Finding the missing baryons with fast radio bursts and Sunyaev-Zeldovich maps

Almost a third of the cosmic baryons are “missing” at low redshifts, as they reside in the invisible warm-hot intergalactic medium (WHIM). The thermal Sunyaev-Zeldovich (tSZ) effect, which measures the line-of-sight integral of the plasma pressure, can potentially detect this WHIM, although its expected signal is hidden below the noise. Extragalactic dispersion measures (DMs)-obtained through observations of fast radio bursts (FRBs)-are excellent tracers of the WHIM, as they measure the column density of plasma, regardless of its temperature. Here we propose cross correlating DMs and tSZ maps as a new way to find and characterize the missing baryons in the WHIM. Our method relies on the precise (∼ arcminute) angular localization of FRBs to assign each burst a DM and a y parameter. We forecast that the signal from the WHIM should be confidently detected in a cross-correlation analysis of ∼104 FRBs, expected to be gathered in a year of operation of the upcoming CHIME and HIRAX radio arrays, confirming the recent tentative detections of filamentary WHIM. Using this technique, future CMB probes (which might lower the tSZ noise) could determine both the temperature of the WHIM and its evolution to within tens of percent. Altogether, DM-tSZ cross correlations hold great promise for studying the baryons in the local Universe.