The Cosmic Background Radiation — Question 6

Question 6

The background dipole can estimate an observer speed

For small beta=v/c, use $T(\theta)=T_0[1+\beta\cos\theta]$. Let T0=2.725 K and dipole amplitude 3.36 mK. Take c=$3.00\times10^5$ km/s.

1. Infer beta and speed.

2. Find the maximum-to-minimum temperature difference and distinguish it from the dipole amplitude.

Question 6 - Solution

The background dipole can estimate an observer speed

(a) Method and calculation

$$\boxed{\beta=A/T_0=.00336/2.725=.00123303}.$$$$\boxed{v=c\beta\simeq369.9\ {\mathrm{km/s}}}.$$

(b) Interpretation and further calculation

$$T_{\max}=T_0+A,\quad T_{\min}=T_0-A.$$$$\boxed{T_{\max}-T_{\min}=2A=6.72\ {\mathrm{mK}}}.$$

Physical check

The exercise assumes a purely kinematic dipole after foreground removal. Amplitude is half the peak-to-peak difference.