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Published August 15, 1998 | Published
Journal Article Open

Calculation of the Ostriker-Vishniac effect in cold dark matter models


We present a new derivation of the cosmic microwave background anisotropy spectrum from the Ostriker-Vishniac effect for an open, flat, or closed universe, and calculate the anisotropy expected in cold dark matter (CDM) models. We provide simple semi-analytic fitting formulas for the Vishniac power spectrum that can be used to evaluate the expected anisotropy in CDM models for any arbitrary ionization history. In a flat universe, CDM models normalized to cluster abundances produce rms temperature anisotropies of 0.8–2.4 μK on arcminute angular scales for a constant ionization fraction of unity, whereas an ionization fraction of 0.2 yields rms anisotropies of 0.3–0.8 μK. In an open and/or high-baryon-density universe, the level of anisotropy is somewhat higher. The signal in some of these models may be detectable with planned interferometry experiments. The damping of the acoustic peaks in the primary-anisotropy spectrum at degree angular scales depends primarily on the optical depth and only secondarily on the epoch of reionization. On the other hand, the amplitude of Ostriker-Vishniac anisotropies depends sensitively on the epoch of reionization. Therefore, when combined with the estimate of the reionization optical depth provided by maps of degree-scale anisotropies, the Ostriker-Vishniac effect can provide a unique probe of the epoch of reionization.

Additional Information

© 1998 The American Physical Society Received 6 January 1998; published 10 July 1998 We thank M. White and W. Hu for useful comments. This work was supported at Columbia by D.O.E. contract No. DEFG02-92-ER 40699, NASA NAG5-3091, and the Alfred P. Sloan Foundation and at Berkeley by NAG5-6552. M.K. would like to acknowledge the hospitality of the Center for Particle Astrophysics where part of this work was completed.

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