The signatures of voids - II. In front of the last scattering surface

Details The signatures of voids - II. In front of the last scattering surface The signatures of voids - II. In front of the last scattering surface

Aug 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998mnras.299..285v&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 299, Issue 1, pp. 285-298.

Astronomy and Astrophysics

Astronomy

3

Hydrodynamics, Methods: Analytical, Methods: Numerical, Cosmic Microwave Background

Scientific paper

We explore the signatures of various compensated, subhorizon-sized, quasi-linear voids in the matter-dominated Universe. We show that the temperature distortion functions (the energy that photons have relative to photons moving outside the void) for cold dark matter voids with positive energy are qualitatively the same and quantitatively similar regardless of the velocity profile. Photons are blueshifted on entering and leaving the void by (costau)deltaRH/(3c), and are redshifted linearly with distance inside the void by a total amount of -2(costau)deltaRH/(3c), where cH^-1 is Hubble's radius, R is the radius of the void and Rsintau is roughly the distance of closest approach. These effects are large since they are first-order in RH/c. We also show that a positive-energy, quasi-linear, cold dark matter void will grow asymptotically (independently of its initial velocity profile) after 10 times the initial time, with relative expansion coefficient inside the void of xi~=2delta/9, where delta is the underdensity of the void. If a quasi-linear, pressureless, positive-energy void is growing asymptotically when cosmic microwave background photons cross it, then it appears as a cold spot surrounded by a hot ring with temperature anisotropy DeltaT/T~=(2/5)delta^2.2(RH/c)^3costau[1-(5/3)cos^2tau]. However, if this same void is not asymptotically evolving when the photons cross it, then even though the temperature distortion functions are changed little, this void can appear as either a cold or a hot spot on the microwave background just by changing the initial velocity profile from unperturbed to perturbed. Thus positive energy, pressureless voids that have equivalent underdensities and sizes can have very similar temperature distortion functions (which ultimately determine the signature of a void on the last scattering surface), but can have very different signatures in front of the last scattering surface unless they are asymptotically evolving. This is due to cancellations to third-order in RH/c. In addition, reduction of the energy of a void to zero completely reverses the temperature distortion functions; photons experience redshifts entering and leaving a zero-energy void, and a blueshift linear with distance crossing the inner void region. However, a zero-energy void can appear as a cold spot but with a signature that is 20 times larger than that for an asymptotically evolving cold dark matter void. We also find that voids with small amounts of pressure have very complicated temperature distortion functions because of the wall explosion and resultant inward and outward-travelling shocks. However, their signatures can be comparable to those of cold dark matter voids.

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