=10^{10}\times10=10^{11}$.

4. CQW main question: yes, quite right! there's aberration due to special relativity in the CMB sky, meaning that all anisotropy patches in the direction of motion appear larger. it influences the CMB spectrum on multipoles larger than $\ell>1/\beta$ with $\beta=\upsilon/c$. for the milky way's velocity of almost $300\mathrm{km}/s$ relative to the CMB rest frame this yields aberration effects on $\ell>1000$.