Is There a Detectable Vishniac Effect?

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Abstract
The dominant linear contribution to cosmic microwave background (CMB) fluctuations at small angular scales (less than one arcsec) is a second-order contribution known as the Vishniac or Ostriker-Vishniac effect. This effect is caused by the scattering of CMB photons off free electrons after the universe has been reionized, and is dominated by linear perturbations near the R_V =2 Mpc/(h Gamma/0.2) scale in the Cold Dark Matter cosmogony. As the reionization of 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 a linear treatment is even feasible in different scenarios of reionization. For an Omega_0 = 1 cosmology normalized to cluster abundances, only about 65% of the linear integral is valid if reionization is due to quasars in halos of mass 10^9 solar, while 75% of the integral is valid if reionization was caused by stars in 10^6 solar mass halos. In lambda or open cosmologies, both the redshift of reionization and z_V are pushed further back, but still only 75% to 85% of the linear integral is valid, independent of the ionization scenario. We point out that all odd higher-order moments from Vishniac fluctuations are zero while even moments are non-zero, regardless of the gaussianity of the density perturbations. This provides a defining characteristic of the Vishniac effect that differentiates it from other secondary perturbations and may be helpful in separating them.

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