Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S2 / 3

Galactic dust emission is concentrated in a bright band along the Galactic plane, with clumps associated with dust-rich regions. It is a foreground with a spectrum different from a 2.7 K blackbody, so multi-frequency observations can help separate it from the CMB. The schematic below illustrates its geometry rather than reproducing observed sky data.

Motion relative to an isotropic radiation field produces a dipole: one broad hot hemisphere and an opposite cool hemisphere. To first order $T(\theta )=T_0[1+(v/c)\cos \theta ]$, where $\theta =0$ is the forward direction. This is not a narrow Galactic-plane feature and is not the intrinsic small-scale CMB pattern.

After foreground and dipole removal, primordial CMB anisotropies are small hot and cold patches across the sky, with characteristic correlated angular scales and amplitudes of order $10^{-5}$ of the mean temperature. They trace perturbations at photon decoupling and subsequent propagation, not simply the current distribution of Milky Way dust.

Expansion redshifts photon energies and preserves a blackbody spectrum, so a comoving observer at $z=2$ sees $T=T_0(1+z)\simeq 8.18$ K. A one-sided dipole excess of 0.105% means $v/c=0.00105$, hence $\boxed{v\simeq 315\mathrm{km}{\mathrm{s}}^{-1}}$. Motion is toward the hotter region. The peak-to-peak contrast is twice this, so using 0.210% for $v/c$ would double the inferred speed incorrectly.

The given calibration yields $M_V=-3.5{\log }_{10}50\simeq -5.946$. The distance modulus is $31.446$, giving $\boxed{d\simeq 19.5\mathrm{Mpc}}$ if extinction is negligible. Hubble's law predicts $v_H\simeq 1400$ km s${}^{-1}$, compared with 1150 km s${}^{-1}$ observed. The approximately $-250$ km s${}^{-1}$ difference can be a line-of-sight peculiar velocity of the cluster and observer, together with distance-calibration uncertainties. The local flow need not follow a perfectly smooth expansion law.