Is There a Detectable Vishniac Effect?

The dominant linear contribution to cosmic microwave background (CMB)fluctuations at small angular scales (less than one arcsec) is a second-ordercontribution known as the Vishniac or Ostriker-Vishniac effect. This effect iscaused by the scattering of CMB photons off free electrons after the universehas been reionized, and is dominated by linear perturbations near the R_V =2Mpc/(h Gamma/0.2) scale in the Cold Dark Matter cosmogony. As the reionizationof the universe requires that nonlinear objects exist on some scale, however,one can compare the scale responsible for reionization to R_V and ask if alinear treatment is even feasible in different scenarios of reionization. Foran Omega_0 = 1 cosmology normalized to cluster abundances, only about 65% ofthe linear integral is valid if reionization is due to quasars in halos of mass10^9 solar, while 75% of the integral is valid if reionization was caused bystars in 10^6 solar mass halos. In lambda or open cosmologies, both theredshift of reionization and z_V are pushed further back, but still only 75% to85% of the linear integral is valid, independent of the ionization scenario. Wepoint out that all odd higher-order moments from Vishniac fluctuations are zerowhile even moments are non-zero, regardless of the gaussianity of the densityperturbations. This provides a defining characteristic of the Vishniac effectthat differentiates it from other secondary perturbations and may be helpful inseparating them.Comment: 21 pages, 5 figures, accepted to the Astrophysical Journa