Limits on the fluctuating part of $y$-type distortion monopole from Planck and SPT results

We use the published Planck and SPT cluster catalogs and recently published $y$-distortion maps to put strong observational limits on the contribution of the fluctuating part of the $y$-type distortions to the $y$-distortion monopole. Our bounds are $5.4\times 10^{-8} < \langle y\rangle < 2.2\times 10^{-6}$. Our upper bound is a factor of 6.8 stronger than the currently best upper $95\%$ confidence limit from COBE-FIRAS of $\langle y\rangle <15\times 10^{-6}$. In the standard cosmology, large scale structure is the only source of such distortions and our limits therefore constrain the baryonic physics involved in the formation of the large scale structure. Our lower limit, from the detected clusters in the Planck and SPT catalogs, also implies that a Pixie-like experiment should detect the $y$-distortion monopole at $>27$-$\sigma$. The biggest sources of uncertainty in our upper limit are the monopole offsets between different HFI channel maps that we estimate to be $<10^{-6}$.