 ![Achievable precision in estimating the velocity through aberration and Doppler effects in an ideal experiment (with $f_{\rm sky} = 0$ and limited by cosmic variance only) for different maps. *Left:* as a function of $\ell_{\rm max}$. *Right:* as a function of $\ell_{\rm     min}$ (with fixed $\ell_{\rm max}=0000$). *Bottom:* for individual bins with $\Delta \ell = 000$. We see that: (i) the first hundred $\ell$s are not important for achieving a high S/N; and (ii) the non-CMB diffuse maps exhibit low precision and are not very useful for measuring $\beta$. Note that for simplicity we have assumed no primordial $B$-modes (our constraints are very weakly sensitive to this choice). \[fig:SN-Ideal\]](Ideal-CMB+tSZ+CIB-v0.pdf "fig:"){width="00.00000%"} ![Achievable precision in estimating the velocity through aberration and Doppler effects in an ideal experiment (with $f_{\rm sky} = 0$ and limited by cosmic variance only) for different maps. *Left:* as a function of $\ell_{\rm max}$. *Right:* as a function of $\ell_{\rm     min}$ (with fixed $\ell_{\rm max}=0000$). *Bottom:* for individual bins with $\Delta \ell = 000$. We see that: (i) the first hundred $\ell$s are not important for achieving a high S/N; and (ii) the non-CMB diffuse maps exhibit low precision and are not very useful for measuring $\beta$. Note that for simplicity we have assumed no primordial $B$-modes (our constraints are very weakly sensitive to this choice). \[fig:SN-Ideal\]](Ideal-CMB+tSZ+CIB-l