Lyman-alpha forest-CMB cross-correlation and the search for the ionized baryons at high redshift

The intergalactic neutral hydrogen which is responsible for the Lyman alpha forest of quasar absorption is a tracer of much larger amounts of ionised hydrogen. The ionised component has yet to be detected directly, but is expected to scatter CMB photons via the Sunyaev-Zel'dovich (SZ) effect. We use hydrodynamic simulations of a LambdaCDM universe to create mock quasar spectra and CMB sky maps. We find that the high-z Lya forest gas causes temperature fluctuations of the order of 1 muK rms in the CMB on arcmin scales. The kinetic and thermal SZ effects have a similar magnitude at z=3, with the thermal effect becoming relatively weaker as expected at higher z. The CMB signal associated with lines of sight having HI column densities > 10^18 cm^-2 is only marginally stronger than that for lower column densities. The strong dependence of rms temperature fluctuation on mean Lya absorbed flux, however, suggests that the CMB signal effectively arises in lower density material. We investigate the use of the cross-correlation of the Lya forest and the microwave background to detect the SZ effect at redshifts 2-4. In so doing we are able to set direct limits on the density of diffuse ionised intergalactic baryons. We carry out a preliminary comparison at a mean redshift z=3 of 3488 quasar spectra from SDSS Data Release 3 and the WMAP first year data. Assuming that the baryons are clustered as in a LambdaCDM cosmology, and have the same mean temperature, the cross-correlation yields a weak limit on the cosmic density of ionised baryons Omega_(b,I), which is Omega_(b,I) < 0.8 at 95% confidence. With data from upcoming CMB telescopes, we anticipate that a direct detection of the high redshift ionised IGM will soon be possible, providing an important consistency check on cosmological models.