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

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