### Abstract

The dominant linear contribution to cosmic microwave background (CMB) fluctuations at small angular scales (≲1′)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/(hΓ/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 whether a linear treatment is even feasible in different scenarios of reionization. For an Ω_{0} = 1 cosmology normalized to cluster abundances, only ∼65% of the linear integral is valid if reionization is due to quasars in halos of mass ∼10^{9} M_{⊙}, while ∼75% of the integral is valid if reionization was caused by stars in halos of ∼10^{6} M_{⊙}. In Λ or open cosmologies, both the redshift of reionization and z_{v} are pushed farther 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 nonzero, regardless of the Gaussianity of the density perturbations. This provides a denning characteristic of the Vishniac effect that differentiates it from other secondary perturbations and may be helpful in separating them.

Original language | English (US) |
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Pages (from-to) | 20-31 |

Number of pages | 12 |

Journal | Astrophysical Journal |

Volume | 540 |

Issue number | 1 PART 1 |

State | Published - Sep 1 2000 |

Externally published | Yes |

### Keywords

- Cosmic microwave background
- Cosmology: theory

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*540*(1 PART 1), 20-31.