The effect of aberration on partial-sky measurements of the cosmic microwave background temperature power spectrum

Understand

Our motion relative to the cosmic-microwave-background (CMB) rest frame deflects light rays giving rise to shifts as large as L -> L(1+beta), where beta=0.00123 is our velocity (in units of the speed of light) on measurements CMB fluctuations.

• Here we present a novel harmonic-space approach to this CMB aberration that improves upon prior work by allowing us to (i) go to higher orders in beta, thus extending the validity of the analysis to measurements at L > 1/beta ~ 800; and (ii) treat the effects of window functions and pixelization in a more accurate and computationally efficient manner.
• We calculate precisely the magnitude of the systematic bias in the power spectrum inferred from the partial sky, and show that aberration shifts the multipole moment by Delta L/L ~ beta<cos(theta)>, with <cos(theta)> averaged over the survey footprint.
• Such a shift, if ignored, would bias the measurement of the sound-horizon size theta_* at the 0.01%-level, which is comparable to the measurement uncertainties of Planck.