A new constraint on the $y$-distortion with FIRAS: robustness of component separation methods

The sky-averaged Compton-$y$ distortion in the cosmic microwave background (CMB) energy spectrum, $\langle y \rangle$, provides information about energy injection in the Universe occurring at $z \lesssim 5\times10^{4}$. It is primarily sourced by the thermal Sunyaev-Zeldovich effect -- the up-scattering of CMB photons on free electrons in collapsed dark matter halos. In this work and our companion paper, Ref. [1], we perform a re-analysis of the archival COBE/FIRAS data to constrain $\langle y \rangle$. We utilize two analysis approaches: (i) fitting the sky-averaged intensity spectrum (frequency monopole) and (ii) fitting the sky spectrum in each pixel (pixel-by-pixel). We obtain the baseline upper limits $\langle y \rangle < 31\times 10^{-6}$ and $\langle y \rangle < 8.3\times 10^{-6}$ (both at $95\%$ C.L.) for these two approaches, respectively. We present the first detailed comparison of these analysis methods on both mock skies and real data. Our findings suggest that accounting for the spatial variability of foregrounds via pixel-by-pixel fitting allows for tighter constraints on $\langle y \rangle$ by a factor of $\approx 3-5$ as compared to the frequency monopole method. We show that our frequency monopole results agree well with predictions from Fisher forecast techniques based on the sky-averaged signal, which have been used for forecasting future spectral distortion experiments. Our results thus suggest that the scientific reach of future spectral distortion experiments can potentially be enhanced by a factor of a few via more optimal component separation methods, and we identify the pixel-by-pixel method as one such robust way to achieve this. We discuss the implications of our improved constraints on $\langle y \rangle$ from the pixel-by-pixel method in Ref. [1].